Finite Group Databasebeta

← #30604479

Subgroups — #30604479

Order 15616.

360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462183C211yesmaximal, characteristic, complemented
2C4×#14519852C211yesmaximal, characteristic, complemented
3Q8⋊#11758187C212yesmaximal, complemented
4#21460770C212yesmaximal, complemented
5C8×#11758226C211yesmaximal, characteristic
6C2×#14519852—21no—
7C4⋊#11758187C2212yes—
8#16840657—21no—
9#16840651—21no—
10#16840651—21no—
11C4×#11758187C2212yes—
12C4×#11758226C411yescharacteristic
13Q8×#92418C2211yescharacteristic
14C8×D244—21no—
15C8×D244C411yescharacteristic
16#16839827—21no—
17#16839827C2211yescharacteristic
18#16839814—21no—
19#16839814C411yescharacteristic
20C4×C8×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C8×Q8×C61C411yescharacteristic
23#14519852—24no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758226C811yescharacteristic
27C2×C8×D61—21no—
28C2×C8×D61—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31Q8×Dic61C811yescharacteristic
32C4×D244—21no—
33C4×D244C2×C411yescharacteristic
34#14519739—21no—
35#14519739C811yescharacteristic
36#14519735—21no—
37#14519735C811yescharacteristic
38C42×D61—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519689—21no—
43#14519689—21no—
44#14519689—21no—
45C4×#92418—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C4×Q8×C61C2×C411yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61C2×C411yescharacteristic
53C4×C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61C2×C811yescharacteristic
56#11758226—22no—
57#11758226—22no—
58C2×D244—21no—
59C2×D244C2×C811yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61C22⋊C411yescharacteristic
64C2×C4×D61C2×C811yescharacteristic
65C2×C4×D61M1611yescharacteristic
66C2×C8×C61—21no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22⋊C411yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61C2×C811yescharacteristic
71C42×C61—21no—
72C42×C61C22×C411yescharacteristic
73#11758198—21no—
74#11758198—21no—
75#11758198—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2×C811yescharacteristic
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61C2×C811yescharacteristic
82C4×Dic61M1611yescharacteristic
83C2×#92418—21no—
84C2×#92418C2×D411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86C8×D61—22no—
87C8×D61—22no—
88C8×D61—42no—
89C8×D61—42no—
90#11758187—24no—
91#11758187—42no—
92C22×D61—21no—
93C22×D61C22⋊C811yescharacteristic
94Q8×C61—21no—
95Q8×C61M3212yescomplemented
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61C22×C811yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C2×Dic61—21no—
102C2×Dic61C22⋊C811yescharacteristic
103C2×Dic61C22⋊C811yescharacteristic
104C2×Dic61C22⋊C811yescharacteristic
105D244—24no—
106D244—21no—
107D244M3212yescomplemented
108C4×D61—24no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—41no—
114C4×D61—42no—
115C4×D61—41no—
116C4×D61—41no—
117C8×C61—21no—
118C8×C61—41no—
119C8×C61#10412yes—
120#92418—21no—
121#92418—41no—
122#92418#13512yes—
123#11615—611nomaximal, Sylow
124C22×C61C2×C22⋊C811yescharacteristic
125C2×D61—21no—
126C2×D61—22no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—41no—
130C2×D61—41no—
131C4×C61—22no—
132C4×C61—21no—
133C4×C61—41no—
134C4×C61#41611yescharacteristic
135C4×C61C2×#10411yescharacteristic
136C4×C61C2×M3211yescharacteristic
137C4×C61C2×M3211yescharacteristic
138Dic61—21no—
139Dic61—21no—
