Finite Group Databasebeta

← #29700506

Subgroups — #29700506

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839896C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic, complemented
5#21446684C211yesmaximal, characteristic, complemented
6#21446505C211yesmaximal, characteristic, complemented
7#21446436C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446066C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14C22⋊C4×#92418C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic, complemented
21C2×#14519737—21no—
22C22×C4⋊Dic61C2211yescharacteristic
23#16839896C418yescomplemented
24C4×#11758199—24no—
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519710C2211yescharacteristic, complemented
27C2×#14519698—24no—
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic, complemented
35C2×#14519697C2211yescharacteristic, complemented
36C2×C22⋊#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic, complemented
38C2×C4×#92418C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic, complemented
40#16839660C2211yescharacteristic, complemented
41#16839654—21no—
42#16839639—21no—
43#16839636—21no—
44C4×C4⋊Dic61C2211yescharacteristic, complemented
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×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199—41no—
69C2×#11758199—41no—
70C2×#11758199C2×C414yescomplemented
71C2×#11758199C2×C414yescomplemented
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751C2×C414yescomplemented
81C4×D244—22no—
82C4×D244—41no—
83#14519737—44no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96#14519710—22no—
97#14519710—41no—
98#14519698—22no—
99#14519698—22no—
100#14519698—22no—
101#14519698C2×C414yescomplemented
102#14519698C2×C414yescomplemented
103#14519698D414yescomplemented
104#14519697—22no—
105#14519697—41no—
106C22⋊#92418C2×C414yescomplemented
107C4×#92418—22no—
108C4×#92418—41no—
109#14519684—21no—
110#14519684—21no—
111C25×C61—21no—
112C22×D4×C61—22no—
113C22×D4×C61—22no—
114C22×D4×C61—21no—
115C22×D4×C61—22no—
116C22×D4×C61—41no—
117C22×D4×C61—41no—
118C22×D4×C61C2×C414yescomplemented
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C23×C4×C61—21no—
123C23×C4×C61C2311yescharacteristic
124C4×D4×C61—22no—
125C4×D4×C61—22no—
126C4×D4×C61—41no—
127C4×D4×C61—41no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
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—21no—
137C2×C22⋊C4×C61—44no—
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C2×C42×C61C2311yescharacteristic
142#95×C61—21no—
143#95×C61D411yescharacteristic
144#95×C61D411yescharacteristic
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—24no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—42no—
152C24×C61—81no—
153C24×C61—81no—
154C24×C61C2×D411yescharacteristic
155C23×D61—21no—
156C2×D4×C61—28no—
157C2×D4×C61—24no—
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—21no—
165C2×D4×C61—21no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—44no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61C22×C412yes—
172C2×D4×C61C22×C412yes—
173C2×D4×C61C2×D412yes—
174C2×D4×C61#4112yes—
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—81no—
186C22×C4×C61—81no—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61#4112yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—42no—
202C22×Dic61—42no—
203C22×Dic61—81no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C22×C412yes—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—81no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—81no—
224C22⋊C4×C61—81no—
225C22⋊C4×C61D814yescomplemented
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230#11758199—28no—
231#11758199—44no—
232#11758198—24no—
233#11758198—42no—
234#11758198—42no—
235#11758198—81no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—42no—
241C4⋊Dic61C22×C412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—42no—
244C4×Dic61—42no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—44no—
255C2×#92418C22×C412yes—
256C2×#92418C22×C412yes—
