Finite Group Databasebeta

← #17241379

Subgroups — #17241379

Order 4352.

2432 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763403C211yesmaximal, characteristic, complemented
2C2×#11763317C211yesmaximal, characteristic, complemented
3#14537075C211yesmaximal, characteristic, complemented
4#14537072C211yesmaximal, characteristic, complemented
5#14535487C211yesmaximal, characteristic, complemented
6#14535444C211yesmaximal, characteristic, complemented
7#14535421C211yesmaximal, characteristic, complemented
8#14535398C211yesmaximal, characteristic, complemented
9#14535355C211yesmaximal, characteristic, complemented
10#14535348C211yesmaximal, characteristic, complemented
11#14535168C211yesmaximal, characteristic, complemented
12#14535153C211yesmaximal, characteristic, complemented
13#14535152C211yesmaximal, characteristic, complemented
14#14535140C211yesmaximal, characteristic, complemented
15#14535134C211yesmaximal, characteristic, complemented
16#14535121C211yesmaximal, characteristic, complemented
17#14535120C211yesmaximal, characteristic, complemented
18#14535111C211yesmaximal, characteristic, complemented
19#14535104C211yesmaximal, characteristic, complemented
20#14534709C211yesmaximal, characteristic, complemented
21#14534632C211yesmaximal, characteristic, complemented
22#14534475C211yesmaximal, characteristic, complemented
23#14534414C211yesmaximal, characteristic, complemented
24#14534378C211yesmaximal, characteristic, complemented
25#14534367C211yesmaximal, characteristic, complemented
26#14534134C211yesmaximal, characteristic, complemented
27#14533983C211yesmaximal, characteristic, complemented
28#14532122C211yesmaximal, characteristic, complemented
29#14532118C211yesmaximal, characteristic, complemented
30#14531425C211yesmaximal, characteristic, complemented
31C17×#2706C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763403—28no—
35C2×#10587584C2211yescharacteristic
36C2×#10587565C2211yescharacteristic, complemented
37C2×#10587576C2211yescharacteristic, complemented
38C2×#10587575C2211yescharacteristic, complemented
39#11763317—28no—
40C2×#10587572C2211yescharacteristic
41C2×#10587572C2211yescharacteristic, complemented
42C2×#10587615C2211yescharacteristic
43C2×#10587615C2211yescharacteristic
44C2×#10587569C2211yescharacteristic
45C2×#10587569C2211yescharacteristic
46C2×#10587621C2211yescharacteristic
47C2×#10587583C2211yescharacteristic
48C2×#10587583C2211yescharacteristic
49C2×#10587610C2211yescharacteristic
50C2×#10587582C2211yescharacteristic
51C2×#10587582C2211yescharacteristic
52C2×#10587564C2211yescharacteristic, complemented
53C2×#10587564C2211yescharacteristic, complemented
54C2×#10587564C2211yescharacteristic, complemented
55C2×#10587570C2211yescharacteristic
56C2×#10587570C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic
59C2×#10587568C2211yescharacteristic
60C2×#10587623C2211yescharacteristic
61C2×#10587623C2211yescharacteristic
62C2×D4×Dic17C2211yescharacteristic, complemented
63C2×#10587579C2211yescharacteristic
64C2×#10587579C2211yescharacteristic
65C2×#10587567C2211yescharacteristic
66C2×#10587567C2211yescharacteristic
67C2×#10587563C2211yescharacteristic
68C22×C4⋊Dic17C2211yescharacteristic, complemented
69#11762747C2211yescharacteristic, complemented
70#11762743C2211yescharacteristic, complemented
71#11762743C2211yescharacteristic, complemented
72#11762742C2211yescharacteristic, complemented
73#11762741C2211yescharacteristic, complemented
74#11762740C2211yescharacteristic, complemented
75#11762740C2211yescharacteristic, complemented
76#11762738C2211yescharacteristic
77#11762738C2211yescharacteristic
78#11762737C2211yescharacteristic, complemented
79#11762736C2211yescharacteristic
80#11762735C2211yescharacteristic, complemented
