Finite Group Databasebeta

← #29696511

Subgroups — #29696511

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#21459383C211yesmaximal, characteristic
2M16×D244C211yesmaximal, characteristic, complemented
3#21448263C211yesmaximal, characteristic, complemented
4#21446800C211yesmaximal, characteristic, complemented
5#21446763C211yesmaximal, characteristic, complemented
6#21446264C211yesmaximal, characteristic, complemented
7#21446259C211yesmaximal, characteristic, complemented
8#21446118C211yesmaximal, characteristic, complemented
9#21446118C211yesmaximal, characteristic, complemented
10#21445917C211yesmaximal, characteristic, complemented
11#21445917C211yesmaximal, characteristic, complemented
12#21445839C211yesmaximal, characteristic, complemented
13#21445527C211yesmaximal, characteristic, complemented
14#339×D61C211yesmaximal, characteristic, complemented
15C61×#1759C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18#16840485C411yescharacteristic, complemented
19#16840477C411yescharacteristic, complemented
20#16840472C411yescharacteristic, complemented
21#16840462C411yescharacteristic, complemented
22#16840462C411yescharacteristic, complemented
23#16840453C411yescharacteristic, complemented
24#16840453C411yescharacteristic, complemented
25#16840452—21no—
26#16840441—21no—
27#16840441—21no—
28#16840417C411yescharacteristic, complemented
29#16840408—21no—
30#16840319C2211yescharacteristic
31#16840296—21no—
32#16840290—21no—
33#16840290—21no—
34#16840269C2211yescharacteristic
35#16840269C2211yescharacteristic
36C4×#11758222—21no—
37C2×C4×D244C2211yescharacteristic
38C2×#14519734C2211yescharacteristic
39#117×D61C2211yescharacteristic
40#117×D61C2211yescharacteristic
41C2×C42×D61C2211yescharacteristic
42#16839841—21no—
43#16839835—21no—
44#16839835—21no—
45C8×D244—21no—
46#16839786C2211yescharacteristic
47C2×#14519704C2211yescharacteristic
48C2×#14519704C2211yescharacteristic
49#16839725C2211yescharacteristic
50#16839725C2211yescharacteristic
51#16839654—21no—
52#16839647—21no—
53#16839640—21no—
54#16839636—21no—
55C4×C4⋊Dic61C2211yescharacteristic
56C4×#11758198C2211yescharacteristic
57C4×#11758198C2211yescharacteristic
58#16839523C2211yescharacteristic
59#16839523C2211yescharacteristic
60#16839523C2211yescharacteristic
61#16839523C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
64#16839522C2211yescharacteristic
65#16839522C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C2×#104×C61C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C4×M16×C61C2211yescharacteristic
72C61×#376C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222—21no—
76C22×D244D411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758189—21no—
83C2×#11758189—21no—
84M16×D61—22no—
85M16×D61—22no—
86M16×D61—41no—
87M16×D61—41no—
88C2×C8×D61—21no—
89C2×C8×D61—21no—
90#14519777C2×C411yescharacteristic, complemented
91#14519777C2×C411yescharacteristic, complemented
92#14519772—21no—
93#14519772—21no—
94#14519771—21no—
95#14519771—21no—
96#14519770—21no—
97#14519770—21no—
98#14519769—21no—
99#14519769C2×C411yescharacteristic, complemented
100#14519769C2×C411yescharacteristic, complemented
101#14519767—21no—
102#14519767—21no—
103#14519765—21no—
104#14519763—21no—
105#14519763—21no—
106#14519762—21no—
107#14519762—21no—
108#14519760—21no—
109#14519760—21no—
110#14519759—21no—
111#14519759—21no—
112#14519758—21no—
113#14519758—21no—
114#14519756—21no—
115#14519756—21no—
116#14519756—21no—
117#14519755—21no—
118#14519755—21no—
119#14519753C2×C411yescharacteristic
120#14519753C2×C411yescharacteristic
121#14519753C2×C411yescharacteristic, complemented
122#14519753C2×C411yescharacteristic, complemented
123#14519751—21no—
124#14519750—21no—
125#14519750—21no—
126#14519748C2×C411yescharacteristic
127#14519748C2×C411yescharacteristic
128#14519748C2×C411yescharacteristic, complemented
129#14519748C2×C411yescharacteristic, complemented
