Finite Group Databasebeta

← #17241193

Subgroups — #17241193

Order 4352.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic, complemented
2C2×#11763321C211yesmaximal, characteristic, complemented
3#14537075C211yesmaximal, characteristic, complemented
4#14537070C211yesmaximal, characteristic, complemented
5#14535337C211yesmaximal, characteristic, complemented
6#14535326C211yesmaximal, characteristic, complemented
7#14535283C211yesmaximal, characteristic, complemented
8#14535272C211yesmaximal, characteristic, complemented
9#14535242C211yesmaximal, characteristic, complemented
10#14535193C211yesmaximal, characteristic, complemented
11#14535182C211yesmaximal, characteristic, complemented
12#14535165C211yesmaximal, characteristic, complemented
13#14535097C211yesmaximal, characteristic, complemented
14#14535091C211yesmaximal, characteristic, complemented
15#14535072C211yesmaximal, characteristic, complemented
16#14535063C211yesmaximal, characteristic, complemented
17#14535041C211yesmaximal, characteristic, complemented
18#14535023C211yesmaximal, characteristic, complemented
19#14535012C211yesmaximal, characteristic, complemented
20#14534990C211yesmaximal, characteristic, complemented
21#14534708C211yesmaximal, characteristic, complemented
22#14534631C211yesmaximal, characteristic, complemented
23#14534402C211yesmaximal, characteristic, complemented
24#14534361C211yesmaximal, characteristic, complemented
25#14534350C211yesmaximal, characteristic, complemented
26#14534143C211yesmaximal, characteristic, complemented
27#14533963C211yesmaximal, characteristic, complemented
28#14532410C211yesmaximal, characteristic, complemented
29#14532391C211yesmaximal, characteristic, complemented
30#14531420C211yesmaximal, characteristic, complemented
31C17×#2609C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763430—28no—
35C2×#10587555C2211yescharacteristic, complemented
36C2×#10587574C2211yescharacteristic, complemented
37C2×#10587584C2211yescharacteristic
38C2×#10587584C2211yescharacteristic, complemented
39C2×#10587561C2211yescharacteristic
40C2×#10587571C2211yescharacteristic
41C2×#10587571C2211yescharacteristic
42C2×#10587571C2211yescharacteristic, complemented
43#11763321—28no—
44C2×#10587572C2211yescharacteristic
45C2×#10587572C2211yescharacteristic
46C2×#10587569C2211yescharacteristic
47C2×#10587569C2211yescharacteristic
48C2×#10587569C2211yescharacteristic, complemented
49C2×#10587583C2211yescharacteristic
50C2×#10587583C2211yescharacteristic
51C2×#10587610C2211yescharacteristic, complemented
52C2×#10587582C2211yescharacteristic
53C2×#10587582C2211yescharacteristic
54C2×#10587582C2211yescharacteristic, complemented
55C2×#10587564C2211yescharacteristic
56C2×#10587581C2211yescharacteristic
57C2×#10587581C2211yescharacteristic
58C2×#10587616C2211yescharacteristic
59C2×#10587570C2211yescharacteristic, complemented
60C2×#10587624C2211yescharacteristic
61C2×#10587568C2211yescharacteristic
62C2×#10587568C2211yescharacteristic
63C2×#10587623C2211yescharacteristic
64C2×C4×Dic34C2211yescharacteristic, complemented
65C2×C4×D68C2211yescharacteristic
66C2×C4×D68C2211yescharacteristic
67C2×C4×D68C2211yescharacteristic
68C2×C4×D68C2211yescharacteristic
69#11762751C2211yescharacteristic, complemented