81#11762734C2211yescharacteristic
82#11762733C2211yescharacteristic
83#11762733C2211yescharacteristic
84#11762733C2211yescharacteristic, complemented
85#11762733C2211yescharacteristic, complemented
86#11762732C2211yescharacteristic
87#11762732C2211yescharacteristic, complemented
88#11762731C2211yescharacteristic
89#11762731C2211yescharacteristic
90#11762731C2211yescharacteristic, complemented
91#11762730C2211yescharacteristic, complemented
92#11762730C2211yescharacteristic, complemented
93#11762729C2211yescharacteristic, complemented
94#11762727C2211yescharacteristic
95#11762726C2211yescharacteristic
96#11762726C2211yescharacteristic
97#11762726C2211yescharacteristic
98#11762725C2211yescharacteristic
99#11762725C2211yescharacteristic
100#11762725C2211yescharacteristic
101#11762725C2211yescharacteristic, complemented
102#11762725C2211yescharacteristic, complemented
103#11762724C2211yescharacteristic
104#11762723C2211yescharacteristic
105#11762723C2211yescharacteristic
106#11762722C2211yescharacteristic, complemented
107#11762718C2211yescharacteristic
108#11762718C2211yescharacteristic
109#11762717C2211yescharacteristic
110#11762717C2211yescharacteristic, complemented
111#11762713C2211yescharacteristic, complemented
112#11762711C2211yescharacteristic
113#11762710C2211yescharacteristic
114#11762709C2211yescharacteristic
115#11762709C2211yescharacteristic
116#11762709C2211yescharacteristic
117#11762709C2211yescharacteristic
118#11762709C2211yescharacteristic, complemented
119#11762707C2211yescharacteristic, complemented
120#11762706C2211yescharacteristic, complemented
121#11762705C2211yescharacteristic, complemented
122#11762705C2211yescharacteristic, complemented
123#11762704C2211yescharacteristic, complemented
124#11762703C2211yescharacteristic
125#11762703C2211yescharacteristic, complemented
126#11762702C2211yescharacteristic, complemented
127#11762702C2211yescharacteristic, complemented
128#11762700C2211yescharacteristic
129#11762699C2211yescharacteristic
130#11762698C2211yescharacteristic
131#11762698C2211yescharacteristic
132#11762698C2211yescharacteristic, complemented
133#11762697C2211yescharacteristic
134#11762697C2211yescharacteristic
135#11762695C2211yescharacteristic, complemented
136#11762695C2211yescharacteristic, complemented
137#11762695C2211yescharacteristic, complemented
138#11762692C2211yescharacteristic, complemented
139#11762689C2211yescharacteristic
140#11762688C2211yescharacteristic
141#11762688C2211yescharacteristic, complemented
142#11762686C2211yescharacteristic
143#11762686C2211yescharacteristic
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic, complemented
147#11762684C2211yescharacteristic
148#11762684C2211yescharacteristic
149#11762684C2211yescharacteristic
150#11762683C2211yescharacteristic
151#11762683C2211yescharacteristic
152#11762683C2211yescharacteristic
153#11762683C2211yescharacteristic
154#11762683C2211yescharacteristic
155#11762683C2211yescharacteristic
156#11762683C2211yescharacteristic, complemented
157#11762683C2211yescharacteristic, complemented
158#11762683C2211yescharacteristic, complemented
159#11762682C2211yescharacteristic
160#11762681C2211yescharacteristic, complemented
161#11762681C2211yescharacteristic, complemented
162#11762678C2211yescharacteristic, complemented
163#11762671C2211yescharacteristic
164#11762671C2211yescharacteristic
165#11762670C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762666C2211yescharacteristic
168#11762666C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762664C2211yescharacteristic
171#11762664C2211yescharacteristic
172C4×#63225C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C17×#123C2211yescharacteristic
175C2×C17×#123C2211yescharacteristic, complemented
176C17×#399C2211yescharacteristic