130#14519745—21no—
131#14519745—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×D244—21no—
136C4×D244C2×C411yescharacteristic
137C4×D244C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244D411yescharacteristic
141C4×D244D411yescharacteristic
142C4×D244D411yescharacteristic
143C4×D244D411yescharacteristic
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150#14519736—21no—
151#14519736C2311yescharacteristic
152#14519736C2311yescharacteristic
153#14519735C2×C411yescharacteristic
154#14519735C2×C411yescharacteristic
155#14519735C2×C411yescharacteristic, complemented
156#14519735C2×C411yescharacteristic, complemented
157#14519734—21no—
158#14519734—21no—
159#14519734—21no—
160#14519734—21no—
161#14519734—22no—
162#14519734—41no—
163#14519733—21no—
164#14519733—21no—
165C2×C4⋊Dic61—21no—
166C2×C4⋊Dic61D411yescharacteristic
167C2×#11758196—21no—
168C4⋊C4×D61C2×C411yescharacteristic
169C4⋊C4×D61C2×C411yescharacteristic
170C4⋊C4×D61C2×C411yescharacteristic, complemented
171C4⋊C4×D61C2×C411yescharacteristic, complemented
172C2×#11758198—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198D411yescharacteristic
176C2×#11758198D411yescharacteristic
177C22⋊C4×D61—21no—
178C22⋊C4×D61—21no—
179C2×C4×Dic61—21no—
180C2×C4×Dic61C2311yescharacteristic
181C2×C4×Dic61C2311yescharacteristic
182C42×D61—21no—
183C42×D61—21no—
184C42×D61—22no—
185C42×D61—41no—
186C4⋊#92418—21no—
187C4⋊#92418—21no—
188#14519704—41no—
189#14519704—41no—
190#14519689—21no—
191#14519689—21no—
192#14519689—21no—
193#14519689—21no—
194#14519684—21no—
195#14519684—21no—
196#14519684—21no—
197C2×#41×C61C2311yescharacteristic
198C2×M16×C61C2311yescharacteristic
199C2×M16×C61C2311yescharacteristic
200C4×Q8×C61C2×C411yescharacteristic, complemented
201C4×Q8×C61C2×C411yescharacteristic, complemented
202C4×D4×C61—21no—
203C4×D4×C61—21no—
204C4×D4×C61C2×C411yescharacteristic, complemented
205C4×D4×C61C2×C411yescharacteristic, complemented
206#117×C61—21no—
207#117×C61C2311yescharacteristic
208C2×C42×C61—21no—
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212#104×C61—22no—
213#104×C61—22no—
214#97×C61—21no—
215C4×C8×C61—21no—
216#95×C61—21no—
217#95×C61—21no—
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—21no—
223#41×C61—21no—
224C2×Q8×C61C22×C411yescharacteristic
225C2×D4×C61—21no—
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758222—44no—
244C2×D244—42no—
245C2×D244C22⋊C411yescharacteristic
246C2×D244C22⋊C411yescharacteristic
247C2×D244C22⋊C411yescharacteristic
248C2×D244C22⋊C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×Dic122—21no—
273C2×Dic122—21no—
274M16×C61—21no—
275M16×C61—21no—
276M16×C61—21no—
277M16×C61#4112yescomplemented
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C42×C61—21no—
288C42×C61—21no—
289C42×C61—21no—
290C42×C61—21no—
291C42×C61—21no—
292C42×C61—21no—
293C42×C61C22×C411yescharacteristic
294C42×C61C22×C411yescharacteristic
295C42×C61C2×D411yescharacteristic
296C42×C61C2×D411yescharacteristic
297C42×C61#4112yescomplemented
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—42no—
313#11758198—42no—
314#11758198—42no—
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317#11758198C22⋊C411yescharacteristic
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320#11758198C22⋊C411yescharacteristic
321#11758198C22⋊C411yescharacteristic
322#11758198C22⋊C411yescharacteristic
323C4⋊Dic61—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—42no—
326C4⋊Dic61C22⋊C411yescharacteristic
327C4⋊Dic61C22⋊C411yescharacteristic
328C4⋊Dic61C22⋊C411yescharacteristic
329C4⋊Dic61C22⋊C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332C4⋊Dic61C22×C411yescharacteristic
333C4⋊Dic61C22×C411yescharacteristic
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—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—42no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—21no—
356C4×Dic61—21no—
