Finite Group Databasebeta

← #29696508

Subgroups — #29696508

Order 15616.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459377C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic, complemented
3#21446800C211yesmaximal, characteristic, complemented
4#21446762C211yesmaximal, characteristic, complemented
5#21446267C211yesmaximal, characteristic, complemented
6#21446262C211yesmaximal, characteristic, complemented
7#21446119C211yesmaximal, characteristic, complemented
8#21446119C211yesmaximal, characteristic, complemented
9#21445919C211yesmaximal, characteristic, complemented
10#21445919C211yesmaximal, characteristic, complemented
11#21445840C211yesmaximal, characteristic, complemented
12#21445630C211yesmaximal, characteristic, complemented
13#21445529C211yesmaximal, characteristic, complemented
14C2×#16839522C211yesmaximal, characteristic, complemented
15C61×#2290C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840482C411yescharacteristic, complemented
19#16840477C411yescharacteristic, complemented
20#16840469C411yescharacteristic, complemented
21#16840458C411yescharacteristic, complemented
22#16840458C411yescharacteristic, complemented
23#16840452C411yescharacteristic, complemented
24#16840452C411yescharacteristic, complemented
25#16840447—21no—
26#16840438—21no—
27#16840438—21no—
28#16840416C411yescharacteristic, complemented
29#16840406—21no—
30#16840319C2211yescharacteristic
31#16840294—21no—
32#16840292—21no—
33#16840292—21no—
34#16840273C2211yescharacteristic
35#16840273C2211yescharacteristic
36C4×#11758222C2211yescharacteristic
37C4×#11758224—21no—
38C2×#14519736C2211yescharacteristic
39C2×#14519736C2211yescharacteristic
40#16839840—21no—
41#16839834—21no—
42#16839834—21no—
43D4×#92418—21no—
44#16839786C2211yescharacteristic
45C2×#14519705C2211yescharacteristic
46C2×#14519705C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49#16839726C2211yescharacteristic
50#16839726C2211yescharacteristic
51C4×#11758194C2211yescharacteristic
52#16839522C2211yescharacteristic
53#16839522C2211yescharacteristic
54#16839522C2211yescharacteristic
55#16839522C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839522C2211yescharacteristic
59#16839522C2211yescharacteristic
60#16839522C2211yescharacteristic
61#16839522C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C2×#117×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C61×#388—21no—
68C61×#387—21no—
69C61×#386—21no—
70C61×#385—21no—
71C4×C4⋊C4×C61C2211yescharacteristic
72C4×C22⋊C4×C61C2211yescharacteristic
73C4×C22⋊C4×C61C2211yescharacteristic
74C61×#376C2211yescharacteristic
75C2×#11758222C2311yescharacteristic
76C2×#11758224—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—22no—
80C2×#11758194—22no—
81C2×#11758194—41no—
82C2×#11758194—41no—
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C2×#11758194C2311yescharacteristic
87C22×#92418—21no—
88C22×#92418—21no—
89#14519777C2×C411yescharacteristic, complemented
90#14519777C2×C411yescharacteristic, complemented
91#14519772—21no—
92#14519772—21no—
93#14519770—21no—
94#14519770—21no—
95#14519770—21no—
96#14519770—21no—
97#14519769C2×C411yescharacteristic, complemented
98#14519769C2×C411yescharacteristic, complemented
99#14519768—21no—
100#14519767—21no—
101#14519767—21no—
102#14519764—21no—
103#14519763—21no—
104#14519763—21no—
105#14519761—21no—
106#14519761—21no—
107#14519760—21no—
108#14519760—21no—
109#14519759—21no—
110#14519759—21no—
111#14519758—21no—
112#14519758—21no—
113#14519757—21no—
114#14519756—21no—