70#11762748C2211yescharacteristic, complemented
71#11762746C2211yescharacteristic
72#11762746C2211yescharacteristic, complemented
73#11762745C2211yescharacteristic, complemented
74#11762744C2211yescharacteristic
75#11762742C2211yescharacteristic, complemented
76#11762741C2211yescharacteristic, complemented
77#11762739C2211yescharacteristic, complemented
78#11762738C2211yescharacteristic
79#11762738C2211yescharacteristic, complemented
80#11762738C2211yescharacteristic, complemented
81#11762736C2211yescharacteristic
82#11762735C2211yescharacteristic
83#11762734C2211yescharacteristic
84#11762732C2211yescharacteristic, complemented
85#11762731C2211yescharacteristic, complemented
86#11762730C2211yescharacteristic, complemented
87#11762730C2211yescharacteristic, complemented
88#11762730C2211yescharacteristic, complemented
89#11762729C2211yescharacteristic, complemented
90#11762727C2211yescharacteristic
91#11762727C2211yescharacteristic
92#11762727C2211yescharacteristic, complemented
93#11762726C2211yescharacteristic
94#11762726C2211yescharacteristic
95#11762726C2211yescharacteristic
96#11762726C2211yescharacteristic, complemented
97#11762725C2211yescharacteristic
98#11762725C2211yescharacteristic
99#11762725C2211yescharacteristic
100#11762725C2211yescharacteristic, complemented
101#11762724C2211yescharacteristic
102#11762724C2211yescharacteristic, complemented
103#11762722C2211yescharacteristic
104#11762722C2211yescharacteristic
105#11762722C2211yescharacteristic, complemented
106#11762722C2211yescharacteristic, complemented
107#11762721C2211yescharacteristic
108#11762721C2211yescharacteristic, complemented
109#11762718C2211yescharacteristic
110#11762718C2211yescharacteristic
111#11762718C2211yescharacteristic
112#11762717C2211yescharacteristic
113#11762713C2211yescharacteristic, complemented
114#11762710C2211yescharacteristic
115#11762710C2211yescharacteristic
116#11762709C2211yescharacteristic
117#11762709C2211yescharacteristic
118#11762708C2211yescharacteristic, complemented
119#11762708C2211yescharacteristic, complemented
120#11762708C2211yescharacteristic, complemented
121#11762702C2211yescharacteristic, complemented
122#11762701C2211yescharacteristic
123#11762700C2211yescharacteristic
124#11762700C2211yescharacteristic, complemented
125#11762699C2211yescharacteristic
126#11762699C2211yescharacteristic
127#11762697C2211yescharacteristic
128#11762697C2211yescharacteristic
129#11762694C2211yescharacteristic, complemented
130#11762694C2211yescharacteristic, complemented
131#11762693C2211yescharacteristic, complemented
132#11762693C2211yescharacteristic, complemented
133#11762690C2211yescharacteristic, complemented
134#11762690C2211yescharacteristic, complemented
135#11762689C2211yescharacteristic
136#11762688C2211yescharacteristic
137#11762688C2211yescharacteristic, complemented
138#11762687C2211yescharacteristic
139#11762687C2211yescharacteristic
140#11762687C2211yescharacteristic
141#11762687C2211yescharacteristic
142#11762687C2211yescharacteristic, complemented
143#11762685C2211yescharacteristic
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic, complemented
147#11762684C2211yescharacteristic
148#11762683C2211yescharacteristic
149#11762683C2211yescharacteristic
150#11762683C2211yescharacteristic
