Finite Group Databasebeta

← #30604451

Subgroups — #30604451

Order 15616.

362 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 110 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#21462152C211yesmaximal, characteristic
2C4×#14519852C211yesmaximal, characteristic
3#21460786C212yesmaximal, complemented
4Q8⋊#11758187C212yesmaximal, complemented
5C8×Q8×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×#14519852—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840651—21no—
11C4×#11758187C2212yes—
12C4×Q8×D61C411yescharacteristic
13Q8×#92418C2211yescharacteristic
14C8×Dic122—21no—
15C8×Dic122C411yescharacteristic
16#16839886—21no—
17#16839886C2211yescharacteristic
18C4⋊C8×D61—21no—
19C4⋊C8×D61C411yescharacteristic
20C4×C8×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C8×Q8×C61C411yescharacteristic
23#14519852—24no—
24#14519852—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×Q8×D61C811yescharacteristic
28C2×C8×D61—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31Q8×Dic61C811yescharacteristic
32C4×Dic122—21no—
33C4×Dic122C2×C411yescharacteristic
34#14519742—21no—
35#14519742C811yescharacteristic
36C4⋊C4×D61—21no—
37C4⋊C4×D61C811yescharacteristic
38C42×D61—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519706—21no—
43#14519706—21no—
44#14519706—21no—
45C4×#92418—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61—21no—
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C4×Q8×C61C2×C411yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61C2×C411yescharacteristic
54C4×C8×C61—21no—
55C4×C8×C61C2×C411yescharacteristic
56C2×Q8×C61C2×C811yescharacteristic
57Q8×D61—22no—
58Q8×D61—22no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61C2×C811yescharacteristic
63C2×C4×D61M1611yescharacteristic
64C2×Dic122—21no—
65C2×Dic122C2×C811yescharacteristic
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
73C4⋊Dic61—21no—
74C4⋊Dic61C2×C811yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61C2×C811yescharacteristic
83C4×Dic61M1611yescharacteristic
84C2×#92418—21no—
85C2×#92418C2×D411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87C8×D61—22no—
88C8×D61—42no—
89C8×D61SD1612yes—
90C8×D61Q1612yes—
91#11758187—24no—
92#11758187—42no—
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×Dic61—21no—
103C2×Dic61C22⋊C811yescharacteristic
104C2×Dic61C22⋊C811yescharacteristic
105C2×Dic61C22⋊C811yescharacteristic
106C4×D61—24no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—41no—
110C4×D61—42no—
111C4×D61#10312yes—
112C4×D61#10412yes—
113Dic122—24no—
114Dic122—21no—
115Dic122M3212yescomplemented
116C8×C61—21no—
117C8×C61—41no—
118C8×C61#10312yes—
119#92418—21no—
120#92418—41no—
121#92418C2×SD1611yescharacteristic
122#92418C2×Q1611yescharacteristic
123#11607—611nomaximal, Sylow
124C22×C61C2×C22⋊C811yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61Q8⋊C812yes—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61C2×#10311yescharacteristic
132C4×C61C2×#10411yescharacteristic
133C4×C61C2×M3211yescharacteristic
134C4×C61C2×M3211yescharacteristic
135Dic61—21no—
136Dic61—22no—
137Dic61—21no—
138Dic61—41no—
139Dic61Q8⋊C812yes—
140C2×C8×Q8—611no—
141#2150—611no—
142C4×M32—611no—
143Q8⋊C16—612no—
144Q8⋊C16—612no—
145C2×C61C2×Q8⋊C811yescharacteristic
146C2×C61#211211yescharacteristic
147C2×C61#211711yescharacteristic
148D61—22no—
149C2×C4×Q8—611no—
150C2×M32—1221no—
151C2×M32—1221no—
152C8×Q8—611no—
153C8×Q8—611no—
154C8×Q8—611no—
155C8×Q8—1221no—
156C8×Q8—1221no—
157C8×Q8#692311yescharacteristic
158C2×C4⋊C8—611no—
159C2×C4⋊C8—1221no—
160C2×C4×C8—611no—
161C2×C4×C8—1221no—
162C4⋊C16—612no—
163C4⋊C16—1221no—
164#346—1221no—
165C4×C16—612no—
166C61#1160711yescharacteristic, complemented, Sylow
167C22×Q8—611no—
168C22×C8—611no—
169C22×C8—611no—
170C22×C8—1221no—
171C4×Q8—611no—
172C4×Q8—611no—
173C4×Q8—611no—
174C4×Q8—1221no—
175C4×Q8—1221no—
176C4×Q8C2×#692311yescharacteristic
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C42—611no—
180C2×C42—1221no—
181M32—1224no—
182M32—2442no—
183C2×C16—1222no—
184C2×C16—1222no—
185C4⋊C8—21no—
186C4⋊C8—611no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189C4⋊C8—1221no—
190C4⋊C8—1221no—
191C4⋊C8C2×#692311yescharacteristic
192C4×C8—21no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8—1221no—
197C4×C8—1221no—
198C4×C8—1221no—
199C4×C8C2×#692311yescharacteristic
200C2×Q8—611no—
201C2×Q8—1221no—
202C2×Q8—1222no—
203C2×Q8—1222no—
204C2×Q8D61⋊C811yescharacteristic
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210C2×C8—21no—
211C2×C8—611no—
212C2×C8—612no—
213C2×C8—612no—
214C2×C8—611no—
215C2×C8—1222no—
216C2×C8—1221no—
217C2×C8—2442no—
218C2×C8C22⋊#692311yescharacteristic
219C2×C8C22⋊#692311yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4D61⋊C811yescharacteristic
227C42—21no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—1221no—
232C42—1221no—
233C42—1221no—
234C42C22×#692311yescharacteristic
235C16—1224no—
236C16—2442no—
237C23—611no—
238Q8—21no—
239Q8—612no—
240Q8—1224no—
241Q8—1221no—
242Q8#1451985212yescomplemented
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—611no—
246C2×C4—612no—
247C2×C4—612no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—1224no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—2441no—
256C2×C4—2442no—
257C2×C4C2×C22⋊#692311yescharacteristic
258C2×C4C2×D61⋊C811yescharacteristic
259C2×C4D61⋊M1611yescharacteristic
260C8—21no—
261C8—41no—
262C8—611no—
263C8—611no—
264C8—1221no—
265C8—2441no—
266C8#1451984012yes—
267C22—612no—
268C22—1221no—
269C22—1221no—
270C22D61⋊(C22⋊C8)11yescharacteristic
271C4—22no—
272C4—21no—
273C4—41no—
274C4—612no—
275C4—1221no—
276C4—1222no—
277C4—1221no—
278C4—2441no—
279C4C2×#1451984011yescharacteristic
280C4D61⋊#10411yescharacteristic
281C4D61⋊M3211yescharacteristic
282C4C2×#1451985211yescharacteristic
283C2—1222no—
284C2D61⋊(Q8⋊C8)11yescharacteristic
285C2#2146204711yescharacteristic
286C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC8×Q8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC22×D61C22⋊C8
cosocleC4×#92418C23
hypercenterC8×Q8#6923
hypocenterC61#11607
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
3. #21460786C2semidirect
4. Q8⋊#11758187C2semidirect
95. Q8×C61M32semidirect
115. Dic122M32semidirect
166. C61#11607semidirect
242. Q8#14519852semidirect

Maximal subgroups

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

subgroupindex
#214621522
C4×#145198522
#214607862
Q8⋊#117581872
C8×Q8×D612
#1160761