177C17×#398C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#396C2211yescharacteristic, complemented
180C17×#394C2211yescharacteristic, complemented
181C17×#392C2211yescharacteristic
182C17×#390C2211yescharacteristic
183C17×#388C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#385C2211yescharacteristic, complemented
187C17×#382C2211yescharacteristic, complemented
188C17×#380C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C2×#63254—24no—
207C2×#63254—42no—
208C2×#63254—42no—
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×C4×D17—24no—
212C22×C4×D17—42no—
213C22×C4×D17—42no—
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C17×#123—24no—
222C17×#123—24no—
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
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×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊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×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257#10587625—24no—
258#10587625—42no—
259#10587623—24no—
260#10587623—42no—
261#10587621—42no—
262D4×Dic17—24no—
263#10587615—24no—
264#10587615—24no—
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⋊Dic17—24no—
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
303C2×C4⋊Dic17C2311yescharacteristic
304#10587610—42no—
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330#10587584—24no—
331#10587583—24no—
332#10587583—42no—
333#10587582—24no—
334#10587582—24no—
335#10587579—24no—
336#10587579—24no—
337#10587576—24no—
338#10587575—24no—
339#10587572—24no—
340#10587572—42no—
341#10587570—24no—
342#10587570—24no—
343#10587569—24no—
344#10587569—42no—
345#10587568—24no—
346#10587567—24no—
347#10587567D418yescomplemented
348#10587565—24no—
349#10587564—24no—
350#10587564—24no—
351#10587564—42no—
352#10587563—24no—
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
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
387C24×C17C2411yescharacteristic
388C23×D17—22no—
389C23×D17—22no—
390C23×D17—22no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17—41no—
394C23×D17—41no—
395C23×D17C2411yescharacteristic
396C23×D17C2411yescharacteristic
397C23×D17C2411yescharacteristic
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—22no—
401C2×D4×C17—22no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C22×C4×C17—22no—
408C22×C4×C17—22no—
409C22×C4×C17—22no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17C2×D414yes—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—22no—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17C2×D414yes—
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471#63254—416no—
472C2×D68—22no—
473C2×D68—22no—
474C2×D68—22no—
475C2×D68—41no—
476C2×D68—41no—
477C2×D68—41no—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
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×D17—416no—
493C2×C4×D17C2×D414yes—
494C2×Dic34—22no—
495C2×Dic34—22no—
496C2×Dic34—22no—
497C2×Dic34—41no—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C4⋊C4×C17—22no—
501C4⋊C4×C17—22no—
502C4⋊C4×C17—22no—
503C4⋊C4×C17—22no—
504C4⋊C4×C17—41no—
505C4⋊C4×C17—41no—
506C4⋊C4×C17—41no—
507C4⋊C4×C17—41no—
508C22⋊C4×C17—22no—
509C22⋊C4×C17—22no—
510C22⋊C4×C17—22no—
511C22⋊C4×C17—22no—
512C22⋊C4×C17—41no—
513C22⋊C4×C17—41no—
514C22⋊C4×C17—41no—
515C22⋊C4×C17—41no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17—41no—
518C22⋊C4×C17—41no—
519C22⋊C4×C17—41no—
520C22⋊C4×C17C2×D414yes—
521C42×C17—41no—
522C22⋊Dic17—22no—
523C22⋊Dic17—22no—
524C22⋊Dic17—22no—
525C22⋊Dic17—22no—
526C22⋊Dic17—22no—
527C22⋊Dic17—22no—
528C22⋊Dic17—22no—
529C22⋊Dic17—22no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534#63227—22no—
535#63227—22no—
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