357C4×Dic61—42no—
358#11758194—21no—
359#11758194—21no—
360#11758194—21no—
361#11758194—21no—
362C2×#92418—21no—
363C2×#92418—21no—
364#11758189—42no—
365#11758189—42no—
366C8×D61—42no—
367C8×D61—42no—
368C23×C61—21no—
369C23×C61C22×D411yescharacteristic
370C22×D61—21no—
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—22no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61C2×C22⋊C411yescharacteristic
379C22×D61C2×C22⋊C411yescharacteristic
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C2×C22⋊C411yescharacteristic
382Q8×C61—21no—
383Q8×C61—21no—
384D4×C61—21no—
385D4×C61—21no—
386D4×C61—41no—
387D4×C61—41no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—22no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—42no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—81no—
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C2×C4×C61C2×C22⋊C411yescharacteristic
405C2×C4×C61C2×C22⋊C411yescharacteristic
406C2×C4×C61C2×C22⋊C411yescharacteristic
407C2×C4×C61C23×C411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C2×#4111yescharacteristic
410C2×C4×C61C2×#4111yescharacteristic
411C2×C4×C61H(5,𝔽2)11yescharacteristic
412C2×C4×C612−1+411yescharacteristic
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—81no—
416C22⋊D61—81no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—22no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C2×C22⋊C411yescharacteristic
434C2×Dic61C2×C22⋊C411yescharacteristic
435D244—22no—
436D244—22no—
437D244—41no—
438D244—41no—
439C4×D61—21no—
440C4×D61—21no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—42no—
456C4×D61—48no—
457C4×D61—42no—
458C4×D61—81no—
459C4×D61—81no—
460Dic122—42no—
461Dic122—81no—
462C8×C61—22no—
463C8×C61—41no—
464#92418—41no—
465#92418—41no—
466#22506—611nomaximal, Sylow
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—41no—
470C22×C61—41no—
471C22×C61—41no—
472C22×C61C22×C22⋊C411yescharacteristic
473C22×C61#54611yescharacteristic
474C22×C61#54711yescharacteristic
475C2×D61—21no—
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—21no—
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—42no—
487C2×D61—42no—
488C2×D61—81no—
489C2×D61—81no—
490C2×D61#42112yes—
491C4×C61—21no—
492C4×C61—21no—
493C4×C61—21no—
494C4×C61—21no—
495C4×C61—42no—
496C4×C61—41no—
497C4×C61—41no—
498C4×C61—41no—
499C4×C61—81no—
500C4×C61C4×#4111yescharacteristic
501C4×C61#52011yescharacteristic
502C4×C61#54611yescharacteristic
503C4×C61#54711yescharacteristic
504Dic61—21no—
505Dic61—21no—
506Dic61—21no—
507Dic61—21no—
508Dic61—42no—
509Dic61—41no—
510Dic61—41no—
511Dic61—41no—
512Dic61—41no—
513Dic61—81no—
514#3475—611no—
515D4×M16—611no—
516#2290—611no—
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#1759D6111yescharacteristic, complemented
527#1733—611no—
528C2×#339—611no—
529C2×C61—21no—
530C2×C61—21no—
531C2×C61—81no—
532C2×C61#233911yescharacteristic
533C2×C61C2×#42111yescharacteristic
534C2×C61#290111yescharacteristic
535D61—22no—
536D61—41no—
537D61—41no—
538D61—41no—
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—1221no—
560C4×#41C2×D6111yescharacteristic
561C2×C4×D4—611no—
562C2×#117—611no—
563C2×#117—611no—
564C2×#117—611no—
565C22×C42—611no—
566#436—1221no—
567#435—1221no—
568#435—1221no—
569C8×D4—1221no—
570#423—611no—
571C2×#104—611no—
572C2×#104—611no—
573C2×#104C2×D6111yescharacteristic
574C2×#104C2×D6111yescharacteristic
575#407—611no—
576#407—611no—
577C4×M16C2×D6111yescharacteristic
578#388—1221no—
579#387—1221no—
580#386—1221no—
581#385—1221no—
582C4×C4⋊C4—611no—
583C4×C22⋊C4—611no—
584C4×C22⋊C4—611no—
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#339C2×D6111yescharacteristic
597#339C2×D6111yescharacteristic
598C61#2250611yescharacteristic, complemented, Sylow
599C2×#41—1221no—
600C2×#41C22×D6111yescharacteristic
601C22×D4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—1221no—
605C2×M16—611no—
606C2×M16—611no—
