Finite Group Databasebeta

← #30616932

Subgroups — #30616932

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840790C211yesmaximal, characteristic, complemented
2C2×#16840789C211yesmaximal, characteristic, complemented
3C2×#16840789C211yesmaximal, characteristic, complemented
4C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
5#21461942C211yesmaximal, characteristic, complemented
6#21461918C211yesmaximal, characteristic, complemented
7#21461890C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461793C211yesmaximal, characteristic, complemented
11#21461676C211yesmaximal, characteristic, complemented
12#21461611C211yesmaximal, characteristic, complemented
13#21461553C211yesmaximal, characteristic, complemented
14C22⋊C4×#92420C211yesmaximal, characteristic, complemented
15#21448331C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840790—24no—
21#16840789—24no—
22#16840789—24no—
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C4×D61⋊C8—24no—
36C2×C4×#92420C2211yescharacteristic
37C2×C4×#92420C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40C2×C4×#92420C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519750C411yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839662C411yescharacteristic
54#16839657C411yescharacteristic
55#16839653C411yescharacteristic
56#16839640C411yescharacteristic
57#16839638C411yescharacteristic
58#16839621C411yescharacteristic
59#16839613C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#388C411yescharacteristic
63C2×D61⋊C8—22no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—22no—
69C2×D61⋊C8—22no—
70C2×D61⋊C8—22no—
71C2×D61⋊C8D414yescomplemented
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—22no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844—22no—
85#14519844—22no—
86C4⋊#92420—22no—
87#14519834—22no—
88#14519834—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95C4×#92420—22no—
96C4×#92420—22no—
97C4×#92420—22no—
98C4×#92420—22no—
99C4×#92420—22no—
100C4×#92420D414yescomplemented
101C22×D244C2×C411yescharacteristic
102C22×C22⋊D61C2×C411yescharacteristic
103C22×C22⋊D61C2×C411yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61C2×C411yescharacteristic
106C22×C4×D61C2×C411yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519750C818yescomplemented
110#14519739—22no—
111#14519739—22no—
112#14519737—22no—
113#14519737—22no—
114#14519737—22no—
115#14519737—22no—
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C42×D61—22no—
133C42×D61—22no—
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C42×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61C2×C814yescomplemented
159C2×C22⋊D61C2×C814yescomplemented
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C2411yescharacteristic
172C2×D244—22no—
173C2×D244—22no—
174C2×D244C2×C814yescomplemented
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61C2×C814yescomplemented
191C2×C4×D61C2×D412yes—
192C2×C4×D61#4112yes—
193C2×#92420—21no—
194C2×#92420—21no—
195C2×#92420—21no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—21no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—44no—
212C2×#92420C2×D412yes—
213C2×#92420C2×D412yes—
214C2×#92420C2×D412yes—
215C2×#92420C2×D412yes—
216C2×#92420#4112yes—
217C2×#92420#4112yes—
218D61⋊C8—28no—
219D61⋊C8—28no—
220D61⋊C8—44no—
221C4⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61C2×C814yescomplemented
225C42×C61—22no—
226C22⋊Dic61—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198C2×C814yescomplemented
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196C2×C814yescomplemented
237C4×Dic61—22no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61C2×D412yes—
245C4×Dic61#4112yes—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61C22×C812yes—
253C23×C61C23×C411yescharacteristic
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61C4×D412yes—
265C22×D61C22×C812yes—
266C22×D61C22×C812yes—
267C22×D61#13112yes—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61C4×D412yes—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C22×C812yes—
285C2×C4×C61C22×C812yes—
286C22⋊D61—28no—
287C22⋊D61—28no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61C4×D412yes—
303C2×Dic61C22×C812yes—
304C2×Dic61C22×C812yes—
305C2×Dic61#13112yes—
306C2×Dic61#13112yes—
307C2×Dic61C22×D411yescharacteristic
308C2×Dic61C22×D411yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61C2×#4111yescharacteristic
313D244—28no—
314C4×D61—28no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—28no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324#92420—22no—
325#92420—22no—
326#92420—22no—
327#92420—41no—
328#92420—41no—
329#92420—41no—
330#92420—41no—
331#92420#12114yescomplemented
332C8×#121—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C4×#4111yescharacteristic
343C22×C61C23×C811yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61C2×#13111yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61C8×D414yescomplemented
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—41no—
367Dic61—22no—
368Dic61—22no—
369Dic61—41no—
370Dic61—41no—
371Dic61C8×D414yescomplemented
372Dic61C2×#12111yescharacteristic
373Dic61#52511yescharacteristic
374Dic61#52911yescharacteristic
375Dic61#53211yescharacteristic
376C2×C8×D4—611no—
377C2×C8×D4—611no—
378C2×C8×D4—611no—
379C22×C4×C8—611no—
380C4×#121—611no—
381#1954—611no—
382#1939—611no—
383#1923—611no—
384#1923—611no—
385#1869—611no—