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#63227C2×D414yes—
561C4⋊Dic17—22no—
562C4⋊Dic17—22no—
563C4⋊Dic17—22no—
564C4⋊Dic17—22no—
565C4⋊Dic17—22no—
566C4⋊Dic17—22no—
567C4⋊Dic17—22no—
568C4⋊Dic17—22no—
569C4⋊Dic17—22no—
570C4⋊Dic17—41no—
571C4⋊Dic17—41no—
572#63225—22no—
573#63225—22no—
574#63225—22no—
575#63225—22no—
576#63225—22no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—41no—
581#63225—41no—
582#63225—41no—
583#63225—41no—
584#63225—41no—
585#63225—41no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225C2×D414yes—
591C4×Dic17—22no—
592C4×Dic17—22no—
593C4×Dic17—41no—
594C4×Dic17—41no—
595C4×Dic17—41no—
596C4×Dic17C2×D414yes—
597#36723—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×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17C22×D412yes—
618C23×C17H(5,𝔽2)12yes—
619C23×C17C2511yescharacteristic
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—21no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17—44no—
645C22×D17—44no—
646C22×D17C22×D412yes—
647C22×D172−1+412yes—
648D4×C17—44no—
649D4×C17—44no—
650D4×C17—82no—
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×C17—44no—
687C2×C4×C17C22×D412yes—
688C2×C4×C17C22×D412yes—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—44no—
693C22⋊D17—82no—
694C22⋊D17—82no—
695C22⋊D17—82no—
696C2×Dic17—28no—
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—21no—
731C2×Dic17—21no—
732C2×Dic17—44no—
733C2×Dic17—82no—
734C2×Dic17—82no—
735C2×Dic17C22×D412yes—
736C2×Dic17C22×D412yes—
737C2×Dic17C22×D412yes—
738C2×Dic17H(5,𝔽2)12yes—
739D68—44no—
740D68—44no—
741C4×D17—44no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—44no—
745C4×D17—44no—
746Dic34—44no—
747Dic34—82no—
748C2×#539—171no—
749C2×#525—171no—
750#2849—171no—
751#2848—171no—
752#2707—171no—
753#2706D1711yescharacteristic, complemented
754#2704—171no—
755#2703—171no—
756#2701—171no—
757#2698—171no—
758#2697—171no—
759#2685—171no—
760#2683—171no—
761#2682—171no—
762#2681—171no—
763#2681—171no—
764#2680—171no—
765#2680—171no—
766#2678—171no—
767#2678—171no—
768#2638—171no—
769#2630—171no—
770#2611—171no—
771#2603—171no—
772#2601—171no—
773#2600—171no—
774#2579—171no—
775#2566—171no—
776#2407—171no—
777#2406—171no—
778#2319—171no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
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×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17C23×D411yescharacteristic
801C22×C17C2×H(5,𝔽2)11yescharacteristic
802C22×C17C2×H(5,𝔽2)11yescharacteristic
803C22×C17C2×2−1+411yescharacteristic
804C22×C17#58511yescharacteristic
805C22×C17#58511yescharacteristic
806C22×C17#58511yescharacteristic
807C2×D17—22no—
808C2×D17—22no—
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—416no—
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—
829C4×C17—22no—
830C4×C17—22no—
831C4×C17—41no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841Dic17—22no—
842Dic17—22no—
843Dic17—22no—
844Dic17—22no—
845Dic17—41no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854C22×#41—171no—
855C24×C4—171no—
856#539—348no—
857C2×#126—171no—
858C2×#126—171no—
859C2×#125—171no—
860C2×#125—171no—
861#525—348no—
862C2×#123—171no—
863C2×#123—171no—
864C2×#123—171no—
865C2×#123—171no—
866C2×#123—171no—
867C2×#123—171no—
868C2×#123—171no—
869C2×#123C2×D1711yescharacteristic
870C2×#123C2×D1711yescharacteristic, complemented
871C2×C22⋊Q8—171no—
872C2×C22⋊Q8—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×#121—171no—
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#120—171no—
884C2×#120—171no—
885C2×#120—171no—
886C2×C4×D4—171no—
887C2×C4×D4—171no—
888C2×C4×D4—171no—
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×#117—171no—
892C22×C4⋊C4—171no—
893#400—171no—
894#399C2×D1711yescharacteristic
895#398—171no—
896#398—171no—
