Finite Group Databasebeta

← #16957118

Subgroups — #16957118

Order 4352.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587610C211yesmaximal, characteristic
2C22×C4×Dic34C211yesmaximal, characteristic, complemented
3C2×#11762715C211yesmaximal, characteristic, complemented
4C2×#11762669C211yesmaximal, characteristic
5#14527035C212yesmaximal, complemented
6#14527027C212yesmaximal
7#14527021C212yesmaximal
8#14527015C212yesmaximal, complemented
9#14527014C211yesmaximal, characteristic, complemented
10#14527014C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
12C23×Dic34C2211yescharacteristic
13C2×#10587610—24no—
14C2×#10587610—24no—
15C2×#10587610C418yescomplemented
16C2×C4×Dic34—24no—
17C2×C4×Dic34—24no—
18C2×C4×Dic34—24no—
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2212yes—
23C22×#63225C2212yes—
24C22×C22⋊Dic17C2212yes—
25C22×C22⋊Dic17C2212yes—
26C22×C4×Dic17C2212yes—
27#11762715—24no—
28#11762669—24no—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C24×C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2211yescharacteristic
38C22×C22⋊C4×C17C2211yescharacteristic
39C22×C42×C17C2211yescharacteristic
40C22×C42×C17C2211yescharacteristic
41C4×C22⋊C4×C17—24no—
42C2×C17×#95C2211yescharacteristic
43C2×C17×#95C2211yescharacteristic
44C25×C17C2311yescharacteristic
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—22no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17C2×C414yes—
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2311yescharacteristic
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×Dic17C2312yes—
59C23×Dic17C2312yes—
60C23×Dic17C2312yes—
61C23×Dic17C2312yes—
62C22×Dic34—22no—
63C22×Dic34—22no—
64C22×Dic34—22no—
65C22×Dic34—22no—
66C22×Dic34C2×C414yes—
67C22×Dic34D414yes—
68C22×Dic34D414yes—
69C2×C22⋊C4×C17—22no—
70C2×C22⋊C4×C17—22no—
71C2×C22⋊C4×C17—22no—
72C2×C22⋊C4×C17—22no—
73C2×C22⋊C4×C17—22no—
74C2×C22⋊C4×C17Q814yescomplemented
75C2×C42×C17—22no—
76C2×C42×C17—22no—
77C2×C42×C17—22no—
78C2×C42×C17—22no—
79C2×C42×C17—22no—
80C2×C42×C17D414yes—
81C2×C22⋊Dic17—24no—
82C2×C22⋊Dic17—24no—
83C2×C22⋊Dic17—24no—
84C2×C22⋊Dic17—24no—
85C2×C22⋊Dic17—42no—
86C2×C22⋊Dic17C2×C418yes—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17—22no—
89C2×C4⋊Dic17—22no—
90C2×C4⋊Dic17—22no—
91C2×C4⋊Dic17—22no—
92C2×C4⋊Dic17—22no—
93C2×C4⋊Dic17—22no—
94C2×C4⋊Dic17C2×C414yes—
95C2×C4⋊Dic17D414yes—
96#10587610—232no—
97C2×#63225—24no—
98C2×#63225—24no—
99C2×#63225—24no—
100C2×#63225—24no—
101C2×#63225—24no—
102C2×#63225C2×C418yes—
103C2×C4×Dic17—24no—
104C2×C4×Dic17—24no—
105C2×C4×Dic17—24no—
106C4×Dic34—232no—
107C17×#95—22no—
108C17×#95—22no—
109#10587502—24no—
110#10587502—24no—
111#10587502—24no—
112#10587502—24no—
113#10587502—24no—
114#10587502—42no—
115#10587502—42no—
116C24×C17—21no—
117C24×C17—21no—
118C24×C17—21no—
119C24×C17—21no—
120C24×C17—21no—
121C24×C17—21no—
122C24×C17—21no—
123C24×C17—21no—
124C24×C17—21no—
125C24×C17—21no—
126C24×C17—21no—
127C24×C17—21no—
128C24×C17C22×C412yes—
129C24×C17C2×Q812yes—
130C24×C17#4112yes—
