Finite Group Databasebeta

← #29589966

Subgroups — #29589966

Order 15616.

296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454748C211yesmaximal, characteristic
2#21447621C211yesmaximal, characteristic
3#21447616C211yesmaximal, characteristic
4#21443799C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443797C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8#16840316C411yescharacteristic
9#16839893C411yescharacteristic
10#16839891—21no—
11#16839889C411yescharacteristic
12C8×Dic122—21no—
13C8×Dic122C2211yescharacteristic
14#16839787—21no—
15#16839784C411yescharacteristic
16#16839716—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839580—21no—
20#16839541—21no—
21#16839541—21no—
22#16839537—21no—
23C4×#11758185C2211yescharacteristic
24C8×Q8×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C4×C16×C61C2211yescharacteristic
27C2×#11758189—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519776C811yescharacteristic
31#14519775C811yescharacteristic
32#14519767—21no—
33#14519757C811yescharacteristic
34#14519755—21no—
35#14519753C811yescharacteristic
36C4×Dic122—21no—
37C4×Dic122C2×C411yescharacteristic
38#14519734—21no—
39C42×D61C2×C411yescharacteristic
40C2×#11758185—21no—
41C2×#11758185—21no—
42C4⋊#92418—21no—
43C4⋊#92418C2×C411yescharacteristic
44#14519706—21no—
45#14519706—21no—
46#14519706—21no—
47#14519688—21no—
48#14519687—21no—
49C4×#92418C2×C411yescharacteristic
50C8×Dic61—21no—
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C4×Q8×C61C2×C411yescharacteristic
54C2×C16×C61—21no—
55C2×C16×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61C2×C411yescharacteristic
58C4×C8×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61C2×C811yescharacteristic
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61C2×C811yescharacteristic
63C2×C4×D61M1611yescharacteristic
64C2×Dic122—21no—
65C2×Dic122C2×C811yescharacteristic
66C2×C8×C61—21no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61C2×C811yescharacteristic
71C42×C61—21no—
72C42×C61C22×C411yescharacteristic
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61C2×C811yescharacteristic
77#11758196—21no—
78#11758196—21no—
79#11758196—21no—
80#11758196—21no—
81#11758196—21no—
82C4×Dic61—21no—
83C4×Dic61C22⋊C411yescharacteristic
84C4×Dic61C2×C811yescharacteristic
85C4×Dic61M1611yescharacteristic
86C2×#92418—21no—
87C2×#92418C22⋊C411yescharacteristic
88C2×#92418C22⋊C411yescharacteristic
89#11758189—42no—
90C8×D61—21no—
91C8×D61—21no—
92C8×D61—41no—
93C16×C61—41no—
94C16×C61—41no—
95#11758185—41no—
96#11758185—41no—
97C22×D61C22⋊C811yescharacteristic
98Q8×C61—21no—
99Q8×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C22×C811yescharacteristic
104C2×C4×C61C2×M1611yescharacteristic
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61C22⋊C811yescharacteristic
108C2×Dic61C22⋊C811yescharacteristic
109C2×Dic61C22⋊C811yescharacteristic
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—41no—
115Dic122—21no—
116Dic122—21no—
117Dic122—42no—
118C8×C61—21no—
119C8×C61—41no—
120C8×C61#13711yescharacteristic
121C8×C61#13711yescharacteristic
122#92418—21no—
123#92418—21no—
124#92418—41no—
125#11640—611nomaximal, Sylow
126C22×C61C2×C22⋊C811yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61#41911yescharacteristic
134C4×C61#42111yescharacteristic
135C4×C61#50411yescharacteristic
