Finite Group Databasebeta

← #30620099

Subgroups — #30620099

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×#16840737C211yesmaximal, characteristic, complemented
4C2×#16840734C211yesmaximal, characteristic, complemented
5#21461945C211yesmaximal, characteristic, complemented
6#21461941C211yesmaximal, characteristic, complemented
7#21461799C211yesmaximal, characteristic, complemented
8#21461798C211yesmaximal, characteristic, complemented
9#21461798C211yesmaximal, characteristic, complemented
10#21461795C211yesmaximal, characteristic, complemented
11#21461678C211yesmaximal, characteristic, complemented
12#21461644C211yesmaximal, characteristic, complemented
13#21461642C211yesmaximal, characteristic, complemented
14#21461548C211yesmaximal, characteristic, complemented
15C2×#16840275C211yesmaximal, 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#16840737—24no—
25#16840734—24no—
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic, complemented
35C2×#14519834C2211yescharacteristic, complemented
36C2×#14519834C2211yescharacteristic, complemented
37C2×#14519834C2211yescharacteristic, complemented
38C2×#14519834C2211yescharacteristic, complemented
39C2×#14519834C2211yescharacteristic, complemented
40C2×C22⋊#92420C2211yescharacteristic
41C2×C22⋊#92420C2211yescharacteristic
42C2×#14519832C2211yescharacteristic, complemented
43C2×C4×#92420C2211yescharacteristic, complemented
44#16840628C2211yescharacteristic, complemented
45#16840628C2211yescharacteristic, complemented
46#16840628C2211yescharacteristic, complemented
47#16840628C2211yescharacteristic, complemented
48C22×#11758226C2211yescharacteristic
49C23×C4×D61C2211yescharacteristic
50#16840275—24no—
51#16840275—24no—
52C2×#14519762C411yescharacteristic
53C2×#14519762C411yescharacteristic
54C2×#14519753C411yescharacteristic
55C2×#14519752C411yescharacteristic
56C2×#14519751C411yescharacteristic
57C2×#14519747C411yescharacteristic
58C2×#14519747C411yescharacteristic
59C2×#14519739C2211yescharacteristic
60C2×#14519739C2211yescharacteristic
61C2×#14519737C2211yescharacteristic
62C2×#14519737C2211yescharacteristic
63C2×#14519735C2211yescharacteristic
64C2×C22⋊Q8×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—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—22no—
93#14519834—22no—
94#14519834—22no—
95#14519834—22no—
96#14519834—41no—
97#14519834—41no—
98#14519834—41no—
99#14519834—41no—
100#14519834D414yescomplemented
101C22⋊#92420—22no—
102C22⋊#92420—22no—
103#14519832—22no—
104C4×#92420—22no—
105C24×D61C2×C411yescharacteristic
106C2×#11758226—22no—
107C2×#11758226—22no—
108C2×#11758226—22no—
109C2×#11758226—22no—
110C2×#11758226—41no—
111C2×#11758226—41no—
112C22×D244C2×C411yescharacteristic
113C22×D244C2×C411yescharacteristic
114C22×D244C2×C411yescharacteristic
115C22×D244C2×C411yescharacteristic
116C22×D244C2×C411yescharacteristic
117C22×C22⋊D61C2×C411yescharacteristic
118C22×C22⋊D61C2×C411yescharacteristic
119C23×Dic61C2311yescharacteristic
120C22×C4×D61—22no—
121C22×C4×D61—22no—
122C22×C4×D61—22no—
123C22×C4×D61—22no—
124C22×C4×D61—41no—
125C22×C4×D61—41no—
126C22×C4×D61C2×C411yescharacteristic
127C22×C4×D61C2×C411yescharacteristic
128C22×C4×D61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C22×C4×D61C2311yescharacteristic
131C22×C4×D61C2311yescharacteristic
132#14519762—24no—
133#14519762—24no—
134#14519753—24no—
135#14519752—24no—
136#14519751—24no—
137#14519747—24no—
138#14519747—24no—
139#14519739—22no—
140#14519739—22no—
141#14519739—22no—
142#14519739—22no—
143#14519737—22no—
144#14519737—22no—
145#14519737D414yes—
146#14519737D414yes—
147#14519735—22no—
148#14519735—22no—
149C2×C4⋊Dic61C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×C4×Dic61C2311yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C22×Q8×C61C2×C411yescharacteristic
163C23×C4×C61C2×C411yescharacteristic
164C22⋊Q8×C61—24no—
165C2×C4⋊C4×C61C2×C411yescharacteristic
166C2×C4⋊C4×C61C2×C411yescharacteristic
167C2×C4⋊C4×C61C2×C411yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C24×C61C22×C411yescharacteristic
171C23×D61—22no—
172C23×D61—22no—
173C23×D61—22no—
174C23×D61—41no—
175C23×D61—41no—
176C23×D61—41no—
177C23×D61—41no—
178C23×D61C22×C411yescharacteristic
179C23×D61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C23×D61C22×C411yescharacteristic
182C2×Q8×C61—22no—
183C2×Q8×C61—22no—
184C2×Q8×C61—41no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—41no—
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C2×C22⋊D61—22no—
