Finite Group Databasebeta

← #30620117

Subgroups — #30620117

Order 15616.

1512 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840794C211yesmaximal, characteristic, complemented
2C2×#16840791C211yesmaximal, characteristic, complemented
3C2×#16840737C211yesmaximal, characteristic, complemented
4C2×#16840735C211yesmaximal, characteristic, complemented
5#21461944C211yesmaximal, characteristic, complemented
6#21461944C211yesmaximal, characteristic, complemented
7#21461798C211yesmaximal, characteristic, complemented
8#21461797C211yesmaximal, characteristic, complemented
9#21461794C211yesmaximal, characteristic, complemented
10#21461793C211yesmaximal, characteristic, complemented
11#21461674C211yesmaximal, characteristic, complemented
12#21461644C211yesmaximal, characteristic, complemented
13#21461643C211yesmaximal, characteristic, complemented
14#21461546C211yesmaximal, characteristic, complemented
15C2×#16840311C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840794—24no—
21#16840791—24no—
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24#16840737—24no—
25#16840735—24no—
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×C22⋊#92420C2211yescharacteristic
41C2×C22⋊#92420C2211yescharacteristic
42C2×#14519832C2211yescharacteristic
43C2×#14519832C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C22×#11758226C2211yescharacteristic
49C22×#11758224C2211yescharacteristic
50#16840311—24no—
51#16840311—24no—
52C2×#14519775C411yescharacteristic
53C2×#14519773C411yescharacteristic
54C2×#14519765C411yescharacteristic
55C2×#14519750C411yescharacteristic
56C2×#14519750C411yescharacteristic
57C2×#14519750C411yescharacteristic
58C2×#14519750C411yescharacteristic
59C2×#14519737C2211yescharacteristic
60C2×#14519737C2211yescharacteristic
61C2×#14519737C2211yescharacteristic
62C2×#14519737C2211yescharacteristic
63C2×C42×D61C2211yescharacteristic
64C2×#124×C61C411yescharacteristic
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—41no—
68C2×#11758217—22no—
69C2×#11758217—22no—
70C2×#11758217—41no—
71C2×D61⋊C8—22no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—41no—
74C22×#92420—22no—
75C22×#92420—22no—
76C22×#92420—41no—
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85C4⋊#92420—22no—
86C4⋊#92420—22no—
87#14519834—22no—
88#14519834—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—22no—
93#14519834—22no—
94#14519834—41no—
95#14519834—41no—
96#14519834D414yescomplemented
97C22⋊#92420—22no—
98C22⋊#92420—22no—
99C22⋊#92420—22no—
100C22⋊#92420—22no—
101C22⋊#92420—41no—
102C22⋊#92420—41no—
103#14519832—22no—
104#14519832—22no—
105C2×#11758226—22no—
106C2×#11758226—22no—
107C2×#11758226—22no—
108C2×#11758226—22no—
109C2×#11758226—41no—
110C2×#11758226—41no—
111C2×#11758224—22no—
112C2×#11758224—22no—
113C2×#11758224—22no—
114C2×#11758224—22no—
115C2×#11758224—41no—
116C2×#11758224—41no—
117C22×Dic122C2×C411yescharacteristic
118C22×D244C2×C411yescharacteristic
119C22×D244C2×C411yescharacteristic
120C22×D244C2×C411yescharacteristic
121C22×C22⋊D61C2×C411yescharacteristic
122C22×C22⋊D61C2×C411yescharacteristic
123C22×C22⋊D61C2×C411yescharacteristic
124C22×C22⋊D61C2×C411yescharacteristic
125C22×C22⋊D61C2×C411yescharacteristic
126C22×C22⋊D61C2×C411yescharacteristic
127C23×Dic61C2311yescharacteristic
128C23×Dic61C2311yescharacteristic
129C22×C4×D61C2×C411yescharacteristic
130C22×C4×D61C2×C411yescharacteristic
131C22×C4×D61C2311yescharacteristic
132C22×C4×D61C2311yescharacteristic
133C22×C4×D61C2311yescharacteristic
134#14519775—24no—
135#14519773—24no—
136#14519765—24no—
137#14519750—24no—
138#14519750—24no—
139#14519750—24no—
140#14519750—24no—
141#14519737—22no—
142#14519737—22no—
143#14519737—22no—
144#14519737—22no—
145#14519737—22no—
146#14519737—22no—
147#14519737D414yes—
148#14519737D414yes—
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×C4×Dic61C2×C411yescharacteristic
