Finite Group Databasebeta

← #17197527

Subgroups — #17197527

Order 4352.

2486 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763317C211yesmaximal, characteristic
2#14531949C211yesmaximal, characteristic, complemented
3#14531946C211yesmaximal, characteristic, complemented
4#14531940C211yesmaximal, characteristic, complemented
5#14531937C211yesmaximal, characteristic, complemented
6#14531780C211yesmaximal, characteristic, complemented
7#14531776C211yesmaximal, characteristic, complemented
8#14531772C211yesmaximal, characteristic, complemented
9#14531754C211yesmaximal, characteristic, complemented
10#14531753C211yesmaximal, characteristic, complemented
11#14531723C211yesmaximal, characteristic, complemented
12#14531718C211yesmaximal, characteristic, complemented
13#14531642C211yesmaximal, characteristic, complemented
14#14531638C211yesmaximal, characteristic, complemented
15#14531610C211yesmaximal, characteristic, complemented
16#14531609C211yesmaximal, characteristic, complemented
17#14531547C211yesmaximal, characteristic, complemented
18#14531544C211yesmaximal, characteristic, complemented
19#14531538C211yesmaximal, characteristic, complemented
20#14531535C211yesmaximal, characteristic, complemented
21#14531447C211yesmaximal, characteristic, complemented
22#14531444C211yesmaximal, characteristic, complemented
23#14531441C211yesmaximal, characteristic, complemented
24#14531438C211yesmaximal, characteristic, complemented
25#14531425C211yesmaximal, characteristic, complemented
26#14531423C211yesmaximal, characteristic, complemented
27#14531416C211yesmaximal, characteristic, complemented
28#14531412C211yesmaximal, characteristic, complemented
29#14531163C211yesmaximal, characteristic, complemented
30C2×#11762671C211yesmaximal, characteristic, complemented
31C17×#2359C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763317C4116yescomplemented
35C2×#10587615C2211yescharacteristic
36C2×#10587582C2211yescharacteristic
37C2×#10587582C2211yescharacteristic
38C2×#10587570C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587568C2211yescharacteristic
41C2×#10587623C2211yescharacteristic
42C2×D4×Dic17C2211yescharacteristic
43C2×#10587579C2211yescharacteristic
44C2×#10587579C2211yescharacteristic
45C2×C4×C22⋊D17C2211yescharacteristic
46C2×#10587567C2211yescharacteristic
47C2×#10587567C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587612C2211yescharacteristic
50C2×#10587563C2211yescharacteristic
51C22×#63227C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53#11762715C2211yescharacteristic, complemented
54#11762714C2211yescharacteristic, complemented
55#11762713C2211yescharacteristic, complemented
56#11762713C2211yescharacteristic, complemented
57#11762711C2211yescharacteristic
58#11762711C2211yescharacteristic
59#11762710C2211yescharacteristic
60#11762710C2211yescharacteristic
61#11762709C2211yescharacteristic
62#11762709C2211yescharacteristic
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762708C2211yescharacteristic, complemented
66#11762706C2211yescharacteristic, complemented
67#11762704C2211yescharacteristic, complemented
68#11762702C2211yescharacteristic, complemented
69#11762702C2211yescharacteristic, complemented
70#11762701C2211yescharacteristic
71#11762701C2211yescharacteristic
72#11762701C2211yescharacteristic
73#11762701C2211yescharacteristic
74#11762701C2211yescharacteristic, complemented
75#11762700C2211yescharacteristic
76#11762700C2211yescharacteristic
77#11762700C2211yescharacteristic
78#11762700C2211yescharacteristic
