Finite Group Databasebeta

← #29737066

Subgroups — #29737066

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D61C211yesmaximal, characteristic
2#21449517C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic
4#21447344C211yesmaximal, characteristic, complemented
5#21447206C211yesmaximal, characteristic, complemented
6#21447202C211yesmaximal, characteristic, complemented
7#21446952C211yesmaximal, characteristic, complemented
8#21446068C211yesmaximal, characteristic, complemented
9#21446066C211yesmaximal, characteristic, complemented
10#21446005C211yesmaximal, characteristic, complemented
11#21445995C211yesmaximal, characteristic, complemented
12#21445845C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic
15C2×C61×#474C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519753—21no—
19C2×D4×Dic61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C22×#11758198—21no—
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519706C2211yescharacteristic, complemented
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31#102×D61—24no—
32C2×#14519689C2211yescharacteristic
33#16839695—21no—
34#16839681—21no—
35#16839664C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839661C2211yescharacteristic, complemented
38#16839660C2211yescharacteristic, complemented
39#16839641—21no—
40#16839639—21no—
41#16839633—21no—
42#16839631C2211yescharacteristic, complemented
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4×#11758198C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×C4⋊Q8×C61C2211yescharacteristic, complemented
54C2×C4×D4×C61C2211yescharacteristic
55C61×#474—24no—
56C2×#107×C61C2211yescharacteristic, complemented
57C2×#107×C61C2211yescharacteristic, complemented
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61Q814yescomplemented
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—41no—
78#14519753—44no—
79D4×Dic61—22no—
80D4×Dic61—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—41no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—44no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519711—41no—
103#14519710—41no—
104#14519706—41no—
105#14519699—22no—
106#14519699—41no—
107#14519698—22no—
108#14519698—22no—
109#14519697—22no—
110#14519697—41no—
111#14519689—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C22×Q8×C61—21no—
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C4⋊Q8×C61—22no—
124C4⋊Q8×C61—41no—
125C4×D4×C61—22no—
126C4×D4×C61—41no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#107×C61—22no—
134#107×C61—22no—
135C4⋊C8×C61—22no—
136#102×C61—22no—
137#102×C61D414yes—
138C24×C61—21no—
139C23×D61—21no—
140C23×D61—24no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61C2×D411yescharacteristic
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×Q8×C61—81no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61C2×D412yes—
155C2×D4×C61C2×Q812yes—
156C2×D4×C61#4112yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—42no—
173C22×Dic61—42no—
174C22×Dic61—81no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178D4×D61—28no—
179D4×D61—44no—
180D4×D61—44no—
181D4×D61—44no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244C2×Q812yes—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—81no—
195C2×C4×D61C2×Q812yes—
196C2×C4×D61#4112yes—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C2×D412yes—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61C2×D412yes—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C22⋊Dic61—42no—
214#11758198—22no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—81no—
220#11758198—81no—
221#11758198D814yes—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229#11758196—42no—
230#11758196—42no—
231#11758196—42no—
232#11758196—81no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C8×D61—44no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—22no—
255C22×D61—48no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—48no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61C22⋊Q812yes—
269C22×D61C2×D812yes—
270C22×D61#13712yes—
271Q8×C61—84no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61C22⋊Q814yescomplemented
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
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—84no—
291C2×C4×C61C2×D812yes—
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×Q811yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C22⋊D61—48no—
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×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316C2×Dic61C22⋊Q812yes—
317C2×Dic61C2×D812yes—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—84no—
327C8×C61—22no—
328C8×C61—41no—
329#92418—41no—
330#92418—41no—
331#25950—611nomaximal, Sylow
332C22×C61—24no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61C2×C22⋊Q811yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61C22×D811yescharacteristic
343C22×C61C2×#13711yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—816no—
356C2×D61—81no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61#47414yescomplemented
361C4×C61—22no—
362C4×C61—41no—
363C4×C61—42no—
364C4×C61—81no—
365C4×C61—81no—
366C4×C61C2×C22⋊Q811yescharacteristic
367C4×C61#54311yescharacteristic
368C4×C61#54611yescharacteristic
369C4×C61#55111yescharacteristic
370Dic61—22no—
371Dic61—22no—
372Dic61—41no—
373Dic61—81no—
374Dic61—81no—
375Dic61—81no—
376C2×#474D6111yescharacteristic, complemented
377C22×#102—611no—
378#2440—611no—
379D4×C22⋊C4—611no—
380#2093—611no—
381#2067—611no—
382#2067—611no—
383#2023—611no—
384#1862—611no—
385#1862—611no—
386#1852—611no—
387#1850—611no—
388#1808—611no—
389#1802—611no—
390#1786—611no—
391C2×C61—44no—
392C2×C61#243711yescharacteristic
393C2×C61C2×#47411yescharacteristic
394C2×C61#308111yescharacteristic
395C2×C61#326611yescharacteristic
396C2×C61D4×D811yescharacteristic
397C2×C61#329411yescharacteristic
398C2×C61#331411yescharacteristic
399D61—24no—
400D61—82no—
401C23×D4—611no—
402C23×C8—611no—
403C2×C4⋊Q8C2×D6111yescharacteristic, complemented
404C2×C22⋊Q8—1221no—
405C2×C4×D4—611no—
406C2×C4×D4C2×D6111yescharacteristic
407C22×C4⋊C4—611no—
408C22×C22⋊C4—1221no—
