Finite Group Databasebeta

← #30621704

Subgroups — #30621704

Order 15616.

1144 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840796C211yesmaximal, characteristic, complemented
2C2×#16840792C211yesmaximal, characteristic, complemented
3C2×#16840737C211yesmaximal, characteristic, complemented
4C2×#16840737C211yesmaximal, characteristic, complemented
5#21461945C211yesmaximal, characteristic, complemented
6#21461894C211yesmaximal, characteristic, complemented
7#21461890C211yesmaximal, characteristic, complemented
8#21461799C211yesmaximal, characteristic, complemented
9#21461799C211yesmaximal, characteristic, complemented
10#21461795C211yesmaximal, characteristic, complemented
11#21461767C211yesmaximal, characteristic, complemented
12#21461764C211yesmaximal, characteristic, complemented
13#21461560C211yesmaximal, characteristic, complemented
14#21461557C211yesmaximal, characteristic, complemented
15#21449037C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758213C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20C22×D61⋊C8C2211yescharacteristic
21#16840796—24no—
22#16840792—24no—
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2211yescharacteristic
25C2×C4⋊#92420C2211yescharacteristic
26#16840737—24no—
27#16840737—24no—
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×#14519834C2211yescharacteristic
37C2×#14519834C2211yescharacteristic
38C2×#14519834C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×#14519832C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C22×#11758226C2211yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519739C2211yescharacteristic
51C2×#14519739C2211yescharacteristic
52#16839679C411yescharacteristic
53#16839679C411yescharacteristic
54#16839679C411yescharacteristic
55#16839673C411yescharacteristic
56#16839672C411yescharacteristic
57#16839672C411yescharacteristic
58#16839672C411yescharacteristic
59#16839609C2211yescharacteristic
60#16839609C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#395C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—22no—
68C2×#11758213—22no—
69C2×#11758213—41no—
70C2×#11758213—41no—
71C2×#11758213—41no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—22no—
74C2×D61⋊C8—22no—
75C2×D61⋊C8—22no—
76C2×D61⋊C8—41no—
77C2×D61⋊C8—41no—
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85C22×#92420C2311yescharacteristic
86#14519844—22no—
87#14519844—41no—
88C4⋊#92420—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—22no—
93#14519834—22no—
94#14519834—22no—
95#14519834—22no—
96#14519834—22no—
97#14519834—41no—
98#14519834D414yescomplemented
99#14519834D414yescomplemented
100#14519832—22no—
101#14519832—41no—
102C4×#92420—22no—
103C2×#11758226—22no—
104C2×#11758226—22no—
105C2×#11758226—22no—
106C2×#11758226—22no—
107C2×#11758226—41no—
108C2×#11758226—41no—
109C22×D244C2×C411yescharacteristic
110C22×D244C2×C411yescharacteristic
111C22×D244C2×C411yescharacteristic
112C22×D244C2×C411yescharacteristic
113C22×D244C2×C411yescharacteristic
114C22×D244C2×C411yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119#14519739—22no—
120#14519739—22no—
121#14519739—22no—
122#14519739—22no—
123#14519739—41no—
124#14519739—41no—
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143C22×Q8×C61C2×C411yescharacteristic
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147#95×C61C2×C411yescharacteristic
148#95×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C2×Q8×C61—22no—
155C2×Q8×C61—22no—
156C2×Q8×C61—41no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C2411yescharacteristic
168#11758226—44no—
169#11758226—44no—
170#11758226—44no—
171#11758226—44no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—41no—
182C2×D244—41no—
183C2×D244—41no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244—41no—
188C2×D244—41no—
189C2×D244—41no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61C2×D412yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61#4112yes—
213C2×C4×D61#4112yes—
214C2×#92420—21no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—21no—
231C2×#92420—21no—
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420C2×D412yes—
235C2×#92420C2×D412yes—
236C2×#92420C2×D412yes—
237C2×#92420C2×D412yes—
238#11758213—44no—
239#11758213—44no—
240#11758213—44no—
241D61⋊C8—44no—
242D61⋊C8—44no—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—22no—
245C4⋊C4×C61—41no—
246#11758198—22no—
247#11758198—22no—
248#11758198—22no—
249#11758198—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—41no—
253#11758198—41no—
254#11758198—41no—
255#11758198—41no—
256#11758198—41no—
257#11758198—41no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263C4×Dic61—21no—
264C23×C61C23×C411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61C4×D412yes—
292C22×D61C4×D412yes—
293Q8×C61—44no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61C4×D412yes—
313C2×C4×C61C4×D412yes—
314C2×C4×C61#13112yes—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61C22×D411yescharacteristic
325C2×Dic61C22×D411yescharacteristic
326C2×Dic61C2×#4111yescharacteristic
327C2×Dic61C2×#4111yescharacteristic
328C2×Dic61H(5,𝔽2)11yescharacteristic
329C2×Dic61H(5,𝔽2)11yescharacteristic
330D244—44no—
331D244—44no—
332D244—44no—
333D244—44no—
334D244—44no—
335D244—44no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352#92420—22no—
353#92420—22no—
354#92420—22no—
355#92420—22no—