79#11762700C2211yescharacteristic, complemented
80#11762699C2211yescharacteristic
81#11762699C2211yescharacteristic
82#11762699C2211yescharacteristic
83#11762699C2211yescharacteristic
84#11762699C2211yescharacteristic, complemented
85#11762698C2211yescharacteristic
86#11762698C2211yescharacteristic
87#11762698C2211yescharacteristic
88#11762698C2211yescharacteristic
89#11762698C2211yescharacteristic, complemented
90#11762696C2211yescharacteristic, complemented
91#11762696C2211yescharacteristic, complemented
92#11762696C2211yescharacteristic, complemented
93#11762695C2211yescharacteristic, complemented
94#11762695C2211yescharacteristic, complemented
95#11762693C2211yescharacteristic, complemented
96#11762693C2211yescharacteristic, complemented
97#11762693C2211yescharacteristic, complemented
98#11762691C2211yescharacteristic, complemented
99#11762691C2211yescharacteristic, complemented
100#11762691C2211yescharacteristic, complemented
101#11762690C2211yescharacteristic, complemented
102#11762690C2211yescharacteristic, complemented
103#11762690C2211yescharacteristic, complemented
104#11762689C2211yescharacteristic
105#11762688C2211yescharacteristic
106#11762688C2211yescharacteristic
107#11762688C2211yescharacteristic
108#11762688C2211yescharacteristic, complemented
109#11762687C2211yescharacteristic
110#11762687C2211yescharacteristic
111#11762687C2211yescharacteristic
112#11762687C2211yescharacteristic
113#11762686C2211yescharacteristic
114#11762686C2211yescharacteristic
115#11762686C2211yescharacteristic
116#11762686C2211yescharacteristic, complemented
117#11762685C2211yescharacteristic, complemented
118#11762685C2211yescharacteristic, complemented
119#11762684C2211yescharacteristic
120#11762684C2211yescharacteristic, complemented
121#11762683C2211yescharacteristic, complemented
122#11762682C2211yescharacteristic
123#11762681C2211yescharacteristic
124#11762680C2211yescharacteristic, complemented
125#11762676C2211yescharacteristic, complemented
126#11762676C2211yescharacteristic, complemented
127#11762674C2211yescharacteristic, complemented
128#11762673C2211yescharacteristic, complemented
129#11762671C2211yescharacteristic
130#11762671C2211yescharacteristic
131#11762671C2211yescharacteristic
132#11762671C2211yescharacteristic
133#11762671C2211yescharacteristic
134#11762671C2211yescharacteristic
135#11762671C2211yescharacteristic
136#11762671C2211yescharacteristic
137#11762671C2211yescharacteristic, complemented
138#11762670C2211yescharacteristic
139#11762670C2211yescharacteristic
140#11762670C2211yescharacteristic, complemented
141#11762667C2211yescharacteristic, complemented
142#11762666C2211yescharacteristic
143#11762666C2211yescharacteristic
144#11762666C2211yescharacteristic
145#11762666C2211yescharacteristic
146#11762666C2211yescharacteristic, complemented
147#11762664C2211yescharacteristic
148#11762664C2211yescharacteristic
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×#63225C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C4×#63227C2211yescharacteristic
159C4×#63227C2211yescharacteristic
160C4×#63227C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic
165#11762656C2211yescharacteristic, complemented
166#11762655C2211yescharacteristic, complemented
167#11762654C2211yescharacteristic, complemented
168C2×#10587502C2211yescharacteristic
169C2×#10587502C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#123C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C17×#117C2211yescharacteristic
176C17×#389C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#387C2211yescharacteristic, complemented
