Finite Group Databasebeta

← #30612259

Subgroups — #30612259

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462750C211yesmaximal, characteristic
2#21462744C211yesmaximal, characteristic
3#21461395C211yesmaximal, characteristic, complemented
4#21461395C211yesmaximal, characteristic, complemented
5#21461391C211yesmaximal, characteristic, complemented
6#21461390C211yesmaximal, characteristic, complemented
7#21461387C211yesmaximal, characteristic, complemented
8#21461386C211yesmaximal, characteristic, complemented
9#21461384C211yesmaximal, characteristic, complemented
10#21461383C211yesmaximal, characteristic, complemented
11#21461373C211yesmaximal, characteristic, complemented
12#21461371C211yesmaximal, characteristic, complemented
13#21461370C211yesmaximal, characteristic, complemented
14#21461366C211yesmaximal, characteristic, complemented
15#21454779C211yesmaximal, characteristic
16#16840814—21no—
17#16840811—21no—
18#16840797—21no—
19#16840795—21no—
20#16840795—21no—
21#16840794—21no—
22#16840793—21no—
23#16840789—21no—
24#16840784C2211yescharacteristic
25#16840783C2211yescharacteristic
26#16840781C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840778C2211yescharacteristic
30#16840766C2211yescharacteristic
31#16840765C2211yescharacteristic
32#16840765C2211yescharacteristic
33#16840765C2211yescharacteristic
34D61⋊(C4⋊C8)C2211yescharacteristic
35C2×C4⋊#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840625C2211yescharacteristic
39#16840625C2211yescharacteristic
40#16840625C2211yescharacteristic
41#16840625C2211yescharacteristic
42#16840624C2211yescharacteristic
43#16840624C2211yescharacteristic
44#16840624C2211yescharacteristic
45#16840624C2211yescharacteristic
46#16840623C2211yescharacteristic
47#16840623C2211yescharacteristic
48#16840623C2211yescharacteristic
49#16840623C2211yescharacteristic
50#16840623C2211yescharacteristic
51#16840623C2211yescharacteristic
52C4×#11758224C2211yescharacteristic
53#16839891C411yescharacteristic
54#16839890C411yescharacteristic
55#16839838C411yescharacteristic
56#16839837C411yescharacteristic
57#16839834C411yescharacteristic
58#16839833C411yescharacteristic
59#16839830C411yescharacteristic
60#16839814C2211yescharacteristic
61#16839812C2211yescharacteristic
62#16839812C2211yescharacteristic
63#16839714C2211yescharacteristic
64M16×Dic61C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C61×#435C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87#14519834—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420—21no—
99C2×#11758224Q811yescharacteristic
100C2×#11758194C2×C411yescharacteristic
101C2×#11758189C2×C411yescharacteristic
102C2×#11758189C2×C411yescharacteristic
103C22×#92418C2×C411yescharacteristic
104C4×Dic122C2×C411yescharacteristic
105#14519742D411yescharacteristic
106D4×Dic61D411yescharacteristic
107C4×C22⋊D61C2×C411yescharacteristic
108C4×C22⋊D61C2×C411yescharacteristic
109#14519737D411yescharacteristic
110#14519737D411yescharacteristic
111#14519735Q811yescharacteristic
112#14519733Q811yescharacteristic
113#14519733Q811yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C42×D61C2311yescharacteristic
117C4⋊#92418C2×C411yescharacteristic
118#14519706C2×C411yescharacteristic
119#14519706C2×C411yescharacteristic
120#14519706C2×C411yescharacteristic
121#14519706C2×C411yescharacteristic
122C22⋊#92418C2×C411yescharacteristic
123C22⋊#92418C2×C411yescharacteristic
124#14519689C2×C411yescharacteristic
125#14519689C2×C411yescharacteristic
126#14519688C2×C411yescharacteristic
127#14519687C2×C411yescharacteristic
128#14519687C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C8×Dic61C2×C411yescharacteristic
131C8×Dic61C2311yescharacteristic
132C8×Dic61C2311yescharacteristic
133C8×Dic61C2311yescharacteristic
134C8×Dic61C2311yescharacteristic
135C2×M16×C61C2×C411yescharacteristic
136C22×C8×C61C2×C411yescharacteristic
137C4×D4×C61C2×C411yescharacteristic
