Finite Group Databasebeta

← #30594563

Subgroups — #30594563

Order 15616.

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

normal subgroups only

This group has 340 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
2#21461491C211yesmaximal, characteristic
3#349×D61C211yesmaximal, characteristic
4C2×#14519856—21no—
5C2×#14519846C411yescharacteristic, complemented
6C2×#14519845C411yescharacteristic, complemented
7#16840704—21no—
8#16840636—21no—
9#16840630—21no—
10#16840630C412yescomplemented
11C2×M16×D61C2211yescharacteristic
12M32×D61—21no—
13#16839544C411yescharacteristic, complemented
14#16839543—21no—
15C61×#349C411yescharacteristic, complemented
16#14519856—22no—
17#14519856—22no—
18#14519856—41no—
19#14519856—41no—
20C2×C4⋊#6923—21no—
21C2×C4⋊#6923—21no—
22C2×C4⋊#6923—41no—
23C2×C22⋊#6923—41no—
24C2×C22⋊#6923—41no—
25C2×C4×#6923—22no—
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×D61D811yescharacteristic
43C22×#6923—42no—
44C22×#6923—41no—
45C22×#6923—41no—
46C22×C4×C61C4⋊C411yescharacteristic
47C22×Dic61Q1611yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×C4×D61C22⋊C411yescharacteristic
54C2×C4×D61SD1611yescharacteristic
55C2×C4×D61SD1611yescharacteristic
56C22⋊#6923—42no—
57C22⋊#6923—42no—
58C22⋊#6923—82no—
59C4⋊#6923—42no—
60C4⋊#6923—42no—
61C4⋊#6923—41no—
62C4⋊#6923—41no—
63C4⋊#6923—41no—
64C4⋊#6923—41no—
65C4×#6923—24no—
66C4×#6923—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#10711yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—41no—
85C22×D61—41no—
86C22×D61#10211yescharacteristic
87C22×D61#10211yescharacteristic
88C2×#6923—44no—
89C2×#6923—82no—
90C2×#6923—82no—
91C2×#6923—81no—
92C2×#6923—81no—
93C2×#6923—81no—
94C2×#6923—81no—
95C2×#6923—81no—
96C2×#6923—81no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61#9511yescharacteristic
100C2×C4×C61#10611yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61#10311yescharacteristic
104C2×Dic61#10311yescharacteristic
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61#9911yescharacteristic
112C4×D61#9911yescharacteristic
113C4×D61#10411yescharacteristic
114C4×D61#10411yescharacteristic
115C8×C61—21no—
116C8×C61—21no—
117#92418—21no—
118#92418—21no—
119#7254—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—41no—
122C22×C61#34011yescharacteristic
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—81no—
130C2×D61#32711yescharacteristic
131C2×D61#32711yescharacteristic
132#6923—84no—
133#6923—161no—
134#6923—161no—
135C4×C61—21no—
136C4×C61#33911yescharacteristic
137C4×C61#34211yescharacteristic
138Dic61—21no—
139Dic61#32811yescharacteristic
140Dic61#32811yescharacteristic
141C2×#349—611no—
142#1809—611no—
143C2×H(3,ℤ/4)—611no—
144C2×C61—21no—
145C2×C61—41no—
146C2×C61#129411yescharacteristic
147D61—21no—
148D61—41no—
149D61#133911yescharacteristic
150D61#134011yescharacteristic
151C22×M16—611no—
152C2×#117—1221no—
153C2×M32—1221no—
154C2×#107—611no—
155C2×#106—611no—
156#380—1221no—
157#349—611no—
158#349—1221no—
159#349#692311yescharacteristic, complemented
160#340—1221no—
161H(3,ℤ/4)—612no—
162H(3,ℤ/4)—1221no—
163C61#725411yescharacteristic, complemented, Sylow
164C23×C4—611no—
165C2×M16—611no—
166C2×M16—611no—
167C2×M16—611no—
168C2×M16—2441no—
169C2×M16—2441no—
170C2×M16C2×#692311yescharacteristic
171C22×C8—611no—
172C22×C8—611no—
173#117—1222no—
174#117—1222no—
175#117—2441no—
176#117—2441no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—2441no—
180C2×C22⋊C4—2441no—
181C2×C22⋊C4—2441no—
182C2×C42—1222no—
183M32—21no—
184M32—1221no—
185M32—2441no—
186C2×C16—2441no—
187#107—2441no—
188#106—2441no—
189#95—2441no—
190C24—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—1221no—
200C22×C4—2441no—
201C22×C4—2441no—
202C22×C4—2442no—
203C22×C4C4⋊#692311yescharacteristic
204M16—41no—
205M16—2441no—
206M16—2441no—
207M16—2441no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1221no—
211C2×C8—1221no—
212C2×C8—1221no—
213C2×C8—1221no—
214C2×C8C4×#692311yescharacteristic
215C2×C8C22⋊#692311yescharacteristic
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C22⋊C4—4882no—
223C22⋊C4—2442no—
224C22⋊C4—2442no—
225C42—1224no—
226C42—2442no—
227C16—41no—
228C16—2441no—
229C23—611no—
230C23—611no—
231C23—1221no—
232C23—1221no—
233C23—2441no—
234C23—2441no—
235C23#1451984611yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—4881no—
253C2×C4—4881no—
254C2×C4—4881no—
255C2×C4—4881no—
256C2×C4—4881no—
257C2×C4—4881no—
258C2×C4—4882no—
259C2×C4—4882no—
260C2×C4—2444no—
261C2×C4(C2×#6923)⋊C411yescharacteristic
262C2×C4#1451984511yescharacteristic
263C8—21no—
264C8—21no—
265C8—1221no—
266C8—1221no—
267C22—21no—
268C22—41no—
269C22—611no—
270C22—611no—
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22—4881no—
275C22—2441no—
276C22—2441no—
277C22—2441no—
278C22#1684063611yescharacteristic
279C4—21no—
280C4—611no—
281C4—611no—
282C4—1221no—
283C4—9761no—
284C4—9761no—
285C4—4884no—
286C4#1684063411yescharacteristic
287C4#1684063911yescharacteristic
288C2—21no—
289C2—41no—
290C2—611no—
291C2—611no—
292C2—1221no—
293C2—2441no—
294C2#2146069411yescharacteristic
subgroupG/H
centerC2#21460694
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×#349C4
socleC2×C61#1294
prime radicalC23×D61D8
cosocleC2×M16×D61C22
hypercenter#349#6923
hypocenterC61#7254
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
5. C2×#14519846C4semidirect
6. C2×#14519845C4semidirect
10. #16840630C4semidirect
13. #16839544C4semidirect
15. C61×#349C4semidirect
159. #349#6923semidirect
163. C61#7254semidirect

Maximal subgroups

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

subgroupindex
#214616972
#214614912
#349×D612
#725461