Finite Group Databasebeta

← #29700447

Subgroups — #29700447

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4#21448839C211yesmaximal, characteristic, complemented
5#21448647C211yesmaximal, characteristic, complemented
6#21446674C211yesmaximal, characteristic, complemented
7#21446510C211yesmaximal, characteristic, complemented
8#21446451C211yesmaximal, characteristic, complemented
9#21446164C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21446081C211yesmaximal, characteristic, complemented
12#21446011C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C61×#1895C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24#16839905C418yescomplemented
25#16839871—24no—
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28#16839764—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839667C2211yescharacteristic
39#16839667C2211yescharacteristic
40#16839665C2211yescharacteristic
41#16839661C2211yescharacteristic
42#16839655—21no—
43#16839642—21no—
44#16839638—21no—
45#16839638—21no—
46#16839637—21no—
47#16839624—21no—
48C4⋊C4×Dic61C2211yescharacteristic
49C4×C22⋊Dic61C2211yescharacteristic
50#95×D61—21no—
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yescomplemented
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×#11758200—41no—
77C2×#11758200—41no—
78C2×#11758200C2×C414yescomplemented
79C2×#11758199—22no—
80C2×#11758199—22no—
81C2×#11758199C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84D4×Dic61—22no—
85D4×Dic61—41no—
86D4×Dic61—44no—
87#14519739—22no—
88#14519739—22no—
89#14519739—41no—
90#14519739—41no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61D411yescharacteristic
101C2×C22⋊Dic61D411yescharacteristic
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107#14519708—22no—
108#14519708—41no—
109#14519702—22no—
110#14519702—22no—
111#14519700C2×C414yescomplemented
112#14519699—22no—
113#14519699D414yescomplemented
114#14519697C2×C414yescomplemented
115C22⋊#92418C2×C414yescomplemented
116#14519687—22no—
117C8×Dic61—41no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684D411yescharacteristic
125#14519684D411yescharacteristic
126C22×D4×C61—21no—
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C2×M16×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134#121×C61—22no—
135#121×C61C2×C414yescomplemented
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141#102×C61—22no—
142#102×C61—41no—
143#95×C61—21no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C23×D61—21no—
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61C22×C412yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61—81no—
178C22×Dic61—81no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183#11758222—28no—
184#11758222—44no—
185#11758222—44no—
186#11758222—44no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C412yes—
191C2×D244C2×D412yes—
192C2×D244#4112yes—
193C2×C4×D61—24no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122C22×C412yes—
208M16×C61—44no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61C2×D412yes—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61C22×C412yes—
221C22⋊C4×C61—24no—
222C22⋊C4×C61—81no—
223C22⋊Dic61—22no—
224C22⋊Dic61—41no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227C22⋊Dic61—81no—
228#11758200—44no—
229#11758199—28no—
230#11758198—42no—
231#11758198—42no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—42no—
236C4⋊Dic61—42no—
237C4⋊Dic61C2×D412yes—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—42no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C22×C412yes—
248C2×#92418C22×C412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C4×D412yes—
263C23×C61C22×D411yescharacteristic
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271D4×C61—22no—
272D4×C61—22no—
273D4×C61—48no—
274D4×C61—41no—
275D4×C61—41no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
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—41no—
291C2×C4×C61C4×D412yes—
292C2×C4×C61C23×C411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
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—22no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—84no—
320C2×Dic61—84no—
321C2×Dic61AGL(1,ℤ/8)12yes—
322D244—22no—
323D244—22no—
324D244—22no—
325D244C4×D414yescomplemented
326C4×D61—48no—
327C4×D61—84no—
328C4×D61—84no—
329Dic122—22no—
330Dic122—22no—
331Dic122—41no—
332Dic122—41no—
333C8×C61—22no—
334C8×C61—41no—
335#92418—22no—
336#92418—22no—
337#22866—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61C2×C4×D411yescharacteristic
353C22×C61D4211yescharacteristic
354C22×C61#54611yescharacteristic
355C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C61#57511yescharacteristic
357C22×C61#57711yescharacteristic
358C22×C61#57711yescharacteristic
359C2×D61—24no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—81no—
369C4×C61—81no—
370C4×C61C2×C4×D411yescharacteristic
371C4×C61#51811yescharacteristic
372C4×C61#54611yescharacteristic
373C4×C61#55111yescharacteristic
374Dic61—22no—
375Dic61—42no—
376Dic61—41no—
377Dic61—42no—
378Dic61—41no—
379Dic61—41no—
380Dic61—81no—
381C2×#449—611no—
382C2×#442—611no—
383C2×#417—611no—
384#2361—611no—
385#2339—611no—
386#1968—611no—
387#1935—611no—
388#1927—611no—
389#1895D6111yescharacteristic, complemented
390#1879—611no—
391#1877—611no—
392#1864—611no—
393#1853—611no—
394C4×#102—611no—
395#1753—611no—
396C2×C61—42no—
397C2×C61—82no—
398C2×C61#235811yescharacteristic
399C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
400C2×C61#295211yescharacteristic
401C2×C61#327211yescharacteristic
402C2×C61#327511yescharacteristic
403C2×C61#330611yescharacteristic
404C2×C61#330711yescharacteristic
405D61—44no—
406C22×#41—611no—
407C22×SD16—611no—
408C22×D8—611no—
409C22×M16C2×D6111yescharacteristic
410C2×#121C2×D6111yescharacteristic
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—1221no—