158C2×C4×Dic61C2311yescharacteristic
159C2×C4×Dic61C2311yescharacteristic
160C42×D61—22no—
161C42×D61—22no—
162C22×Q8×C61C2×C411yescharacteristic
163C22×D4×C61C2×C411yescharacteristic
164#124×C61—24no—
165C2×C22⋊C4×C61C2×C411yescharacteristic
166C2×C22⋊C4×C61C2×C411yescharacteristic
167C2×C22⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C42×C61C2×C411yescharacteristic
170C24×C61C22×C411yescharacteristic
171C24×C61C22×C411yescharacteristic
172C23×D61C22×C411yescharacteristic
173C23×D61C22×C411yescharacteristic
174C23×D61C22×C411yescharacteristic
175C2×Q8×C61—22no—
176C2×Q8×C61—22no—
177C2×Q8×C61—41no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—41no—
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—41no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61C22⋊C414yes—
204C22×Dic61—21no—
205C22×Dic61—21no—
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×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C2×D412yes—
219C22×Dic61C2×D412yes—
220C22×Dic61C2411yescharacteristic
221#11758226—44no—
222#11758226—44no—
223#11758226—44no—
224#11758226—44no—
225#11758224—44no—
226#11758224—44no—
227#11758224—44no—
228#11758224—44no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—22no—
235C2×D244—41no—
236C2×D244—41no—
237C2×D244—41no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—41no—
256C2×C4×D61—41no—
257C2×C4×D61—41no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2×D412yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61#4112yes—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—41no—
265#11758217—44no—
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×#92420—21no—
288C2×#92420—44no—
289C2×#92420C2×D412yes—
290C2×#92420C2×D412yes—
291#11758213—44no—
292D61⋊C8—44no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61C22⋊C414yes—
297C42×C61—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301#11758198C22⋊C414yes—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196C22⋊C414yes—
306C4×Dic61—22no—
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×C61C2×C22⋊C412yes—
325C23×C61C23×C411yescharacteristic
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—21no—
345C22×D61C2×C22⋊C412yes—
346C22×D61C4×D412yes—
347Q8×C61—44no—
348D4×C61—44no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61C2×C22⋊C412yes—
362C2×C4×C61C2×C22⋊C412yes—
363C2×C4×C61C4×D412yes—
364C22⋊D61—44no—
365C22⋊D61—44no—
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—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61C2×C22⋊C412yes—
388C2×Dic61C2×C22⋊C412yes—
389C2×Dic61#13112yes—
390C2×Dic61C22×D411yescharacteristic
391C2×Dic61C22×D411yescharacteristic
392C2×Dic61C22×D411yescharacteristic
393C2×Dic61C2×#4111yescharacteristic
394C2×Dic61H(5,𝔽2)11yescharacteristic
395C2×Dic61H(5,𝔽2)11yescharacteristic
396D244—44no—
397D244—44no—
398D244—44no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—44no—
408C4×D61—44no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413Dic122—44no—
414#92420—22no—
415#92420—22no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#92420—41no—
421#92420—41no—
422#22403—611nomaximal, Sylow
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61C22×C22⋊C411yescharacteristic
438C22×C61C2×C4×D411yescharacteristic
439C22×C61#51811yescharacteristic
440C22×C61C2×#13111yescharacteristic
441C22×C61#56811yescharacteristic
442C22×C61#56811yescharacteristic
443C22×C61#56811yescharacteristic
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—22no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C4×C61—22no—
466C4×C61—22no—
467C4×C61—22no—
468C4×C61—41no—
469C4×C61—41no—
470Dic61—22no—
471Dic61—22no—
472Dic61—22no—
473Dic61—41no—
474Dic61D4211yescharacteristic
475Dic61D4211yescharacteristic
476Dic61#54611yescharacteristic
477Dic61#54611yescharacteristic
478C2×#532—611no—
479C2×#435—611no—
480C2×#435—611no—
