Finite Group Databasebeta

← #30595383

Subgroups — #30595383

Order 15616.

668 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460639C214yesmaximal, complemented
4C2×#16839669C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C22×C4⋊Dic61C411yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13#16839669—21no—
14#16839669—21no—
15#16839669C412yes—
16#16839669C2212yes—
17C2×#14519684—21no—
18C2×#14519684—21no—
19C23×Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—42no—
23C22⋊#92420—24no—
24C22⋊#92420—42no—
25C4×#92420—42no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—42no—
31C2×C4⋊Dic61C2×C412yes—
32C2×C4×Dic61—42no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61C2311yescharacteristic
37#14519684—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41C22×Q8×C61—21no—
42C22×Q8×C61—22no—
43C22×Q8×C61—42no—
44C22×Q8×C61—42no—
45C22×Q8×C61C814yescomplemented
46C22×Q8×C61C2×C412yes—
47C23×C4×C61—21no—
48C23×C4×C61C2×C411yescharacteristic
49C24×C61C22⋊C411yescharacteristic
50C2×Q8×C61—24no—
51C2×Q8×C61—22no—
52C2×Q8×C61—48no—
53C2×Q8×C61—48no—
54C2×Q8×C61—42no—
55C2×Q8×C61—42no—
56C2×Q8×C61—42no—
57C2×Q8×C61—42no—
58C2×Q8×C61C2×C814yes—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—24no—
62C22×C4×C61—22no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C2×C812yes—
67C22×C4×C61M1612yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61SD1612yes—
81C22×Dic61Q1612yes—
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊Dic61—42no—
91C4⋊Dic61—42no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61C22⋊C812yes—
101C23×C61#10312yes—
102C23×C61#10412yes—
103C23×C61C2×C22⋊C411yescharacteristic
104Q8×C61—44no—
105Q8×C61—44no—
106Q8×C61—48no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—24no—
110C2×C4×C61—24no—
111C2×C4×C61—24no—
112C2×C4×C61—48no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61C22⋊C812yes—
116C2×C4×C61#9912yes—
117C2×C4×C61#10012yes—
118C2×C4×C61C22×C811yescharacteristic
119C2×C4×C61C2×M1611yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—44no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—84no—
136C2×Dic61#10312yes—
137C2×Dic61C2×SD1611yescharacteristic
138C2×Dic61C2×Q1611yescharacteristic
139C2×Dic61#13712yes—
140#92420—44no—
141#92420—82no—
142#7575—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61Q8⋊C814yes—
150C22×C61C2×C22⋊C811yescharacteristic
151C22×C61C2×#9911yescharacteristic
152C22×C61C2×#10011yescharacteristic
153C22×C61C2×#10311yescharacteristic
154C22×C61#41911yescharacteristic
155C22×C61C2×#10411yescharacteristic
156C22×C61#42111yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—44no—
160C4×C61#32314yes—
161Dic61—22no—
162Dic61—21no—
163Dic61—22no—
164Dic61—21no—
165Dic61—41no—
166Dic61—82no—
167C2×#391—611no—
168#1797—611no—
169C4×C22⋊C8—611no—
170#1272—614no—
171C2×C61—24no—
172C2×C61C2×#32311yescharacteristic
173C2×C61C2×Q8⋊C811yescharacteristic
174C2×C61#147911yescharacteristic
175C2×C61#150811yescharacteristic
176C2×C61#152011yescharacteristic
177C2×C61#152711yescharacteristic
178C2×C61#154811yescharacteristic
179C23×Q8#692311yescharacteristic
180C22×C4⋊C4—611no—
181C22×C42—611no—
182C2×C4⋊C8—1221no—
183C2×C22⋊C8—1221no—
184C2×C22⋊C8—1221no—
185C2×C4×C8—1221no—
186#391—612no—
187#391—612no—
188#391—1221no—
189#391—1221no—
190C2×#95—1221no—
191C2×#95—1221no—
192#336—612no—
193#336—612no—
194C61#757511yescharacteristic, complemented, Sylow
195C22×Q8—22no—
196C22×Q8—21no—
197C22×Q8—42no—
198C22×Q8—42no—
199C22×Q8#9242014yescomplemented
200C22×Q8C2×#692312yes—
201C23×C4—21no—
202C23×C4—611no—
203C23×C4—611no—
204C23×C4—1221no—
205C23×C4C2×#692311yescharacteristic
206C22×C8—1222no—
207C22×C8—1222no—
208C2×C4⋊C4—612no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—2442no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—2442no—
216C4⋊C8—2442no—
217C22⋊C8—1224no—
218C22⋊C8—2442no—
219C4×C8—2442no—
220#95—1222no—
221#95—1222no—
222#95—1222no—
223#95—1222no—
224C24C22⋊#692311yescharacteristic
225C2×Q8—24no—
226C2×Q8—22no—
227C2×Q8—48no—
228C2×Q8—48no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8C2×#9242014yes—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—611no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—2441no—
250C22×C4—2441no—
251C22×C4—2441no—
252C22×C4—2442no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4C2×#9242012yes—
256C22×C4#1175821712yes—
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259C2×C8—1224no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C42—1222no—
268C42—1222no—
269C42—2441no—
270C42—2441no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23C22⋊#9242012yes—
276C23#1451984012yes—
277C23#1451984212yes—
278C23C2×C22⋊#692311yescharacteristic
279Q8—44no—
280Q8—44no—
281Q8—48no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—48no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—612no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—612no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—4884no—
304C2×C4—2442no—
305C2×C4—2442no—
306C2×C4—2444no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4C22⋊#9242012yes—
311C2×C4#1451983512yes—
312C2×C4#1451983712yes—
313C2×C4C22×#9242011yescharacteristic
314C2×C4C2×#1175821711yescharacteristic
315C8—4882no—
316C8—2444no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22Q8⋊#9242014yes—
324C22C2×C22⋊#9242011yescharacteristic
325C22C2×#1451983511yescharacteristic
326C22C2×#1451983711yescharacteristic
327C22C2×#1451984011yescharacteristic
328C22#1684075511yescharacteristic
329C22C2×#1451984211yescharacteristic
330C22#1684076111yescharacteristic
331C4—21no—
332C4—21no—
333C4—44no—
334C4—1221no—
335C4—1222no—
336C4—1221no—
337C4—1222no—
338C4—4882no—
339C4—2441no—
340C4#1684060514yes—
341C2—24no—
342C2C2×#1684060511yescharacteristic
343C2C2×Q8⋊#9242011yescharacteristic
344C2#2146112111yescharacteristic
345C2#2146121911yescharacteristic
346C2#2146125911yescharacteristic
347C2#2146128011yescharacteristic
348C2#2146133211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC23×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC23×Q8#6923
hypocenterC61#7575
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
3. #21460639C2semidirect
45. C22×Q8×C61C8semidirect
194. C61#7575semidirect
199. C22×Q8#92420semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606392
C2×#168396692
#757561