138C4⋊C8×C61C2×C411yescharacteristic
139C22⋊C8×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141#97×C61C2×C411yescharacteristic
142C2×D4×C61C4⋊C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C2×C22⋊D61C4⋊C411yescharacteristic
146C2×C22⋊D61C4⋊C411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×Q811yescharacteristic
150C22×Dic61C2×Q811yescharacteristic
151#11758224—42no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×Q811yescharacteristic
155C2×Dic122C4⋊C411yescharacteristic
156#11758217—81no—
157#11758217—81no—
158#11758217—81no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—81no—
168#11758213—81no—
169D61⋊C8—81no—
170M16×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C4⋊C4×C61C4⋊C411yescharacteristic
177C22⋊C4×C61C4⋊C411yescharacteristic
178C22⋊C4×C61C4⋊C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180C22⋊Dic61C4⋊C411yescharacteristic
181C22⋊Dic61C4⋊C411yescharacteristic
182#11758198C4⋊C411yescharacteristic
183#11758198C4⋊C411yescharacteristic
184C4⋊Dic61C4⋊C411yescharacteristic
185#11758196C4⋊C411yescharacteristic
186#11758196C4⋊C411yescharacteristic
187#11758196C4⋊C411yescharacteristic
188#11758196C4⋊C411yescharacteristic
189C4×Dic61C22×C411yescharacteristic
190C4×Dic61C22×C411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61C2×Q811yescharacteristic
195C4×Dic61C2×Q811yescharacteristic
196C4×Dic61C2×Q811yescharacteristic
197C4×Dic61C2411yescharacteristic
198#11758194—41no—
199C2×#92418—41no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204#11758189—22no—
205#11758189—41no—
206C23×C61C2×C4⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208C22×D61C2×C4⋊C411yescharacteristic
209D4×C61—41no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C2×C4⋊C411yescharacteristic
216C2×C4×C61C2×C4⋊C411yescharacteristic
217C2×C4×C61C2×C4⋊C411yescharacteristic
218C2×C4×C61C23×C411yescharacteristic
219C22⋊D61—22no—
220C22⋊D61—41no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—22no—
226C2×Dic61—41no—
227C2×Dic61C2×C4⋊C411yescharacteristic
228C2×Dic61C2×C4⋊C411yescharacteristic
229C2×Dic61C2×C4⋊C411yescharacteristic
230C2×Dic61C2×C4⋊C411yescharacteristic
231C2×Dic61C2×C4⋊C411yescharacteristic
232C2×Dic61C22×D411yescharacteristic
233C2×Dic61C22×Q811yescharacteristic
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239Dic122—22no—
240#92420—41no—
241#92420—41no—
242#92420—41no—
243#92420—41no—
244#92420—41no—
245#92420—41no—
246#92420—41no—
247#92420—41no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61#13112yes—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#17841—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61C22×C4⋊C411yescharacteristic
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61C2×#13111yescharacteristic
272C4×C61#56811yescharacteristic
273Dic61—21no—
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61#43012yes—
279Dic61#57711yescharacteristic
280Dic61#57711yescharacteristic
281#2991—611no—
282#2990—611no—
283#2965—611no—
284#1574—611no—
285#1574—611no—
286#1572—611no—
287#1572—611no—
288#1570—611no—
289#1570—611no—
290#1569—611no—
291#1569—611no—
292#1566—611no—
293#1565—611no—
294#1565—611no—
295#1564—611no—
296C2×C61—41no—
297C2×C61—41no—
298C2×C61#290611yescharacteristic
299C2×C61#291211yescharacteristic
300C2×C61C2×#43011yescharacteristic
301D61—41no—
302C4×#41—611no—
303#446—611no—
304#446—611no—
305#446—1221no—
306C8×Q8—1221no—
307#436—611no—
308#436—611no—
309#436—1221no—
310#436—1221no—
311#436—1221no—
312#435—611no—
313#435—611no—
314#435—611no—
315#435—1221no—
316#435—1221no—
317#435#692311yescharacteristic
318C8×D4—1221no—
319#432—611no—
320#432—611no—
321#431—611no—
322#431—611no—
323#431—611no—
324#431—611no—
325#431—611no—
326#431—611no—
327#431—611no—
328#423—611no—
329#423—611no—
330#423—611no—
331#423—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C4×M16—611no—
335C4×M16—611no—