181C17×#386C2211yescharacteristic
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C2×#63254—42no—
204C2×#63254—42no—
205C2×#63254C2×C418yes—
206C22×D68C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×C4×D17—42no—
209C22×C4×D17—42no—
210C22×C4×D17C2×C418yescomplemented
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×Dic34C2311yescharacteristic
219C17×#123C2×C418yescomplemented
220C4×D4×C17—42no—
221C17×#117—42no—
222C2×C4⋊C4×C17C2311yescharacteristic
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×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊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×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248#10587623C2×C418yescomplemented
249D4×Dic17—42no—
250#10587615C2×C418yescomplemented
251C4×C22⋊D17—42no—
252C2×#63227—42no—
253C2×#63227—42no—
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
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
282#10587612—42no—
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311#10587582C2×C418yescomplemented
312#10587582C2×C418yescomplemented
313#10587579C2×C418yescomplemented
314#10587579C2×C418yescomplemented
315#10587570C2×C418yescomplemented
316#10587570C2×C418yescomplemented
317#10587568C2×C418yescomplemented
318#10587567—42no—
319#10587567C2×C418yescomplemented
320#10587567C2×C418yescomplemented
321#10587563C2×C418yescomplemented
322C17×#95C2311yescharacteristic
323C17×#95C2311yescharacteristic
324C17×#95C2311yescharacteristic
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17C22×C414yes—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—22no—
383C2×D4×C17—22no—
384C2×D4×C17C22×C414yes—
385C22×C4×C17—22no—
386C22×C4×C17—22no—
387C22×C4×C17—22no—
388C22×C4×C17—22no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17C22×C414yes—
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C2×C22⋊D17—22no—
411C2×C22⋊D17—22no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17C22×C414yes—
419C2×C22⋊D17C22×C414yes—
420C2×C22⋊D17C22×C414yes—
421C2×C22⋊D17C22×C414yes—
422C22×Dic17—22no—
423C22×Dic17—22no—
424C22×Dic17—22no—
425C22×Dic17—22no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17—41no—
429C22×Dic17—41no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17C22×C414yes—
436C22×Dic17C22×C414yes—
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450#63254—416no—
451C2×D68—41no—
452C2×D68—41no—
453C2×D68—41no—
454C2×D68—41no—
455C2×D68C22×C414yes—
456C2×D68C22×C414yes—
457C2×C4×D17—416no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17C22×C414yes—
475C2×C4×D17C22×C414yes—
476C2×C4×D17C22×C414yes—
477C2×C4×D17C22×C414yes—
478C2×C4×D17C22×C414yes—
479C2×Dic34—41no—
480C2×Dic34—41no—
481C2×Dic34C22×C414yes—
482C4⋊C4×C17—41no—
483C4⋊C4×C17—41no—
484C4⋊C4×C17—41no—
485C4⋊C4×C17—41no—
486C4⋊C4×C17—41no—
487C4⋊C4×C17C22×C414yes—
488C4⋊C4×C17C22×C414yes—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—41no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17C22×C414yes—
495C22⋊C4×C17C22×C414yes—
496C22⋊C4×C17C22×C414yes—
497C42×C17—41no—
498C42×C17—41no—
499C42×C17—41no—
500C42×C17—41no—
501C42×C17—41no—
502C22⋊Dic17—22no—
503C22⋊Dic17—22no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17C22×C414yes—
508#63227—41no—
509#63227—41no—
510#63227—41no—
511#63227—41no—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227—41no—
519#63227—41no—
520#63227—41no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227C22×C414yes—
531#63227C22×C414yes—
532#63227C22×C414yes—
533#63227C22×C414yes—
