Finite Group Databasebeta

← #30594657

Subgroups — #30594657

Order 15616.

324 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 56 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#21461799C211yesmaximal, characteristic
2#21461060C211yesmaximal, characteristic
3#21444136C211yesmaximal, characteristic
4C22×#11758213C411yescharacteristic
5#16840778—21no—
6C2×#14519834—21no—
7C2×#14519834C411yescharacteristic
8#16840628—21no—
9#16840606—21no—
10#16840606C412yes—
11C2×#14519739C2211yescharacteristic
12C22⋊C8×D61—21no—
13#16839488C411yescharacteristic
14#16839485—21no—
15C61×#324C411yescharacteristic
16C2×#11758213—41no—
17C2×#11758213—42no—
18C22×#92420—21no—
19C22×#92420—21no—
20C4⋊#92420—41no—
21#14519834—42no—
22#14519834—41no—
23C22⋊#92420—22no—
24C4×#92420—41no—
25C22×D244Q811yescharacteristic
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×C8×D61—41no—
29#14519739—41no—
30#14519739—41no—
31C2×#11758198C2×C411yescharacteristic
32C2×#11758198D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C22⋊#92418—21no—
35#14519689—41no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C23×D61C4⋊C411yescharacteristic
39C23×D61C4⋊C411yescharacteristic
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C4⋊C411yescharacteristic
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C22⋊C411yescharacteristic
45C2×D244—22no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—41no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57C2×#92420—22no—
58C2×#92420—41no—
59C2×#92420—41no—
60C2×#92420—42no—
61C2×#92420—41no—
62C2×#92420—41no—
63C2×#92420—41no—
64#11758213—42no—
65#11758213—42no—
66C2×C8×C61—41no—
67C4⋊C4×C61—41no—
68#11758198—41no—
69#11758198—41no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C2×#92418—41no—
73C8×D61—81no—
74C8×D61—81no—
75C23×C61#9511yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61—41no—
85C22×D61#10812yes—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61#10811yescharacteristic
93C2×C4×C61#10811yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61#9911yescharacteristic
99C2×Dic61#9911yescharacteristic
100D244—42no—
101D244—42no—
102C4×D61—42no—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—81no—
108#92420—42no—
109#92420—81no—
110#92420—82no—
111C8×C61—81no—
112#92418—81no—
113#7285—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61#34111yescharacteristic
117C22×C61#34111yescharacteristic
118C22×C61#34211yescharacteristic
119C2×D61—22no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—42no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—81no—
127C2×D61—81no—
128C2×D61—81no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133Dic61—21no—
134Dic61—41no—
135Dic61AΣL(1,𝔽16)11yescharacteristic
136Dic61#35211yescharacteristic
137#1870—611no—
138#1460—611no—
139#1459—611no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#129811yescharacteristic
143C2×C61#139011yescharacteristic
144C2×C61#139511yescharacteristic
145D61—42no—
146D61—81no—
147C22×M16—611no—
148C2×C4×D4—611no—
149#431—1221no—
150C2×C22⋊C8—611no—
151C2×C22⋊C8—1221no—
152C2×C22⋊C8—1221no—
153#336—1221no—
154#324—611no—
155#324#692311yescharacteristic
156#323—612no—
157#323—1221no—
158#323—1221no—
159C61#728511yescharacteristic, complemented, Sylow
160C22×D4—611no—
161C23×C4—611no—
162C23×C4—611no—
163C2×M16—2442no—
164C2×M16—2441no—
165C22×C8—1221no—
166C22×C8—1221no—
167C22×C8—2441no—
168C4×D4—2441no—
169C4×D4—2441no—
170C2×C4⋊C4C2×#692311yescharacteristic
171C2×C22⋊C4—611no—
172C2×C22⋊C4—611no—
173C2×C42—611no—
174C4⋊C8—2441no—
175C22⋊C8—21no—
176C22⋊C8—1222no—
177C22⋊C8—1221no—
178C22⋊C8—2441no—
179C22⋊C8—2442no—
180C22⋊C8—2441no—
181C4×C8—2441no—
182C24—611no—
183C24—611no—
184C2×D4—1222no—
185C2×D4—1221no—
186C2×D4—1221no—
187C2×D4—2441no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—2441no—
195C22×C4—2441no—
196C22×C4—2441no—
197C22×C4—2441no—
198C22×C4C4×#692311yescharacteristic
199C22×C4C4⋊#692311yescharacteristic
200C22×C4C22⋊#692311yescharacteristic
201M16—2442no—
202M16—2442no—
203C2×C8—41no—
204C2×C8—1222no—
205C2×C8—4881no—
206C2×C8—4881no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2442no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8—2441no—
213C2×C8—2441no—
214C4⋊C4—41no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C42—1221no—
218C42—1221no—
219C23—612no—
220C23—1221no—
221C23—1221no—
222C23—1221no—
223C23—1221no—
224C23—1221no—
225C23—2441no—
226C23—2441no—
227C23—2441no—
228C23—2441no—
229C23(C2×#6923)⋊C411yescharacteristic
230D4—2442no—
231D4—2442no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—4881no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2442no—
249C2×C4—2441no—
250C2×C4#1451984711yescharacteristic
251C2×C4#1451984811yescharacteristic
252C8—81no—
253C8—4881no—
254C8—4881no—
255C8—4882no—
256C8—2442no—
257C22—21no—
258C22—21no—
259C22—1222no—
260C22—4881no—
261C22—4881no—
262C22—4881no—
263C22—2442no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22—2441no—
269C22#1684063711yescharacteristic
270C22#1684063811yescharacteristic
271C22#1684063911yescharacteristic
272C4—21no—
273C4—21no—
274C4—41no—
275C4—41no—
276C4—611no—
277C4—611no—
278C4—1221no—
279C4—2441no—
280C2—21no—
281C2—21no—
282C2—4881no—
283C2—2442no—
284C2#2146070211yescharacteristic
285C2#2146090211yescharacteristic
286C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC22×D244Q8
cosocleC2×#14519739C22
hypercenter#324#6923
hypocenterC61#7285
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
159. C61#7285semidirect

Maximal subgroups

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

subgroupindex
#214617992
#214610602
#214441362
#728561