Finite Group Databasebeta

← #29679830

Subgroups — #29679830

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic
3#21448408C211yesmaximal, characteristic
4#21445914C211yesmaximal, characteristic, complemented
5#21445913C211yesmaximal, characteristic, complemented
6#21445912C211yesmaximal, characteristic, complemented
7#21445908C211yesmaximal, characteristic, complemented
8#21445907C211yesmaximal, characteristic, complemented
9#21445906C211yesmaximal, characteristic, complemented
10#21445904C211yesmaximal, characteristic, complemented
11#21445537C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1825C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840242—24no—
20#16840242C418yescomplemented
21C2×C4×Dic122—21no—
22C2×C4×D244—21no—
23C2×#14519737—21no—
24C2×#14519737—21no—
25C2×#14519735C2211yescharacteristic
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839727—24no—
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36#16839666—21no—
37#16839662—21no—
38#16839640—21no—
39#16839638—21no—
40#16839622C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222C2×C414yes—
67C2×#11758222D414yes—
68C22×Dic122D411yescharacteristic
69C22×D244D411yescharacteristic
70C22×C22⋊D61D411yescharacteristic
71C22×C22⋊D61D411yescharacteristic
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C4×Dic122—28no—
87C4×D244—28no—
88#14519737—28no—
89#14519737—28no—
90#14519735—22no—
91#14519735—22no—
92#14519735—22no—
93#14519735—22no—
94#14519735C2×C414yes—
95#14519735C2×C414yescomplemented
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61C2×C414yescomplemented
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61C2×C414yes—
111C4⋊C4×D61C2×C414yescomplemented
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C22⋊#92418—22no—
122#14519689—22no—
123#14519689—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#117×C61—22no—
131#117×C61C2×C414yescomplemented
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C22⋊C8×C61—22no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61C22⋊C414yes—
161C2×C22⋊D61C22⋊C414yes—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—24no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—81no—
168C22×Dic61—81no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171#11758222—28no—
172#11758222—28no—
173#11758222—28no—
174#11758222—28no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244C22⋊C414yes—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—42no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61—81no—
188C2×C4×D61—81no—
189C2×C4×D61—81no—
190C2×C4×D61—81no—
191C2×C4×D61C22×C412yes—
192C2×C4×D61C22×C412yes—
193C2×C4×D61C2×D412yes—
194C2×C4×D61C2×D412yes—
195C2×C4×D61#4112yes—
196C2×C4×D61#4112yes—
197C2×C4×D61#4112yes—
198C2×C4×D61#4112yes—
199C2×Dic122—22no—
200C2×Dic122—22no—
201C2×Dic122C22⋊C414yes—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C22×C412yes—
215C4⋊C4×C61C22×C412yes—
216C22⋊C4×C61—24no—
217C22⋊C4×C61—81no—
218C42×C61—24no—
219C22⋊Dic61—81no—
220#11758198—24no—
221#11758198—24no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—24no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61C22×C412yes—
233C4⋊Dic61C22×C412yes—
234#11758196—24no—
235#11758196—24no—
236#11758196—42no—
237C4×Dic61—24no—
238C4×Dic61—24no—
239C4×Dic61—42no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246#11758189—44no—
247C8×D61—44no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61C2×C22⋊C412yes—
255C23×C61C22×D411yescharacteristic
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×D61—21no—
265C22×D61—21no—
266C22×D61C2×C22⋊C412yes—
267C22×D61C2×C22⋊C412yes—
268C22×D61#12312yes—
269C22×D61#12312yes—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61C2×C22⋊C412yes—
289C2×C4×C61C23×C411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C22⋊D61—28no—
296C22⋊D61—28no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—84no—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61#12312yes—
315C2×Dic61#12312yes—
316D244—28no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—84no—
322C4×D61—84no—
323C4×D61—84no—
324C4×D61#11714yes—
325C4×D61#11714yes—
326C4×D61#12314yes—
327C4×D61#12314yes—
328Dic122—28no—
329C8×C61—41no—
330C8×C61—41no—
331#92418—41no—
332#92418—41no—
333#20703—611nomaximal, Sylow
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61C2×#12311yescharacteristic
343C22×C61C2×#12311yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57711yescharacteristic
347C22×C61#57811yescharacteristic
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—22no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61#38114yes—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—81no—
366C4×C61—81no—
367C4×C61C2×#11711yescharacteristic
368C4×C61C2×#11711yescharacteristic
369C4×C61C2×#12311yescharacteristic
370C4×C61C2×#12311yescharacteristic
371Dic61—22no—
372Dic61—42no—
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376Dic61#38114yes—
377C2×#520—611no—
378C2×#408—611no—
379#2311—611no—
380#1825—611no—
381#1825—611no—
382#1825—611no—
383#1825D6111yescharacteristic, complemented
384#1824—611no—
385#1824—611no—
386#1823—611no—
387#1823—611no—
388#1736—611no—
389#1736—611no—
390#1735—611no—
391C2×#340—611no—
392C2×C61—42no—
393C2×C61C2×#38111yescharacteristic
394C2×C61#289711yescharacteristic
395C2×C61#289811yescharacteristic
396C2×C61#309611yescharacteristic
397C2×C61#309711yescharacteristic