409#474—24no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#107C2×D6111yescharacteristic, complemented
413C2×#107C2×D6111yescharacteristic, complemented
414C2×C4⋊C8—611no—
415C2×C4⋊C8C2×D6111yescharacteristic, complemented
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—1224no—
423C2×#102C2×D6111yescharacteristic
424C2×#102C2×D6111yescharacteristic
425C2×C22⋊C8—611no—
426#398—1221no—
427#395—1221no—
428#390—611no—
429#390—611no—
430#389—611no—
431#389—611no—
432#386—1221no—
433#386—1221no—
434#385—1221no—
435#384—611no—
436#380—611no—
437#380—611no—
438#379—1221no—
439C4×C22⋊C4—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2595011yescharacteristic, complemented, Sylow
447C25—1221no—
448C22×Q8—21no—
449C22×D4—614no—
450C22×D4—611no—
451C22×D4—1222no—
452C22×D4—1221no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—2441no—
456C22×D4—2441no—
457C22×D4C22×D6111yescharacteristic
458C23×C4—21no—
459C23×C4—611no—
460C23×C4—1221no—
461C23×C4—1221no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—1222no—
465C22×C8—1222no—
466C22×C8—2441no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—2444no—
472C4×D4—22no—
473C4×D4—41no—
474C4×D4—1222no—
475C4×D4—2441no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—2441no—
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—2444no—
501C2×C42—611no—
502C2×C42C22×D6111yescharacteristic
503#107—22no—
504#107—22no—
505#107—2441no—
506#107—2441no—
507C4⋊C8—22no—
508C4⋊C8—2441no—
509#102—22no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—1222no—
514#102—2441no—
515#102—2441no—
516#102C22⋊D6114yes—
517C22⋊C8—1222no—
518#95—611no—
519#95—611no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524C24—21no—
525C24—611no—
526C24—1224no—
527C24—1221no—
528C24—4881no—
529C24—4881no—
530C24—2442no—
531C24—2442no—
532C24—2442no—
533C24—2442no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—612no—
541C2×D4—1224no—
542C2×D4—1228no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—2444no—
549C2×D4—2444no—
550C2×D4—2444no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4Q8×D6112yes—
554C2×D4#1175822612yes—
555C2×D4C2×C22⋊D6112yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—4881no—
575C22×C4—4881no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4D4×D6111yescharacteristic
581C22×C4D4×D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—2444no—
595C2×C8C2×C22⋊D6112yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—2442no—
610C4⋊C4—2442no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4C2×C22⋊D6112yes—
614C22⋊C4—42no—
615C22⋊C4—614no—
616C22⋊C4—1222no—
617C22⋊C4—4881no—
618C22⋊C4—4881no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C42—21no—
625C42—21no—
626C42—1221no—
627C42—1221no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—612no—
636C23—612no—
637C23—612no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1222no—
643C23—4884no—
644C23—4884no—
645C23—4884no—
646C23—4884no—
647C23—4884no—
648C23—2448no—
649C23—2448no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23C2×D4×D6111yescharacteristic
657Q8—84no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—1222no—
662D4—1222no—
663D4—2448no—
664D4—2441no—
665D4—2441no—
666D4#1451975314yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—612no—
683C2×C4—612no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—4884no—
696C2×C4—4884no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4D8×D6112yes—
707C2×C4C22×C22⋊D6111yescharacteristic
708C2×C4C2×Q8×D6111yescharacteristic
709C2×C4#41×D6111yescharacteristic
710C2×C4C2×#1175822611yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982311yescharacteristic
713C8—22no—
714C8—41no—
715C8—2441no—
716C8—2441no—
717C22—24no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—614no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—48816no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—4881no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22C22⋊Q8×D6111yescharacteristic
740C22D4×C22⋊D6111yescharacteristic
741C22#1684040311yescharacteristic
742C22C2×D8×D6111yescharacteristic
743C22#137×D6111yescharacteristic
744C22#1684056311yescharacteristic
745C22#1684057111yescharacteristic
746C4—22no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4—81no—
751C4—1222no—
752C4—1222no—
753C4—4881no—
754C4—4881no—
755C4—4881no—
756C4—2441no—
757C4C2×#1451975311yescharacteristic
758C4#1684038711yescharacteristic
759C4#1684040011yescharacteristic
760C4#1684043911yescharacteristic
761C2—44no—
762C2—1224no—
763C2—4882no—
764C2#2144948211yescharacteristic
765C2#474×D6111yescharacteristic
766C2#2145564311yescharacteristic
767C2#2145732311yescharacteristic
768C2D8×C22⋊D6111yescharacteristic
769C2#2145762911yescharacteristic
770C2#2145789711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#474C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#474D61
hypocenterC61#25950
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. #21449517C2semidirect
4. #21447344C2semidirect
5. #21447206C2semidirect
6. #21447202C2semidirect
7. #21446952C2semidirect
8. #21446068C2semidirect
9. #21446066C2semidirect
10. #21446005C2semidirect
11. #21445995C2semidirect
12. #21445845C2semidirect
13. #21445817C2semidirect
15. C2×C61×#474C2semidirect
22. C2×#14519711C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519706C22semidirect
37. #16839661C22semidirect
38. #16839660C22semidirect
42. #16839631C22semidirect
47. #16839525C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
53. C2×C4⋊Q8×C61C22semidirect
56. C2×#107×C61C22semidirect
57. C2×#107×C61C22semidirect
58. C2×C4⋊C8×C61C22semidirect
69. C2×D4×D61Q8semidirect
275. D4×C61C22⋊Q8semidirect
360. C2×D61#474semidirect
376. C2×#474D61semidirect
403. C2×C4⋊Q8C2×D61semidirect
412. C2×#107C2×D61semidirect
413. C2×#107C2×D61semidirect
415. C2×C4⋊C8C2×D61semidirect
446. C61#25950semidirect
666. D4#14519753semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D612
#214495172
D4×#117581982
#214473442
#214472062
#214472022
#214469522
#214460682
#214460662
#214460052
#214459952
#214458452
#214458172
#214457482
C2×C61×#4742
#2595061