136C4×C61#50411yescharacteristic
137Dic61—21no—
138Dic61—21no—
139Dic61—21no—
140Dic61—41no—
141Dic61—41no—
142#2960—611no—
143#2163—611no—
144#2162—611no—
145Q8⋊C16—611no—
146Q8⋊C16—611no—
147Q8⋊C16—611no—
148Q8⋊C16D6111yescharacteristic, complemented
149C2×C61#147911yescharacteristic
150C2×C61#211311yescharacteristic
151C2×C61#211711yescharacteristic
152D61—41no—
153#533—611no—
154#446—611no—
155#446—611no—
156#446—1221no—
157C8×Q8—611no—
158C8×Q8—1221no—
159C8×Q8C2×D6111yescharacteristic
160#424—1221no—
161#423—611no—
162#405—1221no—
163C2×C4×C8—611no—
164C4⋊C16—611no—
165C4⋊C16—1221no—
166C4⋊C16C2×D6111yescharacteristic
167C22⋊C16—1221no—
168C22⋊C16—1221no—
169#346—1221no—
170C4×C16—611no—
171C4×C16C2×D6111yescharacteristic
172C61#1164011yescharacteristic, complemented, Sylow
173C2×M16—1221no—
174C22×C8—611no—
175C22×C8—611no—
176C4⋊Q8—611no—
177C4⋊Q8—611no—
178#125—1221no—
179C22⋊Q8—611no—
180C22⋊Q8—611no—
181C22⋊Q8—1221no—
182C4×Q8—611no—
183C4×Q8—1221no—
184C4×Q8C4×D6111yescharacteristic
185#117—1221no—
186C2×C42—611no—
187C2×C16—21no—
188C2×C16—21no—
189C2×C16—1221no—
190C2×C16—1221no—
191C4⋊C8—21no—
192C4⋊C8—611no—
193C4⋊C8—1221no—
194C4⋊C8—1221no—
195C4⋊C8—1221no—
196C4⋊C8—1221no—
197C4⋊C8C4×D6111yescharacteristic
198#97—1221no—
199#97—1221no—
200C4×C8—21no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8—611no—
204C4×C8—1221no—
205C4×C8C22×D6111yescharacteristic
206C2×Q8—611no—
207C2×Q8—1221no—
208C2×Q8C8×D6111yescharacteristic
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212M16—2442no—
213C2×C8—21no—
214C2×C8—611no—
215C2×C8—611no—
216C2×C8—1221no—
217C2×C8—1221no—
218C2×C8—1221no—
219C2×C8—2441no—
220C2×C8D4×D6111yescharacteristic
221C2×C8D4×D6111yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4C8×D6111yescharacteristic
231C22⋊C4—1221no—
232C22⋊C4—1221no—
233C42—21no—
234C42—611no—
235C42—611no—
236C42—611no—
237C42—1221no—
238C42C2×C4×D6111yescharacteristic
239C16—41no—
240C16—41no—
241C16—2441no—
242C16—2441no—
243C23—611no—
244Q8—21no—
245Q8—21no—
246Q8—1221no—
247Q8—1221no—
248Q8—2442no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—2441no—
261C2×C4C22⋊C4×D6111yescharacteristic
262C2×C4C2×C8×D6111yescharacteristic
263C2×C4M16×D6111yescharacteristic
264C8—21no—
265C8—41no—
266C8—1221no—
267C8—1221no—
268C8—2441no—
269C8#1451980611yescharacteristic
270C8#1451980911yescharacteristic
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22C22⋊C8×D6111yescharacteristic
275C4—21no—
276C4—41no—
277C4—41no—
278C4—1221no—
279C4—1221no—
280C4—1221no—
281C4—2441no—
282C4—2441no—
283C4#1683976911yescharacteristic
284C4#1683977711yescharacteristic
285C4#1684017811yescharacteristic
286C4#1684018011yescharacteristic
287C2—2441no—
288C2#2144421211yescharacteristic
289C2#2144743111yescharacteristic
290C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61C2×C22⋊C8
prime radicalC22×D61C22⋊C8
cosocleC4×C8×C61C23
hypercenterQ8⋊C16D61
hypocenterC61#11640
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
4. #21443799C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443797C2semidirect
7. C61×Q8⋊C16C2semidirect
148. Q8⋊C16D61semidirect
172. C61#11640semidirect

Maximal subgroups

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

subgroupindex
#214547482
#214476212
#214476162
#214437992
Q8⋊#117581852
#214437972
C61×Q8⋊C162
#1164061