Finite Group Databasebeta

← C2×#21462685 #30625739

Subgroups — C2×#21462685 #30625739

Order 15616.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462685C2116yesmaximal, direct product factor
2C2×#16840797C211yesmaximal, characteristic, complemented
3C2×#16840795C211yesmaximal, characteristic, complemented
4C2×#16840794C211yesmaximal, characteristic, complemented
5C2×#16840793C211yesmaximal, characteristic, complemented
6C2×#16840793C211yesmaximal, characteristic, complemented
7C2×#16840791C211yesmaximal, characteristic, complemented
8C2×#16840789C211yesmaximal, characteristic, complemented
9C2×D4×#92420C211yesmaximal, characteristic, complemented
10C2×#16840786C211yesmaximal, characteristic, complemented
11C2×#16840786C211yesmaximal, characteristic, complemented
12C2×#16840736C211yesmaximal, characteristic, complemented
13C2×#16840735C211yesmaximal, characteristic, complemented
14C2×#16840732C211yesmaximal, characteristic, complemented
15C22×C22⋊#92420C211yesmaximal, characteristic, complemented
16C2×#16840268C211yesmaximal, characteristic
17C22×#11758213C2211yescharacteristic, complemented
18C22×#11758217C2211yescharacteristic
19C22×#11758217C2211yescharacteristic
20C22×#11758217C2211yescharacteristic, complemented
21C22×D61⋊C8C2211yescharacteristic, complemented
22C23×#92420C2211yescharacteristic
23C23×#92420C2211yescharacteristic
24C23×#92420C2211yescharacteristic, complemented
25#16840797C2218yescomplemented
26#16840795C2218yescomplemented
27#16840794C2218yescomplemented
28#16840793C2218yescomplemented
29#16840793C2218yescomplemented
30#16840791C2218yescomplemented
31#16840789C2218yescomplemented
32D4×#92420C2218yescomplemented
33#16840786C2218yescomplemented
34#16840786C2218yescomplemented
35C2×#14519844C2211yescharacteristic, complemented
36C2×#14519844C2211yescharacteristic, complemented
37C2×C4⋊#92420C2211yescharacteristic, complemented
38C2×C4⋊#92420C2211yescharacteristic, complemented
39#16840736C2218yescomplemented
40#16840735C2218yescomplemented
41#16840732C2218yescomplemented
42C2×#14519834C2211yescharacteristic, complemented
43C2×#14519834C2211yescharacteristic, complemented
44C2×C22⋊#92420C2211yescharacteristic
45C2×C22⋊#92420C2211yescharacteristic
46C2×C22⋊#92420C2211yescharacteristic
47C2×C22⋊#92420C2211yescharacteristic
48C2×C22⋊#92420C2211yescharacteristic
49C2×C22⋊#92420C2211yescharacteristic
50C2×C22⋊#92420C2211yescharacteristic
51C2×C22⋊#92420C2211yescharacteristic
52C2×C22⋊#92420C2218yescomplemented
53C2×C22⋊#92420C2211yescharacteristic, complemented
54C2×C22⋊#92420C2211yescharacteristic, complemented
55C2×#14519832C2211yescharacteristic, complemented
56C2×#14519832C2211yescharacteristic, complemented
57C2×C4×#92420C2211yescharacteristic, complemented
58C2×C4×#92420C2211yescharacteristic, complemented
59C22×#11758224C2211yescharacteristic
60C24×Dic61C2211yescharacteristic
61#16840268C418yes—
62#16840268C2218yes—
63C2×#14519761C411yescharacteristic
64C2×#14519758C411yescharacteristic
65C2×#14519754C411yescharacteristic
66C2×#14519754C411yescharacteristic
67C2×#14519749C411yescharacteristic
68C2×#14519749C411yescharacteristic
69C2×#14519746C411yescharacteristic
70C2×D4×Dic61C2211yescharacteristic
71C2×D4×Dic61C2211yescharacteristic