131C24×C17C2411yescharacteristic
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—28no—
161C22×C4×C17—28no—
162C22×C4×C17—28no—
163C22×C4×C17—44no—
164C22×C4×C17—44no—
165C22×C4×C17—44no—
166C22×C4×C17—44no—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C22×C412yes—
169C22×C4×C17C2×D412yes—
170C22×C4×C17C2×D412yes—
171C22×C4×C17C2×D412yes—
172C22×C4×C17C2×D412yes—
173C22×C4×C17C2×D412yes—
174C22×C4×C17C2×D412yes—
175C22×C4×C17C2×Q812yes—
176C22×C4×C17C2×Q812yes—
177C22×C4×C17#4112yes—
178C22×C4×C17#4112yes—
179C22×C4×C17#4112yes—
180C22×C4×C17#4112yes—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17C22×C414yes—
205C22×Dic17C22×C414yes—
206C22×Dic17C2×D414yes—
207C22×Dic17C2×D414yes—
208C22×Dic17C2×D414yes—
209C2×Dic34—28no—
210C2×Dic34—28no—
211C2×Dic34—28no—
212C2×Dic34—28no—
213C2×Dic34—28no—
214C2×Dic34—28no—
215C2×Dic34C22⋊C4116yescomplemented
216C22⋊C4×C17—28no—
217C22⋊C4×C17—28no—
218C42×C17—28no—
219C42×C17—44no—
220C22⋊Dic17—216no—
221C22⋊Dic17—48no—
222C4⋊Dic17—28no—
223C4⋊Dic17—28no—
224C4⋊Dic17—44no—
225#63225—216no—
226#63225—216no—
227C4×Dic17—216no—
228#13969—171nomaximal, Sylow
229C23×C17—22no—
230C23×C17—22no—
231C23×C17—22no—
232C23×C17—22no—
233C23×C17—22no—
234C23×C17—22no—
235C23×C17—22no—
236C23×C17—22no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—22no—
240C23×C17—22no—
241C23×C17—22no—
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—22no—
246C23×C17—22no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17C4×Q814yescomplemented
264C23×C17C23×C411yescharacteristic
265C23×C17C22×D411yescharacteristic
266C23×C17C22×D411yescharacteristic
267C23×C17C22×D411yescharacteristic
268C23×C17C22×D411yescharacteristic
269C23×C17C22×Q811yescharacteristic
270C23×C17C2×#4111yescharacteristic
271C23×C17C2×#4111yescharacteristic
272C23×C17C2×#4111yescharacteristic
273C23×C17C2×#4111yescharacteristic
274C23×C17C2×#4111yescharacteristic
275C23×C17H(5,𝔽2)11yescharacteristic
276C23×C172−1+411yescharacteristic
277C23×C172−1+411yescharacteristic
278C23×C172−1+411yescharacteristic
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—416no—
314C2×C4×C17C2×C22⋊C414yes—
315C2×C4×C17C4×D414yes—
316C2×C4×C17C4×D414yes—
317C2×C4×C17#12014yes—
318C2×C4×C17#12114yes—
319C2×C4×C17#12114yes—
320C2×C4×C17C22⋊Q814yescomplemented
321C2×C4×C17#12314yes—
322C2×Dic17—24no—
323C2×Dic17—24no—
324C2×Dic17—24no—
325C2×Dic17—24no—
326C2×Dic17—24no—
327C2×Dic17—24no—
328C2×Dic17—24no—
329C2×Dic17—24no—
330C2×Dic17—24no—
331C2×Dic17—24no—
332C2×Dic17—24no—
333C2×Dic17—24no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17—42no—
348C2×Dic17—42no—
349C2×Dic17C2×C22⋊C418yes—
350Dic34—232no—
351C22×C22⋊Q8—171no—
352C22×C4×Q8—171no—
353C2×#391—171no—
354C2×#380—171no—
355C2×C4×C22⋊C4D1711yescharacteristic
356#1441—172no—
357#1439—172no—
358#1437—172no—
359#1436—172no—
360C4⋊#95—171no—
361C4⋊#95—171no—
362C22×C17—24no—
363C22×C17—24no—
364C22×C17—24no—
365C22×C17—42no—
366C22×C17—42no—
367C22×C17—42no—
368C22×C17—42no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—42no—
