Finite Group Databasebeta

← #30594574

Subgroups — #30594574

Order 15616.

302 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#16840659C211yesmaximal, characteristic
2C2×#16840631C211yesmaximal, characteristic
3#21445858C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5C2×#14519851—21no—
6#16840659—21no—
7#16840659C412yes—
8#16840631—21no—
9#16840631C412yes—
10C22×#11758189C2211yescharacteristic
11C2×#14519713C411yescharacteristic
12#16839725—21no—
13#16839526—21no—
14C2×#108×C61C411yescharacteristic
15C2×#11758213—41no—
16D61⋊M16—22no—
17D61⋊M16—22no—
18D61⋊M16—41no—
19D61⋊M16—41no—
20C2×#11758217—41no—
21C2×D61⋊C8—22no—
22#14519851—22no—
23#14519851—41no—
24C2×#11758187—41no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194—21no—
27C2×#11758189—41no—
28C2×#11758189—41no—
29C2×#11758189C2×C411yescharacteristic
30C2×#11758189C2×C411yescharacteristic
31C2×#11758189D411yescharacteristic
32C2×#11758189Q811yescharacteristic
33C22×#92418D411yescharacteristic
34#14519713—41no—
35#14519689—41no—
36#14519689—41no—
37C2×M16×C61—21no—
38C22×C8×C61C2×C411yescharacteristic
39#108×C61—41no—
40C23×D61Q1611yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×Dic61SD1611yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61C22⋊C411yescharacteristic
48C2×C4×D61C4⋊C411yescharacteristic
49C2×C4×D61D811yescharacteristic
50C2×C4×D61SD1611yescharacteristic
51#11758217—42no—
52#11758217—42no—
53C2×#92420—42no—
54#11758213—42no—
55#11758213—42no—
56D61⋊C8—24no—
57D61⋊C8—42no—
58M16×C61—41no—
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C4211yescharacteristic
64C2×C8×C61C4⋊C411yescharacteristic
65#11758194—41no—
66#11758194—41no—
67C2×#92418—21no—
68C2×#92418—21no—
69C2×#92418—41no—
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C4⋊C411yescharacteristic
72#11758189—41no—
73#11758189—41no—
74#11758189—41no—
75#11758189—41no—
76#11758187—42no—
77C23×C61#10311yescharacteristic
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—81no—
81C22×D61#10311yescharacteristic
82C22×D61#10711yescharacteristic
83C2×C4×C61#9511yescharacteristic
84C2×C4×C61#9911yescharacteristic
85C2×C4×C61#9911yescharacteristic
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61#10411yescharacteristic
88C2×C4×C61#10411yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61#10211yescharacteristic
92C2×Dic61#10611yescharacteristic
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101#92420—44no—
102C8×C61—21no—
103C8×C61—21no—
104C8×C61—81no—
105#92418—21no—
106#92418—21no—
107#92418—81no—
108#7257—611nomaximal, Sylow
109C22×C61—41no—
110C22×C61#32811yescharacteristic
111C22×C61#32811yescharacteristic
112C22×C61#34011yescharacteristic
113C2×D61—21no—
114C2×D61—21no—
115C2×D61—42no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—81no—
119C4×C61#32711yescharacteristic
120C4×C61#32711yescharacteristic
121C4×C61#33911yescharacteristic
122C4×C61#34211yescharacteristic
123Dic61—21no—
124Dic61—21no—
125C2×#349—611no—
126#1811—611no—
127C2×#338—611no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61#129411yescharacteristic
132D61—41no—
133D61—41no—
134C22×M16—611no—
135C22×M16—1221no—
136C2×M32—1221no—
137C2×#108—611no—
138C2×#108#692311yescharacteristic
139#407—1221no—
140#349—612no—
141#349—1221no—
142#341—1221no—
143#338—612no—
144#338—1221no—
145C61#725711yescharacteristic, complemented, Sylow
146C23×C4—611no—
147C2×M16—21no—
148C2×M16—611no—
149C2×M16—611no—
150C2×M16—611no—
151C2×M16—611no—
152C2×M16—1222no—
153C2×M16—1222no—
154C2×M16—1221no—
155C2×M16—2441no—
156C2×M16—2441no—
157C2×M16—2441no—
158C2×M16—2441no—
159C2×M16—2441no—
160C2×M16—2441no—
161C22×C8—611no—
162C22×C8—1222no—
163C22×C8C2×#692311yescharacteristic
164M32—1222no—
165M32—2441no—
166C2×C16—2441no—
167#108—41no—
168#108—2441no—
169C22⋊C8—2441no—
170C22⋊C8—2441no—
171C24—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4C22⋊#692311yescharacteristic
182M16—41no—
183M16—41no—
184M16—2441no—
185M16—2441no—
186M16—2441no—
187M16—2441no—
188M16—2441no—
189M16—2441no—
190M16—2442no—
191M16—2442no—
192M16—2442no—
193M16—2442no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—1221no—
200C2×C8—1221no—
201C2×C8—1224no—
202C2×C8—2441no—
203C2×C8—2442no—
204C2×C8—2442no—
205C2×C8C4×#692311yescharacteristic
206C2×C8C4⋊#692311yescharacteristic
207C16—2442no—
208C23—611no—
209C23—611no—
210C23—1221no—
211C23—1221no—
212C23—4881no—
213C23#1451984011yescharacteristic
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4(C2×#6923)⋊C411yescharacteristic
227C2×C4#1451983511yescharacteristic
228C2×C4#1451983611yescharacteristic
229C2×C4#1451983911yescharacteristic
230C2×C4#1451984111yescharacteristic
231C2×C4#1451984211yescharacteristic
232C8—21no—
233C8—21no—
234C8—81no—
235C8—1221no—
236C8—1221no—
237C8—4881no—
238C8—2444no—
239C22—41no—
240C22—1221no—
241C22—1221no—
242C22—4881no—
243C22—2441no—
244C22—2441no—
245C22—2442no—
246C22#1684061511yescharacteristic
247C22#1684061611yescharacteristic
248C22#1684063511yescharacteristic
249C4—1221no—
250C4—1221no—
251C4#1684061311yescharacteristic
252C4#1684061411yescharacteristic
253C4#1684063211yescharacteristic
254C4#1684064011yescharacteristic
255C2—21no—
256C2—21no—
257C2—21no—
258C2—2441no—
259C2—2441no—
260C2#2146069211yescharacteristic
subgroupG/H
centerC4#16840614
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC2×#108×C61C4
socleC2×C61#1294
prime radicalC23×D61Q16
cosocleC22×#11758189C22
hypercenterC2×#108#6923
hypocenterC61#7257
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
145. C61#7257semidirect

Maximal subgroups

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

subgroupindex
C2×#168406592
C2×#168406312
#214458582
#725761