257C2×#92418C2×D412yes—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—48no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—48no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61—84no—
281C23×C61—84no—
282C23×C61—84no—
283C23×C61C4×D412yes—
284C23×C61C2×D812yes—
285C23×C61#13512yes—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—48no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61C4×D414yescomplemented
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—84no—
326C2×C4×C61—84no—
327C2×C4×C61C4×D412yes—
328C2×C4×C61C2×D812yes—
329C2×C4×C61C2×D812yes—
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C22⋊D61—48no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—84no—
347D244—22no—
348D244—22no—
349D244—41no—
350D244—41no—
351C4×D61—84no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#22870—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—24no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—816no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61C4×D814yescomplemented
379C22×C61C2×C4×D411yescharacteristic
380C22×C61D4211yescharacteristic
381C22×C61#54611yescharacteristic
382C22×C61C22×D811yescharacteristic
383C22×C61C2×#13511yescharacteristic
384C22×C61#57611yescharacteristic
385C22×C61#57711yescharacteristic
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C2×D61—81no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—22no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61—81no—
399C4×C61—81no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#51811yescharacteristic
402C4×C61#54611yescharacteristic
403C4×C61#55111yescharacteristic
404Dic61—42no—
405Dic61—42no—
406Dic61—81no—
407C2×#447—611no—
408C2×C4×D8—611no—
409C22×#102—611no—
410#2361—611no—
411D4×C22⋊C4D6111yescharacteristic, complemented
412#1970—611no—
413#1934—611no—
414#1925—611no—
415#1893—611no—
416#1879—611no—
417#1879—611no—
418#1862—611no—
419#1852—611no—
420C4×#102—611no—
421C8×C22⋊C4—611no—
422C2×C61—24no—
423C2×C61—44no—
424C2×C61—82no—
425C2×C61#235811yescharacteristic
426C2×C61C2×C4×D811yescharacteristic
427C2×C61#294611yescharacteristic
428C2×C61D4×D811yescharacteristic
429C2×C61#328211yescharacteristic
430C2×C61#329411yescharacteristic
431C2×C61#329711yescharacteristic
432D61—82no—
433C23×D4C2×D6111yescharacteristic
434C22×D8—611no—
435C22×D8—611no—
436C23×C8—611no—
437C2×#121—611no—
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×C4×D4C2×D6111yescharacteristic
441C2×C4×D4C2×D6111yescharacteristic
442C22×C4⋊C4—611no—
443C22×C22⋊C4—21no—
444#447—618no—
445C4×D8—1224no—
446C2×#107—611no—
447C2×#107—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—1224no—
457C2×C22⋊C8—611no—
458C2×C4×C8—611no—
459C2×C4×C8—611no—
460#390—611no—
461#390C2×D6111yescharacteristic
462#390C2×D6111yescharacteristic
463#389—611no—
464#388—1221no—
465#386—21no—
466#386—21no—
467#386—1221no—
468#385—1221no—
469#380C2×D6111yescharacteristic
470#379—21no—
471C4×C4⋊C4—611no—
472C4×C22⋊C4C2×D6111yescharacteristic
473#340—611no—
474#340—611no—
475#340—611no—
476#340—611no—
477#336—611no—
478#336—611no—
479C61#2287011yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—611no—
488C22×D4—1221no—
489C22×D4C4×D6114yescomplemented
490C22×D4C22×D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1222no—
500C2×D8—1222no—
501C2×D8—2441no—
502C2×D8—2441no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8—1222no—
508C22×C8—1222no—
509C22×C8—2441no—
510#121—614no—
511#121—1222no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—1222no—
517C4×D4—2441no—
518C4×D4—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—2441no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C22⋊C4C22⋊D6111yescharacteristic
542C2×C42—1221no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545#107—1222no—
546#107—2441no—
547#102—614no—
548#102—614no—
549#102—614no—
550#102—1222no—
551#102—1222no—
552#102—1222no—
553#102—1222no—
554#102—2441no—
555C22⋊C8—614no—
556C4×C8—1222no—
557C4×C8—2441no—
558#95—21no—
559#95—1221no—
560#95—1221no—
561#95C22⋊D6111yescharacteristic
562#95C22⋊D6111yescharacteristic
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—1221no—
