Finite Group Databasebeta

← #30604845

Subgroups — #30604845

Order 15616.

432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461524C211yesmaximal, characteristic
2#21461052C211yesmaximal, characteristic
3#21460820C214yesmaximal, complemented
4#21451641C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6#16840778—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840606—21no—
11C2×#14519734C2211yescharacteristic
12#16839700—21no—
13#16839697—21no—
14#16839681C2212yes—
15#16839673C412yes—
16#16839658—21no—
17#16839628C411yescharacteristic
18#16839619—21no—
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758213—41no—
21D61⋊M16—24no—
22D61⋊M16—42no—
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25C4⋊#92420—41no—
26C22⋊#92420—22no—
27C4×#92420—41no—
28C22×C4×D61D411yescharacteristic
29#14519734—41no—
30#14519734—41no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—22no—
33C2×#11758196D411yescharacteristic
34C2×#11758196C2311yescharacteristic
35C2×#11758198—22no—
36C2×#11758198C2×C411yescharacteristic
37C2×#11758198D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39#14519684—21no—
40#14519684—22no—
41#14519684—22no—
42#14519684C2×C412yes—
43C22×Q8×C61C2×C412yes—
44C4⋊Q8×C61—41no—
45C4⋊Q8×C61—41no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C42×C61C2×C411yescharacteristic
49C23×D61C22⋊C411yescharacteristic
50C2×Q8×C61—42no—
51C2×Q8×C61—82no—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—22no—
63C2×C4×D61SD1612yes—
64C2×C4×D61Q1612yes—
65#11758217—24no—
66#11758217—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69#11758213—44no—
70D61⋊C8—44no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61—21no—
75C42×C61—21no—
76#11758198—41no—
77#11758198—41no—
78#11758198—82no—
79C4⋊Dic61—42no—
80#11758196—41no—
81#11758196—41no—
82#11758196—82no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C23×C61C2×C22⋊C411yescharacteristic
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—41no—
89C22×D61—41no—
90C22×D61#10312yes—
91Q8×C61—84no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61#9911yescharacteristic
100C2×C4×C61#9911yescharacteristic
101C2×C4×C61#10312yes—
102C2×C4×C61#10412yes—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61C2×SD1611yescharacteristic
113C2×Dic61C2×Q1611yescharacteristic
114C4×D61—22no—
115C4×D61—22no—
116C4×D61—22no—
117C4×D61—22no—
118#92420—44no—
119#92420—82no—
120#11724—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61C2×#9911yescharacteristic
124C22×C61C2×#10311yescharacteristic
125C22×C61C2×#10411yescharacteristic
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—81no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—82no—
134C4×C61#32812yes—
135C4×C61#32812yes—
136Dic61—21no—
137Dic61—21no—
138Dic61—41no—
139Dic61—41no—
140Dic61—82no—
141#2628—611no—
142#1742—611no—
143#1458—611no—
144#1354—614no—
145C2×C61—21no—
146C2×C61—21no—
147C2×C61C2×#32811yescharacteristic
148C2×C61#212211yescharacteristic
149C2×C61#213511yescharacteristic
150D61—42no—
151C22×M16—1221no—
152C2×C4⋊Q8#692311yescharacteristic
153C2×#117—611no—
154#431—1221no—
155#400—1221no—
156#399—1221no—
157#395—612no—
158#393—612no—
159#389—1221no—
160#382—611no—
161#380—1221no—
162#343—612no—
163#343—1221no—
164#324—612no—
165#323—1221no—
166C61#1172411yescharacteristic, complemented, Sylow
167C22×Q8C2×#692312yes—
168C23×C4—611no—
169C2×M16—1222no—
170C2×M16—1224no—
171C2×M16—2442no—
172C2×M16—2441no—
173C22×C8—2441no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176#117—2441no—
177#117—2441no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4—1221no—
184C2×C22⋊C4—611no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—1222no—
187C2×C42—611no—
188C2×C42C2×#692311yescharacteristic
189C4⋊C8—2441no—
190C22⋊C8—1222no—
191C4×C8—2441no—
192#95—612no—
193#95—1222no—
194#95—1222no—
195#95—1221no—
196C24—611no—
197C2×Q8—42no—
198C2×Q8—82no—
199C22×C4—22no—
200C22×C4—611no—
201C22×C4—612no—
202C22×C4—612no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212M16—1224no—
213M16—2442no—
214M16—2444no—
215C2×C8—2442no—
216C2×C8—2444no—
217C2×C8—2442no—
218C4⋊C4—42no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—4882no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2442no—
225C22⋊C4—4882no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C42—21no—
229C42—21no—
230C42—1221no—
231C42—1221no—
232C23—612no—
233C23—1221no—
234C23—1221no—
235C23—2441no—
236C23—2441no—
237C23C2×C22⋊#692311yescharacteristic
238Q8—84no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4#1451983511yescharacteristic
262C2×C4#1451983511yescharacteristic
263C2×C4#1451984012yes—
264C2×C4#1451984212yes—
265C8—4882no—
266C8—2444no—
267C22—21no—
268C22—21no—
269C22—1222no—
270C22—4881no—
271C22—2442no—
272C22—2441no—
273C22—2441no—
274C22C2×#1451983511yescharacteristic
275C22C2×#1451984011yescharacteristic
276C22C2×#1451984211yescharacteristic
277C4—41no—
278C4—41no—
279C4—82no—
280C4—1221no—
281C4—1221no—
282C4—4882no—
283C4—2441no—
284C4—2441no—
285C4#1684061612yes—
286C4#1684061612yes—
287C2—21no—
288C2—21no—
289C2—2442no—
290C2C2×#1684061611yescharacteristic
291C2#2146207811yescharacteristic
292C2#2146212111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11724
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
166. C61#11724semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610522
#214608202
#214516412
#1172461