72C2×#14519737C2211yescharacteristic
73C2×#14519737C2211yescharacteristic
74C2×#14519733C2211yescharacteristic
75C2×#120×C61C411yescharacteristic
76C2×#11758213—42no—
77C2×#11758213C2314yescomplemented
78C2×#11758217—42no—
79C2×#11758217—42no—
80C2×#11758217—42no—
81C2×#11758217C2314yes—
82C2×#11758217C2314yes—
83C2×#11758217C2314yescomplemented
84C2×D61⋊C8—42no—
85C2×D61⋊C8C2314yescomplemented
86C22×#92420—42no—
87C22×#92420—42no—
88C22×#92420—42no—
89C22×#92420C2311yescharacteristic
90C22×#92420C2311yescharacteristic
91C22×#92420C2311yescharacteristic
92C22×#92420C2311yescharacteristic
93C22×#92420C2311yescharacteristic
94C22×#92420C2311yescharacteristic
95C22×#92420C2311yescharacteristic
96C22×#92420C2311yescharacteristic
97C22×#92420C2314yes—
98C22×#92420C2314yes—
99C22×#92420C2314yescomplemented
100#14519844C2314yescomplemented
101#14519844C2314yescomplemented
102C4⋊#92420C2314yescomplemented
103C4⋊#92420C2314yescomplemented
104#14519834C2314yescomplemented
105#14519834C2314yescomplemented
106C22⋊#92420C2314yes—
107C22⋊#92420C2314yes—
108C22⋊#92420C2314yes—
109C22⋊#92420C2314yes—
110C22⋊#92420C2314yes—
111C22⋊#92420C2314yes—
112C22⋊#92420C2314yes—
113C22⋊#92420C2314yes—
114C22⋊#92420C2314yescomplemented
115C22⋊#92420C2314yescomplemented
116#14519832C2314yescomplemented
117#14519832C2314yescomplemented
118C4×#92420C2314yescomplemented
119C4×#92420C2314yescomplemented
120C2×#11758224—42no—
121C2×#11758224—42no—
122C2×#11758224C2×C414yes—
123C2×#11758224C2314yes—
124C22×Dic122C2×C411yescharacteristic
125C22×C22⋊D61C2×C411yescharacteristic
126C22×C22⋊D61C2×C411yescharacteristic
127C22×C22⋊D61C2×C411yescharacteristic
128C22×C22⋊D61C2×C411yescharacteristic
129C23×Dic61—42no—
130C23×Dic61—42no—
131C23×Dic61C2×C411yescharacteristic
132C23×Dic61C2×C411yescharacteristic
133C23×Dic61C2×C411yescharacteristic
134C23×Dic61C2×C414yes—
135C23×Dic61C2311yescharacteristic
136C23×Dic61C2311yescharacteristic
137C23×Dic61C2311yescharacteristic
138C23×Dic61C2311yescharacteristic
139C23×Dic61C2314yes—
140C22×C4×D61C2311yescharacteristic
141#14519761C2×C418yes—
142#14519758C2×C418yes—
143#14519754C2×C418yes—
144#14519754C2×C418yes—
145#14519749C2×C418yes—
146#14519749C2×C418yes—
147#14519746C2×C418yes—
148D4×Dic61C2×C414yes—
149D4×Dic61C2×C414yes—
150D4×Dic61C2314yes—
151D4×Dic61C2314yes—
152#14519737C2×C414yes—
153#14519737C2×C414yes—
154#14519737C2314yes—
155#14519737C2314yes—
156#14519733C2×C414yes—
157#14519733C2314yes—
158C2×C4⋊Dic61C2×C411yescharacteristic
159C2×C4⋊Dic61C2×C411yescharacteristic
160C2×#11758196C2×C411yescharacteristic
161C2×#11758196C2×C411yescharacteristic
162C2×#11758196C2×C411yescharacteristic
163C2×#11758196C2×C411yescharacteristic
164C2×C22⋊Dic61C2×C411yescharacteristic
165C2×C22⋊Dic61C2×C411yescharacteristic
166C2×C22⋊Dic61C2×C411yescharacteristic
167C2×C22⋊Dic61C2×C411yescharacteristic
168C2×C22⋊Dic61C2×C411yescharacteristic
169C2×#11758198C2×C411yescharacteristic
170C2×#11758198C2×C411yescharacteristic
171C2×C4×Dic61C2311yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173C25×C61C2×C411yescharacteristic
174C22×D4×C61C2×C411yescharacteristic
175C22×D4×C61C2×C411yescharacteristic
176C22×D4×C61C2×C411yescharacteristic
177#120×C61C2×C418yes—
178C2×C22⋊C4×C61C2×C411yescharacteristic