376C22×C17—42no—
377C22×C17C22×C22⋊C411yescharacteristic
378C22×C17C2×C4×D411yescharacteristic
379C22×C17C2×C4×D411yescharacteristic
380C22×C17C2×C4×Q811yescharacteristic
381C22×C17C4×#4111yescharacteristic
382C22×C17#51911yescharacteristic
383C22×C17#52011yescharacteristic
384C22×C17C2×#12011yescharacteristic
385C22×C17C2×#12111yescharacteristic
386C22×C17C2×#12111yescharacteristic
387C22×C17C2×C22⋊Q811yescharacteristic
388C22×C17C2×#12311yescharacteristic
389C22×C17#52511yescharacteristic
390C22×C17#52911yescharacteristic
391C22×C17#53311yescharacteristic
392C22×C17#53611yescharacteristic
393C22×C17#53711yescharacteristic
394C22×C17#54111yescharacteristic
395C22×C17#54211yescharacteristic
396C22×C17#54611yescharacteristic
397C22×C17#54711yescharacteristic
398C22×C17#54811yescharacteristic
399C22×C17#54811yescharacteristic
400C22×C17#54811yescharacteristic
401C22×C17#54811yescharacteristic
402C22×C17#54811yescharacteristic
403C22×C17D4×Q811yescharacteristic
404C22×C17D4×Q811yescharacteristic
405C22×C17D4×Q811yescharacteristic
406C22×C17#55011yescharacteristic
407C22×C17#55011yescharacteristic
408C22×C17#55211yescharacteristic
409C22×C17#55211yescharacteristic
410C22×C17#55411yescharacteristic
411C22×C17#55611yescharacteristic
412C4×C17—24no—
413C4×C17—42no—
414C4×C17—42no—
415C4×C17—42no—
416C4×C17—42no—
417C4×C17#38618yes—
418Dic17—28no—
419Dic17—44no—
420Dic17—44no—
421Dic17—82no—
422C23×Q8—171no—
423C24×C4C2×D1711yescharacteristic
424C2×C22⋊Q8—178no—
425C2×C22⋊Q8—344no—
426C2×C22⋊Q8—344no—
427C2×C4×Q8—344no—
428C2×C4×Q8—344no—
429C2×C4×Q8—344no—
430C22×C4⋊C4—172no—
431C22×C4⋊C4—171no—
432C22×C4⋊C4—171no—
433C22×C4⋊C4—172no—
434C22×C4⋊C4—171no—
435C22×C22⋊C4—172no—
436C22×C22⋊C4—172no—
437C22×C22⋊C4C2×D1711yescharacteristic
438C22×C22⋊C4C2×D1711yescharacteristic
439C22×C42—172no—
440C22×C42C2×D1711yescharacteristic
441C22×C42C2×D1711yescharacteristic
442#391—344no—
443#380—344no—
444C4×C22⋊C4—24no—
445C2×#95—172no—
446C2×#95—172no—
447C2×#95—172no—
448C2×#95—172no—
449C2×#95—172no—
450C2×#95—172no—
451C2×#95—172no—
452C2×#95C2×D1711yescharacteristic
453C2×#95C2×D1711yescharacteristic
454C2×C17—44no—
455C2×C17C2×#38611yescharacteristic
456C2×C17C4×C22⋊Q811yescharacteristic
457C2×C17#232311yescharacteristic
458C2×C17Q8×C22⋊C411yescharacteristic
459C2×C17#234111yescharacteristic
460C2×C17#236011yescharacteristic
461C2×C17#236211yescharacteristic
462C2×C17#240711yescharacteristic
463C2×C17#240911yescharacteristic
464C2×C17#242111yescharacteristic
465C2×C17#242311yescharacteristic
466C2×C17#242611yescharacteristic
467C2×C17#242911yescharacteristic
468C2×C17#253611yescharacteristic
469C2×C17#253811yescharacteristic
470C25C22×D1711yescharacteristic
471C22×Q8—174no—
472C22×Q8—174no—
473C22×Q8—174no—
474C22×Q8—342no—
475C22×Q8—342no—
476C22×Q8—342no—
477C22×Q8—342no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—172no—
485C23×C4—172no—
486C23×C4—172no—
487C23×C4—172no—
488C23×C4C4×D1714yes—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1711yescharacteristic