140Dic61—21no—
141Dic61—41no—
142C8×#41—611no—
143#2163—611no—
144C4×M32—611no—
145Q8⋊C16—612no—
146D4⋊C16—612no—
147C2×C61#147611yescharacteristic
148C2×C61#211211yescharacteristic
149C2×C61#211711yescharacteristic
150D61—41no—
151D61—42no—
152C4×#41—611no—
153C2×M32—1221no—
154C8×Q8—611no—
155C8×Q8#692311yescharacteristic
156C8×D4—611no—
157C8×D4—611no—
158C8×D4—1221no—
159C8×D4—1221no—
160#431—611no—
161#431—1221no—
162C2×C4×C8—611no—
163C2×C4×C8—1221no—
164C4⋊C16—612no—
165C22⋊C16—1221no—
166#346—1221no—
167#346—1221no—
168C4×C16—612no—
169C61#1161511yescharacteristic, complemented, Sylow
170C2×#41—611no—
171C22×C8—611no—
172C22×C8—611no—
173C22×C8—1221no—
174C22×C8—1221no—
175C4×Q8—611no—
176C4×Q8C2×#692311yescharacteristic
177C4×D4—611no—
178C4×D4—611no—
179C4×D4—1221no—
180C4×D4—1221no—
181#117—611no—
182#117—1221no—
183C2×C42—611no—
184C2×C42—1221no—
185M32—1224no—
186C2×C16—1222no—
187C2×C16—1222no—
188C4⋊C8—21no—
189C4⋊C8—611no—
190C4⋊C8—1221no—
191C4⋊C8C2×#692311yescharacteristic
192C22⋊C8—1221no—
193C22⋊C8—1221no—
194C22⋊C8—1221no—
195C4×C8—21no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—611no—
199C4×C8—1221no—
200C4×C8—1221no—
201C4×C8C2×#692311yescharacteristic
202#41—1222no—
203#41—1222no—
204C2×Q8D61⋊C811yescharacteristic
205C2×D4—611no—
206C2×D4—1221no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C2×C8—21no—
214C2×C8—611no—
215C2×C8—611no—
216C2×C8—1222no—
217C2×C8—1222no—
218C2×C8—1221no—
219C2×C8—2442no—
220C2×C8—2442no—
221C2×C8C22⋊#692311yescharacteristic
222C2×C8C22⋊#692311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4D61⋊C811yescharacteristic
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C22⋊C4—1221no—
230C42—21no—
231C42—611no—
232C42—611no—
233C42—611no—
234C42—1221no—
235C42—1221no—
236C42C22×#692311yescharacteristic
237C16—1224no—
238C16—2442no—
239C23—611no—
240C23—1221no—
241Q8—21no—
242Q8#1451985212yescomplemented
243D4—612no—
244D4—1224no—
245D4—1221no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—1224no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—2441no—
258C2×C4—2442no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4C2×C22⋊#692311yescharacteristic
262C2×C4C2×D61⋊C811yescharacteristic
263C2×C4D61⋊M1611yescharacteristic
264C8—21no—
265C8—41no—
266C8—612no—
267C8—1221no—
268C8—2441no—
269C8#1451984212yes—
270C22—1222no—
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22—2441no—
275C22—2441no—
276C22D61⋊(C22⋊C8)11yescharacteristic
277C4—22no—
278C4—21no—
279C4—41no—
280C4—1221no—
281C4—1221no—
282C4—1221no—
283C4—2441no—
284C4#1684075211yescharacteristic
285C4C2×#1451984211yescharacteristic
286C4D61⋊M3211yescharacteristic
287C4C2×#1451985211yescharacteristic
288C2—2441no—
289C2—2442no—
290C2#2146111311yescharacteristic
291C2#2146204711yescharacteristic
292C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC8×Q8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758226C8
cosocleC4×#92418C23
hypercenterC8×Q8#6923
hypocenterC61#11615
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
1. #21462183C2semidirect
2. C4×#14519852C2semidirect
3. Q8⋊#11758187C2semidirect
4. #21460770C2semidirect
95. Q8×C61M32semidirect
107. D244M32semidirect
169. C61#11615semidirect
242. Q8#14519852semidirect

Maximal subgroups

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

subgroupindex
#214621832
C4×#145198522
Q8⋊#117581872
#214607702
C8×#117582262
#1161561