Finite Group Databasebeta

← #30594554

Subgroups — #30594554

Order 15616.

344 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461518C211yesmaximal, characteristic
2#21461052C211yesmaximal, characteristic
3#21445800C211yesmaximal, characteristic
4C2×#14519856—21no—
5#16840778—21no—
6#16840640—21no—
7#16840640C412yes—
8#16840608C412yescomplemented
9#16840606—21no—
10C2×#14519734C2211yescharacteristic
11C2×C4⋊#92418C411yescharacteristic, complemented
12C2×#14519689—21no—
13#16839516—21no—
14C2×C4⋊C8×C61C411yescharacteristic, complemented
15#14519856—22no—
16#14519856—22no—
17#14519856—41no—
18#14519856—41no—
19C2×C4⋊#6923—41no—
20C2×C22⋊#6923—22no—
21C2×C4×#6923—41no—
22C4⋊#92420—41no—
23C22⋊#92420—22no—
24C4×#92420—41no—
25C22×C4×D61D411yescharacteristic
26C22×#92418—21no—
27#14519734—41no—
28#14519734—41no—
29C2×#11758196C2×C411yescharacteristic
30C2×#11758196Q811yescharacteristic
31C2×#11758198C2×C411yescharacteristic
32C2×#11758198D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C4⋊#92418—41no—
35#14519689—41no—
36#14519689—41no—
37C22×C8×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C4⋊C8×C61—41no—
40C23×D61C22⋊C411yescharacteristic
41C22×#6923—42no—
42C22×C4×C61C4211yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C22×Dic61C4⋊C411yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61D811yescharacteristic
53C2×C4×D61SD1611yescharacteristic
54C2×C4×D61SD1611yescharacteristic
55C2×C4×D61Q1611yescharacteristic
56C22⋊#6923—24no—
57C22⋊#6923—42no—
58C2×#92420—42no—
59C4⋊#6923—42no—
60C4⋊#6923—42no—
61C4×#6923—42no—
62C4×#6923—42no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C42×C61—21no—
67C42×C61—21no—
68#11758198—41no—
69#11758198—41no—
70#11758196—41no—
71#11758196—41no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C2×#92418—41no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#9511yescharacteristic
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—41no—
81C22×D61—41no—
82C22×D61#10211yescharacteristic
83C22×D61#10311yescharacteristic
84C2×#6923—44no—
85C2×#6923—82no—
86C2×#6923—82no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61#9911yescharacteristic
92C2×C4×C61#9911yescharacteristic
93C2×C4×C61#10211yescharacteristic
94C2×C4×C61#10311yescharacteristic
95C2×C4×C61#10411yescharacteristic
96C2×C4×C61#10411yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61#10611yescharacteristic
104C2×Dic61#10711yescharacteristic
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113#92420—82no—
114C8×C61—81no—
115#92418—81no—
116#7252—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61#33911yescharacteristic
120C22×C61#34011yescharacteristic
121C22×C61#34211yescharacteristic
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—81no—
129#6923—84no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61#32711yescharacteristic
133C4×C61#32711yescharacteristic
134C4×C61#32811yescharacteristic
135C4×C61#32811yescharacteristic
136Dic61—21no—
137Dic61—21no—
138Dic61—41no—
139Dic61—41no—
140#1798—611no—
141#1740—611no—
142#1458—611no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61#129411yescharacteristic
146C2×C61#139111yescharacteristic
147C2×C61#139511yescharacteristic
148D61—41no—
149D61—41no—
150C2×#117—611no—
151C2×#117—1221no—
152#431—1221no—
153C2×C4⋊C8—611no—
154C2×C4⋊C8#692311yescharacteristic, complemented
155C2×C22⋊C8—1221no—
156#342—612no—
157#342—1221no—
158#336—1221no—
159#324—612no—
160#323—1221no—
161C61#725211yescharacteristic, complemented, Sylow
162C23×C4—611no—
163C22×C8—21no—
164C22×C8—1221no—
165#117—1222no—
166#117—1222no—
167#117—2441no—
168#117—2441no—
169#117—2441no—
170#117—2441no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—2441no—
174C2×C22⋊C4—611no—
175C2×C22⋊C4—611no—
176C2×C22⋊C4—1222no—
177C2×C42—611no—
178C2×C42—2441no—
179C2×C42C2×#692311yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—2441no—
182C4⋊C8—2441no—
183C22⋊C8—1222no—
184C22⋊C8—2441no—
185C22⋊C8—2441no—
186C4×C8—2441no—
187C24—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—2442no—
200C22×C4C4×#692311yescharacteristic
201C22×C4C4⋊#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—2442no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C22⋊C4—1224no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C22⋊C4—2442no—
218C42—21no—
219C42—21no—
220C42—1221no—
221C42—1221no—
222C42—2442no—
223C42—2442no—
224C23—611no—
225C23—611no—
226C23—1221no—
227C23—1221no—
228C23—2441no—
229C23—2441no—
230C23(C2×#6923)⋊C411yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—4882no—
250C2×C4—4882no—
251C2×C4—2444no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4#1451983511yescharacteristic
255C2×C4#1451983611yescharacteristic
256C2×C4#1451983911yescharacteristic
257C2×C4#1451984011yescharacteristic
258C2×C4#1451984111yescharacteristic
259C2×C4#1451984211yescharacteristic
260C8—81no—
261C8—4882no—
262C8—4881no—
263C22—21no—
264C22—21no—
265C22—1221no—
266C22—1221no—
267C22—4881no—
268C22—2441no—
269C22—2441no—
270C22—2441no—
271C22—2441no—
272C22#1684063211yescharacteristic
273C22#1684063511yescharacteristic
274C22#1684064011yescharacteristic
275C4—41no—
276C4—41no—
277C4—1221no—
278C4—1221no—
279C4—4884no—
280C4—2441no—
281C4—2441no—
282C4#1684061311yescharacteristic
283C4#1684061411yescharacteristic
284C4#1684061511yescharacteristic
285C4#1684061611yescharacteristic
286C2—21no—
287C2—21no—
288C2—2441no—
289C2—2441no—
290C2#2146069211yescharacteristic
291C2#2146090811yescharacteristic
292C2#2146091911yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#342
prime radicalC23×D61C22⋊C4
cosocleC2×#14519734C22
hypercenterC2×C4⋊C8#6923
hypocenterC61#7252
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
8. #16840608C4semidirect
11. C2×C4⋊#92418C4semidirect
14. C2×C4⋊C8×C61C4semidirect
154. C2×C4⋊C8#6923semidirect
161. C61#7252semidirect

Maximal subgroups

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

subgroupindex
#214615182
#214610522
#214458002
#725261