573C24C2×C22⋊D6111yescharacteristic
574C2×D4—28no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—24no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—612no—
590C2×D4—1224no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4C2×C4×D6112yes—
599C2×D4C2×C4×D6112yes—
600C2×D4D4×D6112yes—
601C2×D4#1175822412yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4C2×C4×D6112yes—
624C22×C4#1175822212yes—
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631D8—1228no—
632D8—2444no—
633C2×C8—612no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—2444no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—1224no—
667C22⋊C4—4881no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4#1175819914yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—2442no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—1222no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23C4×C22⋊D6112yes—
709C23C2×#1175819912yes—
710C23#1451979712yes—
711C23C22×C22⋊D6111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1222no—
721D4—1222no—
722D4—2448no—
723D4—2441no—
724D4—2441no—
725D4#1451973714yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—4884no—
753C2×C4—4884no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4C4×C22⋊D6112yes—
762C2×C4C2×#1175819912yes—
763C2×C4C2×#1175819912yes—
764C2×C4C22×C4×D6111yescharacteristic
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4C2×#1175822411yescharacteristic
767C2×C4C2×#1175822211yescharacteristic
768C2×C4#1451982211yescharacteristic
769C2×C4#1451982211yescharacteristic
770C8—1222no—
771C8—1222no—
772C8—1222no—
773C8—2441no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—4881no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22C4×#1175819914yescomplemented
803C22C2×C4×C22⋊D6111yescharacteristic
804C22D4×C22⋊D6111yescharacteristic
805C22#1684040611yescharacteristic
806C22C22×#1175819911yescharacteristic
807C22C2×#1451979711yescharacteristic
808C22#1684056511yescharacteristic
809C22#1684057311yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—4881no—
818C4—2442no—
819C4—2442no—
820C4C2×#1451973711yescharacteristic
821C4#1684023511yescharacteristic
822C4#1684040211yescharacteristic
823C4#1684043811yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—4882no—
828C2#2144879811yescharacteristic
829C2C2×C4×#1175819911yescharacteristic
830C2#2145465111yescharacteristic
831C2D4×#1175819911yescharacteristic
832C2#2145752211yescharacteristic
833C2#2145763211yescharacteristic
834C2#2145766911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenterD4×C22⋊C4D61
hypocenterC61#22870
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×C4×#11758199C2semidirect
3. C22×#14519698C2semidirect
4. #21448833C2semidirect
5. #21446684C2semidirect
6. #21446505C2semidirect
7. #21446436C2semidirect
8. #21446245C2semidirect
9. #21446170C2semidirect
10. #21446167C2semidirect
11. #21446066C2semidirect
12. #21446006C2semidirect
13. C4×#14519698C2semidirect
14. C22⋊C4×#92418C2semidirect
15. D4×C22⋊C4×C61C2semidirect
20. C2×C4×D244C22semidirect
23. #16839896C4semidirect
25. C2×#14519710C22semidirect
26. C2×#14519710C22semidirect
34. C2×#14519697C22semidirect
35. C2×#14519697C22semidirect
37. C2×C4×#92418C22semidirect
38. C2×C4×#92418C22semidirect
39. #16839664C22semidirect
40. #16839660C22semidirect
44. C4×C4⋊Dic61C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
70. C2×#11758199C2×C4semidirect
71. C2×#11758199C2×C4semidirect
80. #14519751C2×C4semidirect
101. #14519698C2×C4semidirect
102. #14519698C2×C4semidirect
103. #14519698D4semidirect
106. C22⋊#92418C2×C4semidirect
118. C22×D4×C61C2×C4semidirect
225. C22⋊C4×C61D8semidirect
302. D4×C61C4×D4semidirect
378. C22×C61C4×D8semidirect
411. D4×C22⋊C4D61semidirect
479. C61#22870semidirect
489. C22×D4C4×D61semidirect
670. C22⋊C4#11758199semidirect
725. D4#14519737semidirect
802. C22C4×#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×C4×#117581992
C22×#145196982
#214488332
#214466842
#214465052
#214464362
#214462452
#214461702
#214461672
#214460662
#214460062
C4×#145196982
C22⋊C4×#924182
D4×C22⋊C4×C612
#2287061