Finite Group Databasebeta

← #29680100

Subgroups — #29680100

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic
2C2×#16839820C211yesmaximal, characteristic, complemented
3#21448426C211yesmaximal, characteristic, complemented
4#21445914C211yesmaximal, characteristic, complemented
5#21445828C211yesmaximal, characteristic, complemented
6#21445828C211yesmaximal, characteristic, complemented
7#21445818C211yesmaximal, characteristic, complemented
8#21445818C211yesmaximal, characteristic, complemented
9#21445751C211yesmaximal, characteristic
10#21445749C211yesmaximal, characteristic
11#21445643C211yesmaximal, characteristic, complemented
12#21445643C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1825C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17#16840236—24no—
18#16840236C418yescomplemented
19C2×C4×D244—21no—
20C2×C4×D244—21no—
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×#14519739C2211yescharacteristic
25C2×#14519736C2211yescharacteristic
26C2×C22⋊C4×D61—21no—
27C2×C22⋊C4×D61—21no—
28#16839820—24no—
29C2×#14519706C2211yescharacteristic, complemented
30C2×#14519706C2211yescharacteristic, complemented
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519687C2211yescharacteristic, complemented
41C2×C8×Dic61C2211yescharacteristic, complemented
42#16839656—21no—
43#16839650—21no—
44#16839647—21no—
45#16839645—21no—
46#16839631C2211yescharacteristic, complemented
47#16839627C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C2×#117×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244—21no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244C2×C414yes—
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C4×D244—28no—
79C4×D244—28no—
80#14519739—22no—
81#14519739—22no—
82#14519739—22no—
83#14519739—22no—
84#14519739C2×C414yes—
85#14519739C2×C414yes—
86#14519739C2×C414yes—
87#14519739C2×C414yes—
88#14519736C2×C414yes—
89#14519736D414yes—
90C2×C4⋊Dic61D411yescharacteristic
91C2×C4⋊Dic61D411yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61D411yescharacteristic
98C2×C22⋊Dic61D411yescharacteristic
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C22⋊C4×D61—28no—
104C22⋊C4×D61—28no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519706—22no—
110#14519706—22no—
111#14519699—22no—
112#14519699—22no—
113#14519699—22no—
114#14519699—22no—
115#14519697—22no—
116#14519697—22no—
117#14519697—22no—
118#14519697—22no—
119C22⋊#92418—22no—
120#14519687—22no—
121C8×Dic61—22no—
122#14519684—21no—
123#14519684—21no—
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×C414yes—
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×D61—21no—
143C23×D61—21no—
144C23×D61—24no—
145C23×D61—24no—
146C23×D61—24no—
147C23×D61—81no—
148C23×D61—81no—
149C23×D61—81no—
150C23×D61—81no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×D244—24no—
170C2×D244—24no—
171C2×D244—28no—
172C2×D244—28no—
173C2×D244—24no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—28no—
181C2×D244—28no—
182C2×D244C22×C412yes—
183C2×D244C22×C412yes—
184C2×D244#4112yes—
185C2×D244#4112yes—
186C2×D244#4112yes—
187C2×D244#4112yes—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×C4×D61—81no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C22×C412yes—
213C4⋊C4×C61C22×C412yes—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—81no—
216C42×C61—24no—
217C22⋊Dic61—81no—
218C22⋊Dic61C22⋊C414yes—
219C22⋊Dic61C22⋊C414yes—
220#11758198—24no—
221#11758198—24no—
222#11758198—24no—
223#11758198—24no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22⋊C414yes—
229C4⋊Dic61C22⋊C414yes—
230#11758196—81no—
231#11758196—81no—
232C4×Dic61—81no—
233C4×Dic61—81no—
234C4×Dic61C22×C412yes—
235C4×Dic61C22×C412yes—
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61C2×C22⋊C412yes—
251C23×C61C22×D411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—216no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272C22×D61—84no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
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×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61C2×C22⋊C412yes—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C412yes—
315C2×Dic61C2×C22⋊C412yes—
316D244—216no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244—22no—
322D244—22no—
323D244#11714yes—
324D244#11714yes—
325C4×D61—84no—
326C4×D61—84no—
327C4×D61—84no—
328C4×D61—84no—
329C8×C61—41no—
330C8×C61—41no—
331#92418—41no—
332#92418—41no—
333#20744—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×C61#52511yescharacteristic
343C22×C61#52511yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57611yescharacteristic
346C22×C61#57711yescharacteristic
347C22×C61#57711yescharacteristic
348C2×D61—24no—
349C2×D61—24no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—816no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×#11711yescharacteristic
369C4×C61C2×#11711yescharacteristic
370C4×C61#52511yescharacteristic
371C4×C61#52511yescharacteristic
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—22no—
376Dic61—81no—
377Dic61—81no—
378C2×#518—611no—
379C2×#433—611no—
380#2314—611no—
381#1825—611no—
382#1825D6111yescharacteristic, complemented
383#1804—611no—
384#1804—611no—
385#1802—611no—
386#1802—611no—
387#1786—611no—
388#1786—611no—
389#1762—611no—
390#1762—611no—
391C4×#102—611no—
392C4×#102—611no—
393C2×C61—42no—
394C2×C61#228011yescharacteristic
395C2×C61#289711yescharacteristic
396C2×C61#289711yescharacteristic
397C2×C61#311811yescharacteristic
398C2×C61#311811yescharacteristic
399C2×C61#312211yescharacteristic
400C2×C61#312311yescharacteristic
401D61—44no—
402D61—44no—
