Finite Group Databasebeta

← #30612498

Subgroups — #30612498

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462742C211yesmaximal, characteristic, complemented
2#21462735C211yesmaximal, characteristic, complemented
3#21461443C212yesmaximal, complemented
4#21461440C212yesmaximal, complemented
5#21461429C212yesmaximal, complemented
6#21461422C212yesmaximal, complemented
7D61⋊#334C211yesmaximal, characteristic, complemented
8#21461115C211yesmaximal, characteristic, complemented
9#21461115C211yesmaximal, characteristic, complemented
10#21461033C211yesmaximal, characteristic, complemented
11C4×#14519796C211yesmaximal, characteristic
12#16840812C2212yes—
13#16840811C2212yes—
14#16840797C2212yes—
15#16840794—22no—
16#16840789—22no—
17D4×#92420C2212yes—
18#16840782—21no—
19#16840780C2211yescharacteristic
20#16840780C2211yescharacteristic
21#16840779—21no—
22#16840765—21no—
23C2×#14519844—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25D61⋊(C4⋊C8)C2211yescharacteristic
26#16840624C2212yes—
27#16840623C2212yes—
28#16840612C2212yes—
29#16840612C2212yes—
30D4⋊#92420C2212yes—
31D4⋊#92420C2212yes—
32#92420⋊C8C2212yes—
33#92420⋊C8C2212yes—
34C2×#14519796C411yescharacteristic
35C4×#11758224C2211yescharacteristic
36C4×#11758224C2211yescharacteristic
37C4×Dic244C411yescharacteristic
38#16839856C2211yescharacteristic
39#16839853C2211yescharacteristic
40#16839853C2211yescharacteristic
41C4×#11758200C411yescharacteristic
42C4×#11758200C411yescharacteristic
43D8×Dic61C2211yescharacteristic
44#16839799C411yescharacteristic
45#16839755C411yescharacteristic
46#16839755C411yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×D8×C61C411yescharacteristic
49C2×#11758217—22no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8—21no—
52C22×#92420—22no—
53#14519844—22no—
54#14519844—21no—
55#14519844—21no—
56#14519844—21no—
57#14519844D411yescharacteristic
58#14519844D411yescharacteristic
59C4⋊#92420—22no—
60C4⋊#92420C2312yes—
61C4⋊#92420C2312yes—
62#14519834—21no—
63#14519834D412yes—
64C22⋊#92420—22no—
65C22⋊#92420—22no—
66#14519832—22no—
67C4×#92420—22no—
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C2×#11758224C2×C411yescharacteristic
71C2×#11758224C2×C411yescharacteristic
72#14519796—24no—
73C2×Dic244C2×C411yescharacteristic
74C2×#11758200C2×C411yescharacteristic
75C2×#11758200C2×C411yescharacteristic
76C2×C8×D61C2×C411yescharacteristic
77C2×C8×D61C2×C411yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122C2×C411yescharacteristic
80#14519742C2311yescharacteristic
81#14519742C2311yescharacteristic
82D4×Dic61C2311yescharacteristic
83D4×Dic61C2311yescharacteristic
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86#14519737—21no—
87#14519737—21no—
88#14519735C2×C411yescharacteristic
89#14519735C2×C411yescharacteristic
90#14519733—21no—
91#14519733—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519708C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519702C2×C411yescharacteristic
99#14519702C2×C411yescharacteristic
100#14519700C2×C411yescharacteristic
101#14519700C2×C411yescharacteristic
102#14519698C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104C4×#92418C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C2×D8×C61C2×C411yescharacteristic
108C4×D4×C61C2×C411yescharacteristic
109C4×D4×C61C2×C411yescharacteristic
110#107×C61C2×C411yescharacteristic
111#102×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113C4×C8×C61C2×C411yescharacteristic
114C2×D4×C61C22×C411yescharacteristic
115C2×D4×C61C22×C411yescharacteristic
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C2×C22⋊D61—21no—
119C2×C22⋊D61—21no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124#11758224—22no—
125#11758224—22no—
126#11758224—22no—
127#11758224M1614yescomplemented
