Finite Group Databasebeta

← #29700404

Subgroups — #29700404

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839904C211yesmaximal, characteristic
2C2×#16839859C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4#21448840C211yesmaximal, characteristic, complemented
5#21448658C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446436C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446070C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13C4×#14519702C211yesmaximal, characteristic, complemented
14#21445602C211yesmaximal, characteristic, complemented
15C61×#1970C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519742C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519737—21no—
24C2×C4⋊C4×D61C2211yescharacteristic
25#16839904C418yescomplemented
26#16839859—24no—
27C2×#14519710C2211yescharacteristic
28#16839760—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839662—21no—
39#16839662—21no—
40#16839658C2211yescharacteristic
41#16839650—21no—
42#16839638—21no—
43#16839634—21no—
44#16839620—21no—
45#16839619C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47C22⋊C4×Dic61—21no—
48C4×#11758198C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C4×C8×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C2×#11758224—22no—
63C2×#11758224—22no—
64C2×#11758224—22no—
65C2×#11758224—41no—
66C2×#11758224—41no—
67C2×#11758224C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758200—22no—
76C2×#11758200—22no—
77C2×#11758200C2×C414yescomplemented
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519748—22no—
84#14519748C2×C414yes—
85C4×Dic122—22no—
86C4×Dic122—41no—
87#14519742—22no—
88#14519742—41no—
89D4×Dic61—22no—
90D4×Dic61—41no—
91#14519737—44no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—41no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198D411yescharacteristic
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2311yescharacteristic
112#14519710—22no—
113#14519702C2×C414yescomplemented
114#14519702D414yescomplemented
115#14519700—22no—
116#14519698—22no—
117#14519698—41no—
118#14519698C2×C414yescomplemented
119#14519689C2×C414yescomplemented
120#14519687—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684D411yescharacteristic
125#14519684D411yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C2×D8×C61—41no—
129C2×D8×C61—41no—
130C2×D8×C61C2×C414yescomplemented
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—41no—
141#102×C61—22no—
142#102×C61—22no—
143C4×C8×C61—41no—
144C24×C61—21no—
145C24×C61—21no—
146C23×D61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61C22×C412yes—
158C2×D4×C61C22×C412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—24no—
174C22×Dic61—21no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—81no—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758224—28no—
184#11758224—44no—
185#11758224—44no—
186#11758224—44no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61C22×C412yes—
195C2×C4×D61#4112yes—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122C22×C412yes—
200C2×Dic122C2×D412yes—
201C2×Dic122#4112yes—
202D8×C61—44no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61C22×C412yes—
208C2×C8×C61C2×D412yes—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C42×C61—21no—
218C42×C61—21no—
219C22⋊Dic61—24no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—81no—
223#11758200—28no—
224#11758198—22no—
225#11758198—41no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61C22×C412yes—
232C4⋊Dic61C2×D412yes—
233#11758196—42no—
234#11758196—42no—
235#11758196—42no—
236#11758196—42no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—42no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C22×C412yes—
248#11758189—44no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61C22×D411yescharacteristic
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61C4×D412yes—
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—41no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
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×C61AGL(1,ℤ/8)12yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C22⋊D61—48no—
298C22⋊D61—48no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—22no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—48no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—84no—
321C2×Dic61C4×D412yes—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—84no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
330Dic122C4×D414yescomplemented
331C8×C61—22no—
332C8×C61—22no—
333#92418—22no—
334#92418—41no—
335#22863—611nomaximal, Sylow
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61C2×C4×D411yescharacteristic
351C22×C61D4211yescharacteristic
352C22×C61#54611yescharacteristic
353C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C61#57511yescharacteristic
355C22×C61#57611yescharacteristic
356C22×C61#57811yescharacteristic
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×C4×D411yescharacteristic
369C4×C61#51811yescharacteristic
370C4×C61#54611yescharacteristic
371C4×C61#55111yescharacteristic
372Dic61—24no—
373Dic61—22no—
374Dic61—42no—
375Dic61—42no—
376Dic61—41no—
377Dic61—41no—
378Dic61—81no—
379C2×#449—611no—
380C2×#440—611no—
381C2×#417—611no—
382#2361—611no—
383#2341—611no—
384#1970D6111yescharacteristic, complemented
385#1936—611no—
386#1925—611no—
387#1895—611no—
388#1880—611no—
389#1879—611no—
390#1863—611no—
391#1852—611no—
392C4×#103—611no—
393#1753—611no—
394C2×C61—82no—
395C2×C61—82no—
396C2×C61#235811yescharacteristic
397C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C61#295111yescharacteristic
399C2×C61#327411yescharacteristic
400C2×C61#327711yescharacteristic
401C2×C61#330811yescharacteristic
402C2×C61#330911yescharacteristic
403D61—42no—
404C22×#41—611no—
405C22×SD16—611no—
406C22×D8C2×D6111yescharacteristic