195C2×C22⋊D61—41no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61C22⋊C414yes—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C22×C411yescharacteristic
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C2×D412yes—
208C22×Dic61C2×D412yes—
209C22×Dic61C2411yescharacteristic
210#11758226—44no—
211#11758226—44no—
212#11758226—44no—
213#11758226—44no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—41no—
225C2×D244—41no—
226C2×D244—41no—
227C2×D244—41no—
228C2×D244—41no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—44no—
254C2×C4×D61—44no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61—41no—
258C2×C4×D61—41no—
259C2×C4×D61C2×D412yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D412yes—
262C2×C4×D61#4112yes—
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—
291C4⋊C4×C61—22no—
292C4⋊C4×C61—22no—
293C4⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61C22⋊C414yes—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198C22⋊C414yes—
304C4⋊Dic61—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×C61C2×C22⋊C412yes—
318C23×C61C23×C411yescharacteristic
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
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—44no—
345C22×D61—44no—
346C22×D61—44no—
347C22×D61—44no—
348C22×D61—44no—
349C22×D61—44no—
350C22×D61—44no—
351C22×D61C2×C22⋊C412yes—
352C22×D61C4×D412yes—
353C22×D61#13112yes—
354Q8×C61—44no—
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×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—44no—
371C2×C4×C61C2×C22⋊C412yes—
372C2×C4×C61C2×C22⋊C412yes—
373C2×C4×C61C4×D412yes—
374C22⋊D61—44no—
375C22⋊D61—44no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61C2×C22⋊C412yes—
388C2×Dic61C2×C22⋊C412yes—
389C2×Dic61C22×D411yescharacteristic
390C2×Dic61C22×D411yescharacteristic
391C2×Dic61C22×D411yescharacteristic
392C2×Dic61C2×#4111yescharacteristic
393C2×Dic61H(5,𝔽2)11yescharacteristic
394C2×Dic61H(5,𝔽2)11yescharacteristic
395D244—44no—
396D244—44no—
397D244—44no—
398D244—44no—
399D244—44no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—44no—
409C4×D61—44no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
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—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61C22×C22⋊C411yescharacteristic
435C22×C61C2×C4×D411yescharacteristic
436C22×C61#51811yescharacteristic
437C22×C61C2×#13111yescharacteristic
438C22×C61#56811yescharacteristic
439C22×C61#56811yescharacteristic
440C22×C61#56811yescharacteristic
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—22no—
450C2×D61—416no—
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—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C4×C61—22no—
471C4×C61—22no—
472C4×C61—22no—
473C4×C61—41no—
474C4×C61—41no—
475C4×C61—41no—
476Dic61—22no—
477Dic61—22no—
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×C61D4×C22⋊C411yescharacteristic
500C2×C61#287911yescharacteristic
501C2×C61#288011yescharacteristic
502C2×C61#293011yescharacteristic
503C2×C61#293311yescharacteristic
504C2×C61#297611yescharacteristic
505C2×C61#297811yescharacteristic
506D61—42no—
507D61—42no—
508D61—42no—
509D61—81no—
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#692311yescharacteristic
522C2×#121—611no—
523C2×#121—611no—
524C2×#120—611no—
525C2×#120—611no—
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
560C25—611no—
561C2×#41—1222no—
562C2×#41—1222no—
563C2×#41—1222no—
564C2×#41—1222no—
565C2×#41—2441no—
566C2×#41—2441no—
567C22×Q8C2×#692311yescharacteristic
568C22×D4—611no—
569C22×D4—611no—
570C22×D4—611no—
571C22×D4—611no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—1222no—
583C23×C4—1222no—
584C23×C4—1222no—
585C23×C4—1222no—
586C23×C4—2441no—
587C23×C4—2441no—
588C23×C4C2×#692311yescharacteristic
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—24no—
612C22⋊Q8—1224no—
613#121—1224no—
614#121—1224no—
615#120—1224no—
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⋊C4C2×#692311yescharacteristic
631C2×C4⋊C4C2×#692311yescharacteristic
632C2×C4⋊C4C2×#692311yescharacteristic
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⋊C4—611no—
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—611no—
666C24—611no—
667C24—611no—
668C24—611no—
669C24—1222no—
670C24—1222no—
671C24—1222no—
672C24—2441no—
673C24—2441no—
674C24—2441no—
675C24—2441no—
676C24C22×#692311yescharacteristic
677#41—2444no—
678#41—2444no—
679#41—2444no—
680#41—2444no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—41no—
