Finite Group Databasebeta

← #29712998

Subgroups — #29712998

Order 15616.

1344 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic
2C2×#16840079C211yesmaximal, characteristic, complemented
3C2×#103×D61C211yesmaximal, characteristic, complemented
4#21450132C211yesmaximal, characteristic, complemented
5#21447059C211yesmaximal, characteristic, complemented
6#21447058C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21447015C211yesmaximal, characteristic, complemented
9#21446244C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21446089C211yesmaximal, characteristic, complemented
12#21446085C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445752C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840419—24no—
19#16840419—24no—
20C2×#14519764—21no—
21C2×#14519764C2211yescharacteristic
22C2×#14519756—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519748—21no—
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840079—24no—
31C2×#14519709C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39#103×D61—24no—
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44#16839703—21no—
45#16839698—21no—
46#16839661C2211yescharacteristic
47#16839658C2211yescharacteristic
48#16839638—21no—
49#16839636—21no—
50#16839622C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×#41×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—41no—
69C2×Q8×D61—41no—
70C2×Q8×D61D414yes—
71C22×C22⋊D61—21no—
72C22×C22⋊D61D411yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—22no—
79C2×C8×D61—41no—
80C2×C8×D61—41no—
81#14519764—28no—
82#14519764—22no—
83#14519764—22no—
84#14519756—28no—
85#14519756—22no—
86#14519756—22no—
87#14519748—28no—
88#14519748—22no—
89#14519748D414yes—
90Q8×Dic61—22no—
91Q8×Dic61—22no—
92C4×C22⋊D61—28no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519709—22no—
117#14519708—22no—
118#14519702—22no—
119#14519702—41no—
120#14519701—22no—
121#14519701—22no—
122#14519700—22no—
123#14519700—41no—
124#14519698—22no—
125#14519698—41no—
126C22⋊#92418—41no—
127#14519689—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132C2×#41×C61—22no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—41no—
137C2×#41×C61—41no—
138C22×Q8×C61C2311yescharacteristic
139C22×D4×C61—21no—
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148#103×C61—22no—
149#103×C61—22no—
150#102×C61—22no—
151#102×C61—41no—
152C22⋊C8×C61—41no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C2×D412yes—
165C2×Q8×C61#4112yes—
166C2×Q8×C61#4112yes—
167C2×D4×C61—24no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61C2×D412yes—
176C22×C4×C61—21no—
177C22×C4×C61—24no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203Q8×D61—28no—
204Q8×D61—44no—
205Q8×D61—44no—
206Q8×D61—44no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—24no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—81no—
216C2×C4×D61—81no—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2×D412yes—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—24no—
225C2×Dic122—42no—
226C2×Dic122—42no—
227C2×Dic122C2×D412yes—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C22⋊C4×C61—81no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—22no—
244C22⋊Dic61—81no—
245#11758198—22no—
246#11758198—42no—
247C4⋊Dic61—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—81no—
254C4⋊Dic61C2×D412yes—
255#11758196—24no—
256#11758196—22no—
257#11758196—42no—
258#11758196—81no—
259C4×Dic61—24no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C8×D61—44no—
269C23×C61—21no—
270C23×C61—22no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61#12012yes—
289C22×D61#13512yes—
290C22×D61#13712yes—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61#12314yes—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—48no—
298D4×C61—41no—
299D4×C61—41no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—48no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—44no—
324C22⋊D61—48no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61#12012yes—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—48no—
351C4×D61—84no—
352Dic122—22no—
353Dic122—22no—
354Dic122—48no—
355Dic122—41no—
356Dic122—41no—
357C8×C61—41no—
358C8×C61—41no—
359#92418—41no—
360#92418—41no—
361#24036—611nomaximal, Sylow
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—42no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61C2×#12011yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#54611yescharacteristic
379C22×C61C2×#13511yescharacteristic
380C22×C61C2×#13711yescharacteristic
381C22×C61#57711yescharacteristic
382C22×C61#57711yescharacteristic
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61#45214yes—
390C4×C61—24no—
391C4×C61—41no—
392C4×C61—81no—
393C4×C61—81no—
394C4×C61C2×#12311yescharacteristic
395C4×C61#53411yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#54611yescharacteristic
398Dic61—22no—
399Dic61—42no—
400Dic61—41no—
401Dic61—42no—
402Dic61—41no—
403Dic61—81no—
404Dic61—81no—
405C2×#548—611no—
406C2×#481—611no—
407C22×#103—611no—
408#2487—611no—
409#2042—611no—
410#2042—611no—
411#2035—611no—
412#2035—611no—
413#1893—611no—
414#1869—611no—
415#1865—611no—
416#1865—611no—
417#1788—611no—
418#1788D6111yescharacteristic, complemented
419#1787—611no—
420C2×C61—81no—
421C2×C61—82no—
422C2×C61#240511yescharacteristic
423C2×C61C2×#45211yescharacteristic
424C2×C61#301011yescharacteristic
425C2×C61#330111yescharacteristic
426C2×C61#330111yescharacteristic
427C2×C61#331611yescharacteristic
428C2×C61#331611yescharacteristic
429D61—24no—
430C22×#41C2×D6111yescharacteristic
431C23×Q8—611no—
432C23×C8—611no—
433#548—1224no—
434#548—1224no—
435C2×#124—611no—
436C2×#124—1221no—
437C2×C22⋊Q8—611no—
438C2×C22⋊Q8—1221no—
439C2×#121—611no—
440C2×#121—1221no—