336C2×C4×C8—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#334—611no—
344#334—611no—
345#334—611no—
346#334—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334—611no—
351#334—611no—
352#334—611no—
353C61#1784111yescharacteristic, complemented, Sylow
354C2×#41—611no—
355C2×M16—611no—
356C2×M16—611no—
357C2×M16—611no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16C2×#692311yescharacteristic
363C22×C8—611no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8C2×#692311yescharacteristic
367C4×Q8—611no—
368C4×Q8—611no—
369C4×D4—611no—
370C4×D4—611no—
371C4×D4—611no—
372C4×D4—611no—
373C4×D4—611no—
374C4×D4C2×#692311yescharacteristic
375#117—611no—
376#117—611no—
377#117—611no—
378C2×C42—611no—
379C2×C42—611no—
380C2×C42—611no—
381C4⋊C8—611no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C2×#692311yescharacteristic
401C22⋊C8—611no—
402C22⋊C8—611no—
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C2×#692311yescharacteristic
412C22⋊C8C2×#692311yescharacteristic
413#97—611no—
414#97—611no—
415#97—611no—
416#97—1221no—
417#97—1221no—
418#97C2×#692311yescharacteristic
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429#41—2442no—
430C2×Q8—611no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4C4⋊#692311yescharacteristic
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4C22×#692311yescharacteristic
442C22×C4C22×#692311yescharacteristic
443M16—22no—
444M16—1222no—
445M16—4881no—
446M16—4881no—
447M16—4881no—
448M16—4881no—
449M16—2441no—
450M16—2441no—
451C2×C8—22no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—4881no—
465C2×C8—4881no—
466C2×C8—2441no—
467C2×C8C22×#692311yescharacteristic
468C2×C8C22×#692311yescharacteristic
469C2×C8C22×#692311yescharacteristic
470C2×C8C22×#692311yescharacteristic
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4C4⋊#692311yescharacteristic
477C22⋊C4—611no—
478C22⋊C4—611no—
479C22⋊C4—611no—
480C22⋊C4—611no—
481C22⋊C4C4⋊#692311yescharacteristic
482C22⋊C4C4⋊#692311yescharacteristic
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42C22×#692311yescharacteristic
493C23—611no—
494C23C2×C4⋊#692311yescharacteristic
495C23C2×C4⋊#692311yescharacteristic
496Q8—1222no—
497D4—41no—
498D4—1222no—
499D4—2441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—611no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1222no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4C2×C4⋊#692311yescharacteristic
523C2×C4C2×C4⋊#692311yescharacteristic
524C2×C4C2×C4⋊#692311yescharacteristic
525C2×C4C2×C4⋊#692311yescharacteristic
526C2×C4C23×#692311yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8#1451986412yes—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—1221no—
550C22—1221no—
551C22—1221no—
552C22C22×C4⋊#692311yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—611no—
558C4—611no—
559C4—612no—
560C4—1221no—
561C4—1221no—
562C4—1221no—
563C4—1221no—
564C4—1221no—
565C4C2×#1451986411yescharacteristic
566C4#1684084111yescharacteristic
567C2—41no—
568C2—41no—
569C2—2441no—
570C2#2146246411yescharacteristic
571C2#2146247311yescharacteristic
572C2D61⋊#43011yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#435C4
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758224Q8
cosocleC4×Dic61C24
hypercenter#435#6923
hypocenterC61#17841
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #21461395C2semidirect
4. #21461395C2semidirect
5. #21461391C2semidirect
6. #21461390C2semidirect
7. #21461387C2semidirect
8. #21461386C2semidirect
9. #21461384C2semidirect
10. #21461383C2semidirect
11. #21461373C2semidirect
12. #21461371C2semidirect
13. #21461370C2semidirect
14. #21461366C2semidirect
353. C61#17841semidirect

Maximal subgroups

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

subgroupindex
#214627502
#214627442
#214613952
#214613912
#214613902
#214613872
#214613862
#214613842
#214613832
#214613732
#214613712
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