Finite Group Databasebeta

← #29595198

Subgroups — #29595198

Order 15616.

464 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 113 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#21448537C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal
3#101×Dic61C212yesmaximal
4#21443946C211yesmaximal, characteristic
5C61×#1394C211yesmaximal, characteristic
6C2×#14519775C2211yescharacteristic
7C2×Q8×Dic61C2211yescharacteristic
8C2×#14519742C411yescharacteristic
9C2×#14519696C2212yes—
10M16×Dic61—22no—
11#16839668C411yescharacteristic
12#16839649—22no—
13#16839644—22no—
14#16839627C411yescharacteristic
15#16839608C411yescharacteristic
16#16839560C418yescomplemented
17#16839530—22no—
18C2×#101×C61C2212yes—
19C61×#391C2211yescharacteristic
20C22×Dic122C2×C411yescharacteristic
21C2×#11758194—22no—
22#14519775—21no—
23#14519775—21no—
24#14519775C2×C414yes—
25Q8×Dic61—42no—
26#14519742—42no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35#14519696—22no—
36#14519696C2×C414yes—
37#14519687—42no—
38C8×Dic61—42no—
39#14519684—21no—
40#14519684—21no—
41#14519684—22no—
42#14519684—22no—
43C22×Q8×C61C2311yescharacteristic
44C2×M16×C61—22no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47#101×C61—22no—
48#101×C61C2×C414yes—
49#95×C61—22no—
50C2×Q8×C61—41no—
51C2×Q8×C61—41no—
52C2×Q8×C61C22×C412yes—
53C2×Q8×C61#4111yescharacteristic
54C2×Q8×C61#4111yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D412yes—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122C4212yes—
68M16×C61—24no—
69M16×C61—42no—
70C2×C8×C61—42no—
71C4⋊C4×C61—41no—
72C42×C61—41no—
73C4⋊Dic61—41no—
74C4⋊Dic61—42no—
75#11758196—24no—
76#11758196—24no—
77#11758196—42no—
78C4×Dic61—21no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—42no—
83C4×Dic61C4212yes—
84#11758194—24no—
85#11758194—42no—
86C2×#92418—42no—
87C23×C61C2×C22⋊C411yescharacteristic
88Q8×C61—42no—
89Q8×C61—41no—
90Q8×C61—41no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61C2×C4211yescharacteristic
101C2×C4×C61#11711yescharacteristic
102C2×C4×C61C4×D412yes—
103C2×C4×C61C4×D412yes—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61—41no—
115C2×Dic61#9912yes—
116Dic122—42no—
117Dic122—42no—
118C8×C61—44no—
119#92418—44no—
120#12631—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61C4×C22⋊C411yescharacteristic
124C22×C61C2×#9911yescharacteristic
125C22×C61#41011yescharacteristic
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—81no—
131C4×C61—81no—
132Dic61—22no—
133Dic61—42no—
134Dic61—41no—
135Dic61—42no—
136Dic61—42no—
137#2327—611no—
138C2×#356—612no—
139C4×#101—612no—
140#1394—611no—
141#1394D6111yescharacteristic
142C2×C61—21no—
143C2×C61—21no—
144C2×C61C4×#9911yescharacteristic
145C2×C61#213311yescharacteristic
146C2×C61#213511yescharacteristic
147C2×C4⋊Q8—611no—
148C2×C4×Q8—611no—
149C2×C4×Q8—611no—
150C2×#101—612no—
151C2×#101C2×D6112yes—
152C4×M16—1222no—
153#391—611no—
154#391C2×D6111yescharacteristic
155#387—1222no—
156#387—1222no—
157#382—611no—
158#376—611no—
159#356—618no—
160#343—1222no—
161C61#1263111yescharacteristic, complemented, Sylow
162C22×Q8—611no—
163C22×Q8C22×D6111yescharacteristic
164C2×M16—22no—
165C2×M16—1222no—
166C4⋊Q8—614no—
167C4⋊Q8—1221no—
168C4⋊Q8—1221no—
169C4×Q8—2442no—
170C4×Q8—2442no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—612no—
173C2×C4⋊C4—1222no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4C4×D6111yescharacteristic
176C2×C42—611no—
177C2×C42—611no—
178C2×C42—612no—
179C2×C42—1221no—
180C2×C42C4×D6111yescharacteristic
181#101—22no—
182#101—614no—
183#101—1222no—
184#101C4×D6114yes—
185#97—2442no—
186C4×C8—2442no—
187#95—22no—
188#95—1221no—
189#95—1221no—
190#95—1222no—
191#95—1222no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—612no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C2×Q8—2441no—
198C2×Q8C2×C4×D6112yes—
199C2×Q8#1175822411yescharacteristic
200C2×Q8#1175822611yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—611no—
204C22×C4—612no—
205C22×C4—611no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4C2×C4×D6111yescharacteristic
209C22×C4D4×D6112yes—
210M16—24no—
211M16—42no—
212M16—1224no—
213M16—2442no—
214C2×C8—42no—
215C2×C8—2442no—
216C4⋊C4—41no—
217C4⋊C4—1224no—
218C4⋊C4—1224no—
219C4⋊C4—2441no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C42—41no—
223C42—612no—
224C42—1222no—
225C42—1222no—
226C42—1222no—
227C42—1221no—
228C42—2442no—
229C23C22⋊C4×D6111yescharacteristic
230Q8—42no—
231Q8—41no—
232Q8—41no—
233Q8—2442no—
234Q8—2442no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—612no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2442no—
255C2×C4—2441no—
256C2×C4C42×D6111yescharacteristic
257C2×C4#1451973511yescharacteristic
258C2×C4#1451973712yes—
259C2×C4#1451973912yes—
260C8—44no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22#1683960911yescharacteristic
265C22#99×D6111yescharacteristic
266C22#1683973411yescharacteristic
267C4—22no—
268C4—22no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—1222no—
274C4—2442no—
275C4—2441no—
276C4—2442no—
277C4—2442no—
278C2—21no—
279C2—21no—
280C2#2144560611yescharacteristic
281C2#2144750511yescharacteristic
282C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#12631
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
16. #16839560C4semidirect
161. C61#12631semidirect

Maximal subgroups

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

subgroupindex
#214485372
C2×#168395602
#101×Dic612
#214439462
C61×#13942
#1263161