151#11762683C2211yescharacteristic
152#11762683C2211yescharacteristic, complemented
153#11762683C2211yescharacteristic, complemented
154#11762682C2211yescharacteristic
155#11762682C2211yescharacteristic
156#11762680C2211yescharacteristic
157#11762680C2211yescharacteristic
158#11762680C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic, complemented
161#11762677C2211yescharacteristic, complemented
162#11762671C2211yescharacteristic
163#11762671C2211yescharacteristic
164#11762668C2211yescharacteristic
165#11762668C2211yescharacteristic
166#11762668C2211yescharacteristic, complemented
167#11762667C2211yescharacteristic
168#11762666C2211yescharacteristic, complemented
169#11762664C2211yescharacteristic
170#11762664C2211yescharacteristic
171#11762664C2211yescharacteristic
172#11762656C2211yescharacteristic, complemented
173#95×D17C2211yescharacteristic, complemented
174C2×C17×#117C2211yescharacteristic
175C2×C17×#117C2211yescharacteristic, complemented
176C17×#398C2211yescharacteristic, complemented
177C17×#396C2211yescharacteristic
178C17×#396C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#385C2211yescharacteristic
187C17×#385C2211yescharacteristic, complemented
188C17×#382C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C2×#63252—24no—
201C2×#63252—42no—
202C2×#63252—42no—
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×C4×D17—24no—
209C22×C4×D17—42no—
210C22×C4×D17—42no—
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C22×Dic34C2311yescharacteristic
223C17×#117—24no—
224C17×#117—24no—
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255#10587624—42no—
256#10587623—42no—
257#10587616—24no—
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303#10587610—24no—
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320#10587584—24no—
321#10587584—24no—
322#10587583—24no—
323#10587583—24no—
324#10587582—24no—
325#10587582—24no—
326#10587582—42no—
327#10587581—24no—
328#10587581—24no—
329#10587574—42no—
330#10587572—24no—
331#10587572—24no—
332#10587571—24no—
333#10587571—24no—
334#10587571—42no—
335#10587570—42no—
336#10587569—24no—
337#10587569—24no—
338#10587569—42no—
339#10587568—24no—
340#10587568—24no—
341#10587564—42no—
342#10587561—24no—
343C4×D68—24no—
344C4×D68—24no—
345C4×D68—24no—
346C4×D68D418yescomplemented
347#10587555—24no—
348C4×Dic34—24no—
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C23×D17—22no—
388C23×D17—22no—
389C23×D17—22no—
390C23×D17—41no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17—41no—
394C23×D17C2411yescharacteristic
395C23×D17C2411yescharacteristic
396C23×D17C2411yescharacteristic
397C23×D17C2411yescharacteristic
398C2×D4×C17—22no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C22×C4×C17—22no—
402C22×C4×C17—22no—
403C22×C4×C17—22no—
404C22×C4×C17—22no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C2×C22⋊D17—22no—
421C2×C22⋊D17—22no—
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C22×Dic17—22no—
439C22×Dic17—22no—
440C22×Dic17—41no—
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453#63252—416no—
454C2×D68—22no—
455C2×D68—22no—
456C2×D68—22no—
457C2×D68—22no—
458C2×D68—22no—
459C2×D68—22no—
460C2×D68—22no—
461C2×D68—41no—
462C2×D68—41no—
463C2×D68—41no—
464C2×D68—41no—
465C2×D68—41no—
