Finite Group Databasebeta

← #30604023

Subgroups — #30604023

Order 15616.

382 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462055C212yesmaximal, complemented
2#21460768C212yesmaximal, complemented
3#21460752C212yesmaximal, complemented
4#21454516C211yesmaximal, characteristic
5C2×#14519851—22no—
6#16840658—22no—
7#16840658C2214yes—
8C2×#14519784C2211yescharacteristic
9C22×C8×D61C411yescharacteristic
10#16840269C411yescharacteristic
11#16839836—22no—
12#16839825—22no—
13#16839788C2211yescharacteristic
14#16839725C2211yescharacteristic
15#16839720C411yescharacteristic
16C61×#408C411yescharacteristic
17#14519851—24no—
18#14519851—42no—
19C2×#11758187—42no—
20C22×C4×D61C2×C411yescharacteristic
21#14519784—41no—
22#14519784—41no—
23C2×#11758194D412yes—
24C2×#11758194C2311yescharacteristic
25C22×#92418C2×C411yescharacteristic
26C22×#92418D412yes—
27C2×C8×D61—21no—
28C2×C8×D61—21no—
29C2×C8×D61—41no—
30C2×C8×D61—41no—
31#14519758C812yes—
32#14519753—21no—
33#14519748—21no—
34#14519745C812yes—
35C4×C22⋊D61—22no—
36#14519736C2×C411yescharacteristic
37#14519706—22no—
38#14519689—22no—
39#14519687—21no—
40C8×Dic61—21no—
41C2×#41×C61C2×C411yescharacteristic
42C2×M16×C61C2×C411yescharacteristic
43C22×C8×C61C2×C411yescharacteristic
44C22⋊C8×C61—22no—
45C23×D61C2×C811yescharacteristic
46#41×C61—41no—
47#41×C61—41no—
48C2×Q8×C61M1611yescharacteristic
49C2×D4×C61C2×C812yes—
50C2×D4×C61M1611yescharacteristic
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22×C411yescharacteristic
53C2×C22⋊D61—22no—
54C22×Dic61C2×C811yescharacteristic
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—41no—
58C2×C4×D61—41no—
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C22⋊Dic61—22no—
64C22⋊Dic61C2×C812yes—
65#11758198—22no—
66C4⋊Dic61—21no—
67#11758196—22no—
68C4×Dic61—21no—
69#11758194—42no—
70#11758194—41no—
71C2×#92418—22no—
72C2×#92418—22no—
73C2×#92418—21no—
74C2×#92418—21no—
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C22⋊C411yescharacteristic
77C2×#92418C2×D412yes—
78C8×D61—42no—
79C8×D61—41no—
80C8×D61—41no—
81#11758187—44no—
82C23×C61C22⋊C812yes—
83C23×C61C22×C811yescharacteristic
84C22×D61—21no—
85C22×D61—42no—
86C22×D61—41no—
87Q8×C61—41no—
88D4×C61—42no—
89D4×C61—41no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61C22⋊C812yes—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C22⋊D61—44no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C4×D61—42no—
102C4×D61—41no—
103C4×D61—41no—
104C8×C61—41no—
105C8×C61—41no—
106#92418—22no—
107#92418—21no—
108#92418#9911yescharacteristic
109#92418#9911yescharacteristic
110#11483—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—22no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61C2×C22⋊C811yescharacteristic
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—42no—
121C4×C61—21no—
122C4×C61—22no—
123C4×C61C2×#9911yescharacteristic
124C4×C61#41311yescharacteristic
125Dic61—42no—
126Dic61—41no—
127#2929—611no—
128#2115—612no—
129#1328—612no—
130#1320—612no—
131C2×C61—21no—
132C2×C61—41no—
133C2×C61—42no—
134C2×C61#145911yescharacteristic
135D61—42no—
136C2×#131—611no—
137C23×C8—611no—
138#525—611no—
139C2×M32—1222no—
140#435—1222no—
141C8×D4—1222no—
142#424—611no—
143#408#692311yescharacteristic
144#407—611no—
145#405—611no—
146#349—614no—
147#349—1222no—
148C61#1148311yescharacteristic, complemented, Sylow
149C2×#41C2×#692311yescharacteristic
150C23×C4—611no—
151#131—2441no—
152#131—2441no—
153C2×M16—612no—
154C2×M16—611no—
155C2×M16C2×#692311yescharacteristic
156C22×C8—612no—
157C22×C8—611no—
158C22×C8—1221no—
159C22×C8—1221no—
160C22×C8—2441no—
161C22×C8—2441no—
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—22no—
174C22⋊C8—1222no—
175#97—1221no—
176C4×C8—1221no—
177C24—611no—
178#41—41no—
179#41—41no—
180C2×Q8#1175821311yescharacteristic
181C2×D4—1222no—
182C2×D4D61⋊C812yes—
183C2×D4#1175821311yescharacteristic
184C22×C4—611no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—2441no—
188C22×C4—2441no—
189C22×C4C22⋊#692312yes—
190C22×C4C22×#692311yescharacteristic
191M16—41no—
192M16—2441no—
193M16—2442no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—612no—
200C2×C8—1222no—
201C2×C8—1222no—
202C2×C8—1221no—
203C2×C8—1221no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8—2442no—
207C4⋊C4—1222no—
208C4⋊C4—1221no—
209C22⋊C4—612no—
210C22⋊C4—1222no—
211C22⋊C4—1222no—
212C42—1221no—
213C16—2444no—
214C23—1221no—
215C23—2441no—
216C23—2442no—
217C23#1451983412yes—
218C23C2×D61⋊C811yescharacteristic
219Q8—41no—
220D4—42no—
221D4—41no—
222D4—2444no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—2442no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4#1451983412yes—
234C2×C4C2×C22⋊#692311yescharacteristic
235C2×C4C2×#1175821311yescharacteristic
236C8—41no—
237C8—41no—
238C8—611no—
239C8—611no—
240C8—1222no—
241C8—1221no—
242C22—21no—
243C22—22no—
244C22—42no—
245C22—41no—
246C22—1222no—
247C22—2441no—
248C22—2442no—
249C22—2442no—
250C22—2441no—
251C22C2×#1451983411yescharacteristic
252C4—21no—
253C4—22no—
254C4—2442no—
255C4—2441no—
256C4D61⋊#9911yescharacteristic
257C4#1684074911yescharacteristic
258C2—21no—
259C2—41no—
260C2—42no—
261C2—2442no—
262C2#2146105711yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1459
prime radical#16840269C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11483
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462055C2semidirect
2. #21460768C2semidirect
3. #21460752C2semidirect
148. C61#11483semidirect

Maximal subgroups

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

subgroupindex
#214620552
#214607682
#214607522
#214545162
#1148361