Finite Group Databasebeta

← #29590744

Subgroups — #29590744

Order 15616.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451640C211yesmaximal, characteristic
2#21445896C211yesmaximal, characteristic
3#21443844C214yesmaximal
4C61×#1464C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6#16839701C412yescomplemented
7#16839698C2212yes—
8#16839682—21no—
9#16839674—21no—
10#16839660—21no—
11#16839628C411yescharacteristic, complemented
12#16839625—21no—
13#16839622—21no—
14#16839529—21no—
15#16839529C2212yes—
16C2×#117×C61C2211yescharacteristic
17C61×#432—21no—
18C61×#324—21no—
19C61×#323C2212yes—
20C22×Dic122—21no—
21#14519777—41no—
22#14519777—41no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C412yes—
26C2×#11758196—22no—
27C2×C22⋊Dic61—22no—
28C2×C22⋊Dic61—22no—
29#14519684—22no—
30#14519684—21no—
31#14519684—22no—
32#14519684—41no—
33#14519684—41no—
34#14519684C2×C412yes—
35C23×C4×C61D411yescharacteristic
36#117×C61—41no—
37#117×C61—41no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C22⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61C2311yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C4⋊C8×C61—41no—
45C22⋊C8×C61—22no—
46#97×C61—41no—
47C24×C61C2×D411yescharacteristic
48C22×C4×C61—22no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—41no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—42no—
61C2×Dic122—42no—
62C2×Dic122—82no—
63C2×C8×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C22⋊C4×C61—41no—
67C22⋊C4×C61—41no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C22⋊Dic61—42no—
73C22⋊Dic61—42no—
74C22⋊Dic61—82no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—42no—
79#11758196—82no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61C2×C22⋊C411yescharacteristic
85C23×C61#13712yes—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#9911yescharacteristic
102C2×C4×C61#9911yescharacteristic
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—82no—
110C2×Dic61—82no—
111C2×Dic61—82no—
112Dic122—84no—
113C8×C61—82no—
114#11813—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—22no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—81no—
122C22×C61C2×#9911yescharacteristic
123C22×C61#41911yescharacteristic
124C22×C61#42111yescharacteristic
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61—41no—
131C4×C61—41no—
132Dic61—82no—
133Dic61—82no—
134Dic61—162no—
135#2628—611no—
136#1820—611no—
137#1464D6111yescharacteristic
138#1352—614no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61—42no—
142C2×C61#151111yescharacteristic
143C2×C61#212311yescharacteristic
144C2×C61#212811yescharacteristic
145C2×C4⋊Q8—611no—
146C2×#117C2×D6111yescharacteristic
147#432—21no—
148#400—612no—
149#399—612no—
150#395—1221no—
151#393—1221no—
152#389—1221no—
153#382—611no—
154#381—1221no—
155#380—1221no—
156#342—612no—
157#342—1221no—
158#324—21no—
159#323C2×D6112yes—
160C61#1181311yescharacteristic, complemented, Sylow
161C22×Q8—1221no—
162C23×C4D24411yescharacteristic
163C4⋊Q8—2441no—
164C4⋊Q8—2441no—
165#117—41no—
166#117—41no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4C4×D6111yescharacteristic
172C2×C4⋊C4C22⋊D6111yescharacteristic
173C2×C22⋊C4—1222no—
174C2×C22⋊C4—1222no—
175C2×C22⋊C4D24411yescharacteristic
176C2×C22⋊C4C22×D6111yescharacteristic
177C2×C42C4×D6111yescharacteristic
178C2×C42C22⋊D6111yescharacteristic
179C4⋊C8—41no—
180C22⋊C8—22no—
181#97—41no—
182#95—612no—
183#95—1222no—
184#95—1221no—
185#95—1222no—
186#95—2441no—
187#95—2441no—
188C24C2×D24411yescharacteristic
189C2×Q8—4882no—
190C2×Q8—2442no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4—2442no—
198C22×C4#1175819811yescharacteristic
199C22×C4#1175819811yescharacteristic
200C22×C4#1175819811yescharacteristic
201C22×C4#1175819811yescharacteristic
202C22×C4C2×C4×D6111yescharacteristic
203C22×C4C2×C22⋊D6111yescharacteristic
204C2×C8—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—4882no—
208C4⋊C4—2442no—
209C4⋊C4—2442no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—4882no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×#1175819811yescharacteristic
226C23#1451981012yes—
227Q8—4884no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—4882no—
244C2×C4—4882no—
245C2×C4—4882no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4#1451969111yescharacteristic
253C2×C4#1451969111yescharacteristic
254C8—82no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×#1451969111yescharacteristic
263C22#1683977211yescharacteristic
264C22#1683977811yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—9762no—
273C4—4882no—
274C4—4882no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2#2144435311yescharacteristic
279C2#2144747411yescharacteristic
280C2#2144749011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1464C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1464D61
hypocenterC61#11813
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
5. C2×#14519777C4semidirect
6. #16839701C4semidirect
11. #16839628C4semidirect
160. C61#11813semidirect

Maximal subgroups

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

subgroupindex
#214516402
#214458962
#214438442
C61×#14642
#1181361