Finite Group Databasebeta

← #30620381

Subgroups — #30620381

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#21462558C211yesmaximal, characteristic, complemented
2#21462273C211yesmaximal, characteristic, complemented
3#21462007C211yesmaximal, characteristic, complemented
4#21461994C211yesmaximal, characteristic, complemented
5#21461839C211yesmaximal, characteristic, complemented
6#21461837C211yesmaximal, characteristic, complemented
7#21461803C211yesmaximal, characteristic, complemented
8#21461802C211yesmaximal, characteristic, complemented
9#21461726C211yesmaximal, characteristic, complemented
10#21461725C211yesmaximal, characteristic, complemented
11#21461693C211yesmaximal, characteristic, complemented
12#21461582C211yesmaximal, characteristic, complemented
13#21461498C211yesmaximal, characteristic, complemented
14C2×#16840632C211yesmaximal, characteristic, complemented
15#21459382C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C2×D61⋊M16C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20#16840795—21no—
21#16840793—21no—
22#16840792—21no—
23#16840789—21no—
24#16840767C2211yescharacteristic
25C2×#14519841C2211yescharacteristic
26C2×#14519841C2211yescharacteristic
27C2×#14519841C2211yescharacteristic
28C2×#14519841C2211yescharacteristic
29#16840733C2211yescharacteristic
30#16840733C2211yescharacteristic
31C4×#11758213C2211yescharacteristic
32#16840712—21no—
33#16840711—21no—
34#16840710—21no—
35#16840709—21no—
36C4×C4⋊#6923C2211yescharacteristic
37C4×C22⋊#6923C2211yescharacteristic
38C4×C22⋊#6923C2211yescharacteristic
39#16840698C2211yescharacteristic
40#16840632C2211yescharacteristic
41#16840632C2211yescharacteristic
42#16840632C2211yescharacteristic
43#16840632C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52#16840486C411yescharacteristic, complemented
53#16840477C411yescharacteristic, complemented
54#16840469C411yescharacteristic, complemented
55#16840464C411yescharacteristic, complemented
56#16840464C411yescharacteristic, complemented
57#16840447C411yescharacteristic, complemented
58#16840447C411yescharacteristic, complemented
59#16840446—21no—
60#16840435—21no—
61#16840435—21no—
62#16840400—21no—
63#16840317C2211yescharacteristic
64#16840298—21no—
65#16840289—21no—
66#16840289—21no—
67#16840272C2211yescharacteristic
68#16840272C2211yescharacteristic
69#41×Dic61—21no—
70C4×#11758224C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72C2×#14519735C2211yescharacteristic
73C2×#14519735C2211yescharacteristic
74C61×#547C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—22no—
77C2×#11758213—21no—
78C2×#11758213—41no—
79C2×#11758213C2311yescharacteristic
80C2×#11758213C2311yescharacteristic
81C2×#11758213C2311yescharacteristic
82C2×#11758213C2311yescharacteristic
83D61⋊M16—22no—
84D61⋊M16—41no—
85C2×#11758217—21no—
86C2×D61⋊C8—21no—
87C22×#92420—21no—
88#14519856—22no—
89#14519856—41no—
90C2×C4⋊#6923—21no—
91C2×C4⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C4×#6923—22no—
96C2×C4×#6923—21no—
97C2×C4×#6923—41no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519844—21no—
103#14519844—21no—
104#14519841—22no—
105#14519841—22no—
106#14519841—41no—
107#14519841—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112#14519832—21no—
113C4×#92420—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×#11758224C2311yescharacteristic
120C2×D4×D61D411yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123#14519777C2×C411yescharacteristic, complemented
124#14519772—21no—
125#14519772—21no—
126#14519772—21no—
127#14519772—21no—
128#14519770—21no—
129#14519770—21no—
130#14519768—21no—
131#14519768C2×C411yescharacteristic, complemented