534#63227C22×C414yes—
535#63227C22×C414yes—
536C4⋊Dic17—41no—
537C4⋊Dic17—41no—
538C4⋊Dic17—41no—
539C4⋊Dic17—41no—
540C4⋊Dic17—41no—
541#63225—41no—
542#63225—41no—
543#63225—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225C22×C414yes—
548#63225C22×C414yes—
549#63225C22×C414yes—
550#63225C22×C414yes—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562C4×Dic17C22×C414yes—
563C4×Dic17C22×C414yes—
564#34396—171nomaximal, Sylow
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17C23×C412yes—
576C23×C17C23×C412yes—
577C23×C17H(5,𝔽2)12yes—
578C23×C17H(5,𝔽2)12yes—
579C23×C17C2511yescharacteristic
580C22×D17—28no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—21no—
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—44no—
600C22×D17—44no—
601C22×D17—44no—
602C22×D17—44no—
603C22×D17—44no—
604C22×D17—44no—
605C22×D17C23×C412yes—
606C22×D17C23×C412yes—
607C22×D17C23×C412yes—
608D4×C17—28no—
609C2×C4×C17—28no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—82no—
645C2×C4×C17—82no—
646C2×C4×C17—82no—
647C2×C4×C17C23×C412yes—
648C2×C4×C17C23×C412yes—
649C2×C4×C17C23×C412yes—
650C2×C4×C17C23×C412yes—
651C2×C4×C17C23×C412yes—
652C22⋊D17—28no—
653C22⋊D17—44no—
654C22⋊D17—44no—
655C22⋊D17—44no—
656C2×Dic17—28no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—44no—
692C2×Dic17—82no—
693C2×Dic17—82no—
694C2×Dic17—82no—
695C2×Dic17C23×C412yes—
696C2×Dic17C23×C412yes—
697C2×Dic17C23×C412yes—
698C2×Dic17C23×C412yes—
699C2×Dic17C23×C412yes—
700D68—44no—
701D68—44no—
702C4×D17—44no—
703C4×D17—44no—
704C4×D17—44no—
705C4×D17—44no—
706C4×D17—44no—
707C4×D17—82no—
708C4×D17—82no—
709Dic34—44no—
710C2×#525—171no—
711#2378—171no—
712#2378—171no—
713#2377—171no—
714#2377—171no—
715#2359—171no—
716#2359—171no—
717#2359—171no—
718#2359D1711yescharacteristic, complemented
719#2357—171no—
720#2357—171no—
721#2353—171no—
722#2353—171no—
723#2343—171no—
724#2343—171no—
725#2339—171no—
726#2339—171no—
727#2333—171no—
728#2333—171no—
729#2332—171no—
730#2332—171no—
731#2321—171no—
732#2321—171no—
733#2321—171no—
734#2321—171no—
735#2319—171no—
736#2319—171no—
737#2318—171no—
738#2318—171no—
739#2280—171no—
740C2×#381—171no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—22no—
748C22×C17—22no—
749C22×C17—22no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17#51814yes—
755C22×C17C24×C411yescharacteristic
756C22×C17C2×H(5,𝔽2)11yescharacteristic
757C22×C17C2×H(5,𝔽2)11yescharacteristic
758C22×C17#58511yescharacteristic
759C22×C17#58511yescharacteristic
760C22×C17#58511yescharacteristic
761C22×C17#58511yescharacteristic
762C2×D17—22no—
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—22no—
766C2×D17—22no—
767C2×D17—22no—
768C2×D17—22no—
769C2×D17—22no—
770C2×D17—22no—
771C2×D17—416no—
772C2×D17—41no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—41no—
778C2×D17—41no—
779C2×D17—41no—
780C2×D17—41no—
781C2×D17—41no—
782C2×D17—41no—
783C2×D17—41no—
784C4×C17—22no—
785C4×C17—22no—
786C4×C17—22no—
787C4×C17—22no—
788C4×C17—22no—
789C4×C17—41no—
790C4×C17—41no—
791C4×C17—41no—
792C4×C17—41no—
793C4×C17—41no—
794C4×C17—41no—
795C4×C17—41no—
796C4×C17—41no—
797Dic17—22no—
798Dic17—22no—
799Dic17—22no—
800Dic17—22no—
801Dic17—22no—
802Dic17—41no—
803Dic17—41no—
804Dic17—41no—
805Dic17—41no—
806Dic17—41no—
807Dic17—41no—
808Dic17—41no—
809Dic17—41no—
810C22×#41—171no—
811C24×C4—171no—
812#525—1716no—
813C2×#123—171no—
814C2×#123C2×D1711yescharacteristic
815C2×C22⋊Q8—171no—
816C2×C22⋊Q8—171no—
817C2×#121—171no—
818C2×#121—171no—
819C2×#120—171no—
