Finite Group Databasebeta

← #29598696

Subgroups — #29598696

Order 15616.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#21451031C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21443945C214yesmaximal
4C4×#101×C61C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic
6#16839786—21no—
7C2×#14519696C2212yes—
8#16839701—21no—
9#16839701—21no—
10#16839669C2212yes—
11#16839668—21no—
12#16839668—21no—
13#16839627C412yes—
14C4×C4⋊Dic61C411yescharacteristic
15#16839531—21no—
16C2×C4×Q8×C61C2211yescharacteristic
17C2×#101×C61C2212yes—
18C4×M16×C61—21no—
19C61×#343—21no—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—41no—
23#14519777—41no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4×Dic61C2×C412yes—
28C4⋊#92418—41no—
29C4⋊#92418—41no—
30#14519696—24no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34#14519684—22no—
35#14519684—22no—
36C22×Q8×C61C2311yescharacteristic
37C2×M16×C61—22no—
38C4×Q8×C61—41no—
39C4×Q8×C61—41no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46#101×C61—22no—
47#101×C61Q814yescomplemented
48#97×C61—41no—
49C4×C8×C61—41no—
50C2×Q8×C61—41no—
51C2×Q8×C61—41no—
52C2×Q8×C61C2×Q812yes—
53C2×Q8×C61#4112yes—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—22no—
62C22×Dic61—22no—
63C2×Dic122—44no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66M16×C61—24no—
67M16×C61—42no—
68C2×C8×C61—42no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—21no—
78C4⋊Dic61—42no—
79C4⋊Dic61—42no—
80C4⋊Dic61—42no—
81C4×Dic61—42no—
82#11758194—42no—
83#11758194—42no—
84C2×#92418—42no—
85C23×C61C2×C22⋊C411yescharacteristic
86Q8×C61—42no—
87Q8×C61—42no—
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—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#9911yescharacteristic
102C2×C4×C61#9911yescharacteristic
103C2×C4×C61C4×Q812yes—
104C2×C4×C61C22⋊Q812yes—
105C2×C4×C61#12411yescharacteristic
106C2×C4×C61C4⋊Q811yescharacteristic
107C2×Dic61—42no—
108C2×Dic61—44no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112Dic122—82no—
113Dic122—82no—
114C8×C61—44no—
115#92418—82no—
116#13301—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61#39111yescharacteristic
120C22×C61C2×#9911yescharacteristic
121C22×C61#41011yescharacteristic
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61#35512yes—
131Dic61—82no—
132Dic61—82no—
133#2568—611no—
134#1801—611no—
135C4×#101D6111yescharacteristic
136#1394—614no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#199611yescharacteristic
140C2×C61C2×#35511yescharacteristic
141C2×C61#213511yescharacteristic
142C2×C4⋊Q8—611no—
143C2×C4×Q8C2×D6111yescharacteristic
144#423—1221no—
145C2×#101—612no—
146C2×#101C2×D6112yes—
147C4×M16—21no—
148#400—1221no—
149#400—1221no—
150#391—612no—
151#391—1221no—
152#391—1221no—
153#382—612no—
154C4×C4⋊C4—611no—
155#343—21no—
156#343—1221no—
157C61#1330111yescharacteristic, complemented, Sylow
158C22×Q8—1221no—
159C22×Q8C22×D6111yescharacteristic
160C2×M16—22no—
161C2×M16—1222no—
162C4⋊Q8—2441no—
163C4⋊Q8—2441no—
164C4×Q8—41no—
165C4×Q8—41no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4C4×D6111yescharacteristic
170C2×C4⋊C4D24411yescharacteristic
171C2×C4⋊C4C22⋊D6111yescharacteristic
172C2×C42—612no—
173C2×C42C4×D6111yescharacteristic
174C2×C42D24411yescharacteristic
175C2×C42C22⋊D6111yescharacteristic
176C4⋊C8—2441no—
177C4⋊C8—2441no—
178#101—22no—
179#101—1224no—
180#101Dic12214yescomplemented
181#97—41no—
182C4×C8—41no—
183#95—1221no—
184#95—1222no—
185#95—1222no—
186#95—1222no—
187#95—1222no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—2444no—
191C2×Q8—2441no—
192C2×Q8—2441no—
193C2×Q8C2×Dic12212yes—
194C2×Q8#1175822212yes—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4#1175819811yescharacteristic
198C22×C4#1175819811yescharacteristic
199C22×C4#1175819811yescharacteristic
200C22×C4#1175819811yescharacteristic
201C22×C4C2×C4×D6111yescharacteristic
202C22×C4C2×D24411yescharacteristic
203C22×C4C2×C22⋊D6111yescharacteristic
204M16—24no—
205M16—42no—
206M16—2442no—
207M16—2442no—
208C2×C8—42no—
209C2×C8—2442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—2442no—
214C4⋊C4—2442no—
215C4⋊C4—2442no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—2442no—
223C23C2×#1175819811yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—4882no—
227Q8—4882no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2444no—
244C2×C4—2442no—
245C2×C4—2442no—
246C2×C4#1451969111yescharacteristic
247C2×C4#1451969111yescharacteristic
248C2×C4C4×Dic12212yes—
249C2×C4#1451975612yes—
250C2×C4#1451976511yescharacteristic
251C2×C4#1451977711yescharacteristic
252C8—44no—
253C8—4882no—
254C22—21no—
255C22—21no—
256C22#1683966811yescharacteristic
257C22C2×#1451969111yescharacteristic
258C22#1683973511yescharacteristic
259C4—21no—
260C4—22no—
261C4—21no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—4882no—
268C4—4882no—
269C4#1683955812yes—
270C2—21no—
271C2—21no—
272C2#2144680411yescharacteristic
273C2C2×#1683955811yescharacteristic
274C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC4×#101×C61C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenterC4×#101D61
hypocenterC61#13301
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
47. #101×C61Q8semidirect
157. C61#13301semidirect
180. #101Dic122semidirect

Maximal subgroups

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

subgroupindex
#214510312
#214458152
#214439452
C4×#101×C612
#1330161