466C2×D68—41no—
467C2×D68—41no—
468C2×D68C2×D414yes—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—416no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17C2×D414yes—
493C2×C4×D17C2×D414yes—
494C2×Dic34—22no—
495C2×Dic34—22no—
496C2×Dic34—22no—
497C2×Dic34—22no—
498C2×Dic34—22no—
499C2×Dic34—41no—
500C2×Dic34—41no—
501C2×Dic34—41no—
502C2×Dic34—41no—
503C2×Dic34—41no—
504C2×Dic34—41no—
505C2×Dic34—41no—
506C4⋊C4×C17—22no—
507C4⋊C4×C17—22no—
508C4⋊C4×C17—22no—
509C4⋊C4×C17—22no—
510C4⋊C4×C17—22no—
511C4⋊C4×C17—41no—
512C4⋊C4×C17—41no—
513C4⋊C4×C17—41no—
514C4⋊C4×C17—41no—
515C22⋊C4×C17—22no—
516C22⋊C4×C17—22no—
517C22⋊C4×C17—22no—
518C22⋊C4×C17—22no—
519C22⋊C4×C17—22no—
520C22⋊C4×C17—22no—
521C22⋊C4×C17—41no—
522C22⋊C4×C17—41no—
523C22⋊C4×C17—41no—
524C22⋊C4×C17—41no—
525C42×C17—22no—
526C42×C17—22no—
527C42×C17C2×D414yes—
528C22⋊Dic17—22no—
529C22⋊Dic17—22no—
530C22⋊Dic17—22no—
531C22⋊Dic17—22no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—22no—
544#63227—22no—
545#63227—22no—
546#63227—22no—
547#63227—22no—
548#63227—22no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563#63227—41no—
564#63227—41no—
565#63227—41no—
566#63227—41no—
567#63227—41no—
568#63227C2×D414yes—
569#63227C2×D414yes—
570C4⋊Dic17—22no—
571C4⋊Dic17—22no—
572C4⋊Dic17—22no—
573C4⋊Dic17—22no—
574C4⋊Dic17—22no—
575C4⋊Dic17—22no—
576C4⋊Dic17—41no—
577C4⋊Dic17—41no—
578C4⋊Dic17—41no—
579C4⋊Dic17—41no—
580C4⋊Dic17C2×D414yes—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593C4×Dic17—22no—
594C4×Dic17—22no—
595C4×Dic17—41no—
596C4×Dic17—41no—
597#36712—171nomaximal, Sylow
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17H(5,𝔽2)12yes—
612C23×C17C2511yescharacteristic
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—21no—
637C22×D17—21no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17—44no—
645C22×D17C22×D412yes—
646C22×D17C22×D412yes—
647C22×D172−1+412yes—
648D4×C17—82no—
649C2×C4×C17—28no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—44no—
686C2×C4×C17C22×D412yes—
687C2×C4×C17C22×D412yes—
688C2×C4×C17C22×D412yes—
689C2×C4×C17H(5,𝔽2)12yes—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—82no—
693C22⋊D17—82no—
694C22⋊D17—82no—
695C22⋊D17—82no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—44no—
731C2×Dic17C22×D412yes—
732C2×Dic17C22×D412yes—
733D68—44no—
734D68—44no—
735D68—44no—
736D68—44no—
737D68—44no—
738C4×D17—44no—
739C4×D17—44no—
740C4×D17—44no—
741C4×D17—44no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—82no—
745C4×D17—82no—
746Dic34—44no—
747Dic34—44no—
748Dic34—82no—
749Dic34—82no—
750C2×#542—171no—
751C2×#525—171no—
752#2849—171no—
753#2848—171no—
754#2696—171no—
755#2695—171no—
756#2692—171no—
757#2691—171no—
758#2689—171no—
759#2686—171no—
760#2685—171no—
761#2684—171no—
762#2677—171no—
763#2676—171no—
764#2674—171no—
765#2674—171no—
766#2672—171no—
767#2671—171no—
768#2670—171no—
769#2668—171no—
770#2638—171no—
771#2630—171no—
772#2609D1711yescharacteristic, complemented
773#2602—171no—
774#2599—171no—
775#2598—171no—
776#2580—171no—
777#2564—171no—
778#2432—171no—
779#2430—171no—
780#2318—171no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17C23×D411yescharacteristic
796C22×C17C2×H(5,𝔽2)11yescharacteristic
797C22×C17C2×H(5,𝔽2)11yescharacteristic
