Finite Group Databasebeta

← #29727476

Subgroups — #29727476

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839967C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic
3C2×#16839924C211yesmaximal, characteristic
4C2×C4×#11758200C211yesmaximal, characteristic, complemented
5#21449418C211yesmaximal, characteristic, complemented
6#21447200C211yesmaximal, characteristic, complemented
7#21447022C211yesmaximal, characteristic, complemented
8#21447015C211yesmaximal, characteristic, complemented
9#21446918C211yesmaximal, characteristic, complemented
10#21446679C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446163C211yesmaximal, characteristic, complemented
13#21446153C211yesmaximal, characteristic, complemented
14#21446066C211yesmaximal, characteristic, complemented
15C61×#2339C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C2×#14519777C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×C4×Dic122C2211yescharacteristic
24#16839967—24no—
25#16839924—24no—
26#16839924—24no—
27C4×#11758200—24no—
28C2×#14519710C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839696—21no—
43#16839685—21no—
44#16839668C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839659—21no—
47#16839655—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#386—21no—
58C61×#386—21no—
59C61×#381—21no—
60C61×#380C2211yescharacteristic
61C4×C22⋊C4×C61C2211yescharacteristic
62C2×#95×C61—21no—
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C2×#11758202—41no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—22no—
75C2×#11758200—22no—
76C2×#11758200D414yes—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519777—22no—
82#14519777—41no—
83#14519756—22no—
84#14519756—22no—
85#14519756—41no—
86#14519756—41no—
87C4×Dic122—22no—
88C4×Dic122—41no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C4×Dic61—21no—
100#14519710—41no—
101#14519708—22no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519700—22no—
106#14519700—22no—
107#14519700—22no—
108#14519700—41no—
109#14519698—22no—
110#14519698D414yes—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61C2311yescharacteristic
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61—21no—
128C23×C4×C61—21no—
129C23×C4×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—41no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143#95×C61—21no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152#41×C61—44no—
153#41×C61—44no—
154#41×C61—44no—
155#41×C61—44no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61#4112yes—
162C2×D4×C61—24no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61C2×D412yes—
169C2×D4×C61C2×D412yes—
170C2×D4×C61#4112yes—
171C22×C4×C61—24no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61—81no—
188C22×C4×C61—81no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122C2×D412yes—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—81no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226#11758202—44no—
227#11758202—44no—
228#11758200—28no—
229#11758200—44no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—42no—
234C4⋊Dic61—42no—
235C4⋊Dic61C2×D412yes—
236#11758196—42no—
237#11758196—42no—
238#11758196—42no—
239#11758196—42no—
240C4×Dic61—42no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—48no—
276D4×C61#12114yes—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—48no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—84no—
305C2×C4×C61—84no—
306C2×C4×C61#13512yes—
307C2×C4×C61#13712yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326Dic122—22no—
327Dic122—22no—
328Dic122—41no—
329Dic122—41no—
330Dic122—41no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334#92418—22no—
335#92418—22no—
336#92418—41no—
337#92418—41no—
338#25154—611nomaximal, Sylow
339C22×C61—24no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61#52511yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61D4211yescharacteristic
356C22×C61C2×#13511yescharacteristic
357C22×C61C2×#13711yescharacteristic
358C22×C61#57711yescharacteristic
359C22×C61#57811yescharacteristic
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×#12111yescharacteristic
369C4×C61#53811yescharacteristic
370C4×C61#54611yescharacteristic
371C4×C61#54611yescharacteristic
372Dic61—42no—
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376C2×#461—611no—
377C2×#452—611no—
378C2×#452—611no—
379C2×C4×SD16—611no—
380#2429—611no—
381#2339D6111yescharacteristic
382#2066—611no—
383#2036—611no—
384#2035—611no—
385#2016—611no—
386#1969—611no—
387#1923—611no—
388#1878—611no—
389#1877—611no—
390#1862—611no—
391C2×C61—44no—
392C2×C61—81no—
393C2×C61#242411yescharacteristic
394C2×C61#310711yescharacteristic
395C2×C61#312011yescharacteristic
396C2×C61#326611yescharacteristic
397C2×C61#327611yescharacteristic
398C2×C61#328211yescharacteristic
399C2×C61#328311yescharacteristic
400C22×#41C2×D6111yescharacteristic
401C22×Q16—611no—
