Finite Group Databasebeta

← #30597631

Subgroups — #30597631

Order 15616.

514 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519841C211yesmaximal, characteristic
2C4×#14519831C211yesmaximal, characteristic, complemented
3#21461111C211yesmaximal, characteristic
4#21461029C211yesmaximal, characteristic, complemented
5#21460650C211yesmaximal, characteristic, complemented
6#21460646C211yesmaximal, characteristic, complemented
7C8×#11758224C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519841C412yes—
10C4×#11758213C2211yescharacteristic
11C2×#14519831—21no—
12C2×#14519831—21no—
13C4×D61⋊C8C2211yescharacteristic
14C42×#6923C2211yescharacteristic
15#16840632C412yes—
16#16840612C412yescomplemented
17D4⋊#92420C412yescomplemented
18#92420⋊C8—21no—
19#16840603—21no—
20C4×#11758224C2211yescharacteristic
21C8×Dic122C411yescharacteristic, complemented
22#16839886C411yescharacteristic, complemented
23D4×#92418C411yescharacteristic, complemented
24C8×C22⋊D61—21no—
25#16839825—21no—
26#16839814C2211yescharacteristic
27#16839812—21no—
28C2×C8×Dic61—21no—
29C4×C8×D61C2211yescharacteristic
30C8×D4×C61C411yescharacteristic, complemented
31C2×#11758213C2×C412yes—
32C2×D61⋊C8—21no—
33C2×C4×#6923—21no—
34C2×C4×#6923—21no—
35C2×C4×#6923C2×C412yes—
36C4⋊#92420C2×C412yes—
37#14519841—24no—
38#14519834—21no—
39#14519832—21no—
40#14519831—24no—
41#14519831—24no—
42C4×#92420—21no—
43C4×#92420—21no—
44C4×#92420—21no—
45C4×#92420C2×C412yes—
46C2×#11758224C2×C411yescharacteristic
47C22×#92418—21no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61D411yescharacteristic
50C4×Dic122C2×C411yescharacteristic
51#14519742C2×C411yescharacteristic
52D4×Dic61C2×C411yescharacteristic
53C4×C22⋊D61—21no—
54#14519737—21no—
55#14519735C2×C411yescharacteristic
56#14519733—21no—
57C2×C4×Dic61—21no—
58C42×D61C2311yescharacteristic
59C4⋊#92418C2×C411yescharacteristic
60#14519706—21no—
61#14519706—21no—
62C22⋊#92418—21no—
63#14519689—21no—
64C4×#92418C2×C411yescharacteristic
65C8×Dic61—21no—
66C8×Dic61—21no—
67C8×Dic61—21no—
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C22×C8×C61—21no—
71C4×D4×C61C2×C411yescharacteristic
72C4⋊C8×C61C2×C411yescharacteristic
73C22⋊C8×C61—21no—
74C4×C8×C61C2×C411yescharacteristic
75C22×#6923—22no—
76C2×D4×C61C4211yescharacteristic
77C22×C4×C61—21no—
78C2×C22⋊D61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81#11758224—22no—
82#11758224M1614yes—
83C2×C4×D61C22×C411yescharacteristic
84C2×C4×D61C2×D411yescharacteristic
85C2×C4×D61#4111yescharacteristic
86C2×Dic122C4211yescharacteristic
87C2×#92420—22no—
88C2×#92420—22no—
89C2×#92420—22no—
90C4×#6923—22no—
91C4×#6923—22no—
92C4×#6923—22no—
93C4×#6923—22no—
94C4×#6923—42no—
95#11758213—22no—
96#11758213—22no—
97D61⋊C8—22no—
98D61⋊C8—22no—
99C2×C8×C61—21no—
100C2×C8×C61—42no—
101C2×C8×C61C22⋊C411yescharacteristic
102C2×C8×C61C22⋊C411yescharacteristic
103C4⋊C4×C61C4211yescharacteristic
104C22⋊C4×C61—21no—
105C42×C61C22×C411yescharacteristic
106C22⋊Dic61—21no—
107#11758198—21no—
108C4⋊Dic61C4211yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61C22×C411yescharacteristic
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61#4111yescharacteristic
117C2×#92418—21no—
118C2×#92418—42no—
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C8×D61—22no—
122C8×D61—22no—
123C23×C61—21no—
124C22×D61C4×D411yescharacteristic
125C2×#6923—24no—
126C2×#6923—42no—
127C2×#6923—42no—
128D4×C61—21no—
129D4×C61#9712yescomplemented
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C4211yescharacteristic
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61#11711yescharacteristic
136C22⋊D61—24no—
137C2×Dic61—21no—
138C2×Dic61—24no—
139C2×Dic61—21no—
140C2×Dic61—42no—
141C2×Dic61C4×D411yescharacteristic
142C2×Dic61C4×D411yescharacteristic
143C2×Dic61C4×D411yescharacteristic
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—22no—
147C4×D61C2×M1612yes—
148C4×D61#13112yes—
149Dic122—21no—
150Dic122#9712yescomplemented
151#92420—24no—
152#92420—42no—
153#92420—42no—
154C8×C61—21no—
155C8×C61—41no—
156C8×C61#10412yescomplemented
157#92418—21no—
158#92418—41no—
159#92418#10412yescomplemented
160#8192—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C4×C22⋊C411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61#43512yes—
168#6923—44no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61C2×#9711yescharacteristic
172C4×C61#40511yescharacteristic