115#14519756—21no—
116#14519756C2×C411yescharacteristic
117#14519756C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic, complemented
119#14519756C2×C411yescharacteristic, complemented
120#14519754—21no—
121#14519754—21no—
122#14519751C2×C411yescharacteristic
123#14519751C2×C411yescharacteristic
124#14519751C2×C411yescharacteristic, complemented
125#14519751C2×C411yescharacteristic, complemented
126#14519749—21no—
127#14519749—21no—
128#14519748—21no—
129#14519746—21no—
130#14519746—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122C2×C411yescharacteristic, complemented
134C4×Dic122C2×C411yescharacteristic, complemented
135#14519742—21no—
136C4×D244C2×C411yescharacteristic, complemented
137C4×D244C2×C411yescharacteristic, complemented
138D4×Dic61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145#14519737—21no—
146#14519737—21no—
147#14519736—21no—
148#14519736—21no—
149#14519736—21no—
150#14519736—21no—
151#14519736C2×C411yescharacteristic
152#14519736C2×C411yescharacteristic
153#14519736C2×C411yescharacteristic, complemented
154#14519736C2×C411yescharacteristic, complemented
155#14519736C2311yescharacteristic
156#14519736C2311yescharacteristic
157#14519736C2311yescharacteristic
158#14519735—21no—
159#14519734—21no—
160#14519733—21no—
161#14519733—21no—
162C2×C4⋊Dic61C2×C411yescharacteristic
163C2×C4⋊Dic61C2×C411yescharacteristic
164C2×C4⋊Dic61C2×C411yescharacteristic, complemented
165C2×C4⋊Dic61C2×C411yescharacteristic, complemented
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C42×D61—21no—
171C4⋊#92418—21no—
172C4⋊#92418—21no—
173#14519705—22no—
174#14519705—22no—
175#14519705—41no—
176#14519705—41no—
177C22⋊#92418—21no—
178C22⋊#92418—21no—
179C22⋊#92418—21no—
180C22⋊#92418—21no—
181#14519688—21no—
182C4×#92418—21no—
183C22×D4×C61D411yescharacteristic
184C23×C4×C61—21no—
185C23×C4×C61C2311yescharacteristic
186C23×C4×C61C2311yescharacteristic
187C4×D4×C61C2×C411yescharacteristic
188C4×D4×C61C2×C411yescharacteristic
189C4×D4×C61C2×C411yescharacteristic
190C4×D4×C61C2×C411yescharacteristic
191C4×D4×C61D411yescharacteristic
192C4×D4×C61D411yescharacteristic
193C4×D4×C61D411yescharacteristic
194C4×D4×C61D411yescharacteristic
195#117×C61—22no—
196#117×C61—41no—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61—21no—
199C2×C4⋊C4×C61D411yescharacteristic
200C2×C22⋊C4×C61—21no—
201C2×C22⋊C4×C61—21no—
202C2×C22⋊C4×C61—21no—
203C2×C22⋊C4×C61D411yescharacteristic
204C2×C22⋊C4×C61D411yescharacteristic
205C2×C42×C61—22no—
206C2×C42×C61—21no—
207C2×C42×C61—41no—
208C2×C42×C61C2311yescharacteristic
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C2×C42×C61C2311yescharacteristic
213#95×C61—21no—
214#95×C61—21no—
215#95×C61—21no—
216#95×C61—21no—
217#95×C61—21no—
218C24×C61C2×D411yescharacteristic
219C24×C61C2×D411yescharacteristic
220C2×D4×C61—42no—
221C2×D4×C61C22⋊C411yescharacteristic
222C2×D4×C61C22⋊C411yescharacteristic
223C2×D4×C61C22⋊C411yescharacteristic
224C2×D4×C61C22⋊C411yescharacteristic
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—42no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61—21no—
254C2×C22⋊D61—21no—
255C2×C22⋊D61—21no—
256C2×C22⋊D61—21no—
257C2×C22⋊D61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262#11758224—44no—
263#11758222—21no—
264#11758222—21no—
265#11758222—21no—
266#11758222—21no—
267C2×D244C22×C411yescharacteristic
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122C22×C411yescharacteristic
274C4⋊C4×C61—42no—
275C4⋊C4×C61—42no—
276C4⋊C4×C61C22⋊C411yescharacteristic
