Finite Group Databasebeta

← #30612203

Subgroups — #30612203

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462515C211yesmaximal, characteristic
2#21462514C211yesmaximal, characteristic
3#21461397C211yesmaximal, characteristic, complemented
4#21461395C211yesmaximal, characteristic, complemented
5#21461394C211yesmaximal, characteristic, complemented
6#21461393C211yesmaximal, characteristic, complemented
7#21461390C211yesmaximal, characteristic, complemented
8#21461390C211yesmaximal, characteristic, complemented
9#21461384C211yesmaximal, characteristic, complemented
10#21461383C211yesmaximal, characteristic, complemented
11#21461381C211yesmaximal, characteristic, complemented
12#21461371C211yesmaximal, characteristic, complemented
13#21461370C211yesmaximal, characteristic, complemented
14#21461366C211yesmaximal, characteristic, complemented
15#21454779C211yesmaximal, characteristic
16#16840787—21no—
17#16840786—21no—
18#16840786—21no—
19#16840786—21no—
20#16840784C2211yescharacteristic
21#16840783C2211yescharacteristic
22#16840783C2211yescharacteristic
23#16840783C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840778C2211yescharacteristic
26#16840778C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840766C2211yescharacteristic
29#16840765C2211yescharacteristic
30D61⋊(C4⋊C8)C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32#16840736—21no—
33#16840735—21no—
34#16840727—21no—
35#16840726—21no—
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840625C2211yescharacteristic
39#16840625C2211yescharacteristic
40#16840625C2211yescharacteristic
41#16840625C2211yescharacteristic
42#16840625C2211yescharacteristic
43#16840625C2211yescharacteristic
44#16840624C2211yescharacteristic
45#16840624C2211yescharacteristic
46#16840624C2211yescharacteristic
47#16840624C2211yescharacteristic
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×D61⋊C8—21no—
70C22×#92420—21no—
71#14519844—21no—
72#14519844—21no—
73C4⋊#92420—21no—
74C4⋊#92420—21no—
75C4⋊#92420C2311yescharacteristic
76C4⋊#92420C2311yescharacteristic
77C4⋊#92420C2311yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83#14519834—21no—
84#14519834—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420—21no—
99C2×#11758224D411yescharacteristic
100C2×#11758194C2×C411yescharacteristic
101C2×#11758189C2×C411yescharacteristic
102C2×#11758189C2×C411yescharacteristic
103C22×#92418C2×C411yescharacteristic
104C4×Dic122C2×C411yescharacteristic
105#14519742Q811yescharacteristic
106D4×Dic61Q811yescharacteristic
107C4×C22⋊D61C2×C411yescharacteristic
108C4×C22⋊D61C2×C411yescharacteristic
109#14519737Q811yescharacteristic
110#14519737Q811yescharacteristic
111#14519735D411yescharacteristic
112#14519733D411yescharacteristic
113#14519733D411yescharacteristic
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—41no—
152#11758224—41no—
153C2×C4×D61C22×C411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×Q811yescharacteristic
156C2×Dic122C4⋊C411yescharacteristic
157#11758217—42no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—42no—
167#11758213—42no—
168D61⋊C8—42no—
169M16×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C2×C8×C61C22×C411yescharacteristic
174C2×C8×C61C22×C411yescharacteristic
175C4⋊C4×C61C4⋊C411yescharacteristic
176C22⋊C4×C61C4⋊C411yescharacteristic
177C22⋊C4×C61C4⋊C411yescharacteristic
178C42×C61C22×C411yescharacteristic
179C22⋊Dic61C4⋊C411yescharacteristic
180C22⋊Dic61C4⋊C411yescharacteristic
181#11758198C4⋊C411yescharacteristic
182#11758198C4⋊C411yescharacteristic
183C4⋊Dic61C4⋊C411yescharacteristic
184#11758196C4⋊C411yescharacteristic
185#11758196C4⋊C411yescharacteristic
186#11758196C4⋊C411yescharacteristic
187#11758196C4⋊C411yescharacteristic
188C4×Dic61C22×C411yescharacteristic
189C4×Dic61C22×C411yescharacteristic
190C4×Dic61C2×D411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×Q811yescharacteristic
194C4×Dic61C2×Q811yescharacteristic
195C4×Dic61C2×Q811yescharacteristic
196C4×Dic61C2411yescharacteristic
197#11758194—41no—
198C2×#92418—41no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203#11758189—22no—
204#11758189—41no—
205C23×C61C2×C4⋊C411yescharacteristic
206C23×C61C2×C4⋊C411yescharacteristic
207C22×D61C2×C4⋊C411yescharacteristic
208D4×C61—41no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61C2×C4⋊C411yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C2×C4⋊C411yescharacteristic
216C2×C4×C61C2×C4⋊C411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C22⋊D61—41no—
219C22⋊D61—41no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61C2×C4⋊C411yescharacteristic
227C2×Dic61C2×C4⋊C411yescharacteristic
228C2×Dic61C2×C4⋊C411yescharacteristic
229C2×Dic61C2×C4⋊C411yescharacteristic
230C2×Dic61C2×C4⋊C411yescharacteristic
231C2×Dic61C22×D411yescharacteristic
232C2×Dic61C22×Q811yescharacteristic
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—41no—
238Dic122—41no—
239#92420—41no—
240#92420—41no—
241#92420—41no—
242#92420—41no—
243#92420—41no—
244#92420—41no—
245#92420—41no—
246#92420—41no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61#13112yes—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#17831—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61C22×C4⋊C411yescharacteristic