441C2×C4×Q8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—1221no—
444C22×C4⋊C4—611no—
445#481—1224no—
446C2×#106—611no—
447C2×#106—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—1224no—
455C2×#103C2×D6111yescharacteristic
456C2×#103C2×D6111yescharacteristic
457C2×#102—611no—
458C2×#102—611no—
459C2×#102C2×D6111yescharacteristic
460C2×#102C2×D6111yescharacteristic
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×C22⋊C8C2×D6111yescharacteristic
464#400—1221no—
465#399—1221no—
466#389—611no—
467#389—611no—
468#386—1221no—
469#385—1221no—
470#380—611no—
471#380—611no—
472#380C2×D6111yescharacteristic
473#340—611no—
474#340—611no—
475#336—611no—
476#336—611no—
477C61#2403611yescharacteristic, complemented, Sylow
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—614no—
485C22×Q8—611no—
486C22×Q8—1221no—
487C22×Q8—1222no—
488C22×Q8—1222no—
489C22×Q8—1222no—
490C22×Q8—2441no—
491C22×Q8—2441no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—611no—
495C22×D4—1221no—
496C22×D4C22×D6111yescharacteristic
497C23×C4—21no—
498C23×C4—611no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4C22×D6111yescharacteristic
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—1222no—
505C22×C8—2441no—
506C22×C8—2441no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509#124—1222no—
510#124—1228no—
511#124—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8—1228no—
515#121—614no—
516#121—1222no—
517#121—1228no—
518C4×Q8—1222no—
519C4×Q8—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1228no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1222no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—611no—
546C2×C42—1221no—
547#106—1222no—
548#106—1222no—
549#103—22no—
550#103—22no—
551#103—1222no—
552#103—1222no—
553#103—1222no—
554#103—1222no—
555#103—2441no—
556#103—2441no—
557#102—22no—
558#102—41no—
559#102—1222no—
560#102—2441no—
561C22⋊C8—41no—
562C22⋊C8—1222no—
563C22⋊C8—2441no—
564#95—21no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—21no—
570C24—611no—
571C24D4×D6111yescharacteristic
572#41—44no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—612no—
580C2×Q8—1224no—
581C2×Q8—1221no—
582C2×Q8—1228no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—2442no—
588C2×Q8—2442no—
589C2×Q8—2444no—
590C2×Q8—2444no—
591C2×Q8—2444no—
592C2×Q8#1175822212yes—
593C2×Q8D4×D6112yes—
594C2×Q8#1175822412yes—
595C2×D4—24no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—1224no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—2442no—
608C2×D4—2442no—
609C2×D4D4×D6112yes—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—611no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—1224no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—4881no—
637C22×C4—4881no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4D4×D6111yescharacteristic
642C22×C4C23×D6111yescharacteristic
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—2444no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—612no—
661C4⋊C4—1222no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—4881no—
670C4⋊C4—4881no—
671C4⋊C4—2442no—
672C22⋊C4—81no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—4881no—
680C22⋊C4—2442no—
681C42—1224no—
682C42—1221no—
683C42—1221no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—612no—
699C23—612no—
700C23—612no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23C2×D4×D6111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—1222no—
710Q8—1222no—
711Q8—2448no—
712Q8—2441no—
713Q8—2441no—
714Q8#1451975914yes—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—2444no—
721D4—2448no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—48no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—612no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1222no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—4884no—
755C2×C4—2448no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×#1175822411yescharacteristic
769C2×C4C2×#1175822211yescharacteristic
770C2×C4#1451982211yescharacteristic
771C2×C4#1451982211yescharacteristic
772C8—41no—
773C8—41no—
774C8—2441no—
775C8—2441no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—614no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—1222no—
797C22#120×D6111yescharacteristic
798C22#1684039911yescharacteristic
799C22#1684040211yescharacteristic
800C22#135×D6111yescharacteristic
801C22#137×D6111yescharacteristic
802C22#1684056911yescharacteristic
803C22#1684057211yescharacteristic
804C4—24no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—1222no—
809C4—4881no—
810C4—4881no—
811C4—2441no—
812C4—2442no—
813C4—2442no—
814C4—2441no—
815C4C2×#1451975911yescharacteristic
816C4#1684032211yescharacteristic
817C4#1684039911yescharacteristic
818C4#1684040211yescharacteristic
819C2—81no—
820C2—82no—
821C2—1224no—
822C2#2144914411yescharacteristic
823C2#452×D6111yescharacteristic
824C2#2145510211yescharacteristic
825C2#2145771411yescharacteristic
826C2#2145772211yescharacteristic
827C2#2145792311yescharacteristic
828C2#2145793111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840419C2
hypercenter#1788D61
hypocenterC61#24036
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16840079C2semidirect
3. C2×#103×D61C2semidirect
4. #21450132C2semidirect
5. #21447059C2semidirect
6. #21447058C2semidirect
7. #21447016C2semidirect
8. #21447015C2semidirect
9. #21446244C2semidirect
10. #21446108C2semidirect
11. #21446089C2semidirect
12. #21446085C2semidirect
13. #21445759C2semidirect
14. #21445752C2semidirect
15. C61×#1788C2semidirect
418. #1788D61semidirect
477. C61#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×#168400792
C2×#103×D612
#214501322
#214470592
#214470582
#214470162
#214470152
#214462442
#214461082
#214460892
#214460852
#214457592
#214457522
C61×#17882
#2403661