277C4⋊C4×C61C22⋊C411yescharacteristic
278C4⋊C4×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C22⋊C4×C61—42no—
281C22⋊C4×C61—42no—
282C22⋊C4×C61—42no—
283C22⋊C4×C61C22⋊C411yescharacteristic
284C22⋊C4×C61C22⋊C411yescharacteristic
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C22⋊C4×C61C22⋊C411yescharacteristic
288C22⋊C4×C61C22⋊C411yescharacteristic
289C22⋊C4×C61C22⋊C411yescharacteristic
290C22⋊C4×C61C22⋊C411yescharacteristic
291C42×C61—21no—
292C42×C61—21no—
293C42×C61—21no—
294C42×C61—21no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61—21no—
298C42×C61—42no—
299C42×C61C22×C411yescharacteristic
300C42×C61C22×C411yescharacteristic
301C42×C61C2×D411yescharacteristic
302C42×C61C2×D411yescharacteristic
303C42×C61#4112yescomplemented
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308C22⋊Dic61—21no—
309C22⋊Dic61—21no—
310C22⋊Dic61—21no—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
314C22⋊Dic61—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61C22×C411yescharacteristic
328C4⋊Dic61C22×C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332C4⋊Dic61C22×C411yescharacteristic
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352#11758194—21no—
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357#11758194—21no—
358#11758194—21no—
359#11758194—42no—
360#11758194—42no—
361#11758194#4112yescomplemented
362C2×#92418—21no—
363C2×#92418—21no—
364C2×#92418—21no—
365C2×#92418—21no—
366C2×#92418—42no—
367C2×#92418—42no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—22no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61C2×C22⋊C411yescharacteristic
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C23×C61C2×C22⋊C411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C22×D61—21no—
382D4×C61—22no—
383D4×C61—22no—
384D4×C61—41no—
385D4×C61—41no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—48no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61C2×C22⋊C411yescharacteristic
423C2×C4×C61C2×C22⋊C411yescharacteristic
424C2×C4×C61C2×C22⋊C411yescharacteristic
425C2×C4×C61C2×C22⋊C411yescharacteristic
426C2×C4×C61C2×C22⋊C411yescharacteristic
427C2×C4×C61C2×C22⋊C411yescharacteristic
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C23×C411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C2×#4111yescharacteristic
432C2×C4×C61C2×#4111yescharacteristic
433C2×C4×C61H(5,𝔽2)11yescharacteristic
434C2×C4×C612−1+411yescharacteristic
435C22⋊D61—42no—
436C22⋊D61—41no—
437C22⋊D61—41no—
438C22⋊D61—42no—
439C22⋊D61—81no—
440C22⋊D61—81no—
441C2×Dic61—21no—
442C2×Dic61—21no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—42no—
449C2×Dic61—42no—
450C2×Dic61—81no—
451C2×Dic61—81no—
452D244—21no—
453D244—21no—
454C4×D61—42no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—81no—
458Dic122—21no—
459Dic122—21no—
460Dic122—42no—
461Dic122—81no—
462#92418—22no—
463#92418—41no—
464#92418—41no—
465#92418—41no—
466#22506—611nomaximal, Sylow
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—42no—
481C22×C61—42no—
482C22×C61—81no—
483C22×C61—81no—
484C22×C61#42112yes—
485C22×C61C22×C22⋊C411yescharacteristic
486C22×C61#54611yescharacteristic
487C22×C61#54711yescharacteristic
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C4×C61—21no—
492C4×C61—21no—
493C4×C61—21no—
494C4×C61—21no—
495C4×C61—21no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—81no—
502C4×C61—81no—
503C4×C61C4×#4111yescharacteristic
504C4×C61#52011yescharacteristic
505C4×C61#54611yescharacteristic
506C4×C61#54711yescharacteristic