481C2×#408—611no—
482C2×#408—611no—
483#1955—611no—
484#1955—611no—
485#1870—611no—
486#1870—611no—
487#1869—611no—
488#1869—611no—
489#1797—611no—
490#1780—611no—
491#1780—611no—
492#1749—611no—
493C2×C61—42no—
494C2×C61—81no—
495C2×C61D4×C22⋊C411yescharacteristic
496C2×C61#287911yescharacteristic
497C2×C61#288011yescharacteristic
498C2×C61#293211yescharacteristic
499C2×C61#293511yescharacteristic
500C2×C61#298011yescharacteristic
501C2×C61#298111yescharacteristic
502D61—42no—
503D61—42no—
504D61—81no—
505C22×#41—611no—
506C22×#41—611no—
507C22×M16—611no—
508C22×M16—611no—
509C23×C8—611no—
510C23×C8—611no—
511#532—1224no—
512#532—1224no—
513C2×C4⋊Q8—611no—
514C2×#127—611no—
515C2×#124—611no—
516C2×#124#692311yescharacteristic
517C2×#121—611no—
518C2×#121—611no—
519C2×#121—611no—
520C2×#121—611no—
521C2×C4×D4—611no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×C4×D4—611no—
525C22×C42—611no—
526#435—1224no—
527#435—1224no—
528C2×C4⋊C8—611no—
529C2×C4⋊C8—611no—
530#408—1224no—
531#408—1224no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
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×#97—611no—
549C2×#97—611no—
550#336—611no—
551#336—611no—
552#336—611no—
553#336—611no—
554C61#2240311yescharacteristic, complemented, Sylow
555C2×#41—1222no—
556C2×#41—1222no—
557C2×#41—1222no—
558C2×#41—1222no—
559C2×#41—1222no—
560C2×#41—1222no—
561C2×#41—1222no—
562C2×#41—1222no—
563C2×#41—2441no—
564C2×#41—2441no—
565C2×#41—2441no—
566C2×#41—2441no—
567C22×Q8—611no—
568C22×Q8C2×#692311yescharacteristic
569C22×D4—611no—
570C22×D4—611no—
571C22×D4—611no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—611no—
575C22×D4—611no—
576C22×D4—611no—
577C22×D4—611no—
578C22×D4C2×#692311yescharacteristic
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C2×M16—1222no—
587C2×M16—1222no—
588C2×M16—1222no—
589C2×M16—1222no—
590C2×M16—2441no—
591C2×M16—2441no—
592C22×C8—611no—
593C22×C8—611no—
594C22×C8—611no—
595C22×C8—611no—
596C22×C8—611no—
597C22×C8—611no—
598C22×C8—611no—
599C22×C8—611no—
600C22×C8—1222no—
601C22×C8—1222no—
602C22×C8—1222no—
603C22×C8—1222no—
604C22×C8—2441no—
605C22×C8—2441no—
606C4⋊Q8—1224no—
607#127—1224no—
608#124—24no—
609#124—1224no—
610#121—1224no—
611#121—1224no—
612#121—1224no—
613#121—1224no—
614C4×D4—614no—
615C4×D4—614no—
616C4×D4—1222no—
617C4×D4—1222no—
618C4×D4—1222no—
619C4×D4—1222no—
620C4×D4—1222no—
621C4×D4—1222no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C22⋊C4—611no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—611no—
630C2×C22⋊C4C2×#692311yescharacteristic
631C2×C22⋊C4C2×#692311yescharacteristic
632C2×C22⋊C4C2×#692311yescharacteristic
633C2×C22⋊C4C2×#692311yescharacteristic
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—1222no—
638C2×C42—1222no—
639C2×C42C2×#692311yescharacteristic
640C4⋊C8—1222no—
641C4⋊C8—1222no—
642C22⋊C8—614no—
643C22⋊C8—1222no—
644C22⋊C8—1222no—
645C22⋊C8—1222no—
646C22⋊C8—1222no—
647C22⋊C8—1222no—
648C22⋊C8—1222no—
649C22⋊C8—1222no—
650C22⋊C8—1222no—
651C22⋊C8—1222no—
652C22⋊C8—1222no—
653C22⋊C8—1222no—
654C22⋊C8—2441no—
655C22⋊C8—2441no—
656C22⋊C8—2441no—
657C22⋊C8—2441no—
658#97—1222no—
659#97—1222no—
660C24—611no—
661C24—611no—
662C24—611no—
663C24C22×#692311yescharacteristic
664C24C22×#692311yescharacteristic
665#41—2444no—
666#41—2444no—
667#41—2444no—
668#41—2444no—
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2444no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—41no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—2441no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—41no—
682C2×D4—614no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1222no—
686C2×D4—1222no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—2441no—
699C2×D4—2441no—
700C2×D4—2441no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2441no—
705C2×D4—2441no—
706C2×D4—2441no—
707C2×D4—2441no—
708C2×D4—2441no—