491C23×C4C22×D1711yescharacteristic
492C23×C4C22×D1711yescharacteristic
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C22⋊Q8—3432no—
496C4×Q8—3432no—
497C2×C4⋊C4—178no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—174no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—344no—
502C2×C4⋊C4—344no—
503C2×C4⋊C4—344no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4—342no—
507C2×C4⋊C4—344no—
508C2×C4⋊C4—342no—
509C2×C4⋊C4—342no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—342no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—178no—
518C2×C22⋊C4—344no—
519C2×C22⋊C4—344no—
520C2×C22⋊C4—344no—
521C2×C22⋊C4—344no—
522C2×C22⋊C4—682no—
523C2×C22⋊C4Dic3414yescomplemented
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—344no—
530C2×C42—344no—
531C2×C42—344no—
532C2×C42C22⋊D1714yes—
533#95—22no—
534#95—22no—
535#95—344no—
536#95—344no—
537#95—344no—
538#95—344no—
539#95—344no—
540#95—682no—
541#95—682no—
542C17#1396911yescharacteristic, complemented, Sylow
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24C2×Dic3412yes—
556C24C2×C4×D1712yes—
557C24#6325212yes—
558C24C23×D1711yescharacteristic
559C2×Q8—1716no—
560C2×Q8—348no—
561C2×Q8—348no—
562C2×Q8—348no—
563C2×Q8—348no—
564C2×Q8—348no—
565C2×Q8—348no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—174no—
602C22×C4—174no—
603C22×C4—174no—
604C22×C4—174no—
605C22×C4—174no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—342no—
621C22×C4—342no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4C2×Dic3412yes—
630C22×C4C2×Dic3412yes—
631C22×C4C2×C4×D1712yes—
632C22×C4C2×C4×D1712yes—
633C22×C4#6325212yes—
634C22×C4#6325212yes—
635C22×C4#6325212yes—
636C22×C4D4×D1712yes—
637C22×C4D4×D1712yes—
638C22×C4D4×D1712yes—
639C22×C4#6325412yes—
640C22×C4C2×C22⋊D1712yes—
641C22×C4C2×C22⋊D1712yes—
642C22×C4C2×C22⋊D1712yes—
643C4⋊C4—3416no—
644C4⋊C4—3416no—
645C4⋊C4—348no—
646C4⋊C4—348no—
647C4⋊C4—684no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—3416no—
651C22⋊C4—688no—
652C42—28no—
653C42—44no—
654C42—3416no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C4×Dic3414yescomplemented
690C23C22×Dic3411yescharacteristic
691C23C22×C4×D1711yescharacteristic
692C23C2×#6325211yescharacteristic
693C23C2×#6325211yescharacteristic
694C23C2×#6325211yescharacteristic
695C23C2×#6325211yescharacteristic
696C23C2×D4×D1711yescharacteristic
697C23C2×D4×D1711yescharacteristic
698C23C2×D4×D1711yescharacteristic
699C23C2×#6325411yescharacteristic
700C23#1058769611yescharacteristic
701C23#1058769711yescharacteristic
702C23#1058769711yescharacteristic
703C23#1058769711yescharacteristic
704C23C22×C22⋊D1711yescharacteristic
705Q8—3432no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—416no—
741C2×C4—178no—
742C2×C4—344no—
743C2×C4—344no—
744C2×C4—344no—
745C2×C4—344no—
746C2×C4—344no—
747C2×C4—344no—
748C2×C4—344no—
749C2×C4—344no—
750C2×C4—344no—
751C2×C4—344no—
752C2×C4—344no—
753C2×C4—344no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—682no—