132#14519768C2×C411yescharacteristic, complemented
133#14519767—21no—
134#14519767—21no—
135#14519766—21no—
136#14519763—21no—
137#14519763—21no—
138#14519761—21no—
139#14519761—21no—
140#14519760—21no—
141#14519760—21no—
142#14519759—21no—
143#14519759—21no—
144#14519757—21no—
145#14519757C2×C411yescharacteristic
146#14519757C2×C411yescharacteristic, complemented
147#14519756C2×C411yescharacteristic
148#14519756C2×C411yescharacteristic, complemented
149#14519754—21no—
150#14519754—21no—
151#14519753—21no—
152#14519751—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748C2×C411yescharacteristic
156#14519748C2×C411yescharacteristic, complemented
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61—21no—
160Q8×Dic61—21no—
161C4×Dic122C2×C411yescharacteristic, complemented
162#14519742—21no—
163#14519742C2×C411yescharacteristic, complemented
164C4×D244C2×C411yescharacteristic
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61—21no—
169D4×Dic61—21no—
170D4×Dic61C2×C411yescharacteristic, complemented
171D4×Dic61D411yescharacteristic
172#14519739D411yescharacteristic
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736—21no—
182#14519736—21no—
183#14519736—21no—
184#14519735—21no—
185#14519735—21no—
186#14519735—21no—
187#14519735—21no—
188#14519735C2×C411yescharacteristic
189#14519735C2×C411yescharacteristic
190#14519735C2×C411yescharacteristic, complemented
191#14519735C2×C411yescharacteristic, complemented
192#14519735C2311yescharacteristic
193#14519735C2311yescharacteristic
194#14519735C2311yescharacteristic
195#14519733—21no—
196C2×C4⋊Dic61C2×C411yescharacteristic
197C2×C4⋊Dic61C2×C411yescharacteristic, complemented
198C4⋊C4×D61D411yescharacteristic
199C2×#11758198—21no—
200C2×#11758198—21no—
201C22⋊C4×D61D411yescharacteristic
202C22⋊C4×D61D411yescharacteristic
203C2×C4×Dic61—21no—
204C2×C4×Dic61—21no—
205C2×C4×Dic61—21no—
206C42×D61C2311yescharacteristic
207C2×#41×C61—21no—
208C4⋊Q8×C61C2×C411yescharacteristic, complemented
209#123×C61—21no—
210#123×C61—21no—
211C22⋊Q8×C61—21no—
212#121×C61C2×C411yescharacteristic
213#121×C61C2×C411yescharacteristic, complemented
214C4×D4×C61C2×C411yescharacteristic
215C4×D4×C61C2×C411yescharacteristic, complemented
216C2×C4⋊C4×C61C2×C411yescharacteristic
217C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—42no—
225C22×#6923—42no—
226C22×#6923—42no—
227#41×C61—44no—
228C2×Q8×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61C22⋊C411yescharacteristic
232C2×D4×C61C22×C411yescharacteristic
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C22×C411yescharacteristic
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249#11758224—21no—
250#11758224—21no—
251#11758224—21no—
252#11758224—21no—
253D4×D61—42no—
254C2×D244C22⋊C411yescharacteristic
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—21no—
262C2×C4×D61—21no—
263C2×C4×D61C22×C411yescharacteristic
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2411yescharacteristic
272C2×Dic122—21no—
273C2×Dic122C22×C411yescharacteristic
274C22⋊#6923—42no—
275C22⋊#6923—42no—
276C22⋊#6923—42no—
277#11758217—42no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—42no—
283C4⋊#6923—42no—
284C4⋊#6923—42no—
285C4×#6923—21no—
286C4×#6923—21no—
287C4×#6923—21no—
288C4×#6923—21no—
289C4×#6923—21no—
290C4×#6923—21no—
291C4×#6923—21no—
292C4×#6923—42no—
293C4×#6923#4112yescomplemented
294#11758213—21no—
295#11758213—21no—
296#11758213—21no—
297#11758213—21no—
298#11758213—21no—
299#11758213—21no—
300#11758213—21no—
301#11758213—42no—
302#11758213#4112yescomplemented
303D61⋊C8—42no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61C22⋊C411yescharacteristic
308C4⋊C4×C61C22×C411yescharacteristic