407C22×M16—611no—
408C2×#121—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C22×C4⋊C4—611no—
414#449—618no—
415#440—1224no—
416C2×#107—611no—
417C2×#107C2×D6111yescharacteristic
418#417—1224no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102C2×D6111yescharacteristic
426C2×#102C2×D6111yescharacteristic
427C2×C22⋊C8—611no—
428C2×#97—611no—
429C2×C4×C8C2×D6111yescharacteristic
430#390—611no—
431#390—1221no—
432#390—1221no—
433#390C2×D6111yescharacteristic
434#390C2×D6111yescharacteristic
435#389—611no—
436#388—1221no—
437#386—1221no—
438#385—1221no—
439#380—611no—
440#380—1221no—
441C4×C4⋊C4—611no—
442C4×C22⋊C4—611no—
443C4×C22⋊C4—1221no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#336—611no—
449#336—611no—
450C61#2286311yescharacteristic, complemented, Sylow
451C2×#41—614no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—2441no—
456C2×#41—2441no—
457C22×Q8—611no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4C22×D6111yescharacteristic
461C22×D4C22×D6111yescharacteristic
462C23×C4—611no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C2×SD16—614no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×D8—41no—
470C2×D8—41no—
471C2×D8C4×D6114yescomplemented
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479#121—614no—
480#121—1222no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×Q8—2441no—
484C4×Q8—2441no—
485C4×D4—1222no—
486C4×D4—2441no—
487C4×D4—2444no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—2441no—
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C42—611no—
511C2×C42—1221no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42C22×D6111yescharacteristic
515#107—41no—
516#107—1222no—
517#103—614no—
518#103—614no—
519#103—1222no—
520#102—22no—
521#102—22no—
522#102—614no—
523#102—1222no—
524#102—2441no—
525C22⋊C8—614no—
526#97—1222no—
527C4×C8—41no—
528#95—611no—
529#95—611no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533C24—21no—
534C24—21no—
535C24—611no—
536#41—1228no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540C2×Q8—612no—
541C2×Q8—612no—
542C2×Q8—612no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4C2×C4×D6112yes—
563C2×D4C2×C4×D6112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—611no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—1224no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4D4×D6111yescharacteristic
589C22×C4D4×D6111yescharacteristic
590C22×C4C23×D6111yescharacteristic
591SD16—1228no—
592D8—44no—
593M16—2444no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—612no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8C2×C4×D6112yes—
605C2×C8D4×D6112yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—1224no—
625C22⋊C4—1222no—
626C22⋊C4—4881no—
627C22⋊C4—4881no—
628C22⋊C4—2441no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C42—21no—
632C42—21no—
633C42—1221no—
634C42—1221no—
635C42—2442no—
636C42—2442no—
637C42—2442no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—612no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23C2×D4×D6111yescharacteristic
660Q8—614no—
661Q8—1222no—
662Q8—1222no—
663Q8—1222no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—2448no—
673D4—2448no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—612no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1221no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1222no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—2448no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4#1451980112yes—
714C2×C4C22×C4×D6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4#41×D6111yescharacteristic
718C2×C4#1451982211yescharacteristic
719C2×C4#1451982211yescharacteristic
720C8—22no—
721C8—22no—
722C8—1222no—
723C8—2441no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—1222no—
739C22—1222no—
740C22—1222no—
741C22—2441no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22C4×D4×D6111yescharacteristic
746C22#1684039711yescharacteristic
747C22#1684040111yescharacteristic
748C22C2×#1451980111yescharacteristic
749C22#1684055911yescharacteristic
750C22#1684056311yescharacteristic
751C22#1684057611yescharacteristic
752C4—22no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—1222no—
757C4—1224no—
758C4—4881no—
759C4—2442no—
760C4—2441no—
761C4—2442no—
762C4—2441no—
763C4C4×D4×D6111yescharacteristic
764C4#1684023511yescharacteristic
765C4#1684040111yescharacteristic
766C4#1684044211yescharacteristic
767C2—82no—
768C2—82no—
769C2—2442no—
770C2#2144880011yescharacteristic
771C2C4×#1451980111yescharacteristic
772C2#2145468911yescharacteristic
773C2#2145743811yescharacteristic
774C2#2145747411yescharacteristic
775C2#2145781611yescharacteristic
776C2#2145783111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1970C2
socleC23×C61C22×D4
prime radicalC2×#16839904C2
cosocleC22×C4×C61C24
hypercenter#1970D61
hypocenterC61#22863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#16839859C2semidirect
3. C2×#16839760C2semidirect
4. #21448840C2semidirect
5. #21448658C2semidirect
6. #21446513C2semidirect
7. #21446436C2semidirect
8. #21446254C2semidirect
9. #21446177C2semidirect
10. #21446169C2semidirect
11. #21446070C2semidirect
12. #21446005C2semidirect
13. C4×#14519702C2semidirect
14. #21445602C2semidirect
15. C61×#1970C2semidirect
25. #16839904C4semidirect
67. C2×#11758224C2×C4semidirect
77. C2×#11758200C2×C4semidirect
113. #14519702C2×C4semidirect
114. #14519702D4semidirect
118. #14519698C2×C4semidirect
119. #14519689C2×C4semidirect
130. C2×D8×C61C2×C4semidirect
330. Dic122C4×D4semidirect
384. #1970D61semidirect
450. C61#22863semidirect
471. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399042
C2×#168398592
C2×#168397602
#214488402
#214486582
#214465132
#214464362
#214462542
#214461772
#214461692
#214460702
#214460052
C4×#145197022
#214456022
C61×#19702
#2286361