128C2×C4×D61C22×C411yescharacteristic
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61#4111yescharacteristic
131C2×Dic122C22×C411yescharacteristic
132C2×Dic122C22×C411yescharacteristic
133#11758217—82no—
134C2×#92420—22no—
135C2×#92420—22no—
136C2×#92420—22no—
137C2×#92420—82no—
138C2×#92420C2×D412yes—
139C2×#92420C2×D412yes—
140D61⋊C8—81no—
141D61⋊C8—81no—
142D8×C61—22no—
143C2×C8×C61C22×C411yescharacteristic
144C2×C8×C61C22×C411yescharacteristic
145C4⋊C4×C61C22×C411yescharacteristic
146C4⋊C4×C61C22×C411yescharacteristic
147C22⋊C4×C61—21no—
148C22⋊C4×C61—21no—
149C42×C61C22×C411yescharacteristic
150C22⋊Dic61—21no—
151C22⋊Dic61—21no—
152#11758200—22no—
153#11758200—22no—
154#11758198—21no—
155#11758198—21no—
156C4⋊Dic61C22×C411yescharacteristic
157C4⋊Dic61C22×C411yescharacteristic
158#11758196—21no—
159#11758196—21no—
160#11758196—21no—
161#11758196—21no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61C2×D411yescharacteristic
169C4×Dic61#4111yescharacteristic
170C4×Dic61C2411yescharacteristic
171C2×#92418C22×C411yescharacteristic
172C2×#92418C22×C411yescharacteristic
173Dic244—22no—
174C8×D61—22no—
175C8×D61—22no—
176C23×C61—21no—
177C23×C61—21no—
178C22×D61C4×D411yescharacteristic
179D4×C61—21no—
180D4×C61—21no—
181D4×C61—21no—
182D4×C61C2×M1612yes—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—81no—
186C2×C4×C61—81no—
187C2×C4×C61C4×D411yescharacteristic
188C2×C4×C61C4×D411yescharacteristic
189C2×C4×C61C23×C411yescharacteristic
190C22⋊D61—24no—
191C22⋊D61—42no—
192C2×Dic61—21no—
193C2×Dic61—24no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61C4×D411yescharacteristic
203C2×Dic61C22×D411yescharacteristic
204C2×Dic61C2×#4111yescharacteristic
205C4×D61—21no—
206C4×D61—21no—
207C4×D61—41no—
208C4×D61C2×M1612yes—
209C4×D61#13112yes—
210Dic122—21no—
211Dic122—21no—
212Dic122—21no—
213Dic122C2×M1612yes—
214#92420—22no—
215#92420—22no—
216#92420—42no—
217#92420—42no—
218#92420—42no—
219C8×C61—21no—
220C8×C61—21no—
221#92418—21no—
222#92418—21no—
223#17882—611nomaximal, Sylow
224C22×C61—22no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61C2×C4×D411yescharacteristic
231C2×D61—21no—
232C2×D61—21no—
233C2×D61#43512yes—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61C22×M1611yescharacteristic
239C4×C61C2×#13111yescharacteristic
240Dic61—22no—
241Dic61—21no—
242Dic61—41no—
243Dic61—41no—
244Dic61—41no—
245Dic61#43512yes—
246Dic61#57711yescharacteristic
247Dic61#57711yescharacteristic
248#2989—611no—
249#2988—611no—
250C4×#135—611no—
251#1587—612no—
252#1586—612no—
253#1583—612no—
254#1582—612no—
255C2×#334—611no—
256#1477—611no—
257#1477—611no—
258#1452—611no—
259C2×C61—42no—
260C2×C61—81no—
261C2×C61C2×#43511yescharacteristic
262C2×C61#295211yescharacteristic
263C2×C61#295711yescharacteristic
264D61—22no—
265C2×#135—611no—
266C4×#41—611no—
267C4×#41—611no—
268#446—612no—
269C8×Q8—612no—
270C4×Q16—611no—
271C4×Q16—611no—
272C4×SD16—611no—
273C4×SD16—611no—
274C4×SD16—611no—
275C4×SD16—611no—
276C4×D8—611no—
277C4×D8#692311yescharacteristic
278#436—612no—
279#435—1222no—
280C8×D4—612no—
281C8×D4—1222no—
282#432—1221no—
283#431—611no—
284#431—611no—
285#431—1221no—
286#427—611no—
287#423—1221no—
288C2×C4⋊C8—611no—
289C2×C4⋊C8—611no—
290C2×C4⋊C8—1221no—
291#416—611no—
292#416—611no—
293C2×C4×C8—611no—
294#334—612no—
295#334—612no—
296Q8⋊C8—612no—
297Q8⋊C8—612no—
298D4⋊C8—612no—
299D4⋊C8—612no—
300#322—612no—
301#322—612no—
302C61#1788211yescharacteristic, complemented, Sylow
303C2×#41—611no—
304C2×#41—611no—
305#135—1224no—
306C2×Q16—611no—
307C2×SD16—611no—
308C2×SD16—611no—
309C2×D8C2×#692311yescharacteristic
310C2×M16—1222no—
311C22×C8—611no—
312C22×C8—611no—
313C22×C8—1222no—
314C22×C8—1221no—
315C22×C8—1221no—
316C4×Q8—611no—
317C4×Q8—611no—
318C4×Q8—611no—
319C4×Q8—611no—