402C22×Q16—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C2×C4⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×D4C2×D6111yescharacteristic
410C2×C4×D4C2×D6111yescharacteristic
411#461—1224no—
412#452—1224no—
413#452—1224no—
414C4×SD16—1224no—
415C2×#107—611no—
416C2×#106—611no—
417C2×C4⋊C8—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428C2×C4×C8—611no—
429#398—1221no—
430#396—1221no—
431#391—611no—
432#391C2×D6111yescharacteristic
433#391C2×D6111yescharacteristic
434#389—611no—
435#389—1221no—
436#388—1221no—
437#386—21no—
438#386—21no—
439#381—21no—
440#380C2×D6111yescharacteristic
441C4×C22⋊C4C2×D6111yescharacteristic
442C2×#95—21no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2515411yescharacteristic, complemented, Sylow
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C22×Q8—611no—
455C22×Q8—611no—
456C22×Q8C22×D6111yescharacteristic
457C22×D4—21no—
458C22×D4C22×D6111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—1222no—
464C2×Q16—1222no—
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—2441no—
468C2×Q16—2441no—
469C2×SD16—614no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C4⋊Q8—1222no—
480C4⋊Q8—2441no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483C22⋊Q8—2441no—
484C22⋊Q8—2441no—
485C4×Q8—1222no—
486C4×Q8—2441no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4C22⋊D6111yescharacteristic
507C2×C22⋊C4C22⋊D6111yescharacteristic
508C2×C42—1221no—
509C2×C42C22×D6111yescharacteristic
510C2×C42C22×D6111yescharacteristic
511#107—2441no—
512#106—1222no—
513C4⋊C8—1222no—
514#103—1222no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—2441no—
520#102—614no—
521#102—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C4×C8—1222no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95C22⋊D6111yescharacteristic
534#95C22⋊D6111yescharacteristic
535C24—21no—
536C24C2×C22⋊D6111yescharacteristic
537#41—44no—
538#41—44no—
539#41—44no—
540#41—44no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—612no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8#1175822212yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4#1175822212yes—
566C2×D4D4×D6112yes—
567C2×D4D4×D6112yes—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C23×D6111yescharacteristic
596Q16—2444no—
597Q16—2444no—
598SD16—1228no—
599SD16—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—612no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4—2442no—
623C4⋊C4—2442no—
624C4⋊C4—2442no—
625C4⋊C4—2442no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—2442no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C22×C22⋊D6111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—41no—
656Q8—41no—
657Q8—1222no—
658Q8—1222no—
659Q8—2441no—
660Q8—2441no—
661Q8—2441no—
662Q8—2441no—
663Q8—2441no—
664Q8—2441no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4#1451975014yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—1222no—
700C2×C4—1222no—
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×C4—2441no—
710C2×C4—2441no—
711C2×C4#1451979712yes—
712C2×C4#1451980712yes—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822211yescharacteristic
716C2×C4C2×#1175822211yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C8—1222no—
720C8—1222no—
721C8—2441no—
722C8—2441no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#1684027311yescharacteristic
738C22D4×C22⋊D6111yescharacteristic
739C22D4×C22⋊D6111yescharacteristic
740C22C2×#1451979711yescharacteristic
741C22C2×#1451980711yescharacteristic
742C22#1684057311yescharacteristic
743C22#1684057711yescharacteristic
744C4—22no—
745C4—22no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—81no—
751C4—81no—
752C4—4881no—
753C4—4881no—
754C4—2442no—
755C4—2442no—
756C4C2×#1451975011yescharacteristic
757C4#1684035011yescharacteristic
758C4#1684040211yescharacteristic
759C4#1684040211yescharacteristic
760C2—44no—
761C2—81no—
762C2#2144935511yescharacteristic
763C2#2145589011yescharacteristic
764C2#2145603311yescharacteristic
765C2#2145732511yescharacteristic
766C2#2145746111yescharacteristic
767C2#2145752211yescharacteristic
768C2#2145753711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2339C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenter#2339D61
hypocenterC61#25154
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
1. C2×#16839967C2semidirect
4. C2×C4×#11758200C2semidirect
5. #21449418C2semidirect
6. #21447200C2semidirect
7. #21447022C2semidirect
8. #21447015C2semidirect
9. #21446918C2semidirect
10. #21446679C2semidirect
11. #21446427C2semidirect
12. #21446163C2semidirect
13. #21446153C2semidirect
14. #21446066C2semidirect
447. C61#25154semidirect

Maximal subgroups

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

subgroupindex
C2×#168399672
C2×#168399242
C2×C4×#117582002
#214494182
#214472002
#214470222
#214470152
#214469182
#214466792
#214464272
#214461632
#214461532
#214460662
C61×#23392
#2515461