Finite Group Databasebeta

← #29685751

Subgroups — #29685751

Order 15616.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840236C211yesmaximal, characteristic
2C2×#16839915C211yesmaximal, characteristic
3C2×#16839864C211yesmaximal, characteristic, complemented
4C2×C4×#11758190C211yesmaximal, characteristic, complemented
5#21448501C211yesmaximal, characteristic, complemented
6#21446152C211yesmaximal, characteristic, complemented
7#21446152C211yesmaximal, characteristic, complemented
8#21446129C211yesmaximal, characteristic, complemented
9#21446083C211yesmaximal, characteristic, complemented
10#21446069C211yesmaximal, characteristic, complemented
11#21446020C211yesmaximal, characteristic, complemented
12#21445751C211yesmaximal, characteristic
13#21445645C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20#16840236—24no—
21#16840236—24no—
22C2×C4×Dic122C2211yescharacteristic, complemented
23C2×C4×D244C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519739—21no—
28C2×#14519739—21no—
29C2×#14519736C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C22⋊C4×D61—21no—
32#16839915C418yescomplemented
33#16839864—24no—
34C4×#11758190—24no—
35C2×#14519711C2211yescharacteristic, complemented
36C2×#14519709C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519702C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45#16839668C2211yescharacteristic, complemented
46#16839660C2211yescharacteristic, complemented
47#16839657—21no—
48#16839656—21no—
49#16839650—21no—
50#16839643—21no—
51#16839622C2211yescharacteristic
52C4×C4⋊Dic61C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839525C2211yescharacteristic, complemented
56#16839525C2211yescharacteristic, complemented
57C2×#117×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic, complemented
61C2×C4×C8×C61C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×Dic122C2311yescharacteristic
66C22×D244—21no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—22no—
70C22×D244—22no—
71C22×D244—22no—
72C22×D244C2×C414yes—
73C22×D244C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C2×#11758190—22no—
80C2×#11758190—22no—
81C2×#11758190—22no—
82C2×#11758190—22no—
83C2×#11758190C2×C414yescomplemented
84C2×#11758190C2×C414yescomplemented
85#14519756—22no—
86#14519756C2×C414yescomplemented
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—22no—
94C4×D244—22no—
95C4×D244D414yes—
96C4×D244D414yes—
97#14519739—28no—
98#14519739—28no—
99#14519736—22no—
100#14519736—22no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C22⋊C4×D61—28no—
117C22⋊C4×D61—28no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121#14519711—22no—
122#14519709—22no—
123#14519702—22no—
124#14519702—22no—
125#14519699—22no—
126#14519699—22no—
127#14519699—22no—
128#14519699—22no—
129#14519699C2×C414yescomplemented
130#14519699C2×C414yescomplemented
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141#117×C61—22no—
142#117×C61—22no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C22⋊C8×C61—22no—
150C22⋊C8×C61C2×C414yescomplemented
151#97×C61—22no—
152C4×C8×C61—22no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—24no—
159C23×D61—81no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C22×C412yes—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C2×D244—24no—
182C2×D244—28no—
183C2×D244—28no—
184C2×D244—24no—
185C2×D244—24no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—28no—
193C2×D244—28no—
194C2×D244C22×C412yes—
195C2×D244C22×C412yes—
196C2×D244C2×D412yes—
197C2×D244C2×D412yes—
198C2×D244#4112yes—
199C2×D244#4112yes—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—81no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61—81no—
210C2×C4×D61—81no—
211C2×C4×D61—81no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C22×C412yes—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61C22×C412yes—
229C2×C8×C61C22×C412yes—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61C2×D412yes—
237C42×C61C2×D412yes—
238C22⋊Dic61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—81no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C22×C412yes—
253C4⋊Dic61C2×D412yes—
254C4⋊Dic61C2×D412yes—
255#11758196—24no—
256#11758196—42no—
257#11758196—81no—
258C4×Dic61—24no—
259C4×Dic61—42no—
260C4×Dic61—81no—
261#11758190—28no—
262#11758190—28no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61C4×D412yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—216no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61—84no—