761C2×C4—682no—
762C2×C4—682no—
763C2×C4—682no—
764C2×C4—682no—
765C2×C4—682no—
766C2×C4—682no—
767C2×C4—682no—
768C2×C4—682no—
769C2×C4C22⋊C4×D1714yes—
770C2×C4#1058756714yes—
771C2×C4#1058756914yes—
772C2×C4#1058757014yes—
773C2×C4#1058761014yescomplemented
774C2×C4C4×C22⋊D1714yes—
775C2×C4#1058762314yes—
776C2×C4#1058762414yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×C22⋊C4×D1711yescharacteristic
793C22C2×#1058756711yescharacteristic
794C22C2×C4×C22⋊D1711yescharacteristic
795C22C2×C4×Dic3411yescharacteristic
796C22C4×#6325211yescharacteristic
797C22#1176328611yescharacteristic
798C22#1176328911yescharacteristic
799C22C2×#1058762311yescharacteristic
800C22C2×#1058762411yescharacteristic
801C22C2×#1058757011yescharacteristic
802C22C2×#1058761011yescharacteristic
803C22C2×#1058756911yescharacteristic
804C22#1176332011yescharacteristic
805C22#1176334311yescharacteristic
806C22#1176336611yescharacteristic
807C22#1176338011yescharacteristic
808C22#1176338711yescharacteristic
809C22#1176342111yescharacteristic
810C22#1176343011yescharacteristic
811C22#1176345511yescharacteristic
812C22#1176346411yescharacteristic
813C22#1176346811yescharacteristic
814C22#1176346811yescharacteristic
815C22#1176346811yescharacteristic
816C22#1176346811yescharacteristic
817C22#1176346811yescharacteristic
818C22D4×Dic3411yescharacteristic
819C22D4×Dic3411yescharacteristic
820C22D4×Dic3411yescharacteristic
821C22#1176348011yescharacteristic
822C22#1176348011yescharacteristic
823C22#1176349911yescharacteristic
824C22#1176349911yescharacteristic
825C22#1176351611yescharacteristic
826C22#1176352911yescharacteristic
827C4—24no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—348no—
833C4—684no—
834C4—684no—
835C4—1362no—
836C4#1176268518yes—
837C2—44no—
838C2C2×#1176268511yescharacteristic
839C2C4×#1058761011yescharacteristic
840C2#1453146611yescharacteristic
841C2C22⋊C4×Dic3411yescharacteristic
842C2#1453162411yescharacteristic
843C2#1453178711yescharacteristic
844C2#1453180911yescharacteristic
845C2#1453212911yescharacteristic
846C2#1453214911yescharacteristic
847C2#1453228711yescharacteristic
848C2#1453230911yescharacteristic
849C2#1453235011yescharacteristic
850C2#1453238311yescharacteristic
851C2#1453369311yescharacteristic
852C2#1453370611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#13969
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic34C2semidirect
3. C2×#11762715C2semidirect
5. #14527035C2semidirect
8. #14527015C2semidirect
9. #14527014C2semidirect
10. #14527014C2semidirect
15. C2×#10587610C4semidirect
74. C2×C22⋊C4×C17Q8semidirect
215. C2×Dic34C22⋊C4semidirect
263. C23×C17C4×Q8semidirect
320. C2×C4×C17C22⋊Q8semidirect
523. C2×C22⋊C4Dic34semidirect
542. C17#13969semidirect
689. C23C4×Dic34semidirect
773. C2×C4#10587610semidirect

Maximal subgroups

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

subgroupindex
C22×#105876102
C22×C4×Dic342
C2×#117627152
C2×#117626692
#145270352
#145270272
#145270212
#145270152
#145270142
C2×C4×C22⋊C4×C172
#1396917