356#92420—41no—
357#92420—41no—
358#92420—41no—
359#92420—41no—
360#22849—611nomaximal, Sylow
361C22×C61C2×C4×D411yescharacteristic
362C22×C61C2×C4×D411yescharacteristic
363C22×C61#51811yescharacteristic
364C22×C61C2×#13111yescharacteristic
365C22×C61#56811yescharacteristic
366C22×C61#56811yescharacteristic
367C22×C61#56811yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61D4211yescharacteristic
407Dic61#54611yescharacteristic
408Dic61#54611yescharacteristic
409Dic61#55111yescharacteristic
410C2×#436—611no—
411C2×#435—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388—611no—
415#1955—611no—
416#1924—611no—
417#1923—611no—
418#1870—611no—
419#1870—611no—
420#1869—611no—
421#1851—611no—
422#1850—611no—
423#1753—611no—
424#1752—611no—
425C2×C61#235811yescharacteristic
426C2×C61#293011yescharacteristic
427C2×C61#293211yescharacteristic
428C2×C61#293311yescharacteristic
429C2×C61#293511yescharacteristic
430C2×C61#297811yescharacteristic
431C2×C61#298111yescharacteristic
432D61—42no—
433D61—42no—
434D61—81no—
435D61—81no—
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439C22×M16—611no—
440C23×C8—611no—
441C23×C8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445#436—1224no—
446#435—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450#408—1224no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466#395#692311yescharacteristic
467#394—611no—
468#394—611no—
469#394—611no—
470#393—611no—
471#392—611no—
472#392—611no—
473#392—611no—
474C4×C22⋊C4—611no—
475C4×C22⋊C4—611no—
476C4×C22⋊C4—611no—
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483C61#2284911yescharacteristic, complemented, Sylow
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8C2×#692311yescharacteristic
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—1222no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—1222no—
519C22×C8—1222no—
520C22×C8—1222no—
521C22×C8—1222no—
522C22×C8—2441no—
523C22×C8—2441no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—2441no—
529C4×D4—2441no—
530C2×C4⋊C4C2×#692311yescharacteristic
531C2×C4⋊C4C2×#692311yescharacteristic
532C2×C4⋊C4C2×#692311yescharacteristic
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—2441no—
562#97—1222no—
563#97—2441no—
564C4×C8—1222no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95C2×#692311yescharacteristic
569#95C2×#692311yescharacteristic
570#95C2×#692311yescharacteristic
571C24—611no—
572C24—611no—
573C24—611no—
574C24—611no—
575#41—2444no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—41no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C22×C4—611no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4C22×#692311yescharacteristic
629C22×C4C22×#692311yescharacteristic
630C22×C4C22×#692311yescharacteristic
631C22×C4C22×#692311yescharacteristic
632C22×C4C22×#692311yescharacteristic
633C22×C4C22×#692311yescharacteristic
634C22×C4C22×#692311yescharacteristic
635M16—2444no—
636M16—2444no—
637M16—2444no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—612no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8—2444no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—2441no—
674C22⋊C4—2441no—
675C22⋊C4—2441no—
676C22⋊C4—2441no—
677C22⋊C4—2441no—
678C22⋊C4—2441no—
679C42—1221no—
680C42—1221no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C23—612no—
686C23—612no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23C23×#692311yescharacteristic
714Q8—44no—
715D4—2444no—
716D4—2444no—
717D4—2444no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4D4×#692312yes—
771C2×C4D4×#692312yes—
772C2×C4#1451986512yes—
773C8—1222no—
774C8—1222no—
775C8—1222no—
776C8—1222no—
777C8—2441no—
778C8—2441no—
779C8—2441no—
780C8—2441no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—1222no—
786C22—1222no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×D4×#692311yescharacteristic
810C22C2×D4×#692311yescharacteristic
811C22#1684082911yescharacteristic
812C22C2×#1451986511yescharacteristic
813C22#1684084111yescharacteristic
814C22#1684084211yescharacteristic
815C22#1684084211yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—611no—
824C4—611no—
825C4—611no—
826C4—611no—
827C4—2441no—
828C4—2441no—
829C4—2441no—
830C2—4881no—
831C2—4881no—
832C2—2442no—
833C2—2442no—
834C2#2146234111yescharacteristic
835C2#2146253911yescharacteristic
836C2#2146254611yescharacteristic
837C2#2146255211yescharacteristic
838C2#2146256511yescharacteristic
839C2#2146269811yescharacteristic
840C2#2146271111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#395C4
prime radical#21449037C2
cosocleC22×Dic61C24
hypercenter#395#6923
hypocenterC61#22849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#16840796C2semidirect
2. C2×#16840792C2semidirect
3. C2×#16840737C2semidirect
4. C2×#16840737C2semidirect
5. #21461945C2semidirect
6. #21461894C2semidirect
7. #21461890C2semidirect
8. #21461799C2semidirect
9. #21461799C2semidirect
10. #21461795C2semidirect
11. #21461767C2semidirect
12. #21461764C2semidirect
13. #21461560C2semidirect
14. #21461557C2semidirect
98. #14519834D4semidirect
99. #14519834D4semidirect
483. C61#22849semidirect

Maximal subgroups

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

subgroupindex
C2×#168407962
C2×#168407922
C2×#168407372
#214619452
#214618942
#214618902
#214617992
#214617952
#214617672
#214617642
#214615602
#214615572
#214490372
#2284961