897#398—171no—
898#398—171no—
899#398—171no—
900#398—171no—
901#398C2×D1711yescharacteristic, complemented
902#397—171no—
903#397—171no—
904#397—171no—
905#397—171no—
906#397—171no—
907#397—171no—
908#397C2×D1711yescharacteristic, complemented
909#396—171no—
910#396—171no—
911#396—171no—
912#396—171no—
913#396—171no—
914#396—171no—
915#396—171no—
916#396—171no—
917#396—171no—
918#396C2×D1711yescharacteristic, complemented
919#395—171no—
920#395—171no—
921#395—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#394—171no—
933#394—171no—
934#394C2×D1711yescharacteristic, complemented
935#393—171no—
936#392—171no—
937#392—171no—
938#392—171no—
939#392—171no—
940#392C2×D1711yescharacteristic
941#391—171no—
942#390—171no—
943#390—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#390—171no—
949#390C2×D1711yescharacteristic
950#389—171no—
951#389—171no—
952#389—171no—
953#389—171no—
954#389—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388C2×D1711yescharacteristic, complemented
967#387—171no—
968#387—171no—
969#387—171no—
970#387—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#386C2×D1711yescharacteristic
980#386C2×D1711yescharacteristic
981#385—171no—
982#385—171no—
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#385C2×D1711yescharacteristic, complemented
997#384—171no—
998#382C2×D1711yescharacteristic, complemented
999#381—171no—
1000#381—171no—
1001#381—171no—
1002#380—171no—
1003#380—171no—
1004#380—171no—
1005#380C2×D1711yescharacteristic
1006#379—171no—
1007#379—171no—
1008#379—171no—
1009C4×C4⋊C4—171no—
1010#376—171no—
1011C2×C17—42no—
1012C2×C17—42no—
1013C2×C17—81no—
1014C2×C17#344911yescharacteristic
1015C2×C17#348411yescharacteristic
1016C2×C17#348911yescharacteristic
1017C2×C17#353311yescharacteristic
1018C2×C17#353511yescharacteristic
1019C2×C17#353911yescharacteristic
1020C2×C17#354111yescharacteristic
1021D17—42no—
1022D17—42no—
1023D17—81no—
1024C25—171no—
1025C2×#41—344no—
1026C2×#41—682no—
1027C2×#41—682no—
1028C22×Q8—171no—
1029C22×Q8—171no—
1030C22×D4—171no—
1031C22×D4—171no—
1032C22×D4—171no—
1033C22×D4—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4C22×D1711yescharacteristic
1040C22×D4C22×D1711yescharacteristic
1041C22×D4C22×D1711yescharacteristic
1042C23×C4—171no—
1043C23×C4—171no—
1044C23×C4—171no—
1045C23×C4—171no—
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—344no—
1052C23×C4—682no—
1053C23×C4—682no—
1054C23×C4C22×D1711yescharacteristic
1055C23×C4C22×D1711yescharacteristic
1056#126—344no—
1057#126—344no—
1058#125—344no—
1059#125—344no—
1060#123—24no—
1061#123—24no—
1062#123—344no—
1063#123—344no—
1064#123—344no—
1065#123—344no—
1066#123—682no—
1067#123—682no—
1068#123—682no—
1069C22⋊Q8—344no—
1070C22⋊Q8—344no—
1071C22⋊Q8—344no—
1072C22⋊Q8—344no—
1073C22⋊Q8—344no—
1074C22⋊Q8—682no—
1075C22⋊Q8—682no—
1076C22⋊Q8—682no—
1077#121—344no—
1078#121—344no—
1079#121—344no—
1080#121—682no—
1081#120—344no—
1082#120—344no—
1083#120—682no—
1084C4×D4—178no—
1085C4×D4—344no—
1086C4×D4—344no—
1087C4×D4—344no—
1088C4×D4—344no—
1089#117—344no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
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⋊C4—171no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—344no—
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×C4⋊C4C22×D1711yescharacteristic
1128C2×C4⋊C4C22×D1711yescharacteristic
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⋊C4C22×D1711yescharacteristic
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×C22⋊C4C22×D1711yescharacteristic
1180C2×C22⋊C4C22×D1711yescharacteristic
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42—171no—
1185C2×C42—171no—
1186C2×C42—171no—
1187C2×C42C22×D1711yescharacteristic
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