820C2×#120—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4—171no—
824C2×C4×D4—171no—
825C2×C4×D4—171no—
826C2×C4×D4—171no—
827C2×C4×D4—171no—
828C2×C4×D4C2×D1711yescharacteristic
829C2×#117—171no—
830C2×#117—171no—
831C2×#117C2×D1711yescharacteristic
832C22×C22⋊C4—171no—
833C22×C22⋊C4—171no—
834#391—171no—
835#391—171no—
836#391—171no—
837#391—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390—171no—
842#390—171no—
843#390—171no—
844#390—171no—
845#390—171no—
846#389—171no—
847#389—171no—
848#389—171no—
849#389C2×D1711yescharacteristic, complemented
850#388—171no—
851#388—171no—
852#388—171no—
853#388—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388C2×D1711yescharacteristic, complemented
873#388C2×D1711yescharacteristic, complemented
874#387—171no—
875#387—171no—
876#387—171no—
877#387—171no—
878#387—171no—
879#387—171no—
880#387—171no—
881#387—171no—
882#387—171no—
883#387—171no—
884#387—171no—
885#387—171no—
886#387—171no—
887#387—171no—
888#387C2×D1711yescharacteristic, complemented
889#387C2×D1711yescharacteristic, complemented
890#386—171no—
891#386—171no—
892#386—171no—
893#386—171no—
894#386—171no—
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386—171no—
904#386—171no—
905#386C2×D1711yescharacteristic
906#385—171no—
907#385—171no—
908#385—171no—
909#385—171no—
910#385—171no—
911#385—171no—
912#385C2×D1711yescharacteristic
913#385C2×D1711yescharacteristic, complemented
914#383—171no—
915#383—171no—
916#382—171no—
917#382—171no—
918#381—171no—
919#381—171no—
920#381—171no—
921#381—171no—
922#381—171no—
923#381—171no—
924#381—171no—
925#381—171no—
926#381—171no—
927#381—171no—
928#381—171no—
929#381—171no—
930#380—171no—
931#380—171no—
932#380—171no—
933#380—171no—
934#380—171no—
935#380—171no—
936#379—171no—
937#379—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C4⋊C4—171no—
943C4×C4⋊C4C2×D1711yescharacteristic, complemented
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956C4×C22⋊C4C2×D1711yescharacteristic
957C4×C22⋊C4C2×D1711yescharacteristic, complemented
958#376—171no—
959#376—171no—
960C2×#95—171no—
961C2×#95—171no—
962C2×#95—171no—
963C2×#95—171no—
964C2×#95—171no—
965C2×#95C2×D1711yescharacteristic
966C2×C17—24no—
967C2×C17—42no—
968C2×C17C2×#51811yescharacteristic
969C2×C17#342811yescharacteristic
970C2×C17#342811yescharacteristic
971C2×C17#353311yescharacteristic
972C2×C17#353311yescharacteristic
973C2×C17#353311yescharacteristic
974C2×C17#353311yescharacteristic
975D17—42no—
976D17—42no—
977D17—42no—
978C25—171no—
979C2×#41—178no—
980C2×#41—682no—
981C2×#41—682no—
982C22×Q8—171no—
983C22×D4—171no—
984C22×D4—171no—
985C22×D4—171no—
986C22×D4—171no—
987C22×D4—171no—
988C22×D4—171no—
989C22×D4C22×D1711yescharacteristic
990C23×C4—171no—
991C23×C4—171no—
992C23×C4—178no—
993C23×C4—171no—
994C23×C4—171no—
995C23×C4—171no—
996C23×C4—171no—
997C23×C4—171no—
998C23×C4—171no—
999C23×C4—171no—
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—682no—
1004C23×C4—682no—
1005C23×C4C22×D1711yescharacteristic
1006C23×C4C22×D1711yescharacteristic
1007C23×C4C22×D1711yescharacteristic
1008C23×C4C22×D1711yescharacteristic
1009#123—178no—
1010#123C4×D1718yescomplemented
1011C22⋊Q8—178no—
1012C22⋊Q8—178no—
1013#121—178no—
1014#121—178no—
1015#120—178no—
1016#120—178no—
1017C4×D4—42no—
1018C4×D4—178no—
1019C4×D4—178no—
1020C4×D4—178no—
1021C4×D4—178no—
1022C4×D4—682no—
1023C4×D4—682no—
1024C4×D4—682no—
1025#117—42no—
1026#117—178no—
1027#117—682no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—171no—
1040C2×C4⋊C4—171no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4C22×D1711yescharacteristic
