Finite Group Databasebeta

← #29574966

Subgroups — #29574966

Order 15616.

376 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 89 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#21456343C211yesmaximal, characteristic
2#21454924C211yesmaximal, characteristic
3#21444483C211yesmaximal, characteristic
4#21444293C211yesmaximal, characteristic
5#21444291C211yesmaximal, characteristic
6#21443718C211yesmaximal, characteristic
7C61×#1302C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840319C2211yescharacteristic
10#16840171—21no—
11#16840171—21no—
12#16840171C412yes—
13#16840171C412yes—
14#16839891—22no—
15#16839890—22no—
16#16839820—22no—
17#16839819C2211yescharacteristic
18#16839815C2211yescharacteristic
19#16839800—22no—
20#16839509—21no—
21#16839507—21no—
22#16839494—22no—
23#16839492—22no—
24C61×#432C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27#14519777C2×C411yescharacteristic
28#14519777C2×C411yescharacteristic
29#14519777D411yescharacteristic
30#14519777D411yescharacteristic
31#14519769—21no—
32#14519769C2×C412yes—
33#14519756—21no—
34#14519756—21no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736—21no—
42#14519736D412yes—
43#14519711—22no—
44#14519711—22no—
45#14519709—22no—
46#14519709—22no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519706—24no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519688—21no—
53#14519687—22no—
54C4×#92418—21no—
55C8×Dic61—22no—
56C22×C8×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61D412yes—
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62#97×C61—21no—
63#97×C61—21no—
64#97×C61C2×C412yes—
65C4×C8×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61#4111yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×C8×C61—24no—
74C2×C8×C61—22no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C42×C61C22×C411yescharacteristic
78C42×C61C2×D411yescharacteristic
79C42×C61C2×D411yescharacteristic
80C42×C61C2×D411yescharacteristic
81C22⋊Dic61—22no—
82C22⋊Dic61—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61C22⋊C412yes—
90C4⋊Dic61C22⋊C412yes—
91#11758196—22no—
92#11758196—22no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—22no—
96C4×Dic61—41no—
97C2×#92418—22no—
98C2×#92418—41no—
99C23×C61#12311yescharacteristic
100C2×C4×C61—22no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61C4×D411yescharacteristic
105C2×C4×C61C4×D411yescharacteristic
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12111yescharacteristic
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113Dic122—42no—
114Dic122—42no—
115Dic122—81no—
116Dic122—81no—
117C8×C61—24no—
118C8×C61—42no—
119C8×C61—81no—
120#92418—42no—
121#92418—81no—
122#9006—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61#38611yescharacteristic
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61#45612yes—
133Dic61—42no—
134Dic61—42no—
135Dic61—81no—
136Dic61—81no—
137#3162—611no—
138#2987—611no—
139#1544—611no—
140#1497—611no—
141#1497—611no—
142#1302—611no—
143#1302D6111yescharacteristic
144C2×C61—41no—
145C2×C61#188111yescharacteristic
146C2×C61#188111yescharacteristic
147C2×C61#188611yescharacteristic
148#533—611no—
149#533—611no—
150#501—612no—
151#501—612no—
152#501—1221no—
153#501—1221no—
154#446—1222no—
155#446—1222no—
156#433—1222no—
157#432—611no—
158#432C2×D6111yescharacteristic
159#431—611no—
160#431C2×D6111yescharacteristic
161#427—1222no—
162C2×#97C2×D6111yescharacteristic
163#332—1221no—
164#332—1221no—
165Q8⋊C8—1222no—
166Q8⋊C8—1222no—
167C61#900611yescharacteristic, complemented, Sylow
168C22×C8—21no—
169C4⋊Q8—611no—
170C4⋊Q8—611no—
171C4⋊Q8—611no—
172C4⋊Q8—611no—
173#125—612no—
174#125—1221no—
175C22⋊Q8—1221no—
176C22⋊Q8—1221no—
177C22⋊Q8—1221no—
178C22⋊Q8—1221no—
179C4×Q8—1221no—
180C4×Q8—1221no—
181C4×Q8—1221no—
182C4×Q8—1221no—
183#117—612no—
184#117—1221no—
185C2×C42C22×D6111yescharacteristic
186#107—1222no—
187#107—1222no—
188#106—1222no—
189#106—1222no—
190C4⋊C8—21no—
191C4⋊C8—612no—
192C4⋊C8—1224no—
193C4⋊C8—1221no—
194C4⋊C8D24412yes—
195C22⋊C8—21no—
196C22⋊C8—21no—
197C22⋊C8—1221no—
198C22⋊C8—1221no—
199#97—21no—
200#97—21no—
201#97—1222no—
202#97—1221no—
203#97C4×D6112yes—
204C4×C8—21no—
205C4×C8—1222no—
206C4×C8—1221no—
207C2×Q8—1221no—
208C2×Q8—1221no—
209C2×Q8—1221no—
210C2×Q8—1221no—
211C22×C4#1175822211yescharacteristic
212C22×C4D4×D6111yescharacteristic
213C22×C4#1175822611yescharacteristic
214C2×C8—24no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—1222no—
219C2×C8—2441no—
220C4⋊C4—612no—
221C4⋊C4—612no—
222C4⋊C4—1222no—
223C4⋊C4—1222no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—1222no—
233C22⋊C4—2441no—
234C42—1222no—
235C42—2441no—
236C42C2×C4×D6111yescharacteristic
237C42C2×D24411yescharacteristic
238C42D4×D6111yescharacteristic
239C42D4×D6111yescharacteristic
240C23#1451976211yescharacteristic
241Q8—4881no—
242Q8—4881no—
243Q8—2442no—
244Q8—2442no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4C22⋊C4×D6111yescharacteristic
253C2×C4#1451973911yescharacteristic
254C2×C4C4×D24411yescharacteristic
255C2×C4#1451974711yescharacteristic
256C2×C4#1451975011yescharacteristic
257C2×C4#1451975211yescharacteristic
258C8—24no—
259C8—42no—
260C8—81no—
261C8—4881no—
262C8—2442no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22#1683964011yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—4881no—
273C4—4881no—
274C4—2442no—
275C4—2442no—
276C4#1683994612yes—
277C2—41no—
278C2#2144618011yescharacteristic
279C2#2144618211yescharacteristic
280C2#2144621111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1302C2
socleC22×C61#386
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#1302D61
hypocenterC61#9006
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
167. C61#9006semidirect

Maximal subgroups

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

subgroupindex
#214563432
#214549242
#214444832
#214442932
#214442912
#214437182
C61×#13022
#900661