507Dic61—41no—
508Dic61—41no—
509Dic61—41no—
510Dic61—41no—
511Dic61—41no—
512Dic61—41no—
513Dic61—41no—
514#3475—611no—
515D4×M16—611no—
516#2290D6111yescharacteristic, complemented
517#1995—611no—
518#1986—611no—
519#1897—611no—
520#1896—611no—
521#1871—611no—
522#1871—611no—
523#1826—611no—
524#1826—611no—
525#1806—611no—
526#1759—611no—
527#1733—611no—
528C2×#339—611no—
529C2×C61—21no—
530C2×C61—21no—
531C2×C61—22no—
532C2×C61—41no—
533C2×C61—41no—
534C2×C61—41no—
535C2×C61#233911yescharacteristic
536C2×C61C2×#42111yescharacteristic
537C2×C61#290111yescharacteristic
538D61—81no—
539C22×M16—611no—
540C22×M16—611no—
541#556—611no—
542#555—611no—
543#554—611no—
544#553—611no—
545#553—611no—
546#552—611no—
547#552—611no—
548#552—1221no—
549#551—1221no—
550#551—1221no—
551#547—611no—
552#546—1221no—
553#533—611no—
554#529—1221no—
555#529—1221no—
556#529—1221no—
557#525—611no—
558#525—611no—
559C4×#41—611no—
560C4×#41—1221no—
561C2×C4×D4C2×D6111yescharacteristic
562C2×#117—611no—
563C2×#117—611no—
564C2×#117C2×D6111yescharacteristic
565C22×C42C2×D6111yescharacteristic
566#436—1221no—
567#435—1221no—
568#435—1221no—
569C8×D4—1221no—
570#423—611no—
571C2×#104—611no—
572C2×#104—611no—
573C2×#104—611no—
574C2×#104—611no—
575#407—611no—
576#407—611no—
577C4×M16—611no—
578#388—21no—
579#387—21no—
580#386—21no—
581#385—21no—
582C4×C4⋊C4C2×D6111yescharacteristic
583C4×C22⋊C4C2×D6111yescharacteristic
584C4×C22⋊C4C2×D6111yescharacteristic
585#376C2×D6111yescharacteristic
586#339—611no—
587#339—611no—
588#339—611no—
589#339—611no—
590#339—611no—
591#339—611no—
592#339—611no—
593#339—611no—
594#339—611no—
595#339—611no—
596#339—611no—
597#339—611no—
598C61#2250611yescharacteristic, complemented, Sylow
599C2×#41—611no—
600C2×#41—1221no—
601C22×D4C22⋊D6111yescharacteristic
602C23×C4—21no—
603C23×C4C22×D6111yescharacteristic
604C23×C4C22×D6111yescharacteristic
605C2×M16—611no—
606C2×M16—611no—
607C2×M16—611no—
608C2×M16—611no—
609C2×M16—1221no—
610C2×M16—1221no—
611C2×M16—1222no—
612C2×M16—1222no—
613C2×M16—2441no—
614C2×M16—2441no—
615C22×C8—1221no—
616C22×C8—1221no—
617C4⋊Q8—611no—
618C4⋊Q8—611no—
619#126—1221no—
620#126—1221no—
621#126—1221no—
622#126—1221no—
623#126—1221no—
624#126—1221no—
625#125—611no—
626#125—611no—
627#125—1221no—
628#125—1221no—
629#125—1221no—
630#124—1221no—
631#124—1221no—
632#124—1221no—
633#123—1221no—
634#123—1221no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641C22⋊Q8—611no—
642C22⋊Q8—611no—
643C22⋊Q8—611no—
644C22⋊Q8—611no—
645C22⋊Q8—1221no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650#121—611no—
651#121—611no—
652#121—611no—
653#121—611no—
654#121—1221no—
655#121—1221no—
656#121—1221no—
657#120—1221no—
658#120—1221no—
659C4×Q8—611no—
660C4×Q8—611no—
661C4×Q8—1221no—
662C4×Q8—1221no—
663C4×Q8—1221no—
664C4×D4—611no—
665C4×D4—611no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4C4×D6111yescharacteristic
676C4×D4C4×D6111yescharacteristic
677C4×D4C4×D6111yescharacteristic
678C4×D4C4×D6111yescharacteristic
679C4×D4D24411yescharacteristic
680C4×D4D24411yescharacteristic
681C4×D4D24411yescharacteristic
682C4×D4D24411yescharacteristic
683#117—22no—
684#117—41no—
685#117—611no—
686#117—611no—
687#117—611no—
688#117—611no—
689#117—611no—
690#117—611no—
691#117—611no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117—1221no—
696#117—1221no—
697#117—1221no—
698#117—1221no—
699#117—1221no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4C22⋊D6111yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—1221no—