1044C2×C4⋊C4C22×D1711yescharacteristic
1045C2×C4⋊C4C22×D1711yescharacteristic
1046C2×C4⋊C4C22×D1711yescharacteristic
1047C2×C4⋊C4C22×D1711yescharacteristic
1048C2×C4⋊C4C22×D1711yescharacteristic
1049C2×C4⋊C4C22×D1711yescharacteristic
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—682no—
1085C2×C22⋊C4—682no—
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4C22×D1711yescharacteristic
1092C2×C22⋊C4C22×D1711yescharacteristic
1093C2×C22⋊C4C22×D1711yescharacteristic
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—171no—
1107C2×C42C22×D1711yescharacteristic
1108C2×C42C22×D1711yescharacteristic
1109C2×C42C22×D1711yescharacteristic
1110C2×C42C22×D1711yescharacteristic
1111C2×C42C22×D1711yescharacteristic
1112#95—171no—
1113#95—171no—
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155#95C22×D1711yescharacteristic
1156#95C22×D1711yescharacteristic
1157#95C22×D1711yescharacteristic
1158#95C22×D1711yescharacteristic
1159#95C22×D1711yescharacteristic
1160C17#3439611yescharacteristic, complemented, Sylow
1161C24—171no—
1162C24—171no—
1163C24—171no—
1164C24—174no—
1165C24—342no—
1166C24—342no—
1167C24—681no—
1168C24—681no—
1169C24—681no—
1170C24—681no—
1171C24C23×D1711yescharacteristic
1172C24C23×D1711yescharacteristic
1173#41—6816no—
1174C2×Q8—174no—
1175C2×Q8—681no—
1176C2×Q8—681no—
1177C2×D4—22no—
1178C2×D4—22no—
1179C2×D4—174no—
1180C2×D4—174no—
1181C2×D4—174no—
1182C2×D4—174no—
1183C2×D4—174no—
1184C2×D4—174no—
1185C2×D4—342no—
1186C2×D4—342no—
1187C2×D4—681no—
1188C2×D4—681no—
1189C2×D4—681no—
1190C2×D4—681no—
1191C2×D4—681no—
1192C2×D4—681no—
1193C2×D4—681no—
1194C2×D4—681no—
1195C2×D4—681no—
1196C2×D4—681no—
1197C2×D4C2×C4×D1714yes—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—22no—
1201C22×C4—22no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—41no—
1205C22×C4—41no—
1206C22×C4—41no—
1207C22×C4—41no—
1208C22×C4—41no—
1209C22×C4—174no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—171no—
1213C22×C4—171no—
1214C22×C4—171no—
1215C22×C4—174no—
1216C22×C4—174no—
1217C22×C4—174no—
1218C22×C4—174no—
1219C22×C4—174no—
1220C22×C4—174no—
1221C22×C4—171no—
1222C22×C4—171no—
1223C22×C4—171no—
1224C22×C4—171no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—342no—
1230C22×C4—342no—
1231C22×C4—342no—
1232C22×C4—342no—
1233C22×C4—6816no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4—681no—
1244C22×C4—681no—
1245C22×C4—681no—
1246C22×C4—681no—
1247C22×C4—681no—
1248C22×C4—681no—
1249C22×C4—681no—
1250C22×C4—681no—
1251C22×C4—681no—
1252C22×C4—681no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4C2×C4×D1714yes—
1260C22×C4C23×D1711yescharacteristic
1261C22×C4C23×D1711yescharacteristic
1262C22×C4C23×D1711yescharacteristic
1263C22×C4C23×D1711yescharacteristic
1264C22×C4C23×D1711yescharacteristic
1265C22×C4C23×D1711yescharacteristic
1266C22×C4C23×D1711yescharacteristic
1267C22×C4C23×D1711yescharacteristic
1268C22×C4C23×D1711yescharacteristic
1269C22×C4C23×D1711yescharacteristic
1270C22×C4C23×D1711yescharacteristic
1271C22×C4C23×D1711yescharacteristic
1272C22×C4C23×D1711yescharacteristic
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—41no—
1277C4⋊C4—41no—
1278C4⋊C4—174no—
1279C4⋊C4—174no—
1280C4⋊C4—174no—
1281C4⋊C4—174no—
1282C4⋊C4—681no—
1283C4⋊C4—681no—
1284C4⋊C4—681no—
1285C4⋊C4—681no—
1286C4⋊C4—681no—
1287C4⋊C4—681no—
1288C4⋊C4—681no—
1289C4⋊C4—681no—
1290C4⋊C4—681no—
1291C4⋊C4—681no—
1292C4⋊C4—681no—
1293C4⋊C4C2×C4×D1714yes—
1294C4⋊C4C2×C4×D1714yes—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—174no—