179C2×C22⋊C4×C61C2×C411yescharacteristic
180C2×C22⋊C4×C61C2×C411yescharacteristic
181C24×C61—24no—
182C24×C61—42no—
183C24×C61—42no—
184C24×C61C22×C411yescharacteristic
185C24×C61C22×C411yescharacteristic
186C24×C61C22×C411yescharacteristic
187C24×C61C22×C411yescharacteristic
188C24×C61C22×C414yes—
189C23×D61C22×C411yescharacteristic
190C2×D4×C61—24no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61C22×C414yes—
194C2×D4×C61C22×C414yes—
195C2×D4×C61C22×C414yes—
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61C22×C414yes—
204C2×C22⋊D61C22×C414yes—
205C2×C22⋊D61C22×C414yes—
206C2×C22⋊D61C22×C414yes—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—48no—
216C22×Dic61—44no—
217C22×Dic61—44no—
218C22×Dic61—42no—
219C22×Dic61—42no—
220C22×Dic61—42no—
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C412yes—
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C412yes—
226C22×Dic61C22×C412yes—
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C412yes—
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C22×C414yes—
232C22×Dic61C22×C414yes—
233C22×Dic61C22×C414yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2411yescharacteristic
239#11758224—48no—
240#11758224—44no—
241#11758224—44no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61C22×C412yes—
245C2×C4×D61C2412yes—
246C2×Dic122—42no—
247C2×Dic122C22×C414yes—
248#11758217—44no—
249#11758217—44no—
250#11758217—44no—
251C2×#92420—22no—
252C2×#92420—22no—
253C2×#92420—22no—
254C2×#92420—22no—
255C2×#92420—22no—
256C2×#92420—22no—
257C2×#92420—22no—
258C2×#92420—22no—
259C2×#92420—44no—
260C2×#92420—44no—
261C2×#92420—44no—
262C2×#92420C2412yes—
263C2×#92420C2412yes—
264C2×#92420C2412yes—
265C2×#92420C2412yes—
266C2×#92420C2412yes—
267C2×#92420C2412yes—
268C2×#92420C2412yes—
269C2×#92420C2412yes—
270#11758213—44no—
271D61⋊C8—44no—
272C22⋊C4×C61C22×C414yes—
273C22⋊C4×C61C22×C414yes—
274C22⋊C4×C61C22×C414yes—
275C22⋊Dic61C22×C414yes—
276C22⋊Dic61C22×C414yes—
277C22⋊Dic61C22×C414yes—
278C22⋊Dic61C22×C414yes—
279C22⋊Dic61C22×C414yes—
280#11758198C22×C414yes—
281#11758198C22×C414yes—
282C4⋊Dic61C22×C414yes—
283C4⋊Dic61C22×C414yes—
284#11758196C22×C414yes—
285#11758196C22×C414yes—
286#11758196C22×C414yes—
287#11758196C22×C414yes—
288C4×Dic61C22×C412yes—
289C4×Dic61C22×C412yes—
290C4×Dic61C2412yes—
291C4×Dic61C2412yes—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—28no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—44no—
305C23×C61—44no—
306C23×C61—416no—
307C23×C61#13114yes—
308C23×C61C23×C412yes—
309C23×C61C23×C412yes—
310C23×C61C23×C412yes—
311C23×C61C23×C412yes—
312C23×C61C23×C411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61C23×C412yes—
317D4×C61—28no—
318D4×C61—44no—
319D4×C61—44no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61C23×C412yes—
324C2×C4×C61C23×C412yes—
325C2×C4×C61C23×C412yes—
326C22⋊D61—28no—
327C22⋊D61—44no—
328C22⋊D61—44no—
329C22⋊D61—44no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—24no—
337C2×Dic61—24no—
338C2×Dic61—24no—
339C2×Dic61—24no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61—44no—
351C2×Dic61C23×C412yes—
352C2×Dic61C23×C412yes—
353C2×Dic61C23×C412yes—
354C2×Dic61C23×C412yes—
355C2×Dic61C23×C412yes—