711C2×C22⋊C4—1221no—
712C2×C22⋊C4C22⋊D6111yescharacteristic
713C2×C22⋊C4C22⋊D6111yescharacteristic
714C2×C42—22no—
715C2×C42—21no—
716C2×C42—41no—
717C2×C42—1221no—
718C2×C42—1221no—
719C2×C42—1221no—
720C2×C42C22×D6111yescharacteristic
721C2×C42C22×D6111yescharacteristic
722C2×C42C22×D6111yescharacteristic
723C2×C42C22×D6111yescharacteristic
724C2×C42C22×D6111yescharacteristic
725C4⋊C8—1221no—
726C4⋊C8—1221no—
727#104—1222no—
728#104—1222no—
729#104—2441no—
730#104—2441no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735#97—1221no—
736C4×C8—1221no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742C24C2×C22⋊D6111yescharacteristic
743C24C2×C22⋊D6111yescharacteristic
744#41—1221no—
745#41—1221no—
746#41—1221no—
747#41—1221no—
748#41—2444no—
749C2×Q8—611no—
750C2×Q8—1221no—
751C2×Q8—1221no—
752C2×D4—42no—
753C2×D4—611no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—1221no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4#1175819811yescharacteristic
760C2×D4#1175819811yescharacteristic
761C2×D4#1175819811yescharacteristic
762C2×D4#1175819811yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4C2×C4×D6111yescharacteristic
786C22×C4C2×C4×D6111yescharacteristic
787C22×C4C2×C4×D6111yescharacteristic
788C22×C4C2×C4×D6111yescharacteristic
789C22×C4C2×D24411yescharacteristic
790C22×C4C2×D24411yescharacteristic
791C22×C4C2×D24411yescharacteristic
792C22×C4C2×D24411yescharacteristic
793C22×C4C2×C22⋊D6111yescharacteristic
794C22×C4C2×C22⋊D6111yescharacteristic
795C22×C4C2×C22⋊D6111yescharacteristic
796C22×C4C2×C22⋊D6111yescharacteristic
797C22×C4C23×D6111yescharacteristic
798M16—612no—
799M16—1221no—
800M16—1221no—
801M16—1221no—
802M16—1221no—
803M16—1221no—
804M16—1221no—
805M16—1221no—
806M16—2442no—
807M16—2442no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—2442no—
813C2×C8—2442no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—611no—
817C4⋊C4—611no—
818C4⋊C4—611no—
819C4⋊C4—611no—
820C4⋊C4—611no—
821C4⋊C4—611no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—1221no—
827C4⋊C4—1221no—
828C4⋊C4—1221no—
829C4⋊C4—1221no—
830C4⋊C4—1221no—
831C4⋊C4—1221no—
832C4⋊C4—1221no—
833C4⋊C4—1221no—
834C4⋊C4—1221no—
835C4⋊C4—1221no—
836C4⋊C4—1221no—
837C4⋊C4—1221no—
838C4⋊C4#1175819811yescharacteristic
839C4⋊C4#1175819811yescharacteristic
840C4⋊C4#1175819811yescharacteristic
841C4⋊C4#1175819811yescharacteristic
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—1221no—
846C22⋊C4—1221no—
847C22⋊C4—1221no—
848C22⋊C4—1221no—
849C22⋊C4—1221no—
850C22⋊C4—1221no—
851C22⋊C4—1221no—
852C22⋊C4—1221no—
853C22⋊C4—1221no—
854C22⋊C4—1221no—
855C22⋊C4—1221no—
856C22⋊C4—1221no—
857C22⋊C4—1221no—
858C22⋊C4—1221no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
861C22⋊C4—1221no—
862C22⋊C4#1175819811yescharacteristic
863C22⋊C4#1175819811yescharacteristic
864C22⋊C4#1175819811yescharacteristic
865C22⋊C4#1175819811yescharacteristic
866C22⋊C4#1175819811yescharacteristic
867C22⋊C4#1175819811yescharacteristic
868C22⋊C4#1175819811yescharacteristic
869C22⋊C4#1175819811yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—42no—
878C42—1221no—
879C42—1221no—
880C42—1221no—
881C42—1221no—
882C42—1221no—
883C42—1221no—
884C42—1221no—
885C42—1221no—
886C42—1221no—
887C42C2×C4×D6111yescharacteristic
888C42C2×C4×D6111yescharacteristic
889C42C2×D24411yescharacteristic
890C42C2×D24411yescharacteristic
891C42#1175822412yescomplemented
892C23—22no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—1221no—
901C23C2×#1175819811yescharacteristic
