Finite Group Databasebeta

← #30601858

Subgroups — #30601858

Order 15616.

392 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C4×#14519847C211yesmaximal, characteristic
2#21461277C212yesmaximal
3#21461142C212yesmaximal
4#21461029C211yesmaximal, characteristic
5#21456406C211yesmaximal, characteristic
6#16840781C2211yescharacteristic
7C2×#14519847—21no—
8C4×#11758213C2212yes—
9C4×#11758213C2211yescharacteristic
10#16840638—21no—
11#16840619—24no—
12Q8⋊#92420—24no—
13#92420⋊C8—21no—
14#16840603—21no—
15#16840317C2212yes—
16#16840142C411yescharacteristic
17#16840114C412yes—
18#16840004—21no—
19#16840004—21no—
20#16839856—21no—
21#16839856—21no—
22C4×C8×D61C2211yescharacteristic
23C61×#500C411yescharacteristic
24C2×#11758213—22no—
25C2×#11758213—21no—
26#14519847—24no—
27C4⋊#92420D412yes—
28#14519834—21no—
29#14519832—22no—
30#14519832D412yes—
31C4×#92420—21no—
32C4×#92420—21no—
33C4×#92420—22no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519777C2×C412yes—
39#14519768—22no—
40#14519757—22no—
41#14519753—22no—
42Q8×Dic61—22no—
43#14519742—22no—
44#14519735—22no—
45C42×D61C2311yescharacteristic
46#14519700—22no—
47#14519700—22no—
48C4×#92418C2×C411yescharacteristic
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C4⋊Q8×C61C2×C412yes—
52#107×C61—21no—
53#107×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61—22no—
56C2×C4×D61C2×D411yescharacteristic
57C2×C4×D61#4111yescharacteristic
58C2×C4×D61#4111yescharacteristic
59C2×Dic122—22no—
60C2×#92420—22no—
61C2×#92420—22no—
62C2×#92420—42no—
63#11758213—24no—
64#11758213—42no—
65#11758213—42no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C42×C61C22×C411yescharacteristic
71#11758198—42no—
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61—42no—
75#11758196—42no—
76C4×Dic61—42no—
77C4×Dic61C2×D411yescharacteristic
78C4×Dic61C2×D411yescharacteristic
79C4×Dic61C2×D411yescharacteristic
80C2×#92418C22⋊C411yescharacteristic
81C2×#92418C22⋊C411yescharacteristic
82Dic244—42no—
83Dic244—42no—
84C8×D61—22no—
85C8×D61—41no—
86C22×D61#12411yescharacteristic
87Q8×C61—44no—
88C2×C4×C61—42no—
89C2×C4×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61C4×D411yescharacteristic
91C2×C4×C61C4×D411yescharacteristic
92C2×Dic61—42no—
93C2×Dic61#12111yescharacteristic
94C2×Dic61#12111yescharacteristic
95C2×Dic61#12711yescharacteristic
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—22no—
99C4×D61—22no—
100Dic122—42no—
101Dic122—42no—
102#92420—44no—
103#92420—42no—
104#92420—42no—
105C8×C61—21no—
106C8×C61#10412yes—
107#92418—21no—
108#92418—21no—
109#9727—611nomaximal, Sylow
110C22×C61#39011yescharacteristic
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—21no—
114C4×C61—21no—
115C4×C61—82no—
116C4×C61C2×#10411yescharacteristic
117C4×C61#42111yescharacteristic
118C4×C61#44412yes—
119Dic61—21no—
120Dic61—21no—
121Dic61—82no—
122Dic61#47312yes—
123#3170—611no—
124C4×#108—611no—
125#1526—612no—
126#1485—612no—
127#1451—611no—
128C2×C61#197511yescharacteristic
129C2×C61#197911yescharacteristic
130C2×C61#198011yescharacteristic
131D61—41no—
132#533—612no—
133#500#692311yescharacteristic
134#494—611no—
135#487—612no—
136#467—1221no—
137#467—1221no—
138C4×Q16—1221no—
139C4×Q16—1221no—
140#431—611no—
141C2×#108—1221no—
142C4×M16—611no—
143C4×M16—612no—
144C2×C4×C8—611no—
145#341—1221no—
146#330—1224no—
147Q8⋊C8—1224no—
148#322—1221no—
149#322—1221no—
150C61#972711yescharacteristic, complemented, Sylow
151C2×Q16—1221no—
152C2×Q16—1221no—
153C2×M16—1221no—
154C2×M16—1222no—
155C22×C8—611no—
156C22×C8—611no—
157C4⋊Q8—612no—
158C4⋊Q8C2×#692312yes—
159#125—1222no—
160C22⋊Q8—1222no—
161C22⋊Q8—1222no—
162C4×Q8—1222no—
163C4×Q8—1222no—
164#117—1222no—
165C2×C42—611no—
166#108—1224no—
167#107—21no—
168#107—21no—
169C4⋊C8—612no—
170#103—1222no—
171#103—1222no—
172C22⋊C8—1221no—
173#97—612no—
174#97—1222no—
175C4×C8—611no—
176C4×C8—611no—
177C4×C8—611no—
178C4×C8—1221no—
179C4×C8—1221no—
180C4×C8—1222no—
181C4×C8C2×#692311yescharacteristic
182C2×Q8—22no—
183C2×Q8—1222no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187Q16—2442no—
188Q16—2442no—
189M16—1224no—
190M16—2442no—
191M16—2442no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—1222no—
195C2×C8—1222no—
196C2×C8—1222no—
197C2×C8—2441no—
198C2×C8—2442no—
199C2×C8C22⋊#692311yescharacteristic
200C2×C8C22⋊#692311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—1222no—
204C4⋊C4—1222no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C22⋊C4—2442no—
208C42—611no—
209C42—611no—
210C42—611no—
211C42—2442no—
212C42C22×#692311yescharacteristic
213C23—611no—
214Q8—44no—
215Q8—2442no—
216Q8—2442no—
217C2×C4—42no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1222no—
225C2×C4—2442no—
226C2×C4C2×C22⋊#692311yescharacteristic
227C2×C4D4×#692311yescharacteristic
228C2×C4D4×#692311yescharacteristic
229C8—21no—
230C8—1221no—
231C8—1221no—
232C8—2442no—
233C8—2442no—
234C8—2444no—
235C8#1451984212yes—
236C22—1221no—
237C22—1221no—
238C22—1221no—
239C22#1684071411yescharacteristic
240C4—21no—
241C4—82no—
242C4—612no—
243C4—1221no—
244C4—1221no—
245C4—4882no—
246C4C2×#1451984211yescharacteristic
247C4#1684076111yescharacteristic
248C4#1684080912yes—
249C2—2441no—
250C2#2146197411yescharacteristic
251C2#2146198111yescharacteristic
252C2#2146198211yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9727
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
150. C61#9727semidirect

Maximal subgroups

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

subgroupindex
C4×#145198472
#214612772
#214611422
#214610292
#214564062
#972761