291C22×D61—84no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
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×C61C4×D412yes—
309C2×C4×C61#12012yes—
310C2×C4×C61#12012yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335D244—216no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—22no—
342D244C4×D414yes—
343D244C4×D414yes—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61—84no—
347C4×D61—84no—
348Dic122—22no—
349Dic122—22no—
350Dic122—41no—
351Dic122—41no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—41no—
355C8×C61—41no—
356#21459—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61C2×C4×D411yescharacteristic
365C22×C61C2×#12011yescharacteristic
366C22×C61#52511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57711yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57711yescharacteristic
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—816no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61C2×C4×D411yescharacteristic
392C4×C61C2×C4×D411yescharacteristic
393C4×C61#52511yescharacteristic
394C4×C61#52511yescharacteristic
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61—81no—
400Dic61—81no—
401C2×#518—611no—
402C2×#450—611no—
403C2×#440—611no—
404C2×C4×SD16—611no—
405#2323—611no—
406#1877—611no—
407#1877—611no—
408#1873—611no—
409#1864—611no—
410#1862—611no—
411#1854—611no—
412#1786—611no—
413#1762—611no—
414C4×#102—611no—
415#1750D6111yescharacteristic, complemented
416C2×C61—42no—
417C2×C61C4×#12011yescharacteristic
418C2×C61#294611yescharacteristic
419C2×C61#294911yescharacteristic
420C2×C61#300911yescharacteristic
421C2×C61#301211yescharacteristic
422C2×C61#311811yescharacteristic
423C2×C61#312311yescharacteristic
424D61—44no—
425D61—44no—
426C23×D4—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C2×C22⋊Q8—611no—
430#518—1224no—
431#518—1224no—
432C2×C4×Q8—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×#117—611no—
440C2×#117C2×D6111yescharacteristic
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#450—618no—
444#440—1224no—
445C4×SD16—1224no—
446C2×#107—611no—
447C2×#106—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×C22⋊C8C2×D6111yescharacteristic
457C2×C22⋊C8C2×D6111yescharacteristic
458C2×#97C2×D6111yescharacteristic, complemented
459C2×C4×C8C2×D6111yescharacteristic, complemented
460#391—611no—
461#389—611no—
462#389—1221no—
463#388—1221no—
464#388—1221no—
465#387—1221no—
466#380—611no—
467C4×C4⋊C4—611no—
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#336C2×D6111yescharacteristic, complemented
473#336C2×D6111yescharacteristic, complemented
474C61#2145911yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8—611no—
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—1222no—
481C22×D4—1222no—
482C22×D4—1222no—
483C22×D4—1222no—
484C22×D4—1221no—
485C22×D4—1222no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4C22×D6111yescharacteristic
491C2×SD16—614no—
492C2×SD16—614no—
493C2×SD16—1222no—
494C2×SD16—1222no—
495C2×SD16—1222no—
496C2×SD16—1222no—
497C22×C8C22×D6111yescharacteristic
498C22×C8C22×D6111yescharacteristic
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501C22⋊Q8—614no—
502C22⋊Q8—1222no—
503C4×Q8—1222no—
504C4×Q8—1222no—
505C4×D4—614no—
506C4×D4—614no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1228no—
512C4×D4—1228no—
513C4×D4—1222no—
514C4×D4—1222no—
515#117—22no—
516#117—22no—
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4D24411yescharacteristic
528C2×C4⋊C4D24411yescharacteristic
529C2×C22⋊C4—1228no—
530C2×C22⋊C4—1228no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4D24411yescharacteristic
539C2×C22⋊C4D24411yescharacteristic
540C2×C42—1221no—
541C2×C42—1221no—
542C2×C42—1221no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545#107—1222no—
546#106—1222no—
547#103—1222no—
548#103—1222no—
549#102—614no—
550#102—614no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555C22⋊C8—22no—
556C22⋊C8C4×D6114yescomplemented
557#97—22no—
558C4×C8—22no—
559#95—1221no—
560#95—1221no—
561#95—1221no—
562#95—1221no—
563#95—1221no—
564C24—1224no—
565C24—1224no—
566C24—1224no—
567C24—1221no—
568C24—1221no—
569C24—4881no—
570C24—4881no—
571C24—4881no—
572C24—4881no—
573C24C2×D24411yescharacteristic
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×D4—612no—
581C2×D4—612no—