1220C17#3672311yescharacteristic, complemented, Sylow
1221C24—171no—
1222C24—171no—
1223C24—171no—
1224C24—342no—
1225C24—342no—
1226C24—342no—
1227C24—681no—
1228C24—681no—
1229C24—681no—
1230C24—681no—
1231C24C23×D1711yescharacteristic
1232C24C23×D1711yescharacteristic
1233C24C23×D1711yescharacteristic
1234#41—6816no—
1235C2×Q8—342no—
1236C2×Q8—342no—
1237C2×Q8—342no—
1238C2×Q8—681no—
1239C2×Q8—681no—
1240C2×Q8—681no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—174no—
1251C2×D4—342no—
1252C2×D4—342no—
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—681no—
1263C2×D4—681no—
1264C2×D4—681no—
1265C2×D4—681no—
1266C2×D4—681no—
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—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—41no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—171no—
1287C22×C4—174no—
1288C22×C4—174no—
1289C22×C4—171no—
1290C22×C4—171no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—342no—
1304C22×C4—342no—
1305C22×C4—342no—
1306C22×C4—342no—
1307C22×C4—342no—
1308C22×C4—342no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—681no—
1316C22×C4—681no—
1317C22×C4—6816no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4C23×D1711yescharacteristic
1325C22×C4C23×D1711yescharacteristic
1326C22×C4C23×D1711yescharacteristic
1327C22×C4C23×D1711yescharacteristic
1328C22×C4C23×D1711yescharacteristic
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C22×C4C23×D1711yescharacteristic
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—174no—
1345C4⋊C4—342no—
1346C4⋊C4—342no—
1347C4⋊C4—342no—
1348C4⋊C4—342no—
1349C4⋊C4—342no—
1350C4⋊C4—342no—
1351C4⋊C4—342no—
1352C4⋊C4—342no—
1353C4⋊C4—342no—
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—681no—
1363C4⋊C4—681no—
1364C4⋊C4—681no—
1365C4⋊C4—681no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4—681no—
1370C4⋊C4—681no—
1371C4⋊C4—681no—
1372C4⋊C4—681no—
1373C4⋊C4—681no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—174no—
1387C22⋊C4—342no—
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—681no—
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⋊C4D4×D1714yes—
1426C42—41no—
1427C42—174no—
1428C42—342no—
1429C42—342no—
1430C42—681no—
1431C42—681no—
1432C42—681no—
1433C23—21no—
1434C23—21no—
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—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—172no—
1453C23—172no—
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—684no—
1474C23—684no—
1475C23—684no—
1476C23—684no—
1477C23—684no—
1478C23—684no—
1479C23—684no—
1480C23C2×D4×D1712yes—
1481C23#1058769612yes—
1482C23C24×D1711yescharacteristic
1483Q8—684no—
1484Q8—1362no—
1485D4—44no—
1486D4—44no—
1487D4—82no—
1488D4—684no—
1489D4—684no—
1490D4—684no—
1491D4—684no—
1492D4—684no—
1493D4—684no—
1494D4—1362no—
1495D4—1362no—
1496D4—1362no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
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—44no—
1532C2×C4—44no—
1533C2×C4—172no—
1534C2×C4—172no—
1535C2×C4—172no—
1536C2×C4—172no—
1537C2×C4—348no—
1538C2×C4—341no—
1539C2×C4—341no—
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—684no—
1574C2×C4—684no—
1575C2×C4—684no—
1576C2×C4—684no—
1577C2×C4—684no—
1578C2×C4—684no—
1579C2×C4—1362no—
1580C2×C4—1362no—
1581C2×C4C2×D4×D1712yes—
1582C2×C4C2×D4×D1712yes—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
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—
1626C22C22×D4×D1711yescharacteristic
1627C22H(5,𝔽2)×D1711yescharacteristic
1628C22C2×#1058769611yescharacteristic
1629C222−1+4×D1711yescharacteristic
1630C22#1176364411yescharacteristic
1631C22#1176364411yescharacteristic
1632C22#1176364511yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—342no—
1646C4—342no—
1647C4—342no—
1648C4—342no—
1649C4—681no—
