Finite Group Databasebeta

← #30620097

Subgroups — #30620097

Order 15616.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840795C211yesmaximal, characteristic, complemented
2C2×#16840794C211yesmaximal, characteristic, complemented
3C2×#16840736C211yesmaximal, characteristic, complemented
4C2×#16840732C211yesmaximal, characteristic, complemented
5#21461943C211yesmaximal, characteristic, complemented
6#21461940C211yesmaximal, characteristic, complemented
7#21461797C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461796C211yesmaximal, characteristic, complemented
10#21461793C211yesmaximal, characteristic, complemented
11#21461677C211yesmaximal, characteristic, complemented
12#21461643C211yesmaximal, characteristic, complemented
13#21461641C211yesmaximal, characteristic, complemented
14#21461549C211yesmaximal, characteristic, complemented
15C2×#16840268C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic, complemented
17C22×#11758217C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic, complemented
20#16840795—24no—
21#16840794—24no—
22C2×#14519844C2211yescharacteristic, complemented
23C2×C4⋊#92420C2211yescharacteristic, complemented
24#16840736—24no—
25#16840732—24no—
26C2×#14519834C2211yescharacteristic, complemented
27C2×#14519834C2211yescharacteristic, complemented
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic, complemented
39C2×C22⋊#92420C2211yescharacteristic, complemented
40C2×C22⋊#92420C2211yescharacteristic, complemented
41C2×C22⋊#92420C2211yescharacteristic, complemented
42C2×#14519832C2211yescharacteristic, complemented
43C2×C4×#92420C2211yescharacteristic, complemented
44#16840628C2211yescharacteristic, complemented
45#16840628C2211yescharacteristic, complemented
46#16840628C2211yescharacteristic, complemented
47#16840628C2211yescharacteristic, complemented
48C22×#11758224C2211yescharacteristic
49C24×Dic61C2211yescharacteristic
50#16840268—24no—
51#16840268—24no—
52C2×#14519761C411yescharacteristic
53C2×#14519758C411yescharacteristic
54C2×#14519754C411yescharacteristic
55C2×#14519754C411yescharacteristic
56C2×#14519749C411yescharacteristic
57C2×#14519749C411yescharacteristic
58C2×#14519746C411yescharacteristic
59C2×D4×Dic61C2211yescharacteristic
60C2×D4×Dic61C2211yescharacteristic
61C2×#14519737C2211yescharacteristic
62C2×#14519737C2211yescharacteristic
63C2×#14519733C2211yescharacteristic
64C2×#120×C61C411yescharacteristic
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—41no—
68C2×#11758217—22no—
69C2×#11758217—22no—
70C2×#11758217—22no—
71C2×#11758217—22no—
72C2×#11758217—41no—
73C2×#11758217—41no—
74C2×D61⋊C8—22no—
75C2×D61⋊C8—22no—
76C2×D61⋊C8—41no—
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85#14519844—22no—
86C4⋊#92420—22no—
87#14519834—22no—
88#14519834—22no—
89C22⋊#92420—22no—
90C22⋊#92420—22no—
91C22⋊#92420—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95C22⋊#92420—22no—
96C22⋊#92420—22no—
97C22⋊#92420—22no—
98C22⋊#92420—41no—
99C22⋊#92420—41no—
100C22⋊#92420—41no—
101C22⋊#92420—41no—
102C22⋊#92420D414yescomplemented
103#14519832—22no—
104C4×#92420—22no—
105C2×#11758224—22no—
106C2×#11758224—22no—
107C2×#11758224—22no—
108C2×#11758224—22no—
109C2×#11758224—41no—