356C2×Dic61C23×C412yes—
357C2×Dic61C23×C411yescharacteristic
358C2×Dic61H(5,𝔽2)12yes—
359C2×Dic61H(5,𝔽2)12yes—
360C2×Dic61C2511yescharacteristic
361C4×D61—24no—
362C4×D61—22no—
363C4×D61—22no—
364Dic122—44no—
365#92420—22no—
366#92420—22no—
367#92420—22no—
368#92420—22no—
369#92420—22no—
370#92420—22no—
371#92420—22no—
372#92420—22no—
373C2×#2976—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—28no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—416no—
387C22×C61—44no—
388C22×C61—44no—
389C22×C61—44no—
390C22×C61#51812yes—
391C22×C61C2×#13114yes—
392C22×C61C2×#13112yes—
393C22×C61#56812yes—
394C22×C61C24×C411yescharacteristic
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—44no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402Dic61—22no—
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61#51812yes—
409Dic61C2×H(5,𝔽2)11yescharacteristic
410Dic61C2×H(5,𝔽2)11yescharacteristic
411C2×#525—611no—
412#2976—6116no—
413C2×#436—611no—
414C2×#436—611no—
415C2×#435—611no—
416C2×#435—611no—
417C2×#435—611no—
418C2×#435—611no—
419C2×C8×D4—611no—
420C2×C8×D4—611no—
421C2×#433—611no—
422C2×#433—611no—
423C2×#408—611no—
424C2×#408—611no—
425C2×#407—611no—
426C22×C22⋊C8—611no—
427C2×C61—24no—
428C2×C61—42no—
429C2×C61—42no—
430C2×C61—42no—
431C2×C61#297614yescomplemented
432C2×C61C2×#51811yescharacteristic
433C2×C61C22×#13111yescharacteristic
434C2×C61C2×#56811yescharacteristic
435D61—42no—
436C22×#41—611no—
437C24×C4—611no—
438C22×M16—611no—
439C22×M16—611no—
440C22×M16—611no—
441C22×M16—611no—
442C23×C8—611no—
443C23×C8—611no—
444C23×C8—611no—
445C23×C8—611no—
446#525—618no—
447#525—618no—
448C2×#123—611no—
449C2×#123—611no—
450C2×C22⋊Q8—611no—
451C2×C22⋊Q8—611no—
452C2×#121—611no—
453C2×#121—611no—
454C2×#120—611no—
455C2×#120#692311yescharacteristic
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458C2×C4×D4—611no—
459C2×C4×D4—611no—
460C2×#117—611no—
461#436—618no—
462#436—618no—
463#435—618no—
464#435—618no—
465#435—618no—
466#435—618no—
467C8×D4—618no—
468C8×D4—618no—
469#433—618no—
470#433—618no—
471C2×C4⋊C8—611no—
472C2×C4⋊C8—611no—
473C2×C4⋊C8—611no—
474C2×C4⋊C8—611no—
475#408—618no—
476#408—618no—
477#407—618no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485C2×C22⋊C8—611no—
486C2×C22⋊C8—618no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492C2×#97—611no—
493C2×C4×C8—611no—
494C2×C4×C8—611no—
495C61C2×#297611yescharacteristic, complemented, Sylow
496C25C2×#692311yescharacteristic
497C2×#41—614no—
498C2×#41—614no—
499C2×#41—2442no—
500C2×#41—2442no—
501C22×Q8—611no—
502C22×D4—611no—
503C22×D4—611no—
504C22×D4—611no—
505C22×D4—611no—
506C22×D4C2×#692311yescharacteristic
507C22×D4C2×#692311yescharacteristic
508C22×D4C2×#692311yescharacteristic
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—614no—
517C23×C4—614no—
518C23×C4—611no—
519C23×C4—2442no—
520C23×C4—2442no—
521C2×M16—614no—
522C2×M16—614no—
523C2×M16—614no—
524C2×M16—614no—
525C2×M16—2442no—
526C2×M16—2442no—
527C2×M16—2442no—
528C2×M16—2442no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—611no—
533C22×C8—611no—
534C22×C8—611no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—614no—
538C22×C8—614no—
539C22×C8—614no—
540C22×C8—614no—
541C22×C8—2442no—
542C22×C8—2442no—