320C4×D4—611no—
321C4×D4—611no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—1221no—
326C4×D4C2×#692311yescharacteristic
327C4×D4C2×#692311yescharacteristic
328#117—611no—
329#117—611no—
330#117—1221no—
331#117—1221no—
332C2×C42—611no—
333C2×C42—1221no—
334C2×C42—1221no—
335#107—611no—
336#107C2×#692311yescharacteristic
337#106—611no—
338#106—611no—
339C4⋊C8—611no—
340C4⋊C8—611no—
341C4⋊C8—612no—
342C4⋊C8—612no—
343C4⋊C8—1221no—
344C4⋊C8—1221no—
345C4⋊C8—1221no—
346C4⋊C8—1222no—
347C4⋊C8—1222no—
348#103—611no—
349#103—611no—
350#103—611no—
351#103—611no—
352#102—611no—
353#102—611no—
354#102C2×#692311yescharacteristic
355#102C2×#692311yescharacteristic
356C22⋊C8—612no—
357C22⋊C8—1222no—
358C22⋊C8—1222no—
359C22⋊C8—1221no—
360#97—1222no—
361C4×C8—612no—
362C4×C8—611no—
363C4×C8—611no—
364C4×C8—612no—
365C4×C8—611no—
366C4×C8—1222no—
367C4×C8C2×#692311yescharacteristic
368#41—614no—
369#41—1222no—
370#41—1222no—
371#41—1222no—
372C2×Q8—611no—
373C2×Q8—611no—
374C2×D4—1221no—
375C2×D4—1221no—
376C2×D4C22×#692311yescharacteristic
377C2×D4C22×#692311yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387Q16—1222no—
388SD16—1222no—
389SD16—1222no—
390D8—22no—
391M16—4882no—
392C2×C8—612no—
393C2×C8—612no—
394C2×C8—611no—
395C2×C8—611no—
396C2×C8—1222no—
397C2×C8—1222no—
398C2×C8—1222no—
399C2×C8—1222no—
400C2×C8—1222no—
401C2×C8—4882no—
402C2×C8—4881no—
403C2×C8—4881no—
404C2×C8C22×#692311yescharacteristic
405C2×C8C22×#692311yescharacteristic
406C4⋊C4—611no—
407C4⋊C4—611no—
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4C22×#692311yescharacteristic
413C4⋊C4C22×#692311yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—1221no—
417C22⋊C4—1221no—
418C22⋊C4—1221no—
419C22⋊C4—1221no—
420C42—611no—
421C42—611no—
422C42—611no—
423C42—1221no—
424C42—1221no—
425C42—1221no—
426C42—1221no—
427C42—1221no—
428C42—1221no—
429C42C22×#692311yescharacteristic
430C23—21no—
431C23—21no—
432C23—611no—
433Q8—612no—
434Q8—1221no—
435Q8—1221no—
436Q8—1221no—
437D4—21no—
438D4—21no—
439D4—21no—
440D4—1224no—
441D4—2442no—
442D4D61⋊M1612yes—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—611no—
448C2×C4—611no—
449C2×C4—612no—
450C2×C4—612no—
451C2×C4—611no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1224no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4D4×#692311yescharacteristic
466C2×C4D4×#692311yescharacteristic
467C2×C4C23×#692311yescharacteristic
468C8—21no—
469C8—21no—
470C8—1222no—
471C8—1222no—
472C8—1221no—
473C8—1221no—
474C8—2442no—
475C8—2442no—
476C8—2442no—
477C22—22no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—612no—
484C22—1221no—
485C22—1221no—
486C22C2×D4×#692311yescharacteristic
487C4—21no—
488C4—21no—
489C4—41no—
490C4—41no—
491C4—611no—
492C4—611no—
493C4—612no—
494C4—1221no—
495C4—1222no—
496C4—2441no—
497C4—2441no—
498C4—2441no—
499C4C2×D61⋊M1611yescharacteristic
500C4D61⋊#13111yescharacteristic
501C2—42no—
502C2—81no—
503C2—1222no—
504C2D61⋊#43511yescharacteristic
505C2#2146258211yescharacteristic
506C2#2146259511yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×D8×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519796C4
cosocleC4×Dic61C24
hypercenterC4×D8#6923
hypocenterC61#17882
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462742C2semidirect
2. #21462735C2semidirect
3. #21461443C2semidirect
4. #21461440C2semidirect
5. #21461429C2semidirect
6. #21461422C2semidirect
7. D61⋊#334C2semidirect
8. #21461115C2semidirect
9. #21461115C2semidirect
10. #21461033C2semidirect
127. #11758224M16semidirect
302. C61#17882semidirect

Maximal subgroups

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

subgroupindex
#214627422
#214627352
#214614432
#214614402
#214614292
#214614222
D61⋊#3342
#214611152
#214610332
C4×#145197962
#1788261