110C2×#11758224—41no—
111C22×Dic122C2×C411yescharacteristic
112C22×C22⋊D61C2×C411yescharacteristic
113C22×C22⋊D61C2×C411yescharacteristic
114C22×C22⋊D61C2×C411yescharacteristic
115C22×C22⋊D61C2×C411yescharacteristic
116C23×Dic61—22no—
117C23×Dic61—22no—
118C23×Dic61—22no—
119C23×Dic61—22no—
120C23×Dic61—41no—
121C23×Dic61—41no—
122C23×Dic61C2×C411yescharacteristic
123C23×Dic61C2×C411yescharacteristic
124C23×Dic61C2×C411yescharacteristic
125C23×Dic61C2311yescharacteristic
126C23×Dic61C2311yescharacteristic
127C23×Dic61C2311yescharacteristic
128C23×Dic61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130#14519761—24no—
131#14519758—24no—
132#14519754—24no—
133#14519754—24no—
134#14519749—24no—
135#14519749—24no—
136#14519746—24no—
137D4×Dic61—22no—
138D4×Dic61—22no—
139D4×Dic61—22no—
140D4×Dic61—22no—
141#14519737—22no—
142#14519737—22no—
143#14519737D414yes—
144#14519737D414yes—
145#14519733—22no—
146#14519733—22no—
147C2×C4⋊Dic61C2×C411yescharacteristic
148C2×C4⋊Dic61C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×C22⋊Dic61C2×C411yescharacteristic
154C2×C22⋊Dic61C2×C411yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×C22⋊Dic61C2×C411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×C4×Dic61C2311yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C25×C61C2×C411yescharacteristic
163C22×D4×C61C2×C411yescharacteristic
164C22×D4×C61C2×C411yescharacteristic
165C22×D4×C61C2×C411yescharacteristic
166#120×C61—24no—
167C2×C22⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61—41no—
174C24×C61—41no—
175C24×C61—41no—
176C24×C61—41no—
177C24×C61C22×C411yescharacteristic
178C24×C61C22×C411yescharacteristic
179C24×C61C22×C411yescharacteristic
180C24×C61C22×C411yescharacteristic
181C23×D61C22×C411yescharacteristic
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—41no—
190C2×D4×C61—41no—
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61C22⋊C414yes—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—41no—
233C22×Dic61—41no—
234C22×Dic61—41no—
235C22×Dic61—44no—
236C22×Dic61—44no—
237C22×Dic61—44no—
238C22×Dic61—44no—
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C2×D412yes—
246C22×Dic61C2×D412yes—
247C22×Dic61C2×D412yes—
248C22×Dic61#4112yes—
249C22×Dic61C2411yescharacteristic
250#11758224—44no—
251#11758224—44no—
252#11758224—44no—
253#11758224—44no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2×D412yes—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—41no—
263#11758217—44no—
264#11758217—44no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—21no—
283C2×#92420—21no—
284C2×#92420—21no—
285C2×#92420—21no—
286C2×#92420—21no—
287C2×#92420C2×D412yes—
288C2×#92420C2×D412yes—
289#11758213—44no—
290D61⋊C8—44no—
291C22⋊C4×C61—22no—
292C22⋊C4×C61—22no—
293C22⋊C4×C61C22⋊C414yes—
294C22⋊Dic61—22no—
295C22⋊Dic61—22no—
296C22⋊Dic61—22no—
297C22⋊Dic61—22no—
298C22⋊Dic61—22no—
299#11758198—22no—
300#11758198C22⋊C414yes—
301C4⋊Dic61—22no—
302C4⋊Dic61—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—22no—
306#11758196C22⋊C414yes—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61C2×D412yes—
310C4×Dic61C2×D412yes—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—44no—
337C23×C61—44no—
338C23×C61—44no—