709C22×C4—611no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—611no—
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—1222no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1222no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1222no—
747C22×C4—2441no—
748C22×C4—2441no—
749C22×C4—2441no—
750C22×C4C22×#692311yescharacteristic
751C22×C4C22×#692311yescharacteristic
752C22×C4C22×#692311yescharacteristic
753C22×C4C22×#692311yescharacteristic
754C22×C4C22×#692311yescharacteristic
755M16—2444no—
756M16—2444no—
757C2×C8—612no—
758C2×C8—612no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
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—2444no—
782C2×C8—2444no—
783C4⋊C4—614no—
784C4⋊C4—1222no—
785C4⋊C4—1222no—
786C4⋊C4—1222no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—614no—
791C22⋊C4—1222no—
792C22⋊C4—1222no—
793C22⋊C4—1222no—
794C22⋊C4C22⋊#692314yes—
795C42—22no—
796C42—612no—
797C42—612no—
798C42—1221no—
799C42—1221no—
800C42—1222no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—612no—
815C23—612no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—1221no—
827C23—1221no—
828C23—1221no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—1221no—
833C23—1221no—
834C23—1221no—
835C23C2×C22⋊#692312yes—
836C23C23×#692311yescharacteristic
837Q8—44no—
838Q8—2444no—
839D4—44no—
840D4—2444no—
841D4—2444no—
842D4—2444no—
843D4—2444no—
844D4—2444no—
845D4—2444no—
846D4—2444no—
847D4—2444no—
848D4—2444no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—611no—
867C2×C4—612no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
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—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—2444no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2444no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4C2×C22⋊#692312yes—
902C2×C4C2×C22⋊#692312yes—
903C2×C4D4×#692312yes—
904C8—1222no—
905C8—1222no—
906C8—2441no—
907C8—2441no—
908C8—2441no—
909C8—2441no—
910C8—2441no—
911C8—2441no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—1222no—
927C22—1222no—
928C22—1222no—
929C22—1222no—
930C22—1222no—
931C22—1222no—
932C22—2441no—
933C22—2441no—
934C22—2441no—
935C22—2441no—
936C22—2441no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22C22×C22⋊#692311yescharacteristic
948C22C2×D4×#692311yescharacteristic
949C22#1684082911yescharacteristic
950C22D61⋊#13111yescharacteristic
951C22#1684084111yescharacteristic
952C22#1684084111yescharacteristic
953C22#1684084111yescharacteristic
954C4—22no—
955C4—22no—
956C4—22no—
957C4—41no—
958C4—41no—
959C4—611no—
960C4—611no—
961C4—611no—
962C4—611no—
963C4—1222no—
964C4—1222no—
965C4—1222no—
966C4—2441no—
967C2—42no—
968C2—81no—
969C2—4881no—
970C2—2442no—
971C2—2442no—
972C2D4×C22⋊#692311yescharacteristic
973C2#2146240411yescharacteristic
974C2#2146240911yescharacteristic
975C2#2146254511yescharacteristic
976C2#2146256411yescharacteristic
977C2#2146270511yescharacteristic
978C2#2146271011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#124×C61C4
prime radicalC2×#16840311C2
cosocleC22×Dic61C24
hypercenterC2×#124#6923
hypocenterC61#22403
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840794C2semidirect
2. C2×#16840791C2semidirect
3. C2×#16840737C2semidirect
4. C2×#16840735C2semidirect
5. #21461944C2semidirect
6. #21461944C2semidirect
7. #21461798C2semidirect
8. #21461797C2semidirect
9. #21461794C2semidirect
10. #21461793C2semidirect
11. #21461674C2semidirect
12. #21461644C2semidirect
13. #21461643C2semidirect
14. #21461546C2semidirect
96. #14519834D4semidirect
554. C61#22403semidirect

Maximal subgroups

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

subgroupindex
C2×#168407942
C2×#168407912
C2×#168407372
C2×#168407352
#214619442
#214617982
#214617972
#214617942
#214617932
#214616742
#214616442
#214616432
#214615462
C2×#168403112
#2240361