173C4×C61C2×#10411yescharacteristic
174C4×C61C2×#10411yescharacteristic
175Dic61—22no—
176Dic61—21no—
177Dic61—41no—
178Dic61#43512yes—
179Dic61#44412yes—
180C8×#41—611no—
181C4×#104—611no—
182C4×#97—611no—
183#1476—611no—
184#1451—611no—
185#1278—611no—
186#1276—611no—
187C2×C61—42no—
188C2×C61#175211yescharacteristic
189C2×C61C4×#10411yescharacteristic
190C2×C61#176511yescharacteristic
191D61—22no—
192C4×#41—611no—
193C8×Q8—611no—
194C8×Q8—611no—
195C8×D4—611no—
196C8×D4—1221no—
197C8×D4—1221no—
198C8×D4#692311yescharacteristic, complemented
199#431—611no—
200#431—611no—
201#431—1221no—
202C2×#104—612no—
203C4×M16—611no—
204C2×#97—1221no—
205C2×#97—1221no—
206C2×C4×C8—611no—
207C2×C4×C8—611no—
208C2×C4×C8—1221no—
209C43—611no—
210#339—612no—
211Q8⋊C8—612no—
212D4⋊C8—612no—
213#322—1221no—
214#322—1221no—
215C61#819211yescharacteristic, complemented, Sylow
216C2×#41—611no—
217C2×M16—612no—
218C22×C8—21no—
219C22×C8—611no—
220C22×C8—611no—
221C22×C8—1221no—
222C22×C8—1221no—
223C4×Q8—611no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—1221no—
227C4×D4—1221no—
228C4×D4C2×#692311yescharacteristic
229#117—611no—
230#117—1221no—
231C2×C42—611no—
232C2×C42—612no—
233C2×C42—1221no—
234C2×C42—1221no—
235C2×C42—1221no—
236C4⋊C8—612no—
237C4⋊C8—611no—
238C4⋊C8—1221no—
239C4⋊C8—1221no—
240C4⋊C8C2×#692311yescharacteristic
241#104—1224no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244C22⋊C8—1221no—
245C22⋊C8—1221no—
246#97—1221no—
247#97—1224no—
248#97—1224no—
249C4×C8—611no—
250C4×C8—611no—
251C4×C8—612no—
252C4×C8—611no—
253C4×C8—1221no—
254C4×C8—1221no—
255C4×C8—1221no—
256C4×C8—1221no—
257C4×C8—1221no—
258C4×C8—1221no—
259C4×C8C2×#692311yescharacteristic
260#41—614no—
261#41—1222no—
262C2×Q8—611no—
263C2×D4—1221no—
264C2×D4C4×#692311yescharacteristic
265C22×C4—21no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1222no—
272M16—1222no—
273M16—1222no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—611no—
277C2×C8—611no—
278C2×C8—1222no—
279C2×C8—1222no—
280C2×C8—1222no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—1221no—
286C2×C8—2442no—
287C2×C8C22⋊#692311yescharacteristic
288C2×C8C22⋊#692311yescharacteristic
289C4⋊C4—611no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4C4×#692311yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C42—611no—
297C42—611no—
298C42—611no—
299C42—1221no—
300C42—1221no—
301C42—1222no—
302C42—1222no—
303C42—1222no—
304C42—1222no—
305C42—1221no—
306C42—2442no—
307C42C22×#692311yescharacteristic
308C23—21no—
309C23—611no—
310Q8—612no—
311Q8—1221no—
312D4—21no—
313D4—1224no—
314D4#1451983112yescomplemented
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—611no—
323C2×C4—1222no—
324C2×C4—1224no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1224no—
329C2×C4—1221no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4C2×C4×#692311yescharacteristic
334C2×C4C2×C22⋊#692311yescharacteristic
335C2×C4#1451985611yescharacteristic
336C8—21no—
337C8—41no—
338C8—612no—
339C8—1224no—
340C8—1221no—
341C8—2442no—
342C8—2442no—
343C8—2441no—
344C8#1451984112yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—612no—
349C22—1221no—
350C22—1221no—
351C22C4×C22⋊#692311yescharacteristic
352C4—21no—
353C4—41no—
354C4—612no—
355C4—612no—
356C4—1222no—
357C4—1221no—
358C4—2444no—
359C4—2441no—
360C4C2×#1451983111yescharacteristic
361C4#1684072511yescharacteristic
362C4C2×#1451984111yescharacteristic
363C4D61⋊#10411yescharacteristic
364C2—42no—
365C2—1222no—
366C2#2146155511yescharacteristic
367C2C4×#1451984111yescharacteristic
368C2#2146159711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#11758224C2×C4
cosocleC42×D61C23
hypercenterC8×D4#6923
hypocenterC61#8192
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. C4×#14519831C2semidirect
4. #21461029C2semidirect
5. #21460650C2semidirect
6. #21460646C2semidirect
16. #16840612C4semidirect
17. D4⋊#92420C4semidirect
21. C8×Dic122C4semidirect
22. #16839886C4semidirect
23. D4×#92418C4semidirect
30. C8×D4×C61C4semidirect
129. D4×C61#97semidirect
150. Dic122#97semidirect
156. C8×C61#104semidirect
159. #92418#104semidirect
198. C8×D4#6923semidirect
215. C61#8192semidirect
314. D4#14519831semidirect
344. C8#14519841semidirect

Maximal subgroups

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

subgroupindex
C4×#145198412
C4×#145198312
#214611112
#214610292
#214606502
#214606462
C8×#117582242
#819261