798C22×C17C2×2−1+411yescharacteristic
799C22×C17#58511yescharacteristic
800C22×C17#58511yescharacteristic
801C22×C17#58511yescharacteristic
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—416no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C4×C17—22no—
832C4×C17—22no—
833C4×C17—22no—
834C4×C17—22no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843C4×C17—41no—
844Dic17—22no—
845Dic17—22no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856C22×#41—171no—
857C24×C4—171no—
858#542—348no—
859C2×C4⋊Q8—171no—
860C2×C4⋊Q8—171no—
861C2×#126—171no—
862C2×#126—171no—
863C2×#124—171no—
864C2×#124—171no—
865C2×#124—171no—
866C2×#124—171no—
867#525—348no—
868C2×#123—171no—
869C2×#123—171no—
870C2×#123—171no—
871C2×#123—171no—
872C2×#123—171no—
873C2×C22⋊Q8—171no—
874C2×C22⋊Q8—171no—
875C2×C22⋊Q8—171no—
876C2×C22⋊Q8—171no—
877C2×C22⋊Q8—171no—
878C2×C22⋊Q8—171no—
879C2×C22⋊Q8—171no—
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#121—171no—
884C2×#121—171no—
885C2×#120—171no—
886C2×#120—171no—
887C2×#120—171no—
888C2×C4×Q8—171no—
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×C4×D4—171no—
892C2×C4×D4—171no—
893C2×#117C2×D1711yescharacteristic
894C2×#117C2×D1711yescharacteristic, complemented
895#400—171no—
896#400—171no—
897#399—171no—
898#399—171no—
899#399—171no—
900#399—171no—
901#398—171no—
902#398—171no—
903#398—171no—
904#398C2×D1711yescharacteristic, complemented
905#397—171no—
906#397—171no—
907#397—171no—
908#397—171no—
909#397—171no—
910#397—171no—
911#396—171no—
912#396—171no—
913#396C2×D1711yescharacteristic
914#396C2×D1711yescharacteristic, complemented
915#395—171no—
916#395—171no—
917#395—171no—
918#395—171no—
919#394—171no—
920#394—171no—
921#394—171no—
922#394—171no—
923#394—171no—
924#394—171no—
925#394—171no—
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394—171no—
931#394—171no—
932#394C2×D1711yescharacteristic
933#393—171no—
934#393—171no—
935#393—171no—
936#393—171no—
937#393—171no—
938#393—171no—
939#392—171no—
940#392—171no—
941#392—171no—
942#392—171no—
943#391—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#389—171no—
949#389—171no—
950#389—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388C2×D1711yescharacteristic
960#388C2×D1711yescharacteristic, complemented
961#387—171no—
962#387—171no—
963#387—171no—
964#387—171no—
965#387—171no—
966#387—171no—
967#387C2×D1711yescharacteristic, complemented
968#387C2×D1711yescharacteristic, complemented
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386C2×D1711yescharacteristic
982#386C2×D1711yescharacteristic
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385C2×D1711yescharacteristic
998#385C2×D1711yescharacteristic, complemented
999#383—171no—
1000#382C2×D1711yescharacteristic, complemented
1001#381—171no—
1002#381—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#379—171no—
1009#379—171no—
1010#379—171no—
1011C4×C22⋊C4—171no—
1012C2×#95—171no—
1013C2×C17—42no—
1014C2×C17—81no—
1015C2×C17#344911yescharacteristic
1016C2×C17#348411yescharacteristic
1017C2×C17#348911yescharacteristic
1018C2×C17#353311yescharacteristic
1019C2×C17#353511yescharacteristic
1020C2×C17#354011yescharacteristic
1021C2×C17#354111yescharacteristic
1022D17—42no—
1023D17—42no—
1024D17—42no—