902C23C2×#1175819811yescharacteristic
903C23C2×#1175819811yescharacteristic
904C23C2×#1175819811yescharacteristic
905C23C22×C22⋊D6111yescharacteristic
906Q8—1221no—
907Q8—1221no—
908Q8—4881no—
909Q8—2442no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—1221no—
915D4—1221no—
916D4—4881no—
917D4—4881no—
918D4—2442no—
919D4—2442no—
920D4—2441no—
921D4—2441no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—48no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—4881no—
965C2×C4—4881no—
966C2×C4—4881no—
967C2×C4—2442no—
968C2×C4—2442no—
969C2×C4—2442no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4C2×#1175819811yescharacteristic
973C2×C4C2×#1175819811yescharacteristic
974C2×C4C2×#1175819811yescharacteristic
975C2×C4C2×#1175819811yescharacteristic
976C2×C4C2×#1175819811yescharacteristic
977C2×C4C2×#1175819811yescharacteristic
978C2×C4C2×#1175819811yescharacteristic
979C2×C4C2×#1175819811yescharacteristic
980C2×C4C22×C4×D6111yescharacteristic
981C2×C4C22×D24411yescharacteristic
982C2×C4#41×D6111yescharacteristic
983C2×C4C2×#1175822411yescharacteristic
984C2×C4#1451982211yescharacteristic
985C2×C4#1451982411yescharacteristic
986C8—1222no—
987C8—2441no—
988C8—2441no—
989C8—2441no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—2441no—
1008C22—2441no—
1009C22—2441no—
1010C22#1683978012yes—
1011C22C22×#1175819811yescharacteristic
1012C22#1684040611yescharacteristic
1013C22#1684041111yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—2441no—
1027C4—2441no—
1028C4—2441no—
1029C4—2441no—
1030C4—2441no—
1031C4—2441no—
1032C4—2441no—
1033C4C4×#1175822411yescharacteristic
1034C4#1684024111yescharacteristic
1035C4#1684040711yescharacteristic
1036C4#1684041611yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—4881no—
1044C2#2144864411yescharacteristic
1045C2C2×#1683978011yescharacteristic
1046C2#2145436711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2290C2
socleC22×C61C22×C22⋊C4
prime radical#21459377C2
cosocleC22×C4×C61C24
hypercenter#2290D61
hypocenterC61#22506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. D4×#11758194C2semidirect
3. #21446800C2semidirect
4. #21446762C2semidirect
5. #21446267C2semidirect
6. #21446262C2semidirect
7. #21446119C2semidirect
8. #21446119C2semidirect
9. #21445919C2semidirect
10. #21445919C2semidirect
11. #21445840C2semidirect
12. #21445630C2semidirect
13. #21445529C2semidirect
14. C2×#16839522C2semidirect
15. C61×#2290C2semidirect
18. #16840482C4semidirect
19. #16840477C4semidirect
20. #16840469C4semidirect
21. #16840458C4semidirect
22. #16840458C4semidirect
23. #16840452C4semidirect
24. #16840452C4semidirect
28. #16840416C4semidirect
89. #14519777C2×C4semidirect
90. #14519777C2×C4semidirect
97. #14519769C2×C4semidirect
98. #14519769C2×C4semidirect
118. #14519756C2×C4semidirect
119. #14519756C2×C4semidirect
124. #14519751C2×C4semidirect
125. #14519751C2×C4semidirect
133. C4×Dic122C2×C4semidirect
134. C4×Dic122C2×C4semidirect
136. C4×D244C2×C4semidirect
137. C4×D244C2×C4semidirect
153. #14519736C2×C4semidirect
154. #14519736C2×C4semidirect
164. C2×C4⋊Dic61C2×C4semidirect
165. C2×C4⋊Dic61C2×C4semidirect
303. C42×C61#41semidirect
361. #11758194#41semidirect
516. #2290D61semidirect
598. C61#22506semidirect
891. C42#11758224semidirect

Maximal subgroups

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

subgroupindex
#214593772
D4×#117581942
#214468002
#214467622
#214462672
#214462622
#214461192
#214459192
#214458402
#214456302
#214455292
C2×#168395222
C61×#22902
#2250661