Finite Group Databasebeta

← #30595836

Subgroups — #30595836

Order 15616.

410 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461747C211yesmaximal, characteristic
2#21461536C211yesmaximal, characteristic
3#21460639C214yesmaximal
4#21454196C211yesmaximal, characteristic
5C2×#14519832—21no—
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12#16839669C412yes—
13#16839669C2212yes—
14#16839667—21no—
15#16839667—21no—
16#16839627—21no—
17#16839627—21no—
18C42×Dic61C2211yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519832—24no—
23C22×Dic122—21no—
24#14519777—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61C2311yescharacteristic
33#14519684—22no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37C22×Q8×C61C2×C412yes—
38C4⋊Q8×C61—42no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C42×C61C2×C411yescharacteristic
42C2×Q8×C61—24no—
43C2×Q8×C61—42no—
44C2×Q8×C61—42no—
45C22×C4×C61—22no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22×C411yescharacteristic
49C22×Dic61—22no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C2×D411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122—42no—
57C2×#92420—24no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C2×#92420—42no—
62C2×#92420—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—42no—
65C42×C61—22no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C4×Dic61—41no—
74C23×C61C2×C22⋊C411yescharacteristic
75Q8×C61—84no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61#10012yes—
86C2×C4×C61#10412yes—
87C2×C4×C61#13112yes—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61#13712yes—
102C2×Dic61#13712yes—
103Dic122—84no—
104#92420—44no—
105#92420—82no—
106#7702—611nomaximal, Sylow
107C22×C61#40811yescharacteristic
108C22×C61#41011yescharacteristic
109C22×C61C2×#10011yescharacteristic
110C22×C61#41911yescharacteristic
111C22×C61#41911yescharacteristic
112C22×C61C2×#10411yescharacteristic
113C22×C61#42111yescharacteristic
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—22no—
117C4×C61—82no—
118Dic61—22no—
119Dic61—22no—
120Dic61—41no—
121Dic61—41no—
122Dic61—82no—
123#2862—611no—
124#1839—611no—
125#1745—611no—
126#1272—614no—
127C2×C61#146911yescharacteristic
128C2×C61#148511yescharacteristic
129C2×C61#149711yescharacteristic
130C2×C61#150611yescharacteristic
131C2×C61#151511yescharacteristic
132C2×C61#152711yescharacteristic
133C2×C61#155811yescharacteristic
134C2×C4⋊Q8—611no—
135C2×C4⋊Q8#692311yescharacteristic
136C2×#97—1221no—
137#391—612no—
138#391—612no—
139#391—1221no—
140#391—1221no—
141#382—1221no—
142#382—1221no—
143C43—611no—
144#336—612no—
145#336—612no—
146#336—1221no—
147#336—1221no—
148#336—1221no—
149C61#770211yescharacteristic, complemented, Sylow
150C22×Q8—1221no—
151C22×Q8C2×#692312yes—
152C22×C8—1222no—
153C22×C8—1222no—
154C4⋊Q8—42no—
155C4⋊Q8—2442no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—1221no—
160C2×C42—611no—
161C2×C42—611no—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42—611no—
166C2×C42C2×#692311yescharacteristic
167#97—1224no—
168#95—1222no—
169#95—1222no—
170#95—1222no—
171#95—1222no—
172C2×Q8—24no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8—2442no—
176C2×Q8—2442no—
177C2×Q8—2442no—
178C22×C4—22no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—1222no—
184C22×C4C22⋊#692311yescharacteristic
185C22×C4C22⋊#692311yescharacteristic
186C22×C4C22×#692311yescharacteristic
187C2×C8—1224no—
188C2×C8—2442no—
189C2×C8—2442no—
190C2×C8—2442no—
191C2×C8—2442no—
192C2×C8—2442no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C42—22no—
198C42—1222no—
199C42—1222no—
200C42—1222no—
201C42—1222no—
202C42—2441no—
203C42—2441no—
204C23C2×C22⋊#692311yescharacteristic
205Q8—84no—
206Q8—4884no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4#1451983712yes—
232C2×C4#1451984212yes—
233C2×C4#1451986412yes—
234C8—4882no—
235C8—2444no—
236C22#1684073611yescharacteristic
237C22#1684074211yescharacteristic
238C22C2×#1451983711yescharacteristic
239C22#1684075511yescharacteristic
240C22#1684075511yescharacteristic
241C22C2×#1451984211yescharacteristic
242C22#1684076111yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—82no—
247C4—1222no—
248C4—1222no—
249C4—4882no—
250C4—2441no—
251C4—2441no—
252C2#2146108911yescharacteristic
253C2#2146114211yescharacteristic
254C2#2146118211yescharacteristic
255C2#2146121311yescharacteristic
256C2#2146124311yescharacteristic
257C2#2146128011yescharacteristic
258C2#2146135211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7702
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
149. C61#7702semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214615362
#214606392
#214541962
#770261