1301C22⋊C4—174no—
1302C22⋊C4—174no—
1303C22⋊C4—174no—
1304C22⋊C4—174no—
1305C22⋊C4—174no—
1306C22⋊C4—174no—
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—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—681no—
1330C22⋊C4—681no—
1331C22⋊C4—681no—
1332C22⋊C4—681no—
1333C22⋊C4—681no—
1334C22⋊C4C2×C4×D1714yes—
1335C22⋊C4C2×C4×D1714yes—
1336C22⋊C4C2×C4×D1714yes—
1337C42—41no—
1338C42—41no—
1339C42—41no—
1340C42—41no—
1341C42—41no—
1342C42—174no—
1343C42—174no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C42—681no—
1348C42—681no—
1349C42—681no—
1350C42—681no—
1351C42—681no—
1352C42—681no—
1353C42—681no—
1354C42—681no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—172no—
1366C23—172no—
1367C23—172no—
1368C23—348no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—341no—
1374C23—341no—
1375C23—341no—
1376C23—341no—
1377C23—341no—
1378C23—341no—
1379C23—341no—
1380C23—341no—
1381C23—341no—
1382C23—341no—
1383C23—341no—
1384C23—341no—
1385C23—341no—
1386C23—341no—
1387C23—684no—
1388C23—684no—
1389C23—684no—
1390C23—684no—
1391C23—684no—
1392C23—684no—
1393C23C22×C4×D1712yes—
1394C23C22×C4×D1712yes—
1395C23#1058769112yes—
1396C23#1058769612yes—
1397C23C24×D1711yescharacteristic
1398Q8—684no—
1399D4—28no—
1400D4—348no—
1401D4—684no—
1402D4—684no—
1403D4—684no—
1404D4—684no—
1405D4—684no—
1406C2×C4—28no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—82no—
1442C2×C4—82no—
1443C2×C4—82no—
1444C2×C4—172no—
1445C2×C4—172no—
1446C2×C4—172no—
1447C2×C4—172no—
1448C2×C4—172no—
1449C2×C4—348no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—684no—
1485C2×C4—684no—
1486C2×C4—684no—
1487C2×C4—684no—
1488C2×C4—684no—
1489C2×C4—684no—
1490C2×C4—1362no—
1491C2×C4—1362no—
1492C2×C4—1362no—
1493C2×C4—1362no—
1494C2×C4—1362no—
1495C2×C4C22×C4×D1712yes—
1496C2×C4C22×C4×D1712yes—
1497C2×C4C22×C4×D1712yes—
1498C2×C4C22×C4×D1712yes—
1499C2×C4C22×C4×D1712yes—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—22no—
1504C22—22no—
1505C22—22no—
1506C22—22no—
1507C22—22no—
1508C22—22no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—342no—
1514C22—342no—
1515C22—342no—
1516C22—342no—
1517C22—342no—
1518C22—342no—
1519C22—342no—
1520C22—342no—
1521C22—342no—
1522C22—6816no—
1523C22—681no—
1524C22—681no—
1525C22—681no—
1526C22—681no—
1527C22—681no—
1528C22—681no—
1529C22—681no—
1530C22—681no—
1531C22—681no—
1532C22—681no—
1533C22—681no—
1534C22—681no—
1535C22#1176328114yes—
1536C22C23×C4×D1711yescharacteristic
1537C22C2×#1058769111yescharacteristic
1538C22C2×#1058769611yescharacteristic
1539C22#1176364411yescharacteristic
1540C22#1176364511yescharacteristic
1541C22#1176364511yescharacteristic
1542C22#1176364611yescharacteristic
1543C4—22no—
1544C4—22no—
1545C4—22no—
1546C4—22no—
1547C4—22no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—342no—
1557C4—342no—
1558C4—342no—
1559C4—342no—
1560C4—342no—
1561C4—681no—
1562C4—681no—
1563C4—681no—
1564C4—681no—
1565C4—681no—
1566C4—681no—
1567C4—681no—
1568C4—681no—
1569C2—24no—
1570C2—42no—
1571C2—682no—
1572C2—682no—
1573C2—682no—
1574C2C2×#1176328111yescharacteristic
1575C2#1454198311yescharacteristic
1576C2#1454198411yescharacteristic
1577C2#1454294311yescharacteristic
1578C2#1454295011yescharacteristic
1579C2#1454295411yescharacteristic
1580C2#1454295611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2359C2
socle, cosocleC23×C17C25
prime radicalC2×#11763317C2
hypercenter#2359D17
hypocenterC17#34396
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #14531949C2semidirect
3. #14531946C2semidirect