339C23×C61—44no—
340C23×C61—44no—
341C23×C61—44no—
342C23×C61—44no—
343C23×C61C2×C22⋊C412yes—
344C23×C61C4×D412yes—
345C23×C61#13112yes—
346C23×C61C23×C411yescharacteristic
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—21no—
353C22×D61C2×C22⋊C412yes—
354D4×C61—44no—
355D4×C61—44no—
356D4×C61—44no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C2×C22⋊C412yes—
366C22⋊D61—44no—
367C22⋊D61—44no—
368C22⋊D61—44no—
369C22⋊D61—44no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—44no—
394C2×Dic61—44no—
395C2×Dic61—44no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61C2×C22⋊C412yes—
405C2×Dic61C2×C22⋊C412yes—
406C2×Dic61C4×D412yes—
407C2×Dic61C22×D411yescharacteristic
408C2×Dic61C22×D411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410C2×Dic61C2×#4111yescharacteristic
411C2×Dic61H(5,𝔽2)11yescharacteristic
412C2×Dic61H(5,𝔽2)11yescharacteristic
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417Dic122—44no—
418#92420—22no—
419#92420—22no—
420#92420—41no—
421#92420—41no—
422#92420—41no—
423#92420—41no—
424#92420—41no—
425#92420—41no—
426#22400—611nomaximal, Sylow
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—22no—
434C22×C61—22no—
435C22×C61—22no—
436C22×C61—416no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61C22×C22⋊C411yescharacteristic
457C22×C61C2×C4×D411yescharacteristic
458C22×C61#51811yescharacteristic
459C22×C61C2×#13111yescharacteristic
460C22×C61#56811yescharacteristic
461C22×C61#56811yescharacteristic
462C22×C61#56811yescharacteristic
463C2×D61—22no—
464C2×D61—22no—
465C2×D61—22no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C4×C61—22no—
471C4×C61—22no—
472C4×C61—41no—
473Dic61—22no—
474Dic61—22no—
475Dic61—22no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479Dic61D4211yescharacteristic
480Dic61D4211yescharacteristic
481Dic61#54611yescharacteristic
482Dic61#54611yescharacteristic
483C2×#525—611no—
484C2×#436—611no—
485C2×#435—611no—
486C2×#408—611no—
487C2×#407—611no—
488#1955—611no—
489#1954—611no—
490#1870—611no—
491#1870—611no—
492#1870—611no—
493#1869—611no—
494#1798—611no—
495#1780—611no—
496#1779—611no—
497#1750—611no—
498C2×C61—42no—
499C2×C61—42no—
500C2×C61—42no—
501C2×C61—81no—
502C2×C61D4×C22⋊C411yescharacteristic
503C2×C61#287911yescharacteristic
504C2×C61#288011yescharacteristic
505C2×C61#293011yescharacteristic
506C2×C61#293311yescharacteristic
507C2×C61#297611yescharacteristic
508C2×C61#297811yescharacteristic
509D61—42no—
510C22×#41—611no—
511C24×C4—611no—
512C22×M16—611no—
513C22×M16—611no—
514C22×M16—611no—
515C23×C8—611no—
516#525—1224no—
517#525—1224no—
518C2×#123—611no—
519C2×#123—611no—
520C2×C22⋊Q8—611no—
521C2×C22⋊Q8—611no—
522C2×#121—611no—
523C2×#121—611no—
524C2×#120—611no—
525C2×#120#692311yescharacteristic
526C2×C4×D4—611no—
527C2×C4×D4—611no—
528C2×C4×D4—611no—
529C2×C4×D4—611no—
530C2×#117—611no—
531#436—1224no—
532#435—1224no—
533C2×C4⋊C8—611no—
534C2×C4⋊C8—611no—
535#408—1224no—
536#407—1224no—
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—611no—
540C2×C22⋊C8—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543C2×C22⋊C8—611no—
544C2×C22⋊C8—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×C22⋊C8—611no—
548C2×C22⋊C8—611no—
