Finite Group Databasebeta

← #30594659

Subgroups — #30594659

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#21461797C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21444138C211yesmaximal, characteristic
4C22×#11758213C411yescharacteristic
5C2×#14519834C411yescharacteristic
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8#16840628—21no—
9#16840608C412yes—
10#16840606—21no—
11C2×#14519737C2211yescharacteristic
12#16839812—21no—
13#16839486C411yescharacteristic
14#16839485—21no—
15C61×#323C411yescharacteristic
16C2×#11758213—41no—
17C2×#11758213—42no—
18C22×#92420—21no—
19C22×#92420—21no—
20C22×#92420—41no—
21#14519834—41no—
22C22⋊#92420—22no—
23C22⋊#92420—42no—
24C22⋊#92420—41no—
25C22×C22⋊D61Q811yescharacteristic
26C23×Dic61D411yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28#14519737—41no—
29#14519737—41no—
30C2×#11758196C2×C411yescharacteristic
31C2×#11758198D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33#14519706—41no—
34C22⋊#92418—21no—
35C8×Dic61—41no—
36C2×C22⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C24×C61C4⋊C411yescharacteristic
39C23×D61C4⋊C411yescharacteristic
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C2×C22⋊D61—21no—
43C2×C22⋊D61—21no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—41no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—41no—
49C22×Dic61—41no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C4⋊C411yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61—21no—
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—
64C2×#92420—81no—
65C2×#92420—81no—
66#11758213—42no—
67#11758213—42no—
68C2×C8×C61—41no—
69C22⋊C4×C61—41no—
70#11758198—41no—
71#11758196—41no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C2×#92418—41no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61#9511yescharacteristic
80C23×C61#10811yescharacteristic
81C23×C61#10811yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C22⋊D61—42no—
92C22⋊D61—42no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—81no—
102C2×Dic61#9911yescharacteristic
103C2×Dic61#9911yescharacteristic
104C2×Dic61#10812yes—
105C4×D61—42no—
106C4×D61—41no—
107C4×D61—41no—
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—21no—
117C22×C61—21no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—81no—
123C22×C61#34111yescharacteristic
124C22×C61#34111yescharacteristic
125C22×C61#34211yescharacteristic
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—81no—
130C2×D61—81no—
131C4×C61—41no—
132C4×C61—41no—
133Dic61—22no—
134Dic61—21no—
135Dic61—41no—
136Dic61AΣL(1,𝔽16)11yescharacteristic
137Dic61#35211yescharacteristic
138#1870—611no—
139#1460—611no—
140#1459—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—41no—
144C2×C61—41no—
145C2×C61#129811yescharacteristic
146C2×C61#139011yescharacteristic
147C2×C61#139511yescharacteristic
148D61—81no—
149C22×M16—611no—
150C2×C4×D4—611no—
151#431—1221no—
152C2×C22⋊C8—611no—
153C2×C22⋊C8—1221no—
154C2×C22⋊C8—1221no—
155#336—1221no—
156#324—612no—
157#323—611no—
158#323—1221no—
159#323—1221no—
160#323#692311yescharacteristic
161C61#728511yescharacteristic, complemented, Sylow
162C22×D4—611no—
163C23×C4—611no—
164C23×C4—611no—
165C2×M16—2442no—
166C2×M16—2441no—
167C22×C8—1221no—
168C22×C8—1221no—
169C22×C8—2441no—
170C4×D4—2441no—
171C4×D4—2441no—
172C2×C4⋊C4—611no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4C2×#692311yescharacteristic
175C2×C42—611no—
176C4⋊C8—2441no—
177C22⋊C8—21no—
178C22⋊C8—1222no—
179C22⋊C8—1221no—
180C22⋊C8—2442no—
181C22⋊C8—2441no—
182C22⋊C8—2441no—
183C4×C8—2441no—
184C24—611no—
185C24C4⋊#692311yescharacteristic
186C2×D4—1222no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—2441no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—2441no—
198C22×C4—2441no—
199C22×C4—2441no—
200C22×C4—2441no—
201C22×C4C4×#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203M16—2442no—
204M16—2442no—
205C2×C8—41no—
206C2×C8—1222no—
207C2×C8—4881no—
208C2×C8—4881no—
209C2×C8—2441no—
210C2×C8—2441no—
211C2×C8—2442no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8—2441no—
216C4⋊C4—2441no—
217C22⋊C4—41no—
218C22⋊C4—2441no—
219C42—1221no—
220C42—1221no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23—1221no—
226C23—1221no—
227C23—1221no—
228C23—2441no—
229C23—2441no—
230C23(C2×#6923)⋊C411yescharacteristic
231C23#1451984711yescharacteristic
232C23#1451984811yescharacteristic
233D4—2442no—
234D4—2442no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—611no—
240C2×C4—612no—
241C2×C4—611no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—4881no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2442no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C8—81no—
255C8—4881no—
256C8—4881no—
257C8—4882no—
258C8—2442no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22—4881no—
269C22—4881no—
270C22—2441no—
271C22—2441no—
272C22—2441no—
273C22#1684063711yescharacteristic
274C22#1684063811yescharacteristic
275C22#1684063911yescharacteristic
276C4—41no—
277C4—41no—
278C4—611no—
279C4—611no—
280C4—1221no—
281C4—1222no—
282C4—2441no—
283C2—21no—
284C2—21no—
285C2—41no—
286C2—41no—
287C2—4881no—
288C2#2146070211yescharacteristic
289C2#2146090511yescharacteristic
290C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC22×C22⋊D61Q8
cosocleC2×#14519737C22
hypercenter#323#6923
hypocenterC61#7285
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
161. C61#7285semidirect

Maximal subgroups

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

subgroupindex
#214617972
#214610572
#214441382
#728561