684C2×D4—614no—
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—2441no—
697C2×D4—2441no—
698C2×D4—2441no—
699C2×D4—2441no—
700C2×D4—2441no—
701C2×D4—2441no—
702C2×D4—2441no—
703C2×D4—2441no—
704C2×D4—2441no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—41no—
708C22×C4—611no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
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—1222no—
737C22×C4—1222no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1222no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1222no—
746C22×C4—2441no—
747C22×C4—2441no—
748C22×C4—2444no—
749C22×C4—2444no—
750C22×C4—2444no—
751C22×C4—2444no—
752C22×C4C22×#692311yescharacteristic
753C22×C4C22×#692311yescharacteristic
754C22×C4C22×#692311yescharacteristic
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—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—614no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C22⋊C4—22no—
793C22⋊C4—614no—
794C22⋊C4—1222no—
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—612no—
813C23—612no—
814C23—612no—
815C23—1221no—
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—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1221no—
839C23—1221no—
840C23—2444no—
841C23—2444no—
842C23—2444no—
843C23—2444no—
844C23—2444no—
845C23—2444no—
846C23—2444no—
847C23C2×C22⋊#692312yes—
848C23C23×#692311yescharacteristic
849Q8—44no—
850D4—2444no—
851D4—2444no—
852D4—2444no—
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—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—44no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—611no—
876C2×C4—611no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—612no—
880C2×C4—612no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1221no—
894C2×C4—1221no—
895C2×C4—1221no—
896C2×C4—1221no—
897C2×C4—1221no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—2444no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2444no—
910C2×C4C2×C22⋊#692312yes—
911C2×C4C2×C22⋊#692312yes—
912C2×C4D4×#692312yes—
913C8—1222no—
914C8—1222no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C8—2441no—
920C8—2441no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—1222no—
929C22—1222no—
930C22—1222no—
931C22—1222no—
932C22—1222no—
933C22—1222no—
934C22—1222no—
935C22—1222no—
936C22—1222no—
937C22—24416no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22—2441no—
942C22—2441no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22—2441no—
952C22—2441no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22C22×C22⋊#692311yescharacteristic
958C22C2×D4×#692311yescharacteristic
959C22#1684082911yescharacteristic
960C22D61⋊#13111yescharacteristic
961C22#1684084111yescharacteristic
962C22#1684084211yescharacteristic
963C22#1684084211yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—611no—
971C4—611no—
972C4—611no—
973C4—611no—
974C4—1222no—
975C4—1222no—
976C4—2441no—
977C2—42no—
978C2—4881no—
979C2—2442no—
980C2—2442no—
981C2—2442no—
982C2D4×C22⋊#692311yescharacteristic
983C2#2146240611yescharacteristic
984C2#2146240911yescharacteristic
985C2#2146253911yescharacteristic
986C2#2146255411yescharacteristic
987C2#2146269011yescharacteristic
988C2#2146269811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C22⋊Q8×C61C4
prime radicalC2×#16840275C2
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22400
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840795C2semidirect
2. C2×#16840794C2semidirect
3. C2×#16840737C2semidirect
4. C2×#16840734C2semidirect
5. #21461945C2semidirect
6. #21461941C2semidirect
7. #21461799C2semidirect
8. #21461798C2semidirect
9. #21461798C2semidirect
10. #21461795C2semidirect
11. #21461678C2semidirect
12. #21461644C2semidirect
13. #21461642C2semidirect
14. #21461548C2semidirect
16. C22×#11758213C22semidirect
19. C22×D61⋊C8C22semidirect
22. C2×#14519844C22semidirect
23. C2×C4⋊#92420C22semidirect
34. C2×#14519834C22semidirect
35. C2×#14519834C22semidirect
36. C2×#14519834C22semidirect
37. C2×#14519834C22semidirect
38. C2×#14519834C22semidirect
39. C2×#14519834C22semidirect
42. C2×#14519832C22semidirect
43. C2×C4×#92420C22semidirect
44. #16840628C22semidirect
45. #16840628C22semidirect
46. #16840628C22semidirect
47. #16840628C22semidirect
100. #14519834D4semidirect
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×#168407372
C2×#168407342
#214619452
#214619412
#214617992
#214617982
#214617952
#214616782
#214616442
#214616422
#214615482
C2×#168402752
#2240061