398C2×C61#309811yescharacteristic
399C2×C61#309911yescharacteristic
400D61—24no—
401D61—42no—
402C22×#41—611no—
403C22×M16—611no—
404C23×C8—611no—
405#520—618no—
406#520—1224no—
407C2×C4×Q8—1221no—
408C2×C4×D4—1221no—
409C2×C4×D4—1221no—
410C2×C4×D4—1221no—
411C2×#117—611no—
412C2×#117—611no—
413C2×#117—611no—
414C2×#117C2×D6111yescharacteristic
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—611no—
419#408—1224no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8C2×D6111yescharacteristic
424#391—1221no—
425#390—1221no—
426#386—1221no—
427#386—1221no—
428#380—611no—
429#380—611no—
430#380—611no—
431#380C2×D6111yescharacteristic
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340C2×D6111yescharacteristic
445#340C2×D6111yescharacteristic
446#340C2×D6111yescharacteristic
447#340C2×D6111yescharacteristic
448C61#2070311yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—614no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C22×Q8—611no—
456C22×D4—611no—
457C22×D4—611no—
458C22×D4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4C22×D6111yescharacteristic
466C2×M16—1222no—
467C2×M16—1222no—
468C2×M16—1222no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C22×C8C22×D6111yescharacteristic
475C22×C8C22×D6111yescharacteristic
476C4×Q8—1228no—
477C4×D4—1228no—
478C4×D4—1228no—
479C4×D4—1228no—
480#117—22no—
481#117—614no—
482#117—614no—
483#117—1222no—
484#117—1222no—
485#117—1222no—
486#117—1222no—
487#117C4×D6114yescomplemented
488C2×C4⋊C4—614no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—614no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1222no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C42—21no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C22⋊C8—22no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524#95—21no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—611no—
529C24—611no—
530C24D4×D6111yescharacteristic
531#41—1228no—
532#41—1228no—
533#41—1228no—
534#41—1228no—
535C2×Q8—614no—
536C2×Q8—1222no—
537C2×Q8—1222no—
538C2×D4—614no—
539C2×D4—614no—
540C2×D4—614no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—611no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1224no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—4881no—
577C22×C4—4881no—
578C22×C4—4881no—
579C22×C4—4881no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—2442no—
585C22×C4C2×C4×D6112yes—
586C22×C4D4×D6112yes—
587C22×C4D4×D6111yescharacteristic
588C22×C4C23×D6111yescharacteristic
589M16—2444no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—2444no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—612no—
610C4⋊C4—612no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—2442no—
621C4⋊C4C2×C4×D6112yes—
622C4⋊C4C2×C4×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—81no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—4881no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—2442no—
631C42—24no—
632C42—1224no—
633C42—1224no—
634C42—2442no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—612no—
642C23—612no—
643C23—612no—
644C23—612no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23C22⋊C4×D6112yes—
656C23C2×D4×D6111yescharacteristic
657Q8—1228no—
658D4—1228no—
659D4—1228no—
660D4—1228no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—614no—
683C2×C4—614no—
684C2×C4—614no—
685C2×C4—614no—
686C2×C4—612no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—4884no—
696C2×C4—4884no—
697C2×C4—4884no—
698C2×C4—4884no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C22⋊C4×D6112yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C8—41no—
717C8—41no—
718C8—2441no—
719C8—2441no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—614no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22C2×C22⋊C4×D6111yescharacteristic
742C22#123×D6111yescharacteristic
743C22#123×D6111yescharacteristic
744C22#1684056411yescharacteristic
745C22#1684056911yescharacteristic
746C22#1684057211yescharacteristic
747C22#1684057811yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—614no—
754C4—1222no—
755C4—4881no—
756C4—4881no—
757C4—2442no—
758C4—2442no—
759C4#117×D6111yescharacteristic
760C4#117×D6111yescharacteristic
761C4#123×D6111yescharacteristic
762C4#123×D6111yescharacteristic
763C2—42no—
764C2—1224no—
765C2—2442no—
766C2#381×D6111yescharacteristic
767C2#2145434111yescharacteristic
768C2#2145435011yescharacteristic
769C2#2145577411yescharacteristic
770C2#2145578511yescharacteristic
771C2#2145580011yescharacteristic
772C2#2145581111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1825C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1825D61
hypocenterC61#20703
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #21445914C2semidirect
5. #21445913C2semidirect
6. #21445912C2semidirect
7. #21445908C2semidirect
8. #21445907C2semidirect
9. #21445906C2semidirect
10. #21445904C2semidirect
11. #21445537C2semidirect
12. #21445537C2semidirect
13. #21445534C2semidirect
14. #340×D61C2semidirect
15. C61×#1825C2semidirect
20. #16840242C4semidirect
95. #14519735C2×C4semidirect
98. C2×C4⋊Dic61C2×C4semidirect
111. C4⋊C4×D61C2×C4semidirect
131. #117×C61C2×C4semidirect
383. #1825D61semidirect
448. C61#20703semidirect
487. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402422
C2×#168397272
#214484082
#214459142
#214459132
#214459122
#214459082
#214459072
#214459062
#214459042
#214455372
#214455342
#340×D612
C61×#18252
#2070361