309C4⋊C4×C61C22×C411yescharacteristic
310C4⋊C4×C61C22×C411yescharacteristic
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61C22⋊C411yescharacteristic
315C22⋊C4×C61C22⋊C411yescharacteristic
316C42×C61C22×C411yescharacteristic
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61C22⋊C411yescharacteristic
323C22⋊Dic61C22⋊C411yescharacteristic
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198C22⋊C411yescharacteristic
334#11758198C22⋊C411yescharacteristic
335#11758198C22⋊C411yescharacteristic
336#11758198C22⋊C411yescharacteristic
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61C22⋊C411yescharacteristic
345C4⋊Dic61C22×C411yescharacteristic
346C4⋊Dic61C22×C411yescharacteristic
347C4⋊Dic61C22×C411yescharacteristic
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196C22⋊C411yescharacteristic
355#11758196C22⋊C411yescharacteristic
356C4×Dic61—21no—
357C4×Dic61—21no—
358C4×Dic61—21no—
359C4×Dic61—21no—
360C4×Dic61—21no—
361C4×Dic61—21no—
362C4×Dic61—21no—
363C4×Dic61—21no—
364C4×Dic61—21no—
365C4×Dic61C22×C411yescharacteristic
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C23×C61—21no—
369C23×C61C2×C22⋊C411yescharacteristic
370C23×C61C2×C22⋊C411yescharacteristic
371C22×D61—22no—
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61C2×C22⋊C411yescharacteristic
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C22×D411yescharacteristic
382C2×#6923—22no—
383C2×#6923—22no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—48no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395Q8×C61—42no—
396D4×C61—22no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—42no—
400D4×C61—42no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C23×C411yescharacteristic
416C22⋊D61—22no—
417C22⋊D61—41no—
418C22⋊D61—41no—
419C22⋊D61—41no—
420C22⋊D61—81no—
421C22⋊D61—81no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—81no—
433C2×Dic61—81no—
434C2×Dic61—81no—
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440D244—41no—
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—41no—
454C4×D61—41no—
455C4×D61C2×#4111yescharacteristic
456C4×D61C2×#4111yescharacteristic
457C4×D61H(5,𝔽2)11yescharacteristic
458C4×D612−1+411yescharacteristic
459Dic122—21no—
460Dic122—21no—
461Dic122—81no—
462#92420—22no—
463#92420—41no—
464#92420—41no—
465#92420—41no—
466#22506—611nomaximal, Sylow
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61#42112yes—
476C22×C61C22×C22⋊C411yescharacteristic
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—42no—
486C2×D61—42no—
487C2×D61—81no—
488C2×D61—81no—
489C2×D61#54611yescharacteristic
490C2×D61#54711yescharacteristic
491#6923—42no—
492#6923—42no—
493#6923—81no—
494#6923—81no—
495C4×C61—21no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—41no—
500C4×C61—41no—
501C4×C61—41no—
502C4×C61C4×#4111yescharacteristic
503C4×C61#52011yescharacteristic
504Dic61—21no—
505Dic61—21no—
506Dic61—21no—
507Dic61—21no—
508Dic61—41no—
509Dic61—41no—
510Dic61—41no—
511Dic61—41no—
512Dic61#54611yescharacteristic
513Dic61#54711yescharacteristic
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#1759—611no—
527#1733—611no—
528C2×#339—611no—
529C2×C61—22no—
530C2×C61—41no—
531C2×C61—81no—
532C2×C61#233911yescharacteristic
533C2×C61C2×#42111yescharacteristic
534C2×C61#290111yescharacteristic
535D61—21no—
536D61—21no—
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#692311yescharacteristic, complemented
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×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×#104—611no—
574C2×#104—611no—
575#407—611no—
576#407—611no—
577C4×M16—611no—
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#376—611no—