1650C4—681no—
1651C4—681no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C2—42no—
1659C2—42no—
1660C2—81no—
1661C2—682no—
1662C2—682no—
1663C2—1361no—
1664C2#1454211511yescharacteristic
1665C2#1454241411yescharacteristic
1666C2#1454245811yescharacteristic
1667C2#1454295611yescharacteristic
1668C2#1454299111yescharacteristic
1669C2#1454303611yescharacteristic
1670C2#1454306611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2706C2
hypercenter#2706D17
hypocenterC17#36723
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2706

Complements

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

NH ≅ G/Ntype
1. C2×#11763403C2semidirect
2. C2×#11763317C2semidirect
3. #14537075C2semidirect
4. #14537072C2semidirect
5. #14535487C2semidirect
6. #14535444C2semidirect
7. #14535421C2semidirect
8. #14535398C2semidirect
9. #14535355C2semidirect
10. #14535348C2semidirect
11. #14535168C2semidirect
12. #14535153C2semidirect
13. #14535152C2semidirect
14. #14535140C2semidirect
15. #14535134C2semidirect
16. #14535121C2semidirect
17. #14535120C2semidirect
18. #14535111C2semidirect
19. #14535104C2semidirect
20. #14534709C2semidirect
21. #14534632C2semidirect
22. #14534475C2semidirect
23. #14534414C2semidirect
24. #14534378C2semidirect
25. #14534367C2semidirect
26. #14534134C2semidirect
27. #14533983C2semidirect
28. #14532122C2semidirect
29. #14532118C2semidirect
30. #14531425C2semidirect
31. C17×#2706C2semidirect
36. C2×#10587565C22semidirect
37. C2×#10587576C22semidirect
38. C2×#10587575C22semidirect
41. C2×#10587572C22semidirect
52. C2×#10587564C22semidirect
53. C2×#10587564C22semidirect
54. C2×#10587564C22semidirect
62. C2×D4×Dic17C22semidirect
68. C22×C4⋊Dic17C22semidirect
69. #11762747C22semidirect
70. #11762743C22semidirect
71. #11762743C22semidirect
72. #11762742C22semidirect
73. #11762741C22semidirect
74. #11762740C22semidirect
75. #11762740C22semidirect
78. #11762737C22semidirect
80. #11762735C22semidirect
84. #11762733C22semidirect
85. #11762733C22semidirect
87. #11762732C22semidirect
90. #11762731C22semidirect
91. #11762730C22semidirect
92. #11762730C22semidirect
93. #11762729C22semidirect
101. #11762725C22semidirect
102. #11762725C22semidirect
106. #11762722C22semidirect
110. #11762717C22semidirect
111. #11762713C22semidirect
118. #11762709C22semidirect
119. #11762707C22semidirect
120. #11762706C22semidirect
121. #11762705C22semidirect
122. #11762705C22semidirect
123. #11762704C22semidirect
125. #11762703C22semidirect
126. #11762702C22semidirect
127. #11762702C22semidirect
132. #11762698C22semidirect
135. #11762695C22semidirect
136. #11762695C22semidirect
137. #11762695C22semidirect
138. #11762692C22semidirect
141. #11762688C22semidirect
146. #11762685C22semidirect
156. #11762683C22semidirect
157. #11762683C22semidirect
158. #11762683C22semidirect
160. #11762681C22semidirect
161. #11762681C22semidirect
162. #11762678C22semidirect
165. #11762670C22semidirect
166. #11762667C22semidirect
172. C4×#63225C22semidirect
173. #11762654C22semidirect
175. C2×C17×#123C22semidirect
177. C17×#398C22semidirect
178. C17×#397C22semidirect
179. C17×#396C22semidirect
180. C17×#394C22semidirect
183. C17×#388C22semidirect
186. C17×#385C22semidirect
187. C17×#382C22semidirect
347. #10587567D4semidirect
753. #2706D17semidirect
870. C2×#123C2×D17semidirect
901. #398C2×D17semidirect
908. #397C2×D17semidirect
918. #396C2×D17semidirect
934. #394C2×D17semidirect
966. #388C2×D17semidirect
996. #385C2×D17semidirect
998. #382C2×D17semidirect
1220. C17#36723semidirect

Maximal subgroups

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

subgroupindex
C2×#117634032
C2×#117633172
#145370752
#145370722
#145354872
#145354442
#145354212
#145353982
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