Finite Group Databasebeta

← #30604510

Subgroups — #30604510

Order 15616.

352 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 102 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#21462176C211yesmaximal, characteristic, complemented
2#21462151C211yesmaximal, characteristic, complemented
3#21460786C212yesmaximal, complemented
4#21460770C212yesmaximal, complemented
5#21454775C211yesmaximal, characteristic
6C2×#14519851—21no—
7C4⋊#11758187—21no—
8C4⋊#11758187—21no—
9C4⋊#11758187C2212yes—
10C22⋊#11758187—21no—
11C4×#11758187C2212yes—
12C4×#11758222C411yescharacteristic
13#16839886C411yescharacteristic
14#16839886C2211yescharacteristic
15#16839827C411yescharacteristic
16#16839827C2211yescharacteristic
17#16839825—21no—
18#16839825—21no—
19#16839813—21no—
20C2×C4×#92418C2211yescharacteristic
21C4×C8×D61—21no—
22C61×#431C411yescharacteristic
23#14519851—42no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758222C811yescharacteristic
27C22×#92418D411yescharacteristic
28C22×#92418D411yescharacteristic
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C4×Dic122C811yescharacteristic
32C4×Dic122C2×C411yescharacteristic
33C4×D244C811yescharacteristic
34C4×D244C2×C411yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37#14519736C811yescharacteristic
38#14519734—21no—
39C42×D61—21no—
40#14519706—21no—
41#14519706—21no—
42#14519689—21no—
43#14519689—21no—
44C4×#92418C2×C411yescharacteristic
45C4×#92418D411yescharacteristic
46C4×#92418D411yescharacteristic
47C4×#92418C2311yescharacteristic
48C8×Dic61—21no—
49C8×Dic61—21no—
50C2×C42×C61C2×C411yescharacteristic
51C4⋊C8×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C2×C811yescharacteristic
57C22×C4×C61M1611yescharacteristic
58C2×C22⋊D61—21no—
59#11758222—22no—
60#11758222—22no—
61C2×D244C2×C811yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×Dic122C2×C811yescharacteristic
66C2×C8×C61—21no—
67C2×C8×C61—21no—
68C42×C61C22⋊C411yescharacteristic
69C42×C61C2×C811yescharacteristic
70C42×C61M1611yescharacteristic
71C42×C61C22×C411yescharacteristic
72C22⋊Dic61—21no—
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61C2×C811yescharacteristic
76C4⋊Dic61C2×C811yescharacteristic
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C2×#92418—21no—
83C2×#92418—21no—
84C2×#92418—41no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89C8×D61—42no—
90C8×D61—41no—
91C8×D61—41no—
92#11758187—42no—
93#11758187—42no—
94C23×C61C22⋊C811yescharacteristic
95C22×D61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61C22⋊C811yescharacteristic
102C2×C4×C61C22⋊C811yescharacteristic
103C2×C4×C61C22⋊C811yescharacteristic
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61C22×C811yescharacteristic
106C2×C4×C61C2×M1611yescharacteristic
107C22⋊D61—24no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111D244—21no—
112D244M3212yescomplemented
113C4×D61—24no—
114C4×D61—42no—
115C4×D61—41no—
116C4×D61—41no—
117Dic122—21no—
118Dic122M3212yescomplemented
119C8×C61—41no—
120C8×C61—41no—
121#92418—21no—
122#92418—21no—
123#92418—21no—
124#92418AGL(1,ℤ/8)11yescharacteristic
125#92418#13711yescharacteristic
126#11623—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61C2×C22⋊C811yescharacteristic
131C2×D61—22no—
132C2×D61—41no—
133C2×D61—41no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61#35012yes—
138C4×C61#41711yescharacteristic
139C4×C61#42111yescharacteristic
140C4×C61C2×M3211yescharacteristic
141C4×C61C2×M3211yescharacteristic