415C22×C4⋊C4—611no—
416#449—618no—
417#442—1224no—
418C2×#106—611no—
419C2×#106—611no—
420#417—1224no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#102C2×D6111yescharacteristic
428C2×#102C2×D6111yescharacteristic
429C2×C22⋊C8—611no—
430C2×#97—611no—
431C2×C4×C8—611no—
432#391—611no—
433#391—611no—
434#390—611no—
435#389—611no—
436#388—1221no—
437#386—1221no—
438#386—1221no—
439#386—1221no—
440#385—1221no—
441#381—1221no—
442#380C2×D6111yescharacteristic
443C4×C4⋊C4—611no—
444C4×C22⋊C4—611no—
445C2×#95—1221no—
446#340—611no—
447#340—611no—
448#340C2×D6111yescharacteristic
449#340C2×D6111yescharacteristic
450#336—611no—
451#336—611no—
452C61#2286611yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—2441no—
458C2×#41—2441no—
459C22×Q8—611no—
460C22×D4—21no—
461C22×D4—611no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4C22×D6111yescharacteristic
470C2×SD16—614no—
471C2×SD16—2441no—
472C2×SD16—2441no—
473C2×D8—614no—
474C2×D8—1222no—
475C2×D8—1222no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483#121—22no—
484#121C4×D6114yescomplemented
485C4×D4—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—2441no—
489C4×D4—2441no—
490C4×D4—2441no—
491C4×D4—2444no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—1222no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—2441no—
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
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—611no—
512C2×C42—1221no—
513#106—1222no—
514#106—2441no—
515#103—614no—
516#103—1222no—
517#103—1222no—
518#102—22no—
519#102—41no—
520#102—614no—
521#102—614no—
522#102—1222no—
523C22⋊C8—614no—
524#97—1222no—
525C4×C8—2441no—
526#95—21no—
527#95—611no—
528#95—611no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535C24—21no—
536C24—1221no—
537C24D4×D6111yescharacteristic
538#41—1228no—
539#41—2444no—
540#41—2444no—
541#41—2444no—
542C2×Q8—612no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—612no—
557C2×D4—612no—
558C2×D4—612no—
559C2×D4—1224no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—2442no—
564C2×D4—2442no—
565C2×D4C2×C4×D6112yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1224no—
580C22×C4—1221no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—4881no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4C2×C4×D6112yes—
596C22×C4D4×D6111yescharacteristic
597C22×C4#1175822412yes—
598C22×C4C23×D6111yescharacteristic
599SD16—2444no—
600D8—1228no—
601M16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8D4×D6112yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—612no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—2442no—
624C4⋊C4—2442no—
625C4⋊C4C2×C4×D6112yes—
626C22⋊C4—24no—
627C22⋊C4—81no—
628C22⋊C4—1222no—
629C22⋊C4—4881no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C22⋊C4—2441no—
634C22⋊C4—2442no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—2442no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23#1451973712yes—
661C23C2×D4×D6111yescharacteristic
662Q8—1222no—
663Q8—1222no—
664Q8—2441no—
665Q8—2441no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—41no—
670D4—41no—
671D4—614no—
672D4—1222no—
673D4—1222no—
674D4—1222no—
675D4—2448no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—612no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1222no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1222no—
704C2×C4—1221no—
705C2×C4—4884no—
706C2×C4—4884no—
707C2×C4—4884no—
708C2×C4—4884no—
709C2×C4—2448no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4#1451973712yes—
718C2×C4C22×C4×D6111yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4#41×D6111yescharacteristic
721C2×C4C2×#1175822411yescharacteristic
722C2×C4#1451982211yescharacteristic
723C2×C4#1451982311yescharacteristic
724C8—22no—
725C8—41no—
726C8—1222no—
727C8—1222no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—1224no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22—2442no—
749C22C2×#1451973711yescharacteristic
750C22#1684039611yescharacteristic
751C22#1684040111yescharacteristic
752C22AGL(1,ℤ/8)×D6111yescharacteristic
753C22#1684055811yescharacteristic
754C22#1684057111yescharacteristic
755C22#1684057211yescharacteristic
756C4—22no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—1222no—
761C4—4881no—
762C4—2441no—
763C4—2442no—
764C4—2441no—
765C4—2442no—
766C4—2441no—
767C4C4×D4×D6111yescharacteristic
768C4#1684023411yescharacteristic
769C4#1684039911yescharacteristic
770C4#1684043511yescharacteristic
771C2—42no—
772C2—82no—
773C2—2444no—
774C2#2144879911yescharacteristic
775C2#2145462311yescharacteristic
776C2#2145469811yescharacteristic
777C2#2145741611yescharacteristic
778C2#2145745711yescharacteristic
779C2#2145777511yescharacteristic
780C2#2145779011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1895C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
cosocleC22×C4×C61C24
hypercenter#1895D61
hypocenterC61#22866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×#16839764C2semidirect
4. #21448839C2semidirect
5. #21448647C2semidirect
6. #21446674C2semidirect
7. #21446510C2semidirect
8. #21446451C2semidirect
9. #21446164C2semidirect
10. #21446151C2semidirect
11. #21446081C2semidirect
12. #21446011C2semidirect
13. #21445633C2semidirect
14. #21445600C2semidirect
15. C61×#1895C2semidirect
24. #16839905C4semidirect
67. C2×#11758222C2×C4semidirect
78. C2×#11758200C2×C4semidirect
81. C2×#11758199C2×C4semidirect
111. #14519700C2×C4semidirect
113. #14519699D4semidirect
114. #14519697C2×C4semidirect
115. C22⋊#92418C2×C4semidirect
135. #121×C61C2×C4semidirect
325. D244C4×D4semidirect
389. #1895D61semidirect
452. C61#22866semidirect
484. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168398712
C2×#168397642
#214488392
#214486472
#214466742
#214465102
#214464512
#214461642
#214461512
#214460812
#214460112
#214456332
#214456002
C61×#18952
#2286661