4. #14531940C2semidirect
5. #14531937C2semidirect
6. #14531780C2semidirect
7. #14531776C2semidirect
8. #14531772C2semidirect
9. #14531754C2semidirect
10. #14531753C2semidirect
11. #14531723C2semidirect
12. #14531718C2semidirect
13. #14531642C2semidirect
14. #14531638C2semidirect
15. #14531610C2semidirect
16. #14531609C2semidirect
17. #14531547C2semidirect
18. #14531544C2semidirect
19. #14531538C2semidirect
20. #14531535C2semidirect
21. #14531447C2semidirect
22. #14531444C2semidirect
23. #14531441C2semidirect
24. #14531438C2semidirect
25. #14531425C2semidirect
26. #14531423C2semidirect
27. #14531416C2semidirect
28. #14531412C2semidirect
29. #14531163C2semidirect
30. C2×#11762671C2semidirect
31. C17×#2359C2semidirect
34. #11763317C4semidirect
53. #11762715C22semidirect
54. #11762714C22semidirect
55. #11762713C22semidirect
56. #11762713C22semidirect
65. #11762708C22semidirect
66. #11762706C22semidirect
67. #11762704C22semidirect
68. #11762702C22semidirect
69. #11762702C22semidirect
74. #11762701C22semidirect
79. #11762700C22semidirect
84. #11762699C22semidirect
89. #11762698C22semidirect
90. #11762696C22semidirect
91. #11762696C22semidirect
92. #11762696C22semidirect
93. #11762695C22semidirect
94. #11762695C22semidirect
95. #11762693C22semidirect
96. #11762693C22semidirect
97. #11762693C22semidirect
98. #11762691C22semidirect
99. #11762691C22semidirect
100. #11762691C22semidirect
101. #11762690C22semidirect
102. #11762690C22semidirect
103. #11762690C22semidirect
108. #11762688C22semidirect
116. #11762686C22semidirect
117. #11762685C22semidirect
118. #11762685C22semidirect
120. #11762684C22semidirect
121. #11762683C22semidirect
124. #11762680C22semidirect
125. #11762676C22semidirect
126. #11762676C22semidirect
127. #11762674C22semidirect
128. #11762673C22semidirect
137. #11762671C22semidirect
140. #11762670C22semidirect
141. #11762667C22semidirect
146. #11762666C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. C4×#63225C22semidirect
152. C4×#63225C22semidirect
153. #11762660C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
165. #11762656C22semidirect
166. #11762655C22semidirect
167. #11762654C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
176. C17×#389C22semidirect
177. C17×#388C22semidirect
178. C17×#388C22semidirect
179. C17×#387C22semidirect
180. C17×#387C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
210. C22×C4×D17C2×C4semidirect
219. C17×#123C2×C4semidirect
248. #10587623C2×C4semidirect
250. #10587615C2×C4semidirect
311. #10587582C2×C4semidirect
312. #10587582C2×C4semidirect
313. #10587579C2×C4semidirect
314. #10587579C2×C4semidirect
315. #10587570C2×C4semidirect
316. #10587570C2×C4semidirect
317. #10587568C2×C4semidirect
319. #10587567C2×C4semidirect
320. #10587567C2×C4semidirect
321. #10587563C2×C4semidirect
718. #2359D17semidirect
849. #389C2×D17semidirect
872. #388C2×D17semidirect
873. #388C2×D17semidirect
888. #387C2×D17semidirect
889. #387C2×D17semidirect
913. #385C2×D17semidirect
943. C4×C4⋊C4C2×D17semidirect
957. C4×C22⋊C4C2×D17semidirect
1010. #123C4×D17semidirect
1160. C17#34396semidirect

Maximal subgroups

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

subgroupindex
C2×#117633172
#145319492
#145319462
#145319402
#145319372
#145317802
#145317762
#145317722
#145317542
#145317532
#145317232
#145317182
#145316422
#145316382
#145316102
#145316092
#145315472
#145315442
#145315382
#145315352
#145314472
#145314442
#145314412
#145314382
#145314252
#145314232
#145314162
#145314122
#145311632
C2×#117626712
C17×#23592
#3439617