1025D17—81no—
1026C25—171no—
1027C2×#41—344no—
1028C2×#41—682no—
1029C2×#41—682no—
1030C22×Q8—171no—
1031C22×Q8—171no—
1032C22×Q8—171no—
1033C22×Q8—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4—171no—
1044C22×D4—171no—
1045C22×D4C22×D1711yescharacteristic
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—344no—
1056C23×C4—682no—
1057C23×C4—682no—
1058C23×C4C22×D1711yescharacteristic
1059C23×C4C22×D1711yescharacteristic
1060C4⋊Q8—344no—
1061C4⋊Q8—682no—
1062#126—344no—
1063#126—344no—
1064#124—344no—
1065#124—344no—
1066#124—344no—
1067#124—682no—
1068#123—344no—
1069#123—344no—
1070#123—344no—
1071#123—344no—
1072#123—682no—
1073C22⋊Q8—344no—
1074C22⋊Q8—344no—
1075C22⋊Q8—344no—
1076C22⋊Q8—344no—
1077C22⋊Q8—344no—
1078C22⋊Q8—682no—
1079C22⋊Q8—682no—
1080#121—344no—
1081#121—344no—
1082#121—344no—
1083#121—682no—
1084#121—682no—
1085#120—344no—
1086#120—344no—
1087#120—682no—
1088C4×Q8—344no—
1089C4×D4—178no—
1090C4×D4—344no—
1091C4×D4—344no—
1092C4×D4—344no—
1093#117—24no—
1094#117—24no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4C22×D1711yescharacteristic
1119C2×C4⋊C4C22×D1711yescharacteristic
1120C2×C4⋊C4C22×D1711yescharacteristic
1121C2×C4⋊C4C22×D1711yescharacteristic
1122C2×C4⋊C4C22×D1711yescharacteristic
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42C22×D1711yescharacteristic
1184C2×C42C22×D1711yescharacteristic
1185C2×C42C22×D1711yescharacteristic
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95C22×D1711yescharacteristic
1213#95C22×D1711yescharacteristic
1214#95C22×D1711yescharacteristic
1215#95C22×D1711yescharacteristic
1216#95C22×D1711yescharacteristic
1217#95C22×D1711yescharacteristic
1218#95C22×D1711yescharacteristic
1219#95C22×D1711yescharacteristic
1220#95C22×D1711yescharacteristic
1221#95C22×D1711yescharacteristic
1222C17#3671211yescharacteristic, complemented, Sylow
1223C24—171no—
1224C24—171no—
1225C24—171no—
1226C24—171no—
1227C24—342no—
1228C24—342no—
1229C24—342no—
1230C24—681no—
1231C24—681no—
1232C24—681no—
1233C24—681no—
1234C24C23×D1711yescharacteristic
1235C24C23×D1711yescharacteristic
1236#41—6816no—
1237C2×Q8—342no—
1238C2×Q8—342no—
1239C2×Q8—342no—
1240C2×Q8—342no—
1241C2×Q8—342no—
1242C2×Q8—681no—
1243C2×Q8—681no—
1244C2×Q8—681no—
1245C2×Q8—681no—
1246C2×Q8—681no—
1247C2×Q8—681no—
1248C2×Q8—681no—
1249C2×D4—22no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—174no—
1253C2×D4—342no—
1254C2×D4—342no—
1255C2×D4—342no—
1256C2×D4—342no—
1257C2×D4—342no—
1258C2×D4—342no—
1259C2×D4—342no—
1260C2×D4—342no—
1261C2×D4—342no—
1262C2×D4—342no—
1263C2×D4—342no—
1264C2×D4—342no—
1265C2×D4—342no—
1266C2×D4—342no—
1267C2×D4—681no—
1268C2×D4—681no—
1269C2×D4—681no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—681no—
1282C2×D4—681no—
1283C2×D4—681no—
1284C2×D4—681no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—174no—
1294C22×C4—174no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
1305C22×C4—342no—
1306C22×C4—342no—
1307C22×C4—342no—
1308C22×C4—342no—
1309C22×C4—342no—
1310C22×C4—342no—
1311C22×C4—342no—
1312C22×C4—342no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4—6816no—
1330C22×C4—681no—
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C22×C4C23×D1711yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—174no—