582C2×D4—612no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—1228no—
587C2×D4—1228no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1228no—
591C2×D4—1228no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1224no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—4881no—
620C22×C4—4881no—
621C22×C4C2×C4×D6112yes—
622C22×C4C2×D24411yescharacteristic
623C22×C4C2×D24411yescharacteristic
624C22×C4C2×D24411yescharacteristic
625C22×C4C2×D24411yescharacteristic
626C22×C4C2×D24411yescharacteristic
627C22×C4#1175822212yes—
628C22×C4C23×D6111yescharacteristic
629SD16—1228no—
630SD16—1228no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8C2×C4×D6112yes—
642C2×C8C2×C4×D6112yes—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—612no—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1224no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—4881no—
657C4⋊C4—2442no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—4881no—
667C42—21no—
668C42—21no—
669C42—1224no—
670C42—4881no—
671C42—2442no—
672C42D4×D6112yes—
673C42D4×D6112yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—12216no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—4884no—
688C23—4884no—
689C23—4884no—
690C23—4884no—
691C23—4884no—
692C23—4884no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23C4×D24412yes—
702C23C22×D24411yescharacteristic
703Q8—1222no—
704Q8—1222no—
705Q8—2441no—
706Q8—2441no—
707D4—614no—
708D4—614no—
709D4—12216no—
710D4—1222no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—4884no—
739C2×C4—4884no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4C4×D24412yes—
755C2×C4#1451974712yes—
756C2×C4#1451974712yes—
757C2×C4C22×C4×D6111yescharacteristic
758C2×C4C2×D4×D6111yescharacteristic
759C2×C4C2×D4×D6111yescharacteristic
760C2×C4#41×D6111yescharacteristic
761C2×C4#41×D6111yescharacteristic
762C2×C4C2×#1175822211yescharacteristic
763C8—22no—
764C8—22no—
765C8—41no—
766C8—41no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—1224no—
775C22—1224no—
776C22—48816no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22C2×C4×D24411yescharacteristic
790C22C2×#1451974711yescharacteristic
791C22#1684027411yescharacteristic
792C22#1684056711yescharacteristic
793C22#1684057411yescharacteristic
794C22#1684057411yescharacteristic
795C22#1684057411yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—4881no—
802C4—4881no—
803C4—2442no—
804C4—2442no—
805C4—2442no—
806C4—2442no—
807C4C4×D4×D6111yescharacteristic
808C4C4×D4×D6111yescharacteristic
809C4#1684027111yescharacteristic
810C4#1684027111yescharacteristic
811C2—42no—
812C2—2444no—
813C2—2444no—
814C2C4×#1451974711yescharacteristic
815C2#2145465311yescharacteristic
816C2#2145468011yescharacteristic
817C2#2145509811yescharacteristic
818C2#2145512611yescharacteristic
819C2#2145600511yescharacteristic
820C2#2145607211yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1750C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#1750D61
hypocenterC61#21459
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
3. C2×#16839864C2semidirect
4. C2×C4×#11758190C2semidirect
5. #21448501C2semidirect
6. #21446152C2semidirect
7. #21446152C2semidirect
8. #21446129C2semidirect
9. #21446083C2semidirect
10. #21446069C2semidirect
11. #21446020C2semidirect
13. #21445645C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1750C2semidirect
22. C2×C4×Dic122C22semidirect
32. #16839915C4semidirect
35. C2×#14519711C22semidirect
36. C2×#14519709C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519702C22semidirect
45. #16839668C22semidirect
46. #16839660C22semidirect
52. C4×C4⋊Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839525C22semidirect
56. #16839525C22semidirect
60. C2×#97×C61C22semidirect
61. C2×C4×C8×C61C22semidirect
62. C61×#336C22semidirect
63. C61×#336C22semidirect
83. C2×#11758190C2×C4semidirect
84. C2×#11758190C2×C4semidirect
86. #14519756C2×C4semidirect
129. #14519699C2×C4semidirect
130. #14519699C2×C4semidirect
150. C22⋊C8×C61C2×C4semidirect
415. #1750D61semidirect
458. C2×#97C2×D61semidirect
459. C2×C4×C8C2×D61semidirect
472. #336C2×D61semidirect
473. #336C2×D61semidirect
474. C61#21459semidirect
556. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402362
C2×#168399152
C2×#168398642
C2×C4×#117581902
#214485012
#214461522
#214461292
#214460832
#214460692
#214460202
#214457512
#214456452
C4×#145196992
C61×#17502
#2145961