607C2×M16—1221no—
608C2×M16—1221no—
609C2×M16—1222no—
610C2×M16—1222no—
611C2×M16—2441no—
612C2×M16—2441no—
613C2×M16C22×D6111yescharacteristic
614C2×M16C22×D6111yescharacteristic
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—1221no—
660C4×Q8—1221no—
661C4×Q8—1221no—
662C4×Q8C4×D6111yescharacteristic, complemented
663C4×Q8C4×D6111yescharacteristic, complemented
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—611no—
667C4×D4—611no—
668C4×D4—611no—
669C4×D4—611no—
670C4×D4—611no—
671C4×D4—611no—
672C4×D4—611no—
673C4×D4—611no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4C4×D6111yescharacteristic, complemented
682C4×D4C4×D6111yescharacteristic, complemented
683#117—21no—
684#117—611no—
685#117—611no—
686#117—611no—
687#117—611no—
688#117—611no—
689#117—611no—
690#117—1221no—
691#117—1221no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117—1221no—
696#117—1221no—
697#117—1222no—
698#117—2441no—
699#117C22×D6111yescharacteristic
700C2×C4⋊C4—611no—
701C2×C4⋊C4—611no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—1221no—
706C2×C4⋊C4—1221no—
707C2×C22⋊C4—611no—
708C2×C22⋊C4—611no—
709C2×C22⋊C4—1221no—
710C2×C22⋊C4—1221no—
711C2×C22⋊C4—1221no—
712C2×C22⋊C4—1221no—
713C2×C22⋊C4—1221no—
714C2×C42—21no—
715C2×C42—611no—
716C2×C42—611no—
717C2×C42—1221no—
718C2×C42—1221no—
719C2×C42—1222no—
720C2×C42—1221no—
721C2×C42—2441no—
722C2×C42C22×D6111yescharacteristic
723C2×C42C22×D6111yescharacteristic
724C2×C42C22×D6111yescharacteristic
725C4⋊C8—1221no—
726C4⋊C8—1221no—
727#104—22no—
728#104—22no—
729#104—2441no—
730#104—2441no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735#97—21no—
736C4×C8—21no—
737#95—21no—
738#95—21no—
739#95—1221no—
740#95—1221no—
741#95—1221no—
742C24—611no—
743C24—611no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—2444no—
749C2×Q8—1221no—
750C2×Q8—1221no—
751C2×Q8C2×C4×D6111yescharacteristic
752C2×D4—21no—
753C2×D4—611no—
754C2×D4—611no—
755C2×D4—611no—
756C2×D4—611no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—2442no—
762C2×D4C2×C4×D6111yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—2442no—
793C22×C4—2442no—
794C22×C4—2442no—
795C22×C4D4×D6111yescharacteristic
796C22×C4D4×D6111yescharacteristic
797C22×C4C23×D6111yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—1221no—
802M16—1221no—
803M16—1221no—
804M16—1221no—
805M16—2442no—
806M16—2442no—
807M16#1175822212yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—2442no—
813C2×C8—2442no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—611no—
817C4⋊C4—611no—
818C4⋊C4—611no—
819C4⋊C4—611no—
820C4⋊C4—611no—
821C4⋊C4—611no—
822C4⋊C4—611no—
823C4⋊C4—611no—
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—2442no—
839C4⋊C4—2442no—
840C4⋊C4C2×C4×D6111yescharacteristic
841C4⋊C4C2×C4×D6111yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—611no—
846C22⋊C4—611no—
847C22⋊C4—611no—
848C22⋊C4—611no—
849C22⋊C4—611no—
850C22⋊C4—611no—
851C22⋊C4—611no—
852C22⋊C4—611no—
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—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—2442no—
868C22⋊C4—2442no—
869C22⋊C4—2442no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—1221no—
877C42—1221no—
878C42—1221no—
879C42—1221no—
880C42—1221no—
881C42—1221no—
882C42—1221no—
883C42—1221no—
884C42—1221no—
885C42—1221no—
886C42—2442no—
887C42C2×C4×D6111yescharacteristic
888C42C2×C4×D6111yescharacteristic
889C42#1175822212yescomplemented
890C42D4×D6111yescharacteristic
891C42D4×D6111yescharacteristic
892C23—21no—
893C23—611no—
894C23—611no—
895C23—611no—
896C23—611no—
897C23—1222no—
898C23—1221no—
899C23—1221no—
900C23—1221no—
901C23—1221no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23C2×D4×D6111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—4881no—
909Q8—2442no—
910D4—21no—
911D4—21no—
912D4—41no—
913D4—41no—
914D4—1222no—
915D4—1222no—
916D4—4881no—
917D4—4881no—
918D4—2441no—