543C22×C8—2442no—
544C22×C8—2442no—
545#123—618no—
546#123—618no—
547C22⋊Q8—618no—
548C22⋊Q8—618no—
549#121—618no—
550#121—618no—
551#120—618no—
552#120C2×#692318yes—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—614no—
559C4×D4—614no—
560C4×D4—614no—
561#117—614no—
562#117—614no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—611no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4C2×#692311yescharacteristic
577C2×C22⋊C4C2×#692311yescharacteristic
578C2×C22⋊C4C2×#692311yescharacteristic
579C2×C42—611no—
580C2×C42—611no—
581C4⋊C8—614no—
582C4⋊C8—614no—
583C4⋊C8—614no—
584C4⋊C8—614no—
585C22⋊C8—614no—
586C22⋊C8—614no—
587C22⋊C8—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590C22⋊C8—614no—
591C22⋊C8—614no—
592C22⋊C8—614no—
593C22⋊C8—614no—
594C22⋊C8—614no—
595C22⋊C8—614no—
596C22⋊C8—614no—
597#97—614no—
598#97—614no—
599C4×C8—614no—
600C4×C8—614no—
601C24—24no—
602C24—42no—
603C24—42no—
604C24—611no—
605C24C22×#692311yescharacteristic
606C24C22×#692311yescharacteristic
607C24C22×#692311yescharacteristic
608C24C22×#692311yescharacteristic
609C24C22×#692314yes—
610#41—2444no—
611#41—2444no—
612#41—2448no—
613C2×Q8—614no—
614C2×Q8—2442no—
615C2×D4—24no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—614no—
619C2×D4—614no—
620C2×D4—614no—
621C2×D4—614no—
622C2×D4—1224no—
623C2×D4—2442no—
624C2×D4—2442no—
625C2×D4—2442no—
626C2×D4C22×#692314yes—
627C2×D4C22×#692314yes—
628C2×D4C22×#692314yes—
629C22×C4—611no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—614no—
645C22×C4—614no—
646C22×C4—614no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—2444no—
660C22×C4—2444no—
661C22×C4—2448no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4C22×#692311yescharacteristic
666C22×C4C22×#692311yescharacteristic
667C22×C4C22×#692311yescharacteristic
668M16—2444no—
669M16—2444no—
670M16—2444no—
671M16—2444no—
672C2×C8—612no—
673C2×C8—612no—
674C2×C8—612no—
675C2×C8—612no—
676C2×C8—612no—
677C2×C8—612no—
678C2×C8—612no—
679C2×C8—612no—
680C2×C8—1222no—
681C2×C8—1222no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—1222no—
685C2×C8—1222no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8—2444no—
689C2×C8—2444no—
690C2×C8—2444no—
691C2×C8—2444no—
692C4⋊C4—614no—
693C4⋊C4—614no—
694C4⋊C4—614no—
695C4⋊C4—614no—
696C4⋊C4—614no—
697C4⋊C4—614no—
698C22⋊C4—614no—
699C22⋊C4—614no—
700C22⋊C4—614no—
701C22⋊C4—614no—
702C22⋊C4—614no—
703C22⋊C4—614no—
704C22⋊C4—614no—
705C22⋊C4C22×#692314yes—
706C22⋊C4C22×#692314yes—
707C22⋊C4C22×#692314yes—
708C42—612no—
709C42—612no—
710C42—612no—
711C42—612no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—44no—
725C23—44no—
726C23—416no—
727C23—612no—
728C23—1222no—
729C23—1222no—
730C23—1222no—
731C23#1451986414yes—
732C23C23×#692312yes—
733C23C23×#692312yes—
734C23C23×#692312yes—
735C23C23×#692312yes—
736C23C23×#692311yescharacteristic
737Q8—2444no—
738D4—28no—
739D4—44no—
740D4—44no—
741D4—1228no—
742D4—2444no—
743D4—2444no—
744D4—2444no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1224no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1224no—
768C2×C4—1224no—
769C2×C4—1224no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1224no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—2444no—