386#1869—611no—
387#1797—611no—
388C8×C4⋊C4—611no—
389C8×C22⋊C4—611no—
390C8×C22⋊C4—611no—
391C2×C61—42no—
392C2×C61C4×#12111yescharacteristic
393C2×C61C2×C8×D411yescharacteristic
394C2×C61C2×C8×D411yescharacteristic
395C2×C61#292911yescharacteristic
396C2×C61#293111yescharacteristic
397C2×C61C8×#4111yescharacteristic
398C2×C61#296611yescharacteristic
399D61—24no—
400D61—42no—
401C23×C8—611no—
402C23×C8—611no—
403C23×C8—611no—
404C23×C8—611no—
405C2×#121—611no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C42—611no—
410C8×D4—1224no—
411C8×D4—1224no—
412C8×D4—1224no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C4×C8—611no—
426C2×C4×C8—611no—
427C2×C4×C8—611no—
428C2×C4×C8—611no—
429C2×C4×C8—611no—
430C2×C4×C8—611no—
431C2×C4×C8—1224no—
432#390—611no—
433#389—611no—
434#388—611no—
435#388#692311yescharacteristic
436#386—611no—
437#386—611no—
438#380—611no—
439C4×C4⋊C4—611no—
440C4×C22⋊C4—611no—
441C4×C22⋊C4—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336—611no—
447#336—611no—
448C61C8×#12111yescharacteristic, complemented, Sylow
449C22×D4—611no—
450C22×D4—611no—
451C22×D4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—614no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—1222no—
469C22×C8—1222no—
470C22×C8—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C22×C8—1222no—
475C22×C8—1222no—
476C22×C8—1222no—
477#121—618no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4C2×#692311yescharacteristic
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4C2×#692311yescharacteristic
497C2×C22⋊C4C2×#692311yescharacteristic
498C2×C22⋊C4C2×#692311yescharacteristic
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—611no—
503C2×C42—611no—
504C2×C42—1222no—
505C2×C42—1222no—
506C2×C42C2×#692311yescharacteristic
507C4⋊C8—1222no—
508C4⋊C8—1222no—
509C4⋊C8—1222no—
510C4⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C4×C8—614no—
520C4×C8—1222no—
521C4×C8—1222no—
522C4×C8—1222no—
523C4×C8—1222no—
524C4×C8—1222no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95C2×#692311yescharacteristic
530#95C2×#692311yescharacteristic
531C24—611no—
532C24—611no—
533C24C22×#692311yescharacteristic
534C2×D4—614no—
535C2×D4—614no—
536C2×D4—614no—
537C2×D4—1222no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—614no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4C22×#692311yescharacteristic
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—1228no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1228no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—2444no—
606C2×C8—2444no—
607C4⋊C4—22no—
608C4⋊C4—614no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—614no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4D61⋊C814yescomplemented
622C42—22no—
623C42—612no—
624C42—612no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—1222no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—612no—
639C23—612no—
640C23—612no—
641C23—612no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23C2×D61⋊C812yes—
653C23C23×#692311yescharacteristic
654D4—1228no—
655D4—1228no—
656D4—1228no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—612no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1228no—
687C2×C4—1228no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4D4×#692312yes—
707C2×C4D4×#692312yes—
708C2×C4C2×D61⋊C812yes—
709C2×C4C2×D61⋊C812yes—
710C8—614no—
711C8—1222no—
712C8—1222no—
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—614no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C2×D4×#692311yescharacteristic
740C22C2×D4×#692311yescharacteristic
741C22#41×#692311yescharacteristic
742C22C22×D61⋊C811yescharacteristic
743C22D61⋊#13111yescharacteristic
744C22D61⋊#13111yescharacteristic
745C22D61⋊#13111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—611no—
753C4—611no—
754C4—611no—
755C4—611no—
756C4—614no—
757C4—1222no—
758C4—1222no—
759C4—2441no—
760C4—2441no—
761C2—42no—
762C2—1224no—
763C2—2442no—
764C2#121×#692311yescharacteristic
765C2D4×D61⋊C811yescharacteristic
766C2D4×D61⋊C811yescharacteristic
767C2#2146253611yescharacteristic
768C2#2146254311yescharacteristic
769C2#2146262311yescharacteristic
770C2#2146263711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C23×C8
FittingC61×#388C4
socleC23×C61C23×C4
prime radicalC2×#14519750C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61C8×#121
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840790C2semidirect
2. C2×#16840789C2semidirect
3. C2×#16840789C2semidirect
4. C2×C4×D61⋊C8C2semidirect
5. #21461942C2semidirect
6. #21461918C2semidirect
7. #21461890C2semidirect
8. #21461888C2semidirect
9. #21461795C2semidirect
10. #21461793C2semidirect
11. #21461676C2semidirect
12. #21461611C2semidirect
13. #21461553C2semidirect
14. C22⋊C4×#92420C2semidirect
71. C2×D61⋊C8D4semidirect
100. C4×#92420D4semidirect
109. #14519750C8semidirect
158. C2×C22⋊D61C2×C8semidirect
159. C2×C22⋊D61C2×C8semidirect
174. C2×D244C2×C8semidirect
190. C2×C4×D61C2×C8semidirect
224. C22⋊C4×C61C2×C8semidirect
232. #11758198C2×C8semidirect
236. #11758196C2×C8semidirect
331. #92420#121semidirect
360. C2×D61C8×D4semidirect
371. Dic61C8×D4semidirect
448. C61C8×#121semidirect
621. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#168407902
C2×#168407892
C2×C4×D61⋊C82
#214619422
#214619182
#214618902
#214618882
#214617952
#214617932
#214616762
#214616112
#214615532
C22⋊C4×#924202
#214483312
C8×#12161