Finite Group Databasebeta

← #29700266

Subgroups — #29700266

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2C2×#16839862C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic
4#21448822C211yesmaximal, characteristic, complemented
5#21446699C211yesmaximal, characteristic, complemented
6#21446519C211yesmaximal, characteristic, complemented
7#21446436C211yesmaximal, characteristic, complemented
8#21446240C211yesmaximal, characteristic, complemented
9#21446177C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic, complemented
21C22×C4⋊Dic61C2211yescharacteristic
22#16839913C418yescomplemented
23#16839862—24no—
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519700C2211yescharacteristic, complemented
27C2×#14519700C2211yescharacteristic, complemented
28C2×#14519698—24no—
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic, complemented
37C2×#14519688C2211yescharacteristic, complemented
38#16839668C2211yescharacteristic, complemented
39#16839660C2211yescharacteristic, complemented
40#16839659—21no—
41#16839649—21no—
42#16839634—21no—
43C4×C4⋊Dic61C2211yescharacteristic, complemented
44C22⋊C4×Dic61—21no—
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51C23×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C22×C22⋊C4×C61—21no—
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#386—21no—
58C61×#386—21no—
59C61×#380C2211yescharacteristic
60C61×#379—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C23×Dic61—21no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—41no—
67C2×#11758200—41no—
68C2×#11758200C2×C414yescomplemented
69C2×#11758200C2×C414yescomplemented
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519756—22no—
78#14519756C2×C414yescomplemented
79C4×Dic122—22no—
80C4×Dic122—41no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93#14519710—22no—
94#14519710—41no—
95#14519700—22no—
96#14519700—41no—
97#14519698—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698C2×C414yescomplemented
101#14519698C2×C414yescomplemented
102#14519698D414yes—
103C22⋊#92418C2×C414yescomplemented
104#14519688—22no—
105#14519688—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C25×C61—21no—
111C22×D4×C61—22no—
112C22×D4×C61—22no—
113C22×D4×C61—21no—
114C22×D4×C61—22no—
115C22×D4×C61—41no—
116C22×D4×C61—41no—
117C22×D4×C61C2×C414yes—
118C22×D4×C61C2311yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C4×D4×C61—41no—
126C4×D4×C61—41no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—44no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141#95×C61—21no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C2×D4×C61—28no—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—44no—
165C2×D4×C61—44no—
166C2×D4×C61—44no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61C22×C412yes—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C2×D412yes—
172C2×D4×C61#4112yes—
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—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—42no—
183C22×C4×C61—81no—
184C22×C4×C61—81no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61#4112yes—
192C22×C4×C61C2411yescharacteristic
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—81no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C22×C412yes—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—81no—
218C22⋊C4×C61—81no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C22⋊Dic61—24no—
224#11758200—28no—
225#11758200—44no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231C4⋊Dic61C22×C412yes—
232C4⋊Dic61C2×D412yes—
233#11758196—24no—
234#11758196—42no—
235#11758196—81no—
236C4×Dic61—42no—
237C4×Dic61—81no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—44no—
248C2×#92418C22×C412yes—
249C2×#92418C22×C412yes—
250C2×#92418C2×D412yes—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—48no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—48no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61C4×D412yes—
277C23×C61AGL(1,ℤ/8)12yes—
278C23×C61#13712yes—
279C23×C61C22×D411yescharacteristic
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—48no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61C4×D414yes—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
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—84no—
314C2×C4×C61—84no—
315C2×C4×C61C4×D412yes—
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—84no—
335Dic122—22no—
336Dic122—22no—
337Dic122—41no—
338Dic122—41no—
339#92418—22no—
340#92418—22no—
341#92418—22no—
342#92418—41no—
343#22854—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—24no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—816no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61#44014yescomplemented
366C22×C61C2×C4×D411yescharacteristic
367C22×C61D4211yescharacteristic
368C22×C61#54611yescharacteristic
369C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C61C2×#13711yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57711yescharacteristic
373C4×C61—22no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—81no—
379C4×C61—81no—
380C4×C61C2×C4×D411yescharacteristic
381C4×C61#51811yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#55111yescharacteristic
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—81no—
388C2×#450—611no—
389C2×#440—611no—
390C22×#102—611no—
391#2360—611no—
392D4×C22⋊C4D6111yescharacteristic
393#1973—611no—
394#1936—611no—
395#1925—611no—
396#1892—611no—
397#1880—611no—
398#1877—611no—
399#1862—611no—
400#1852—611no—
401#1762—611no—
402#1752—611no—
403C2×C61—24no—
404C2×C61—44no—
405C2×C61—82no—
406C2×C61#235811yescharacteristic
407C2×C61C2×#44011yescharacteristic