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—21no—
600C2×#41—611no—
601C22×D4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—1221no—
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⋊Q8C2×#692311yescharacteristic, complemented
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—21no—
634#123—21no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641C22⋊Q8—21no—
642C22⋊Q8—611no—
643C22⋊Q8—611no—
644C22⋊Q8—611no—
645C22⋊Q8—611no—
646C22⋊Q8—1221no—
647C22⋊Q8—1221no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650#121—611no—
651#121—611no—
652#121—1221no—
653#121—1221no—
654#121—1221no—
655#121C2×#692311yescharacteristic
656#121C2×#692311yescharacteristic, complemented
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—611no—
667C4×D4—611no—
668C4×D4—611no—
669C4×D4—611no—
670C4×D4—611no—
671C4×D4—611no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4—1221no—
675C4×D4—1221no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4C2×#692311yescharacteristic
682C4×D4C2×#692311yescharacteristic, complemented
683#117—611no—
684#117—611no—
685#117—611no—
686#117—611no—
687#117—611no—
688#117—611no—
689#117—611no—
690#117—1221no—
691#117—1222no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117—1221no—
696#117—1221no—
697#117—1221no—
698#117—1221no—
699#117—2441no—
700C2×C4⋊C4—611no—
701C2×C4⋊C4—611no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—1221no—
704C2×C4⋊C4—1221no—
705C2×C4⋊C4C2×#692311yescharacteristic
706C2×C4⋊C4C2×#692311yescharacteristic, complemented
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—611no—
715C2×C42—611no—
716C2×C42—611no—
717C2×C42—611no—
718C2×C42—611no—
719C2×C42—1221no—
720C2×C42—1222no—
721C2×C42—1221no—
722C2×C42—1221no—
723C2×C42—1221no—
724C2×C42—2441no—
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—1221no—
738#95—1221no—
739#95—1221no—
740#95—1221no—
741#95—1221no—
742C24—611no—
743C24—611no—
744#41—44no—
745#41—1221no—
746#41—1221no—
747#41—1221no—
748#41—1221no—
749C2×Q8—21no—
750C2×Q8—611no—
751C2×Q8—1221no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—611no—
755C2×D4—611no—
756C2×D4—611no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—2442no—
761C2×D4C22⋊#692311yescharacteristic
762C2×D4C22×#692311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—611no—
767C22×C4—611no—
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—1221no—
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—1221no—
793C22×C4—2442no—
794C22×C4—2442no—
795C22×C4—2442no—
796C22×C4C22×#692311yescharacteristic
797C22×C4C22×#692311yescharacteristic
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—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—611no—
818C4⋊C4—611no—
819C4⋊C4—611no—
820C4⋊C4—611no—
821C4⋊C4—611no—
822C4⋊C4—611no—
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—2442no—
837C4⋊C4—2442no—
838C4⋊C4C22⋊#692311yescharacteristic
839C4⋊C4C22×#692311yescharacteristic
840C4⋊C4C22×#692311yescharacteristic
841C4⋊C4C22×#692311yescharacteristic
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—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—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—2442no—
866C22⋊C4—2442no—
867C22⋊C4—2442no—
868C22⋊C4C22⋊#692311yescharacteristic
869C22⋊C4C22⋊#692311yescharacteristic
870C42—611no—
871C42—611no—
872C42—611no—
873C42—612no—
874C42—1221no—
875C42—1221no—
876C42—1221no—
877C42—1221no—
878C42—1221no—
879C42—1221no—
880C42—1221no—
881C42—1221no—
882C42—1221no—
883C42—1221no—
884C42—1221no—
885C42—1221no—
886C42—1221no—
887C42—1221no—
888C42—1221no—
889C42—1221no—
890C42—2442no—
891C42C22×#692311yescharacteristic