919D4—2441no—
920D4—2442no—
921D4—2442no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—42no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—81no—
937C2×C4—611no—
938C2×C4—611no—
939C2×C4—611no—
940C2×C4—611no—
941C2×C4—1221no—
942C2×C4—1221no—
943C2×C4—1221no—
944C2×C4—1221no—
945C2×C4—1221no—
946C2×C4—1221no—
947C2×C4—1221no—
948C2×C4—1221no—
949C2×C4—1221no—
950C2×C4—1221no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1221no—
954C2×C4—1221no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1222no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—4881no—
967C2×C4—4881no—
968C2×C4—2442no—
969C2×C4—2442no—
970C2×C4—2448no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4C22⋊C4×D6111yescharacteristic
977C2×C4C22⋊C4×D6111yescharacteristic
978C2×C4C22⋊C4×D6111yescharacteristic
979C2×C4C22⋊C4×D6111yescharacteristic
980C2×C4C22×C4×D6111yescharacteristic
981C2×C4C2×D4×D6111yescharacteristic
982C2×C4C2×#1175822211yescharacteristic
983C2×C4C2×#1175822211yescharacteristic
984C2×C4#1451982311yescharacteristic
985C2×C4#1451982411yescharacteristic
986C8—22no—
987C8—41no—
988C8—2441no—
989C8—2441no—
990C22—21no—
991C22—21no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—612no—
996C22—1221no—
997C22—1221no—
998C22—1221no—
999C22—1221no—
1000C22—1221no—
1001C22—1221no—
1002C22—1221no—
1003C22—1221no—
1004C22—1221no—
1005C22—1221no—
1006C22—1221no—
1007C22—4881no—
1008C22—4881no—
1009C22—2442no—
1010C22—2442no—
1011C22C2×C22⋊C4×D6111yescharacteristic
1012C22#1684040811yescharacteristic
1013C22#1684041711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—42no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—81no—
1023C4—1221no—
1024C4—1221no—
1025C4—1221no—
1026C4—1221no—
1027C4—4881no—
1028C4—2442no—
1029C4—2441no—
1030C4—2441no—
1031C4—2441no—
1032C4—2441no—
1033C4C4×#1175822211yescharacteristic
1034C4#1684024211yescharacteristic
1035C4#1684040811yescharacteristic
1036C4#1684041711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—81no—
1040C2—1222no—
1041C2—2441no—
1042C2—2441no—
1043C2—2441no—
1044C2#2144865011yescharacteristic
1045C2#421×D6111yescharacteristic
1046C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C22×C22⋊C4
prime radical#21459383C2
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#22506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. M16×D244C2semidirect
3. #21448263C2semidirect
4. #21446800C2semidirect
5. #21446763C2semidirect
6. #21446264C2semidirect
7. #21446259C2semidirect
8. #21446118C2semidirect
9. #21446118C2semidirect
10. #21445917C2semidirect
11. #21445917C2semidirect
12. #21445839C2semidirect
13. #21445527C2semidirect
14. #339×D61C2semidirect
15. C61×#1759C2semidirect
18. #16840485C4semidirect
19. #16840477C4semidirect
20. #16840472C4semidirect
21. #16840462C4semidirect
22. #16840462C4semidirect
23. #16840453C4semidirect
24. #16840453C4semidirect
28. #16840417C4semidirect
90. #14519777C2×C4semidirect
91. #14519777C2×C4semidirect
99. #14519769C2×C4semidirect
100. #14519769C2×C4semidirect
121. #14519753C2×C4semidirect
122. #14519753C2×C4semidirect
128. #14519748C2×C4semidirect
129. #14519748C2×C4semidirect
155. #14519735C2×C4semidirect
156. #14519735C2×C4semidirect
170. C4⋊C4×D61C2×C4semidirect
171. C4⋊C4×D61C2×C4semidirect
200. C4×Q8×C61C2×C4semidirect
201. C4×Q8×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
205. C4×D4×C61C2×C4semidirect
277. M16×C61#41semidirect
297. C42×C61#41semidirect
526. #1759D61semidirect
598. C61#22506semidirect
662. C4×Q8C4×D61semidirect
663. C4×Q8C4×D61semidirect
681. C4×D4C4×D61semidirect
682. C4×D4C4×D61semidirect
807. M16#11758222semidirect
889. C42#11758222semidirect

Maximal subgroups

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

subgroupindex
#214593832
M16×D2442
#214482632
#214468002
#214467632
#214462642
#214462592
#214461182
#214459172
#214458392
#214455272
#339×D612
C61×#17592
#2250661