780C2×C4—2444no—
781C2×C4—2444no—
782C2×C4C23×#692312yes—
783C2×C4C23×#692312yes—
784C2×C4C23×#692312yes—
785C8—1222no—
786C8—1222no—
787C8—1222no—
788C8—1222no—
789C8—1222no—
790C8—1222no—
791C8—1222no—
792C8—1222no—
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—416no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—1222no—
810C22—1222no—
811C22—1222no—
812C22—2444no—
813C22#1684082912yes—
814C22C2×#1451986414yes—
815C22C2×#1451986412yes—
816C22#1684084012yes—
817C22C24×#692311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—612no—
822C4—611no—
823C4—611no—
824C4—1222no—
825C4—1222no—
826C4—1222no—
827C4—1222no—
828C4—1222no—
829C4—1222no—
830C2—24no—
831C2—42no—
832C2—42no—
833C2—42no—
834C2—2442no—
835C2#2146268514yesdirect product factor
836C2C2×#1684082911yescharacteristic
837C2C22×#1451986411yescharacteristic
838C2C2×#1684084011yescharacteristic
subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#120×C61C4
socleC23×C61C23×C4
prime radicalC2×#16840268C2
cosocleC2×Dic61C25
hypercenterC2×#120#6923
hypocenterC61C2×#2976
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #21462685C2direct (N × H)
2. C2×#16840797C2semidirect
3. C2×#16840795C2semidirect
4. C2×#16840794C2semidirect
5. C2×#16840793C2semidirect
6. C2×#16840793C2semidirect
7. C2×#16840791C2semidirect
8. C2×#16840789C2semidirect
9. C2×D4×#92420C2semidirect
10. C2×#16840786C2semidirect
11. C2×#16840786C2semidirect
12. C2×#16840736C2semidirect
13. C2×#16840735C2semidirect
14. C2×#16840732C2semidirect
15. C22×C22⋊#92420C2semidirect
17. C22×#11758213C22semidirect
20. C22×#11758217C22semidirect
21. C22×D61⋊C8C22semidirect
24. C23×#92420C22semidirect
25. #16840797C22semidirect
26. #16840795C22semidirect
27. #16840794C22semidirect
28. #16840793C22semidirect
29. #16840793C22semidirect
30. #16840791C22semidirect
31. #16840789C22semidirect
32. D4×#92420C22semidirect
33. #16840786C22semidirect
34. #16840786C22semidirect
35. C2×#14519844C22semidirect
36. C2×#14519844C22semidirect
37. C2×C4⋊#92420C22semidirect
38. C2×C4⋊#92420C22semidirect
39. #16840736C22semidirect
40. #16840735C22semidirect
41. #16840732C22semidirect
42. C2×#14519834C22semidirect
43. C2×#14519834C22semidirect
52. C2×C22⋊#92420C22semidirect
53. C2×C22⋊#92420C22semidirect
54. C2×C22⋊#92420C22semidirect
55. C2×#14519832C22semidirect
56. C2×#14519832C22semidirect
57. C2×C4×#92420C22semidirect
58. C2×C4×#92420C22semidirect
77. C2×#11758213C23semidirect
83. C2×#11758217C23semidirect
85. C2×D61⋊C8C23semidirect
99. C22×#92420C23semidirect
100. #14519844C23semidirect
101. #14519844C23semidirect
102. C4⋊#92420C23semidirect
103. C4⋊#92420C23semidirect
104. #14519834C23semidirect
105. #14519834C23semidirect
114. C22⋊#92420C23semidirect
115. C22⋊#92420C23semidirect
116. #14519832C23semidirect
117. #14519832C23semidirect
118. C4×#92420C23semidirect
119. C4×#92420C23semidirect
431. C2×C61#2976semidirect
495. C61C2×#2976semidirect
835. C2#21462685direct (N × H)

Maximal subgroups

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

subgroupindex
#214626852
C2×#168407972
C2×#168407952
C2×#168407942
C2×#168407932
C2×#168407912
C2×#168407892
C2×D4×#924202
C2×#168407862
C2×#168407362
C2×#168407352
C2×#168407322
C22×C22⋊#924202
C2×#168402682
C2×#297661