1354C4⋊C4—342no—
1355C4⋊C4—342no—
1356C4⋊C4—342no—
1357C4⋊C4—342no—
1358C4⋊C4—342no—
1359C4⋊C4—342no—
1360C4⋊C4—342no—
1361C4⋊C4—342no—
1362C4⋊C4—342no—
1363C4⋊C4—342no—
1364C4⋊C4—342no—
1365C4⋊C4—342no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4—681no—
1370C4⋊C4—681no—
1371C4⋊C4—681no—
1372C4⋊C4—681no—
1373C4⋊C4—681no—
1374C4⋊C4—681no—
1375C4⋊C4—681no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—22no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—174no—
1387C22⋊C4—174no—
1388C22⋊C4—342no—
1389C22⋊C4—342no—
1390C22⋊C4—342no—
1391C22⋊C4—342no—
1392C22⋊C4—342no—
1393C22⋊C4—342no—
1394C22⋊C4—342no—
1395C22⋊C4—342no—
1396C22⋊C4—342no—
1397C22⋊C4—342no—
1398C22⋊C4—342no—
1399C22⋊C4—342no—
1400C22⋊C4—342no—
1401C22⋊C4—342no—
1402C22⋊C4—342no—
1403C22⋊C4—342no—
1404C22⋊C4—342no—
1405C22⋊C4—681no—
1406C22⋊C4—681no—
1407C22⋊C4—681no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4—681no—
1426C22⋊C4—681no—
1427C22⋊C4—681no—
1428C42—22no—
1429C42—22no—
1430C42—342no—
1431C42—342no—
1432C42—681no—
1433C42—681no—
1434C42D4×D1714yes—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—172no—
1449C23—172no—
1450C23—172no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23—341no—
1474C23—341no—
1475C23—341no—
1476C23—684no—
1477C23—684no—
1478C23—684no—
1479C23—684no—
1480C23—684no—
1481C23—684no—
1482C23—684no—
1483C23#1058769612yes—
1484C23C24×D1711yescharacteristic
1485Q8—684no—
1486Q8—684no—
1487Q8—1362no—
1488Q8—1362no—
1489D4—82no—
1490D4—684no—
1491D4—684no—
1492D4—684no—
1493D4—684no—
1494D4—684no—
1495D4—684no—
1496D4—684no—
1497D4—1362no—
1498D4—1362no—
1499D4—1362no—
1500D4—1362no—
1501C2×C4—28no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—44no—
1538C2×C4—172no—
1539C2×C4—172no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—684no—
1575C2×C4—684no—
1576C2×C4—684no—
1577C2×C4—684no—
1578C2×C4—684no—
1579C2×C4—684no—
1580C2×C4—684no—
1581C2×C4—1362no—
1582C2×C4—1362no—
1583C2×C4C2×D4×D1712yes—
1584C2×C4C2×D4×D1712yes—
1585C2×C4C2×D4×D1712yes—
1586C2×C4#1058769612yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—342no—
1602C22—342no—
1603C22—342no—
1604C22—342no—
1605C22—342no—
1606C22—342no—
1607C22—342no—
1608C22—342no—
1609C22—342no—
1610C22—6816no—
1611C22—681no—
1612C22—681no—
1613C22—681no—
1614C22—681no—
1615C22—681no—
1616C22—681no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22C22×D4×D1711yescharacteristic
1631C22C2×#1058769611yescharacteristic
1632C22C2×#1058769611yescharacteristic
1633C222−1+4×D1711yescharacteristic
1634C22#1176364411yescharacteristic
1635C22#1176364511yescharacteristic
1636C22#1176364511yescharacteristic
1637C4—22no—
1638C4—22no—
1639C4—22no—
1640C4—22no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—342no—
1651C4—342no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C2—42no—
1663C2—81no—
1664C2—682no—
1665C2—682no—
1666C2—682no—
1667C2—1361no—
1668C2#1454211411yescharacteristic
1669C2#1454241711yescharacteristic
1670C2#1454245911yescharacteristic
1671C2#1454295611yescharacteristic
1672C2#1454299611yescharacteristic
1673C2#1454305411yescharacteristic
1674C2#1454308011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2609C2
hypercenter#2609D17
hypocenterC17#36712