892C23—21no—
893C23—611no—
894C23—611no—
895C23—611no—
896C23—1221no—
897C23—1221no—
898C23—1221no—
899C23—1221no—
900C23—1222no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23C2×C22⋊#692311yescharacteristic
905C23C2×C22⋊#692311yescharacteristic
906Q8—42no—
907Q8—1221no—
908Q8—1221no—
909Q8—4881no—
910D4—22no—
911D4—21no—
912D4—21no—
913D4—42no—
914D4—42no—
915D4—1222no—
916D4—4881no—
917D4—4881no—
918D4—2441no—
919D4—2441no—
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—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—611no—
933C2×C4—611no—
934C2×C4—611no—
935C2×C4—611no—
936C2×C4—611no—
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—1222no—
958C2×C4—1222no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—4881no—
964C2×C4—4881no—
965C2×C4—4881no—
966C2×C4—2441no—
967C2×C4—2441no—
968C2×C4—2441no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2448no—
981C2×C4C2×C22⋊#692311yescharacteristic
982C2×C4C2×C22⋊#692311yescharacteristic
983C2×C4C2×C22⋊#692311yescharacteristic
984C2×C4C2×C22⋊#692311yescharacteristic
985C2×C4C23×#692311yescharacteristic
986C8—1222no—
987C8—2441no—
988C8—2441no—
989C8—2441no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—611no—
999C22—611no—
1000C22—1221no—
1001C22—1221no—
1002C22—1221no—
1003C22—1221no—
1004C22—1221no—
1005C22—1221no—
1006C22—1221no—
1007C22—1221no—
1008C22—4881no—
1009C22—4881no—
1010C22—2442no—
1011C22—2442no—
1012C22#1684076012yes—
1013C22C22×C22⋊#692311yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—41no—
1019C4—41no—
1020C4—41no—
1021C4—611no—
1022C4—611no—
1023C4—1221no—
1024C4—1221no—
1025C4—1221no—
1026C4—1221no—
1027C4—4881no—
1028C4—4881no—
1029C4—2442no—
1030C4—2442no—
1031C4—2441no—
1032C4—2441no—
1033C4—2441no—
1034C4—2441no—
1035C4#41×#692311yescharacteristic
1036C4#1684083111yescharacteristic
1037C2—22no—
1038C2—41no—
1039C2—81no—
1040C2—1221no—
1041C2—1221no—
1042C2—2441no—
1043C2—2441no—
1044C2#2146232211yescharacteristic
1045C2C2×#1684076011yescharacteristic
1046C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459382C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#22506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462558C2semidirect
2. #21462273C2semidirect
3. #21462007C2semidirect
4. #21461994C2semidirect
5. #21461839C2semidirect
6. #21461837C2semidirect
7. #21461803C2semidirect
8. #21461802C2semidirect
9. #21461726C2semidirect
10. #21461725C2semidirect
11. #21461693C2semidirect
12. #21461582C2semidirect
13. #21461498C2semidirect
14. C2×#16840632C2semidirect
52. #16840486C4semidirect
53. #16840477C4semidirect
54. #16840469C4semidirect
55. #16840464C4semidirect
56. #16840464C4semidirect
57. #16840447C4semidirect
58. #16840447C4semidirect
74. C61×#547C4semidirect
123. #14519777C2×C4semidirect
131. #14519768C2×C4semidirect
132. #14519768C2×C4semidirect
146. #14519757C2×C4semidirect
148. #14519756C2×C4semidirect
156. #14519748C2×C4semidirect
161. C4×Dic122C2×C4semidirect
163. #14519742C2×C4semidirect
170. D4×Dic61C2×C4semidirect
190. #14519735C2×C4semidirect
191. #14519735C2×C4semidirect
197. C2×C4⋊Dic61C2×C4semidirect
208. C4⋊Q8×C61C2×C4semidirect
213. #121×C61C2×C4semidirect
215. C4×D4×C61C2×C4semidirect
217. C2×C4⋊C4×C61C2×C4semidirect
293. C4×#6923#41semidirect
302. #11758213#41semidirect
551. #547#6923semidirect
598. C61#22506semidirect
618. C4⋊Q8C2×#6923semidirect
656. #121C2×#6923semidirect
682. C4×D4C2×#6923semidirect
706. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625582
#214622732
#214620072
#214619942
#214618392
#214618372
#214618032
#214618022
#214617262
#214617252
#214616932
#214615822
#214614982
C2×#168406322
#214593822
#2250661