549C2×C22⋊C8—611no—
550C2×C22⋊C8—611no—
551C2×C22⋊C8—611no—
552C2×C22⋊C8—611no—
553C2×#97—611no—
554C2×C4×C8—611no—
555#336—611no—
556#336—611no—
557#336—611no—
558#336—611no—
559C61#2240011yescharacteristic, complemented, Sylow
560C25C2×#692311yescharacteristic
561C2×#41—1222no—
562C2×#41—1222no—
563C2×#41—1222no—
564C2×#41—1222no—
565C2×#41—2441no—
566C2×#41—2441no—
567C22×Q8—611no—
568C22×D4—611no—
569C22×D4—611no—
570C22×D4—611no—
571C22×D4—611no—
572C22×D4C2×#692311yescharacteristic
573C22×D4C2×#692311yescharacteristic
574C22×D4C2×#692311yescharacteristic
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—1222no—
584C23×C4—1222no—
585C23×C4—1222no—
586C23×C4—1222no—
587C23×C4—2441no—
588C23×C4—2441no—
589C2×M16—1222no—
590C2×M16—1222no—
591C2×M16—1222no—
592C2×M16—1222no—
593C2×M16—1222no—
594C2×M16—1222no—
595C2×M16—2441no—
596C2×M16—2441no—
597C2×M16—2441no—
598C22×C8—611no—
599C22×C8—611no—
600C22×C8—611no—
601C22×C8—611no—
602C22×C8—611no—
603C22×C8—611no—
604C22×C8—611no—
605C22×C8—611no—
606C22×C8—1222no—
607C22×C8—1222no—
608C22×C8—2441no—
609#123—1224no—
610#123—1224no—
611C22⋊Q8—1224no—
612C22⋊Q8—1224no—
613#121—1224no—
614#121—1224no—
615#120—24no—
616#120—1224no—
617C4×D4—614no—
618C4×D4—614no—
619C4×D4—1222no—
620C4×D4—1222no—
621C4×D4—1222no—
622C4×D4—1222no—
623C4×D4—1222no—
624C4×D4—1222no—
625#117—1222no—
626#117—1222no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—611no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4C2×#692311yescharacteristic
641C2×C22⋊C4C2×#692311yescharacteristic
642C2×C22⋊C4C2×#692311yescharacteristic
643C2×C42—611no—
644C2×C42—611no—
645C4⋊C8—1222no—
646C4⋊C8—1222no—
647C22⋊C8—614no—
648C22⋊C8—1222no—
649C22⋊C8—1222no—
650C22⋊C8—1222no—
651C22⋊C8—1222no—
652C22⋊C8—1222no—
653C22⋊C8—1222no—
654C22⋊C8—1222no—
655C22⋊C8—1222no—
656C22⋊C8—1222no—
657C22⋊C8—1222no—
658C22⋊C8—1222no—
659C22⋊C8—2441no—
660C22⋊C8—2441no—
661C22⋊C8—2441no—
662C22⋊C8—2441no—
663#97—1222no—
664C4×C8—1222no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—41no—
669C24—41no—
670C24—41no—
671C24—41no—
672C24—611no—
673C24C22×#692311yescharacteristic
674C24C22×#692311yescharacteristic
675C24C22×#692311yescharacteristic
676C24C22×#692311yescharacteristic
677#41—2444no—
678#41—2444no—
679#41—2444no—
680#41—2444no—
681C2×Q8—1222no—
682C2×Q8—1222no—
683C2×Q8—2441no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—41no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—41no—
693C2×D4—614no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—1222no—
700C2×D4—2441no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2441no—
705C22×C4—611no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1222no—
741C22×C4—1222no—
742C22×C4—1221no—
743C22×C4—1222no—
744C22×C4—1222no—
745C22×C4—1221no—
746C22×C4—1222no—
747C22×C4—1222no—
748C22×C4—2441no—
749C22×C4—2441no—
750C22×C4—2441no—
751C22×C4—2444no—
752C22×C4—2444no—
753C22×C4—2444no—
754C22×C4—2444no—
755C22×C4C22×#692311yescharacteristic
756C22×C4C22×#692311yescharacteristic
757C22×C4C22×#692311yescharacteristic
758M16—2444no—
759M16—2444no—
760M16—2444no—
761C2×C8—612no—
762C2×C8—612no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—2444no—
