Finite Group Databasebeta

← #30604020

Subgroups — #30604020

Order 15616.

382 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462056C212yesmaximal, complemented
2#21460768C212yesmaximal, complemented
3#21460751C212yesmaximal, complemented
4#21454513C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×#14519783C2211yescharacteristic
9#16840273C411yescharacteristic
10#16839833—22no—
11C8×C22⋊D61—22no—
12#16839788C2211yescharacteristic
13#16839728C411yescharacteristic
14#16839726C2211yescharacteristic
15#16839717C411yescharacteristic
16C23×C8×C61C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758222C2×C411yescharacteristic
21#14519783—41no—
22#14519783—41no—
23C2×#11758194C2×C411yescharacteristic
24C2×#11758194C2311yescharacteristic
25C2×#11758189D412yes—
26C2×C8×D61D412yes—
27#14519760C812yes—
28#14519756—21no—
29#14519751—21no—
30#14519746C812yes—
31C4×C22⋊D61—22no—
32#14519736C2×C411yescharacteristic
33#14519706—22no—
34C22⋊#92418—22no—
35#14519689—22no—
36#14519687—21no—
37C8×Dic61—21no—
38C23×C4×C61C2×C411yescharacteristic
39C22×C8×C61—21no—
40C22×C8×C61—21no—
41C22×C8×C61—41no—
42C22×C8×C61—41no—
43C22×C8×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C24×C61C2×C811yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61C2×C811yescharacteristic
51C22×C4×C61C22×C411yescharacteristic
52C2×C22⋊D61—22no—
53C2×C22⋊D61C2×C812yes—
54#11758222—41no—
55#11758222—41no—
56C2×D244M1611yescharacteristic
57C2×C4×D61C22⋊C412yes—
58C2×Dic122M1611yescharacteristic
59C2×C8×C61—21no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61—42no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C22⋊Dic61—22no—
69C22⋊Dic61C2×C812yes—
70#11758198—22no—
71C4⋊Dic61—21no—
72#11758196—22no—
73C4×Dic61—21no—
74#11758194—41no—
75#11758194—41no—
76C2×#92418—21no—
77C2×#92418C2×D412yes—
78#11758189—42no—
79C8×D61—22no—
80C8×D61—22no—
81#11758187—44no—
82C23×C61—21no—
83C23×C61—41no—
84C23×C61—42no—
85C23×C61C22×C811yescharacteristic
86C22×D61C22⋊C812yes—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61C2×M1611yescharacteristic
96C22⋊D61—42no—
97C22⋊D61—44no—
98C2×Dic61—22no—
99C2×Dic61C22⋊C812yes—
100D244—41no—
101C4×D61—22no—
102C4×D61—22no—
103Dic122—41no—
104C8×C61—21no—
105C8×C61—41no—
106C8×C61#9911yescharacteristic
107C8×C61#9911yescharacteristic
108#92418—22no—
109#92418—41no—
110#11483—611nomaximal, Sylow
111C22×C61—22no—
112C22×C61—21no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—41no—
118C22×C61C2×C22⋊C811yescharacteristic
119C2×D61—22no—
120C2×D61—42no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61C2×#9911yescharacteristic
124C4×C61#41311yescharacteristic
125Dic61—22no—
126Dic61—42no—
127#2929—611no—
128#2115—612no—
129#1328—612no—
130#1320—612no—
131C2×C61—21no—
132C2×C61—42no—
133C2×C61—41no—
134C2×C61#145911yescharacteristic
135D61—42no—
136C2×#131—611no—
137C23×C8#692311yescharacteristic
138#525—611no—
139C2×M32—1222no—
140#435—1222no—
141C8×D4—1222no—
142#424—611no—
143#408—611no—
144#407—611no—
145#405—611no—
146#349—614no—
147#349—1222no—
148C61#1148311yescharacteristic, complemented, Sylow
149C2×#41—611no—
150C23×C4C2×#692311yescharacteristic
151#131—2441no—
152#131—2441no—
153C2×M16—611no—
154C2×M16—612no—
155C2×M16—611no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—41no—
159C22×C8—41no—
160C22×C8—612no—
161C22×C8C2×#692311yescharacteristic
162C22×C8C2×#692311yescharacteristic
163#123—612no—
164C22⋊Q8—1221no—
165#121—1221no—
166#120—612no—
167C4×D4—1222no—
168#117—611no—
169M32—1224no—
170M32—2442no—
171C2×C16—2442no—
172C4⋊C8—1222no—
173C22⋊C8—1222no—
174C22⋊C8—1222no—
175#97—1221no—
176C4×C8—1221no—
177C24D61⋊C811yescharacteristic
178#41—2441no—
179#41—2441no—
180C2×Q8—611no—
181C2×D4—612no—
182C2×D4—611no—
183C2×D4—1222no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—612no—
189C22×C4D61⋊C811yescharacteristic
190C22×C4C22×#692311yescharacteristic
191M16—2442no—
192M16—2441no—
193M16—2441no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—612no—
202C2×C8—1222no—
203C2×C8—1222no—
204C2×C8—1221no—
205C2×C8C22⋊#692311yescharacteristic
206C2×C8C22⋊#692311yescharacteristic
207C4⋊C4—1222no—
208C4⋊C4—1221no—
209C22⋊C4—612no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C42—1221no—
213C16—2444no—
214C23—21no—
215C23—41no—
216C23—42no—
217C23—612no—
218C23C2×D61⋊C811yescharacteristic
219Q8—2441no—
220D4—2441no—
221D4—2442no—
222D4—2444no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—612no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4C2×C22⋊#692311yescharacteristic
235C2×C4D61⋊M1611yescharacteristic
236C8—21no—
237C8—41no—
238C8—1222no—
239C8—2441no—
240C8#1451983511yescharacteristic
241C8#1451983511yescharacteristic
242C22—22no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—1222no—
250C22—2442no—
251C22D61⋊(C22⋊C8)11yescharacteristic
252C4—21no—
253C4—41no—
254C4—1222no—
255C4—2442no—
256C4C2×#1451983511yescharacteristic
257C4#1684074811yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—2442no—
262C2#2146105411yescharacteristic
subgroupG/H
centerC8#14519835
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC2×C61#1459
prime radical#16840273C4
cosocleC2×#11758194C23
hypercenterC23×C8#6923
hypocenterC61#11483
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21460768C2semidirect
3. #21460751C2semidirect
148. C61#11483semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214607682
#214607512
#214545132
#1148361