408C2×C61#294611yescharacteristic
409C2×C61#326411yescharacteristic
410C2×C61#326611yescharacteristic
411C2×C61#331011yescharacteristic
412C2×C61#331411yescharacteristic
413C23×D4C2×D6111yescharacteristic
414C22×SD16—611no—
415C22×SD16—611no—
416C23×C8—611no—
417C2×C22⋊Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×D4C2×D6111yescharacteristic
420C2×C4×D4C2×D6111yescharacteristic
421C22×C4⋊C4—611no—
422C22×C22⋊C4—21no—
423#450—618no—
424#440—1224no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—1224no—
436C2×C22⋊C8—611no—
437C2×#97—611no—
438C2×#97—611no—
439#391—611no—
440#390C2×D6111yescharacteristic
441#390C2×D6111yescharacteristic
442#389—611no—
443#389—1221no—
444#387—1221no—
445#386—21no—
446#386—21no—
447#385—1221no—
448#380C2×D6111yescharacteristic
449#379—21no—
450C4×C4⋊C4—611no—
451C4×C22⋊C4—1221no—
452C4×C22⋊C4C2×D6111yescharacteristic
453#340—611no—
454#340—611no—
455#340—611no—
456#340—611no—
457#336—611no—
458#336—611no—
459C61#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8—611no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C4×D6114yes—
469C22×D4C22×D6111yescharacteristic
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—1221no—
474C23×C4C22×D6111yescharacteristic
475C2×SD16—614no—
476C2×SD16—614no—
477C2×SD16—1222no—
478C2×SD16—1222no—
479C2×SD16—2441no—
480C2×SD16—2441no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—2441no—
488C22⋊Q8—614no—
489C22⋊Q8—1222no—
490C4×Q8—1222no—
491C4×Q8—2441no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—2441no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4C22⋊D6111yescharacteristic
517C2×C22⋊C4C22⋊D6111yescharacteristic
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42C22×D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522#107—1222no—
523#107—2441no—
524#103—1222no—
525#103—2441no—
526#102—614no—
527#102—614no—
528#102—614no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532C22⋊C8—614no—
533#97—1222no—
534#97—2441no—
535#95—21no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95C22⋊D6111yescharacteristic
541#95C22⋊D6111yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×C22⋊D6111yescharacteristic
552C2×Q8—612no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×D4—28no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—24no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D6112yes—
574C2×D4C2×C4×D6112yes—
575C2×D4D4×D6112yes—
576C2×D4#1175822412yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—4881no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4C2×C4×D6112yes—
597C22×C4#1175822212yes—
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C23×D6111yescharacteristic
604SD16—1228no—
605SD16—2444no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—2444no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—4881no—
631C4⋊C4—2442no—
632C4⋊C4—2442no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—1224no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—4881no—
648C42—2442no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×C22⋊D6112yes—
675C23#1451980312yes—
676C23#1451980712yes—
677C23C22×C22⋊D6111yescharacteristic
678Q8—1222no—
679Q8—1222no—
680Q8—2441no—
681Q8—2441no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4#1451973714yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—4884no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4C4×C22⋊D6112yes—
731C2×C4C22×C4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982211yescharacteristic
737C8—1222no—
738C8—1222no—
739C8—1222no—
740C8—2441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1683986214yescomplemented
763C22C2×C4×C22⋊D6111yescharacteristic
764C22D4×C22⋊D6111yescharacteristic
765C22#1684040611yescharacteristic
766C22C2×#1451980311yescharacteristic
767C22C2×#1451980711yescharacteristic
768C22#1684056511yescharacteristic
769C22#1684057311yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—4881no—
778C4—2442no—
779C4—2442no—
780C4—2442no—
781C4C2×#1451973711yescharacteristic
782C4#1684023511yescharacteristic
783C4#1684040211yescharacteristic
784C4#1684043811yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2144879811yescharacteristic
789C2C2×#1683986211yescharacteristic
790C2#2145465111yescharacteristic
791C2#2145729511yescharacteristic
792C2#2145732511yescharacteristic
793C2#2145784011yescharacteristic
794C2#2145790011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenterD4×C22⋊C4D61
hypocenterC61#22854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839862C2semidirect
4. #21448822C2semidirect
5. #21446699C2semidirect
6. #21446519C2semidirect
7. #21446436C2semidirect
8. #21446240C2semidirect
9. #21446177C2semidirect
10. #21446153C2semidirect
11. #21446066C2semidirect
12. #21446006C2semidirect
13. #21445644C2semidirect
14. #21445597C2semidirect
20. C2×C4×Dic122C22semidirect
22. #16839913C4semidirect
24. C2×#14519710C22semidirect
25. C2×#14519710C22semidirect
26. C2×#14519700C22semidirect
27. C2×#14519700C22semidirect
36. C2×#14519688C22semidirect
37. C2×#14519688C22semidirect
38. #16839668C22semidirect
39. #16839660C22semidirect
43. C4×C4⋊Dic61C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
68. C2×#11758200C2×C4semidirect
69. C2×#11758200C2×C4semidirect
78. #14519756C2×C4semidirect
100. #14519698C2×C4semidirect
101. #14519698C2×C4semidirect
103. C22⋊#92418C2×C4semidirect
365. C22×C61#440semidirect
459. C61#22854semidirect
762. C22#16839862semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
C2×#168398622
C22×#145196982
#214488222
#214466992
#214465192
#214464362
#214462402
#214461772
#214461532
#214460662
#214460062
#214456442
#214455972
D4×C22⋊C4×C612
#2285461