142Dic61—22no—
143Dic61—41no—
144Dic61—41no—
145C8×#41—611no—
146#2162—611no—
147#2150—611no—
148Q8⋊C16—612no—
149D4⋊C16—612no—
150C2×C61—41no—
151C2×C61#147711yescharacteristic
152C2×C61#211211yescharacteristic
153C2×C61C2×#35011yescharacteristic
154D61—42no—
155C4×#41—611no—
156C2×M32—1221no—
157C8×Q8—611no—
158C8×Q8—611no—
159C8×D4—611no—
160C8×D4—611no—
161C8×D4—1221no—
162C8×D4—1221no—
163#431—1221no—
164#431#692311yescharacteristic
165C2×C4×C8—611no—
166C2×C4×C8—1221no—
167C4⋊C16—612no—
168C4⋊C16—1221no—
169C4⋊C16—1221no—
170C22⋊C16—1221no—
171C4×C16—612no—
172C61#1162311yescharacteristic, complemented, Sylow
173C2×#41—611no—
174C22×C8—611no—
175C22×C8—611no—
176C22×C8—1221no—
177C22×C8—1221no—
178C4×Q8—611no—
179C4×Q8—611no—
180C4×D4—611no—
181C4×D4—611no—
182C4×D4—1221no—
183C4×D4—1221no—
184#117—611no—
185#117—1221no—
186C2×C42—1221no—
187C2×C42C2×#692311yescharacteristic
188M32—2442no—
189C2×C16—1222no—
190C2×C16—1222no—
191C4⋊C8—1221no—
192C4⋊C8—1221no—
193C4⋊C8C2×#692311yescharacteristic
194C4⋊C8C2×#692311yescharacteristic
195C22⋊C8—21no—
196C22⋊C8—1221no—
197C22⋊C8—1221no—
198C4×C8—21no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8—1221no—
204C4×C8—1221no—
205#41—1222no—
206#41—1222no—
207C2×Q8—611no—
208C2×D4—611no—
209C2×D4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4D61⋊C811yescharacteristic
214C22×C4#1175821311yescharacteristic
215C22×C4C22⋊#692311yescharacteristic
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—1221no—
223C2×C8—1221no—
224C2×C8—2441no—
225C2×C8—2441no—
226C2×C8—2442no—
227C2×C8—2441no—
228C4⋊C4—611no—
229C4⋊C4—611no—
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C22⋊C4—1221no—
235C42—1221no—
236C42—1221no—
237C42—1221no—
238C42D61⋊C811yescharacteristic
239C42#1175821311yescharacteristic
240C42C22⋊#692311yescharacteristic
241C42C22×#692311yescharacteristic
242C16—2442no—
243C16—2442no—
244C23—1221no—
245C23#1451983411yescharacteristic
246Q8—612no—
247Q8—1221no—
248D4—612no—
249D4—1224no—
250D4—1221no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—1224no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2442no—
263C2×C4#1451983411yescharacteristic
264C2×C4#1451983411yescharacteristic
265C2×C4#1451983411yescharacteristic
266C2×C4C2×C22⋊#692311yescharacteristic
267C2×C4C2×D61⋊C811yescharacteristic
268C2×C4C2×#1175821311yescharacteristic
269C8—41no—
270C8—41no—
271C8—611no—
272C8—611no—
273C8—1221no—
274C8—1221no—
275C8—1221no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—1222no—
280C22—2441no—
281C22—2441no—
282C22C2×#1451983411yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—1222no—
287C4—2441no—
288C4—2441no—
289C4#1684066112yes—
290C4#1684075311yescharacteristic
291C4#1684075911yescharacteristic
292C4D61⋊M3211yescharacteristic
293C4D61⋊M3211yescharacteristic
294C2—41no—
295C2—2442no—
296C2#2146111611yescharacteristic
297C2#2146204811yescharacteristic
298C2C2×#1684066111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#431C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758222C8
cosocleC4×#92418C23
hypercenter#431#6923
hypocenterC61#11623
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #21462176C2semidirect
2. #21462151C2semidirect
3. #21460786C2semidirect
4. #21460770C2semidirect
112. D244M32semidirect
118. Dic122M32semidirect
172. C61#11623semidirect

Maximal subgroups

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

subgroupindex
#214621762
#214621512
#214607862
#214607702
#214547752
#1162361