Finite Group Databasebeta

← #30604763

Subgroups — #30604763

Order 15616.

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

normal subgroups only

This group has 452 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#21460803C214yesmaximal, complemented
4#21451586C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6#16840778—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840606—21no—
11C2×#14519753—21no—
12C2×#14519734C2211yescharacteristic
13#16839693—21no—
14#16839693C2212yes—
15#16839688—21no—
16#16839688C412yes—
17#16839669—21no—
18#16839628C411yescharacteristic
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#14519753—42no—
30#14519753—42no—
31#14519734—41no—
32#14519734—41no—
33C2×C4⋊Dic61—21no—
34C2×#11758196—22no—
35C2×#11758196D411yescharacteristic
36C2×#11758196C2311yescharacteristic
37C2×#11758198—22no—
38C2×#11758198C2×C411yescharacteristic
39C2×#11758198D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519684—21no—
42#14519684—22no—
43#14519684—22no—
44#14519684C2×C412yes—
45C22×Q8×C61—21no—
46C4⋊Q8×C61—41no—
47C4⋊Q8×C61—41no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2×C412yes—
50C2×C42×C61C2×C411yescharacteristic
51C23×D61C22⋊C411yescharacteristic
52C2×Q8×C61—41no—
53C2×Q8×C61—41no—
54C2×Q8×C61—42no—
55C2×Q8×C61—42no—
56C22×C4×C61—22no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—22no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—22no—
67C2×C4×D61D812yes—
68C2×C4×D61SD1612yes—
69#11758217—24no—
70#11758217—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73#11758213—44no—
74D61⋊C8—44no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—21no—
79#11758198—41no—
80#11758198—41no—
81#11758198—44no—
82C4⋊Dic61—42no—
83#11758196—41no—
84#11758196—41no—
85#11758196—42no—
86#11758196—42no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—41no—
93C22×D61—41no—
94C22×D61#10212yes—
95Q8×C61—82no—
96Q8×C61—82no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61#9911yescharacteristic
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#10212yes—
107C2×C4×C61#10412yes—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61C2×D811yescharacteristic
118C2×Dic61C2×SD1611yescharacteristic
119C4×D61—22no—
120C4×D61—22no—
121C4×D61—22no—
122C4×D61—22no—
123#92420—44no—
124#92420—82no—
125#11700—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#10211yescharacteristic
130C22×C61C2×#10411yescharacteristic
131C2×D61—22no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—42no—
135C2×D61—81no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—82no—
139C4×C61#32712yes—
140C4×C61#32712yes—
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61—41no—
145Dic61—82no—
146#2621—611no—
147#1742—611no—
148#1458—611no—
149#1346—614no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61C2×#32711yescharacteristic
153C2×C61#212311yescharacteristic
154C2×C61#213511yescharacteristic
155D61—42no—
156C22×M16—1221no—
157C2×C4⋊Q8#692311yescharacteristic
158C2×C22⋊Q8—1221no—
159C2×#117—611no—
160#431—1221no—
161#398—612no—
162#398—1221no—
163#397—612no—
164#397—1221no—
165#391—1221no—
166#382—611no—
167#343—612no—
168#343—1221no—
169#324—612no—
170#323—1221no—
171C61#1170011yescharacteristic, complemented, Sylow
172C22×Q8—21no—
173C23×C4—611no—
174C2×M16—1222no—
175C2×M16—1224no—
176C2×M16—2442no—
177C2×M16—2441no—
178C22×C8—2441no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C22⋊Q8—2442no—
182C22⋊Q8—2442no—
183#117—2441no—
184#117—2441no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—1222no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4C2×#692312yes—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—611no—
193C2×C22⋊C4—1222no—
194C2×C42—611no—
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—2441no—
197C22⋊C8—1222no—
198C4×C8—2441no—
199#95—612no—
200#95—1222no—
201#95—1222no—
202#95—1221no—
203C24—611no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—42no—
207C2×Q8—42no—
208C22×C4—22no—
209C22×C4—611no—
210C22×C4—612no—
211C22×C4—612no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1222no—
217C22×C4—1222no—
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22×#692311yescharacteristic
221M16—1224no—
222M16—2442no—
223M16—2444no—
224C2×C8—2442no—
225C2×C8—2444no—
226C2×C8—2442no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2442no—
232C4⋊C4—2442no—
233C4⋊C4—2442no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C22⋊C4—2444no—
237C42—21no—
238C42—21no—
239C42—1221no—
240C42—1221no—
241C23—612no—
242C23—1221no—
243C23—1221no—
244C23—2441no—
245C23—2441no—
246C23C2×C22⋊#692311yescharacteristic
247Q8—82no—
248Q8—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2442no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4#1451983511yescharacteristic
272C2×C4#1451983511yescharacteristic
273C2×C4#1451983912yes—
274C2×C4#1451984112yes—
275C8—4882no—
276C8—2444no—
277C22—21no—
278C22—21no—
279C22—1222no—
280C22—4881no—
281C22—2442no—
282C22—2441no—
283C22—2441no—
284C22C2×#1451983511yescharacteristic
285C22C2×#1451983911yescharacteristic
286C22C2×#1451984111yescharacteristic
287C4—41no—
288C4—41no—
289C4—82no—
290C4—1221no—
291C4—1221no—
292C4—4882no—
293C4—2441no—
294C4—2441no—
295C4#1684061312yes—
296C4#1684061312yes—
297C2—21no—
298C2—21no—
299C2—2442no—
300C2C2×#1684061311yescharacteristic
301C2#2146208111yescharacteristic
302C2#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#11700
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. #21460803C2semidirect
171. C61#11700semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610522
#214608032
#214515862
#1170061