403C23×D4—611no—
404#518—618no—
405#518—1224no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—1221no—
411C2×C4×D4—1221no—
412C2×#117—611no—
413C2×#117C2×D6111yescharacteristic
414C22×C22⋊C4—1221no—
415C22×C22⋊C4—1221no—
416#433—1224no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×C22⋊C8—611no—
428C2×C22⋊C8C2×D6111yescharacteristic
429C2×#97—611no—
430C2×C4×C8—611no—
431#388—1221no—
432#388—1221no—
433#387—1221no—
434#387—1221no—
435#384—611no—
436#382—611no—
437#380—611no—
438#380C2×D6111yescharacteristic
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340C2×D6111yescharacteristic, complemented
446#340C2×D6111yescharacteristic, complemented
447#340C2×D6111yescharacteristic, complemented
448#340C2×D6111yescharacteristic, complemented
449C61#2074411yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×D4—614no—
452C22×D4—611no—
453C22×D4—611no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1222no—
458C22×D4—1221no—
459C22×D4—1222no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4×D4—614no—
470C4×D4—614no—
471C4×D4—614no—
472C4×D4—614no—
473C4×D4—1228no—
474C4×D4—1228no—
475C4×D4—1222no—
476C4×D4—1222no—
477C4×D4—1222no—
478C4×D4—1222no—
479#117—22no—
480#117—614no—
481#117—614no—
482#117C4×D6114yes—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—1228no—
498C2×C22⋊C4—1228no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—1221no—
508C2×C42—1221no—
509C4⋊C8—1222no—
510C4⋊C8—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102—1222no—
518#102—1222no—
519C22⋊C8—22no—
520C22⋊C8—1222no—
521#97—1222no—
522C4×C8—1222no—
523#95—21no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529C24—1224no—
530C24—1224no—
531C24—1224no—
532C24—1221no—
533C24—1221no—
534C24—4881no—
535C24—4881no—
536C24—4881no—
537C24—4881no—
538C24D4×D6111yescharacteristic
539C2×D4—612no—
540C2×D4—612no—
541C2×D4—612no—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—1228no—
546C2×D4—1228no—
547C2×D4—1224no—
548C2×D4—1224no—
549C2×D4—1228no—
550C2×D4—1228no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1224no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—1224no—
571C22×C4—1224no—
572C22×C4—1224no—
573C22×C4—1224no—
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×C4C2×C4×D6112yes—
585C22×C4D4×D6112yes—
586C22×C4D4×D6111yescharacteristic
587C22×C4C23×D6111yescharacteristic
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—614no—
607C4⋊C4—614no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—4881no—
613C4⋊C4—4881no—
614C4⋊C4C2×C4×D6112yes—
615C4⋊C4C2×C4×D6112yes—
616C22⋊C4—24no—
617C22⋊C4—81no—
618C22⋊C4—614no—
619C22⋊C4—614no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C22⋊C4—4881no—
625C42—24no—
626C42—612no—
627C42—612no—
628C42—612no—
629C42—612no—
630C42—4881no—
631C42—4881no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—12216no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—4884no—
646C23—4884no—
647C23—4884no—
648C23—4884no—
649C23—4884no—
650C23—4884no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C22⋊C4×D6112yes—
660C23C2×D4×D6111yescharacteristic
661D4—614no—
662D4—614no—
663D4—12216no—
664D4—1222no—
665D4—1222no—
666D4—1222no—
667D4—1222no—
668D4—1222no—
669D4—1222no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—4884no—
701C2×C4—4884no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4C22⋊C4×D6112yes—
711C2×C4C22×C4×D6111yescharacteristic
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C8—41no—
718C8—41no—
719C8—2441no—
720C8—2441no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—1224no—
729C22—1224no—
730C22—48816no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22C2×C22⋊C4×D6111yescharacteristic
744C22#1684027011yescharacteristic
745C22#1684027011yescharacteristic
746C22#1684056411yescharacteristic
747C22#1684056611yescharacteristic
748C22#1684056911yescharacteristic
749C22#1684057111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—81no—
754C4—81no—
755C4—1222no—
756C4—1222no—
757C4—1222no—
758C4—1222no—
759C4—4881no—
760C4—4881no—
761C4#117×D6111yescharacteristic
762C4#117×D6111yescharacteristic
763C4#1684027011yescharacteristic
764C4#1684027011yescharacteristic
765C2—42no—
766C2—2444no—
767C2—2444no—
768C2#2144819911yescharacteristic
769C2#2145434111yescharacteristic
770C2#2145434311yescharacteristic
771C2#2145599811yescharacteristic
772C2#2145600611yescharacteristic
773C2#2145605811yescharacteristic
774C2#2145606711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1825C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#1825D61
hypocenterC61#20744
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
2. C2×#16839820C2semidirect
3. #21448426C2semidirect
4. #21445914C2semidirect
5. #21445828C2semidirect
6. #21445828C2semidirect
7. #21445818C2semidirect
8. #21445818C2semidirect
11. #21445643C2semidirect
12. #21445643C2semidirect
13. #21445633C2semidirect
14. #21445633C2semidirect
15. C61×#1825C2semidirect
18. #16840236C4semidirect
29. C2×#14519706C22semidirect
30. C2×#14519706C22semidirect
40. C2×#14519687C22semidirect
41. C2×C8×Dic61C22semidirect
46. #16839631C22semidirect
47. #16839627C22semidirect
49. C4⋊C4×Dic61C22semidirect
50. C4⋊C4×Dic61C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
382. #1825D61semidirect
445. #340C2×D61semidirect
446. #340C2×D61semidirect
447. #340C2×D61semidirect
448. #340C2×D61semidirect
449. C61#20744semidirect

Maximal subgroups

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

subgroupindex
C2×#168402362
C2×#168398202
#214484262
#214459142
#214458282
#214458182
#214457512
#214457492
#214456432
#214456332
C61×#18252
#2074461