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2609

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763430C2semidirect
2. C2×#11763321C2semidirect
3. #14537075C2semidirect
4. #14537070C2semidirect
5. #14535337C2semidirect
6. #14535326C2semidirect
7. #14535283C2semidirect
8. #14535272C2semidirect
9. #14535242C2semidirect
10. #14535193C2semidirect
11. #14535182C2semidirect
12. #14535165C2semidirect
13. #14535097C2semidirect
14. #14535091C2semidirect
15. #14535072C2semidirect
16. #14535063C2semidirect
17. #14535041C2semidirect
18. #14535023C2semidirect
19. #14535012C2semidirect
20. #14534990C2semidirect
21. #14534708C2semidirect
22. #14534631C2semidirect
23. #14534402C2semidirect
24. #14534361C2semidirect
25. #14534350C2semidirect
26. #14534143C2semidirect
27. #14533963C2semidirect
28. #14532410C2semidirect
29. #14532391C2semidirect
30. #14531420C2semidirect
31. C17×#2609C2semidirect
35. C2×#10587555C22semidirect
36. C2×#10587574C22semidirect
38. C2×#10587584C22semidirect
42. C2×#10587571C22semidirect
48. C2×#10587569C22semidirect
51. C2×#10587610C22semidirect
54. C2×#10587582C22semidirect
59. C2×#10587570C22semidirect
64. C2×C4×Dic34C22semidirect
69. #11762751C22semidirect
70. #11762748C22semidirect
72. #11762746C22semidirect
73. #11762745C22semidirect
75. #11762742C22semidirect
76. #11762741C22semidirect
77. #11762739C22semidirect
79. #11762738C22semidirect
80. #11762738C22semidirect
84. #11762732C22semidirect
85. #11762731C22semidirect
86. #11762730C22semidirect
87. #11762730C22semidirect
88. #11762730C22semidirect
89. #11762729C22semidirect
92. #11762727C22semidirect
96. #11762726C22semidirect
100. #11762725C22semidirect
102. #11762724C22semidirect
105. #11762722C22semidirect
106. #11762722C22semidirect
108. #11762721C22semidirect
113. #11762713C22semidirect
118. #11762708C22semidirect
119. #11762708C22semidirect
120. #11762708C22semidirect
121. #11762702C22semidirect
124. #11762700C22semidirect
129. #11762694C22semidirect
130. #11762694C22semidirect
131. #11762693C22semidirect
132. #11762693C22semidirect
133. #11762690C22semidirect
134. #11762690C22semidirect
137. #11762688C22semidirect
142. #11762687C22semidirect
146. #11762685C22semidirect
152. #11762683C22semidirect
153. #11762683C22semidirect
158. #11762680C22semidirect
159. #11762680C22semidirect
160. #11762680C22semidirect
161. #11762677C22semidirect
166. #11762668C22semidirect
168. #11762666C22semidirect
172. #11762656C22semidirect
173. #95×D17C22semidirect
175. C2×C17×#117C22semidirect
176. C17×#398C22semidirect
178. C17×#396C22semidirect
181. C17×#388C22semidirect
182. C17×#387C22semidirect
183. C17×#387C22semidirect
187. C17×#385C22semidirect
188. C17×#382C22semidirect
346. C4×D68D4semidirect
772. #2609D17semidirect
894. C2×#117C2×D17semidirect
904. #398C2×D17semidirect
914. #396C2×D17semidirect
960. #388C2×D17semidirect
967. #387C2×D17semidirect
968. #387C2×D17semidirect
998. #385C2×D17semidirect
1000. #382C2×D17semidirect
1222. C17#36712semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117634302
C2×#117633212
#145370752
#145370702
#145353372
#145353262
#145352832
#145352722
#145352422
#145351932
#145351822
#145351652
#145350972
#145350912
#145350722
#145350632
#145350412
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