Finite Group Databasebeta

← #30594567

Subgroups — #30594567

Order 15616.

324 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461697C211yesmaximal, characteristic
2D61⋊#338C211yesmaximal, characteristic
3#349×D61C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5C2×#14519846C411yescharacteristic
6C2×#14519845C411yescharacteristic
7#16840704—21no—
8#16840636—21no—
9#16840631—21no—
10#16840631C412yescomplemented
11C2×M16×D61C2211yescharacteristic
12M32×D61—21no—
13#16839544C411yescharacteristic, complemented
14#16839543—21no—
15C61×#349C411yescharacteristic, complemented
16C2×#11758213—41no—
17D61⋊M16—22no—
18D61⋊M16—22no—
19D61⋊M16—41no—
20D61⋊M16—41no—
21C2×#11758217—41no—
22C2×D61⋊C8—22no—
23C2×C4⋊#6923—21no—
24C2×C4⋊#6923—21no—
25C2×C22⋊#6923—41no—
26#14519846—41no—
27#14519845—41no—
28(C2×#6923)⋊C4—41no—
29C22×C4×D61D411yescharacteristic
30C2×#11758194Q811yescharacteristic
31C2×#11758189C2×C411yescharacteristic
32C2×#11758189D411yescharacteristic
33M16×D61—41no—
34M16×D61—41no—
35C2×C8×D61C2×C411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519717—21no—
38#14519716—41no—
39C16×D61—41no—
40C2×M16×C61C2×C411yescharacteristic
41M32×C61—21no—
42C23×D61SD1611yescharacteristic
43C22×#6923—41no—
44C22×#6923—41no—
45C22×C4×C61C4⋊C411yescharacteristic
46C22×Dic61SD1611yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61C22⋊C411yescharacteristic
52C2×C4×D61C22⋊C411yescharacteristic
53C2×C4×D61D811yescharacteristic
54C2×C4×D61Q1611yescharacteristic
55C22⋊#6923—82no—
56#11758217—42no—
57#11758217—42no—
58C2×#92420—42no—
59C4⋊#6923—41no—
60C4⋊#6923—41no—
61C4⋊#6923—41no—
62C4⋊#6923—41no—
63#11758213—42no—
64#11758213—42no—
65D61⋊C8—24no—
66D61⋊C8—42no—
67M16×C61—41no—
68C2×C8×C61C4211yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70#11758194—41no—
71C2×#92418C4⋊C411yescharacteristic
72C2×#92418C4⋊C411yescharacteristic
73#11758189—41no—
74#11758189—41no—
75C8×D61—21no—
76C8×D61—21no—
77C8×D61—21no—
78C8×D61—21no—
79C16×C61—41no—
80#11758185—41no—
81C23×C61#10611yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—41no—
85C22×D61—41no—
86C22×D61#10211yescharacteristic
87C22×D61#10311yescharacteristic
88C2×#6923—81no—
89C2×#6923—81no—
90C2×#6923—81no—
91C2×#6923—81no—
92C2×#6923—81no—
93C2×#6923—81no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61#9511yescharacteristic
97C2×C4×C61#10711yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61#10211yescharacteristic
101C2×Dic61#10311yescharacteristic
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61#9911yescharacteristic
109C4×D61#9911yescharacteristic
110C4×D61#10411yescharacteristic
111C4×D61#10411yescharacteristic
112#92420—44no—
113C8×C61—21no—
114C8×C61—21no—
115#92418—21no—
116#92418—21no—
117#7255—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—41no—
120C22×C61#34011yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—41no—
127C2×D61—81no—
128C2×D61#32711yescharacteristic
129C2×D61#32711yescharacteristic
130#6923—161no—
131#6923—161no—
132C4×C61—21no—
133C4×C61#33911yescharacteristic
134C4×C61#34211yescharacteristic
135Dic61—21no—
136Dic61#32811yescharacteristic
137Dic61#32811yescharacteristic
138C2×#349—611no—
139#1809—611no—
140C2×#338—611no—
141C2×C61—21no—
142C2×C61—41no—
143C2×C61#129411yescharacteristic
144D61—21no—
145D61—41no—
146D61#134111yescharacteristic
147D61#134211yescharacteristic
148C22×M16—611no—
149C22×M16—1221no—
150C2×M32—1221no—
151C2×#107—611no—
152C2×#106—611no—
153#380—1221no—
154#349—611no—
155#349—1221no—
156#349#692311yescharacteristic, complemented
157#340—1221no—
158#338—612no—
159#338—1221no—
160C61#725511yescharacteristic, complemented, Sylow
161C23×C4—611no—
162C2×M16—611no—
163C2×M16—611no—
164C2×M16—611no—
165C2×M16—1222no—
166C2×M16—1222no—
167C2×M16—2441no—
168C2×M16—2441no—
169C2×M16—2441no—
170C2×M16—2441no—
171C2×M16—2441no—
172C2×M16—2441no—
173C2×M16C2×#692311yescharacteristic
174C22×C8—611no—
175C22×C8—611no—
176C22×C8—1222no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1221no—
179C2×C22⋊C4—2441no—
180M32—21no—
181M32—1221no—
182M32—2441no—
183C2×C16—2441no—
184#107—2441no—
185#106—2441no—
186#95—2441no—
187C24—611no—
188C22×C4—611no—
189C22×C4—611no—
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×C4C4⋊#692311yescharacteristic
200M16—41no—
201M16—2441no—
202M16—2441no—
203M16—2441no—
204M16—2442no—
205M16—2442no—
206M16—2442no—
207M16—2442no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1221no—
211C2×C8—1221no—
212C2×C8—1221no—
213C2×C8—1221no—
214C2×C8—1224no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8C4×#692311yescharacteristic
218C2×C8C22⋊#692311yescharacteristic
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—4882no—
224C16—41no—
225C16—2441no—
226C23—611no—
227C23—611no—
228C23—1221no—
229C23—1221no—
230C23—2441no—
231C23—2441no—
232C23#1451984511yescharacteristic
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
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—4881no—
250C2×C4—4881no—
251C2×C4—4881no—
252C2×C4—4881no—
253C2×C4—4881no—
254C2×C4—4881no—
255C2×C4(C2×#6923)⋊C411yescharacteristic
256C2×C4#1451984611yescharacteristic
257C8—21no—
258C8—21no—
259C8—1221no—
260C8—1221no—
261C8—2444no—
262C22—21no—
263C22—41no—
264C22—611no—
265C22—611no—
266C22—1221no—
267C22—1221no—
268C22—1221no—
269C22—4881no—
270C22—2441no—
271C22—2441no—
272C22—2441no—
273C22#1684063611yescharacteristic
274C4—21no—
275C4—611no—
276C4—611no—
277C4—1221no—
278C4—9761no—
279C4—9761no—
280C4#1684063411yescharacteristic
281C4#1684063911yescharacteristic
282C2—21no—
283C2—41no—
284C2—611no—
285C2—611no—
286C2—1221no—
287C2—2441no—
288C2#2146069411yescharacteristic
subgroupG/H
centerC2#21460694
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×#349C4
socleC2×C61#1294
prime radicalC23×D61SD16
cosocleC2×M16×D61C22
hypercenter#349#6923
hypocenterC61#7255
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
10. #16840631C4semidirect
13. #16839544C4semidirect
15. C61×#349C4semidirect
156. #349#6923semidirect
160. C61#7255semidirect

Maximal subgroups

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

subgroupindex
#214616972
D61⋊#3382
#349×D612
#725561