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61C2×#13111yescharacteristic
271C4×C61#56811yescharacteristic
272Dic61—21no—
273Dic61—21no—
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61#57511yescharacteristic
279Dic61#57511yescharacteristic
280#2965—611no—
281#2925—611no—
282#2925—611no—
283#1574—611no—
284#1574—611no—
285#1573—611no—
286#1573—611no—
287#1572—611no—
288#1572—611no—
289#1569—611no—
290#1569—611no—
291#1568—611no—
292#1565—611no—
293#1565—611no—
294#1564—611no—
295C2×C61—41no—
296C2×C61—41no—
297C2×C61#290611yescharacteristic
298C2×C61#291111yescharacteristic
299C2×C61#291611yescharacteristic
300D61—41no—
301C4×#41—611no—
302#446—611no—
303#446—611no—
304#436—611no—
305#436—611no—
306#435—611no—
307#435—611no—
308#435—611no—
309#435#692311yescharacteristic
310#433—1221no—
311#433—1221no—
312#433—1221no—
313#433—1221no—
314#432—611no—
315#432—611no—
316#432—611no—
317#432—611no—
318#431—611no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431—611no—
324#431—611no—
325#423—611no—
326#423—611no—
327C2×C4⋊C8—611no—
328C2×C4⋊C8—611no—
329#408—1221no—
330#408—1221no—
331#405—1221no—
332#405—1221no—
333C4×M16—611no—
334C4×M16—611no—
335C2×C4×C8—611no—
336#335—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—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—
352C61#1783111yescharacteristic, complemented, Sylow
353C2×#41—611no—
354C2×M16—611no—
355C2×M16—611no—
356C2×M16—611no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16C2×#692311yescharacteristic
360C22×C8—611no—
361C22×C8—1221no—
362C22×C8—1221no—
363C22×C8C2×#692311yescharacteristic
364C4×Q8—611no—
365C4×Q8—611no—
366C4×D4—611no—
367C4×D4—611no—
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—611no—
371C4×D4C2×#692311yescharacteristic
372#117—611no—
373#117—611no—
374#117—611no—
375C2×C42—611no—
376C2×C42—611no—
377C2×C42—611no—
378C4⋊C8—611no—
379C4⋊C8—611no—
380C4⋊C8—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—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C2×#692311yescharacteristic
396C22⋊C8—611no—
397C22⋊C8—611no—
398C22⋊C8—611no—
399C22⋊C8—611no—
400C22⋊C8—1221no—
401C22⋊C8—1221no—
402C22⋊C8—1221no—
403C22⋊C8—1221no—
404C22⋊C8—1221no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8C2×#692311yescharacteristic
409C22⋊C8C2×#692311yescharacteristic
410#97—611no—
411#97—611no—
412#97—611no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417#97C2×#692311yescharacteristic
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428#41—2441no—
429#41—2441no—
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—2441no—
446M16—2441no—
447M16—2442no—
448M16—2442no—
449C2×C8—22no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—2441no—
463C2×C8—2442no—
464C2×C8—2442no—
465C2×C8C22×#692311yescharacteristic
466C2×C8C22×#692311yescharacteristic
467C2×C8C22×#692311yescharacteristic
468C2×C8C22×#692311yescharacteristic
469C4⋊C4—611no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4C4⋊#692311yescharacteristic
475C22⋊C4—611no—
476C22⋊C4—611no—
477C22⋊C4—611no—
478C22⋊C4—611no—
479C22⋊C4C4⋊#692311yescharacteristic
480C22⋊C4C4⋊#692311yescharacteristic
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42C22×#692311yescharacteristic
491C23—611no—
492C23C2×C4⋊#692311yescharacteristic
493C23C2×C4⋊#692311yescharacteristic
494Q8—2441no—
495D4—41no—
496D4—2441no—
497D4—2441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—611no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4C2×C4⋊#692311yescharacteristic
521C2×C4C2×C4⋊#692311yescharacteristic
522C2×C4C2×C4⋊#692311yescharacteristic
523C2×C4C2×C4⋊#692311yescharacteristic
524C2×C4C23×#692311yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8#1451986412yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—1221no—
548C22—1221no—
549C22—1221no—
550C22C22×C4⋊#692311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—611no—
556C4—611no—
557C4—1221no—
558C4—1221no—
559C4—1221no—
560C4—1221no—
561C4—1221no—
562C4—1221no—
563C4C2×#1451986411yescharacteristic
564C4#1684084111yescharacteristic
565C2—41no—
566C2—41no—
567C2—2441no—
568C2#2146246411yescharacteristic
569C2#2146247211yescharacteristic
570C2#2146248111yescharacteristic
subgroupG/H
centerC22C22×C4⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#435C4
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758224D4
cosocleC4×Dic61C24
hypercenter#435#6923
hypocenterC61#17831
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. #21461397C2semidirect
4. #21461395C2semidirect
5. #21461394C2semidirect
6. #21461393C2semidirect
7. #21461390C2semidirect
8. #21461390C2semidirect
9. #21461384C2semidirect
10. #21461383C2semidirect
11. #21461381C2semidirect
12. #21461371C2semidirect
13. #21461370C2semidirect
14. #21461366C2semidirect
352. C61#17831semidirect

Maximal subgroups

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

subgroupindex
#214625152
#214625142
#214613972
#214613952
#214613942
#214613932
#214613902
#214613842
#214613832
#214613812
#214613712
#214613702
#214613662
#214547792
#1783161