786C4⋊C4—614no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—614no—
795C22⋊C4—1222no—
796C22⋊C4—1222no—
797C22⋊C4—1222no—
798C22⋊C4—1222no—
799C22⋊C4—1222no—
800C22⋊C4—1222no—
801C22⋊C4C22⋊#692314yes—
802C42—612no—
803C42—612no—
804C42—1221no—
805C42—1221no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—612no—
839C23—1221no—
840C23—1221no—
841C23—1221no—
842C23—1221no—
843C23—1221no—
844C23—1221no—
845C23C2×C22⋊#692312yes—
846C23D4×#692312yes—
847C23#1451986412yes—
848C23C23×#692311yescharacteristic
849Q8—2444no—
850D4—44no—
851D4—44no—
852D4—44no—
853D4—2444no—
854D4—2444no—
855D4—2444no—
856D4—2444no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—611no—
867C2×C4—611no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—612no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2444no—
909C2×C4—2444no—
910C2×C4—2444no—
911C2×C4C2×C22⋊#692312yes—
912C2×C4C2×C22⋊#692312yes—
913C8—1222no—
914C8—1222no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C8—2441no—
920C8—2441no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—416no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—1222no—
951C22—1222no—
952C22—1222no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22C22×C22⋊#692311yescharacteristic
958C22C2×D4×#692311yescharacteristic
959C22#1684082911yescharacteristic
960C22C2×#1451986411yescharacteristic
961C22#1684084011yescharacteristic
962C22#1684084011yescharacteristic
963C22#1684084011yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—611no—
968C4—611no—
969C4—611no—
970C4—611no—
971C4—1222no—
972C4—1222no—
973C4—1222no—
974C4—2441no—
975C4—2441no—
976C4—2441no—
977C2—42no—
978C2—42no—
979C2—42no—
980C2—81no—
981C2—2442no—
982C2D4×C22⋊#692311yescharacteristic
983C2#2146240511yescharacteristic
984C2#2146240711yescharacteristic
985C2#2146253811yescharacteristic
986C2#2146255111yescharacteristic
987C2#2146268511yescharacteristic
988C2#2146269511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#120×C61C4
prime radicalC2×#16840268C2
cosocleC22×Dic61C24
hypercenterC2×#120#6923
hypocenterC61#22400
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#16840795C2semidirect
2. C2×#16840794C2semidirect
3. C2×#16840736C2semidirect
4. C2×#16840732C2semidirect
5. #21461943C2semidirect
6. #21461940C2semidirect
7. #21461797C2semidirect
8. #21461796C2semidirect
9. #21461796C2semidirect
10. #21461793C2semidirect
11. #21461677C2semidirect
12. #21461643C2semidirect
13. #21461641C2semidirect
14. #21461549C2semidirect
16. C22×#11758213C22semidirect
19. C22×D61⋊C8C22semidirect
22. C2×#14519844C22semidirect
23. C2×C4⋊#92420C22semidirect
26. C2×#14519834C22semidirect
27. C2×#14519834C22semidirect
38. C2×C22⋊#92420C22semidirect
39. C2×C22⋊#92420C22semidirect
40. C2×C22⋊#92420C22semidirect
41. C2×C22⋊#92420C22semidirect
42. C2×#14519832C22semidirect
43. C2×C4×#92420C22semidirect
44. #16840628C22semidirect
45. #16840628C22semidirect
46. #16840628C22semidirect
47. #16840628C22semidirect
102. C22⋊#92420D4semidirect
559. C61#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#168407952
C2×#168407942
C2×#168407362
C2×#168407322
#214619432
#214619402
#214617972
#214617962
#214617932
#214616772
#214616432
#214616412
#214615492
C2×#168402682
#2240061