Finite Group Databasebeta

← #30594648

Subgroups — #30594648

Order 15616.

388 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C4×#14519837C211yesmaximal, characteristic
2C4×#14519835C211yesmaximal, characteristic
3#21446114C211yesmaximal, characteristic
4C2×#14519837—21no—
5C2×#14519835—21no—
6C4×#11758217—21no—
7C4×C22⋊#6923—21no—
8#16840642C412yescomplemented
9#16840640C412yes—
10C22×#11758194C411yescharacteristic, complemented
11C2×C4×C22⋊D61C2211yescharacteristic
12C2×#14519689—21no—
13#16839516—21no—
14C2×C22⋊C8×C61C411yescharacteristic, complemented
15C2×#11758217—22no—
16C2×C22⋊#6923—22no—
17C2×C4×#6923—41no—
18#14519837—24no—
19#14519835—24no—
20#14519832—41no—
21C4×#92420—41no—
22(C2×#6923)⋊C4—41no—
23C22×C22⋊D61D411yescharacteristic
24C22×C4×D61D411yescharacteristic
25C2×#11758194—42no—
26C2×#11758194—41no—
27C22×#92418—21no—
28C4×C22⋊D61—41no—
29C4×C22⋊D61—41no—
30C2×#11758196C2×C411yescharacteristic
31C2×C22⋊Dic61Q811yescharacteristic
32C2×#11758198C2×C411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34#14519689—42no—
35C23×C4×C61C2×C411yescharacteristic
36C22×C8×C61—21no—
37C22⋊C8×C61—41no—
38C24×C61C4⋊C411yescharacteristic
39C23×D61C22⋊C411yescharacteristic
40C22×#6923—42no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61C4211yescharacteristic
46C22×C4×C61C22⋊C411yescharacteristic
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—41no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C4⋊C411yescharacteristic
52C22×Dic61C4⋊C411yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57C22⋊#6923—24no—
58C22⋊#6923—42no—
59#11758217—24no—
60#11758217—42no—
61C2×#92420—42no—
62C4×#6923—81no—
63C4×#6923—81no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C22⋊Dic61—41no—
68#11758198—41no—
69#11758196—41no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72#11758194—42no—
73#11758194—42no—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—21no—
80C23×C61—41no—
81C23×C61—41no—
82C23×C61#9511yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61#10412yes—
88C2×#6923—44no—
89C2×#6923—82no—
90C2×#6923—82no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#9911yescharacteristic
100C22⋊D61—44no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61#10412yes—
108C4×D61—41no—
109C4×D61—41no—
110C4×D61—81no—
111#92420—44no—
112C8×C61—81no—
113#92418—42no—
114#7282—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—81no—
121C22×C61—81no—
122C22×C61#33911yescharacteristic
123C22×C61#33911yescharacteristic
124C22×C61#34211yescharacteristic
125C2×D61—22no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—42no—
129C2×D61—81no—
130#6923—84no—
131C4×C61—21no—
132C4×C61—41no—
133C4×C61AΣL(1,𝔽16)11yescharacteristic
134C4×C61#35211yescharacteristic
135Dic61—22no—
136Dic61—41no—
137Dic61—41no—
138#1870—611no—
139C4×#100—611no—
140C4×#99—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61—81no—
144C2×C61#129711yescharacteristic
145C2×C61#139011yescharacteristic
146C2×C61#139511yescharacteristic
147D61—42no—
148C22×M16—611no—
149C2×C4×D4—611no—
150C2×#100—1221no—
151C2×#99—1221no—
152C2×C22⋊C8—1221no—
153C2×C22⋊C8#692311yescharacteristic, complemented
154C4×M16—1221no—
155C4×C22⋊C4—1221no—
156#343—612no—
157#342—612no—
158#336—1221no—
159C61#728211yescharacteristic, complemented, Sylow
160C22×D4—611no—
161C23×C4—611no—
162C23×C4C2×#692311yescharacteristic
163C2×M16—1222no—
164C2×M16—2442no—
165C2×M16—2441no—
166C22×C8—21no—
167C22×C8—1221no—
168C4×D4—2441no—
169C4×D4—2441no—
170C2×C4⋊C4—611no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—611no—
173C2×C22⋊C4—1222no—
174C2×C42—611no—
175C2×C42—2441no—
176#100—1224no—
177#99—1224no—
178C22⋊C8—41no—
179C22⋊C8—2442no—
180#97—2441no—
181C4×C8—2441no—
182#95—2441no—
183C24—611no—
184C24C4⋊#692311yescharacteristic
185C2×D4—1222no—
186C2×D4—1222no—
187C2×D4—2441no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—2441no—
198C22×C4—2441no—
199C22×C4—2442no—
200C22×C4C4×#692311yescharacteristic
201C22×C4C22⋊#692311yescharacteristic
202M16—1224no—
203M16—2442no—
204M16—2442no—
205M16—2442no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—1222no—
210C2×C8—2441no—
211C2×C8—2442no—
212C2×C8—2441no—
213C4⋊C4—2441no—
214C22⋊C4—1224no—
215C22⋊C4—2441no—
216C22⋊C4—2441no—
217C22⋊C4—2442no—
218C42—1221no—
219C42—1221no—
220C42—4881no—
221C42—4881no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—41no—
226C23—41no—
227C23—612no—
228C23—1221no—
229C23—1221no—
230C23—2441no—
231C23—2441no—
232C23(C2×#6923)⋊C411yescharacteristic
233D4—2444no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—612no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—4881no—
247C2×C4—4882no—
248C2×C4—4882no—
249C2×C4—2444no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4#1451983511yescharacteristic
255C2×C4#1451983611yescharacteristic
256C8—81no—
257C8—2444no—
258C8—2442no—
259C22—21no—
260C22—21no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22—81no—
266C22—1222no—
267C22—4881no—
268C22—2442no—
269C22—2441no—
270C22—2441no—
271C22#1684063411yescharacteristic
272C22#1684063411yescharacteristic
273C22#1684064011yescharacteristic
274C4—21no—
275C4—41no—
276C4—1222no—
277C4—4884no—
278C4—2441no—
279C4—2441no—
280C4#1684066311yescharacteristic
281C4#1684066511yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—2442no—
286C2#2146069911yescharacteristic
287C2#2146090411yescharacteristic
288C2#2146091911yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#342
prime radicalC22×C22⋊D61D4
cosocleC2×C4×C22⋊D61C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7282
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
8. #16840642C4semidirect
10. C22×#11758194C4semidirect
14. C2×C22⋊C8×C61C4semidirect
153. C2×C22⋊C8#6923semidirect
159. C61#7282semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
C4×#145198352
#214461142
#728261