Finite Group Databasebeta

← #30604521

Subgroups — #30604521

Order 15616.

328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 88 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#21462182C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3#21460788C212yesmaximal, complemented
4#21460771C212yesmaximal, complemented
5#21454782C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840683—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840657—21no—
11#16840650C2212yes—
12C4×#11758224C411yescharacteristic
13#16839892C411yescharacteristic
14#16839889C2211yescharacteristic
15#16839840C2211yescharacteristic
16#16839836—21no—
17#16839831—21no—
18#16839814C411yescharacteristic
19#16839812—21no—
20M16×Dic61—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23D61⋊C16—42no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758224C811yescharacteristic
27C2×#11758194—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30C4×Dic122C2×C411yescharacteristic
31#14519742C811yescharacteristic
32D4×Dic61C811yescharacteristic
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735C811yescharacteristic
36#14519733—21no—
37C2×C4×Dic61—21no—
38C42×D61C2×C411yescharacteristic
39C4⋊#92418C2×C411yescharacteristic
40#14519706—21no—
41#14519706—21no—
42C22⋊#92418—21no—
43#14519689—21no—
44#14519687—21no—
45#14519687—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×M16×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61C2×C811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60#11758224—42no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61C2×C811yescharacteristic
63C2×C4×D61M1611yescharacteristic
64C2×Dic122C2×C811yescharacteristic
65M16×C61—42no—
66C2×C8×C61—21no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22⋊C411yescharacteristic
69C4⋊C4×C61C2×C811yescharacteristic
70C22⋊C4×C61—21no—
71C42×C61C22×C411yescharacteristic
72C22⋊Dic61—21no—
73#11758198—21no—
74C4⋊Dic61C2×C811yescharacteristic
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61C2×C811yescharacteristic
82C4×Dic61M1611yescharacteristic
83#11758194—41no—
84#11758194—41no—
85C2×#92418—21no—
86C2×#92418C2×D411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88C8×D61—21no—
89C8×D61—21no—
90C8×D61—41no—
91#11758187—42no—
92#11758187—42no—
93C23×C61—21no—
94C22×D61C22⋊C811yescharacteristic
95D4×C61—41no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61C22×C811yescharacteristic
101C2×C4×C61C2×M1611yescharacteristic
102C22⋊D61—42no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61C22⋊C811yescharacteristic
108C2×Dic61C22⋊C811yescharacteristic
109C2×Dic61C22⋊C811yescharacteristic
110C4×D61—22no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—22no—
114Dic122—41no—
115C8×C61—21no—
116C8×C61—21no—
117C8×C61—41no—
118#92418—21no—
119#92418—41no—
120#92418AGL(1,ℤ/8)11yescharacteristic
121#92418#13711yescharacteristic
122#11626—611nomaximal, Sylow
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61C2×C22⋊C811yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61#34912yes—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61#41711yescharacteristic
134C4×C61#42111yescharacteristic
135Dic61—21no—
136Dic61—21no—
137Dic61—41no—
138Dic61—41no—
139Dic61#35012yes—
140#2965—611no—
141#2163—611no—
142C2×C4⋊C16—611no—
143#1338—612no—
144#1330—612no—
145C2×C61—81no—
146C2×C61#147711yescharacteristic
147C2×C61C2×#34911yescharacteristic
148C2×C61C2×#35011yescharacteristic
149D61—22no—
150C4×#41—611no—
151C22×C16—1221no—
152#446—611no—
153#446—611no—
154#436—611no—
155#436#692311yescharacteristic
156#435—1221no—
157#435—1221no—
158#431—611no—
159#431—1221no—
160C4×M16—1221no—
161C2×C4×C8—611no—
162C4⋊C16—612no—
163C4⋊C16—1221no—
164C4⋊C16—1221no—
165C22⋊C16—1221no—
166#346—612no—
167C61#1162611yescharacteristic, complemented, Sylow
168C2×#41—611no—
169C2×M16—21no—
170C2×M16—1221no—
171C22×C8—611no—
172C22×C8—611no—
173C4×Q8—611no—
174C4×Q8—611no—
175C4×D4—611no—
176C4×D4—1221no—
177C4×D4—1221no—
178C4×D4C2×#692311yescharacteristic
179#117—611no—
180#117—1221no—
181C2×C42—611no—
182C2×C42—1221no—
183C2×C16—1222no—
184C2×C16—1222no—
185C2×C16—2442no—
186C4⋊C8—611no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189C4⋊C8C2×#692311yescharacteristic
190C22⋊C8—21no—
191C22⋊C8—1221no—
192C22⋊C8—1221no—
193#97—1221no—
194#97—1221no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—1221no—
199C4×C8C2×#692311yescharacteristic
200#41—2442no—
201C2×Q8—611no—
202C2×D4—1221no—
203C2×D4D61⋊C811yescharacteristic
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210M16—42no—
211M16—2441no—
212M16—2441no—
213C2×C8—21no—
214C2×C8—611no—
215C2×C8—611no—
216C2×C8—1221no—
217C2×C8—1221no—
218C2×C8—1221no—
219C2×C8—2441no—
220C2×C8C22⋊#692311yescharacteristic
221C2×C8C22⋊#692311yescharacteristic
222C4⋊C4—611no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4D61⋊C811yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—1221no—
233C42—1221no—
234C42—1221no—
235C42C22×#692311yescharacteristic
236C16—2442no—
237C16—2442no—
238C23—21no—
239C23—611no—
240Q8—2441no—
241D4—41no—
242D4—2442no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4C2×C22⋊#692311yescharacteristic
258C2×C4C2×D61⋊C811yescharacteristic
259C2×C4D61⋊M1611yescharacteristic
260C8—21no—
261C8—21no—
262C8—41no—
263C8—611no—
264C8—611no—
265C8—1221no—
266C8—2441no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—612no—
271C22—1221no—
272C22—1221no—
273C22D61⋊(C22⋊C8)11yescharacteristic
274C4—21no—
275C4—21no—
276C4—41no—
277C4—612no—
278C4—1221no—
279C4—1221no—
280C4—2441no—
281C4—2441no—
282C4#1684075311yescharacteristic
283C4#1684076011yescharacteristic
284C2—81no—
285C2—1222no—
286C2#2146111511yescharacteristic
287C2D61⋊#34911yescharacteristic
288C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758224C8
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11626
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462182C2semidirect
2. D61⋊(C4⋊C16)C2semidirect
3. #21460788C2semidirect
4. #21460771C2semidirect
167. C61#11626semidirect

Maximal subgroups

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

subgroupindex
#214621822
D61⋊(C4⋊C16)2
#214607882
#214607712
#214547822
#1162661