Finite Group Databasebeta

← #30604039

Subgroups — #30604039

Order 15616.

418 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462181C212yesmaximal, complemented
2#21460740C212yesmaximal, complemented
3#21460739C212yesmaximal, complemented
4C2×C8×C22⋊D61C211yesmaximal, characteristic
5#16840683—22no—
6C22⋊#11758187C2214yes—
7#16840651—22no—
8C22×C8×D61C411yescharacteristic
9C2×C4×C22⋊D61C411yescharacteristic
10C8×C22⋊D61—22no—
11C8×C22⋊D61—22no—
12C2×#14519706C411yescharacteristic
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519689C2211yescharacteristic
15C2×C8×Dic61C2211yescharacteristic
16C23×C8×C61C411yescharacteristic
17C2×#11758187—24no—
18C22×C22⋊D61C811yescharacteristic
19C22×C4×D61C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21C22×#92418C2311yescharacteristic
22C2×C8×D61—21no—
23C2×C8×D61—21no—
24C2×C8×D61—42no—
25C4×C22⋊D61—22no—
26C4×C22⋊D61—22no—
27C2×#11758196C811yescharacteristic
28C2×C22⋊Dic61C811yescharacteristic
29C2×#11758198C811yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31#14519706—22no—
32C22⋊#92418—22no—
33#14519689—22no—
34C8×Dic61D412yes—
35C8×Dic61D412yes—
36C23×C4×C61C2×C411yescharacteristic
37C22×C8×C61—21no—
38C22×C8×C61—21no—
39C22×C8×C61—42no—
40C22×C8×C61C2×C411yescharacteristic
41C22×C8×C61C2×C411yescharacteristic
42C24×C61C2×C811yescharacteristic
43C23×D61C2×C811yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61C2×C811yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C22×Dic61C2×C811yescharacteristic
54C22×Dic61C2×C811yescharacteristic
55C22×Dic61C2×C811yescharacteristic
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—41no—
59C2×C4×D61—41no—
60C2×C8×C61—22no—
61C2×C8×C61—21no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22⋊C411yescharacteristic
67C22⋊Dic61—22no—
68#11758198—22no—
69#11758196—22no—
70C4×Dic61C22⋊C412yes—
71C4×Dic61M1612yes—
72C2×#92418—21no—
73C2×#92418—41no—
74C2×#92418—41no—
75C2×#92418C2×D412yes—
76C8×D61—42no—
77C8×D61—42no—
78#11758187—44no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61M3212yes—
84C23×C61C22×C811yescharacteristic
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—41no—
88C22×D61—41no—
89C22×D61M3212yes—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×C4×C61C2×M1611yescharacteristic
99C22⋊D61—28no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61C22⋊C812yes—
106C2×Dic61C22⋊C812yes—
107C4×D61—42no—
108C4×D61—41no—
109C4×D61—41no—
110C8×C61—21no—
111C8×C61—41no—
112C8×C61#10012yes—
113#92418—22no—
114#92418—41no—
115#11488—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—22no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C2×C22⋊C811yescharacteristic
124C22×C61C2×M3211yescharacteristic
125C22×C61C2×M3211yescharacteristic
126C2×D61—22no—
127C2×D61—42no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—42no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61#41011yescharacteristic
134C4×C61C2×#10011yescharacteristic
135Dic61—22no—
136Dic61—22no—
137Dic61—41no—
138C2×C8×D4—611no—
139#2163—612no—
140#1314—612no—
141#1314—612no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61—42no—
145C2×C61#146011yescharacteristic
146C2×C61#211211yescharacteristic
147C2×C61#211511yescharacteristic
148D61—42no—
149C23×C8—611no—
150C23×C8#692311yescharacteristic
151C2×C4×D4—611no—
152C8×D4—1222no—
153C8×D4—1222no—
154C2×C4⋊C8—611no—
155C2×C22⋊C8—611no—
156C2×C22⋊C8—611no—
157C2×C4×C8—611no—
158C4⋊C16—1222no—
159C22⋊C16—614no—
160#346—1222no—
161C61#1148811yescharacteristic, complemented, Sylow
162C22×D4—611no—
163C23×C4—611no—
164C23×C4C2×#692311yescharacteristic
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—42no—
168C22×C8—611no—
169C22×C8—611no—
170C22×C8—1221no—
171C22×C8—1221no—
172C22×C8—2442no—
173C22×C8C2×#692311yescharacteristic
174C22×C8C2×#692311yescharacteristic
175C4×D4—1222no—
176C4×D4—1222no—
177C2×C4⋊C4—611no—
178C2×C22⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C42—611no—
181C2×C16—1224no—
182C4⋊C8—1222no—
183C22⋊C8—1222no—
184C22⋊C8—1222no—
185C4×C8—612no—
186C4×C8—612no—
187C24—611no—
188C24D61⋊C811yescharacteristic
189C2×D4—1222no—
190C2×D4—1222no—
191C2×D4—1222no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4—2441no—
202C22×C4—2441no—
203C22×C4D61⋊C811yescharacteristic
204C22×C4C22×#692311yescharacteristic
205C2×C8—22no—
206C2×C8—21no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—41no—
210C2×C8—612no—
211C2×C8—1221no—
212C2×C8—2442no—
213C2×C8—2441no—
214C2×C8—2442no—
215C2×C8—2441no—
216C2×C8C22⋊#692311yescharacteristic
217C2×C8C22⋊#692311yescharacteristic
218C4⋊C4—1222no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C42—612no—
222C42—612no—
223C16—2444no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23—612no—
229C23—1221no—
230C23—1221no—
231C23—2441no—
232C23—2441no—
233C23#1451985212yes—
234C23C2×D61⋊C811yescharacteristic
235D4—1228no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—612no—
244C2×C4—612no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—2442no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4C2×C22⋊#692311yescharacteristic
254C2×C4D61⋊M1611yescharacteristic
255C8—21no—
256C8—41no—
257C8—1222no—
258C8—2441no—
259C8#1451983712yes—
260C22—21no—
261C22—21no—
262C22—22no—
263C22—42no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—1222no—
268C22—2442no—
269C22—2442no—
270C22—2441no—
271C22—2441no—
272C22D61⋊(C22⋊C8)11yescharacteristic
273C22D61⋊M3211yescharacteristic
274C22C2×#1451985211yescharacteristic
275C4—21no—
276C4—41no—
277C4—1222no—
278C4—1222no—
279C4—2441no—
280C4#1684074111yescharacteristic
281C4C2×#1451983711yescharacteristic
282C2—21no—
283C2—21no—
284C2—42no—
285C2—2442no—
286C2#2146105811yescharacteristic
287C2#2146204711yescharacteristic
288C2#2146205611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC22×C22⋊D61C8
cosocleC22×#92418C23
hypercenterC23×C8#6923
hypocenterC61#11488
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #21462181C2semidirect
2. #21460740C2semidirect
3. #21460739C2semidirect
161. C61#11488semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214607402
#214607392
C2×C8×C22⋊D612
#1148861