Finite Group Databasebeta

← #30599795

Subgroups — #30599795

Order 15616.

412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462700C211yesmaximal, characteristic
2#21461953C211yesmaximal, characteristic
3#21461397C212yesmaximal, complemented
4#21460646C212yesmaximal, complemented
5#21444478C211yesmaximal, characteristic
6#16840797—22no—
7D4×#92420—22no—
8#16840781C2212yes—
9#16840766C2211yescharacteristic
10C2×#14519841—22no—
11#16840735—22no—
12C42×#6923C2211yescharacteristic
13#16840625—22no—
14#16840624—22no—
15#16840310C2211yescharacteristic
16#16839814C2212yes—
17#16839510C412yescomplemented
18#16839506C411yescharacteristic, complemented
19C61×#331C411yescharacteristic, complemented
20C2×#11758213—21no—
21C2×#11758217—22no—
22C22×#92420—22no—
23C2×C4×#6923—21no—
24C2×C4×#6923—22no—
25C4⋊#92420—22no—
26C4⋊#92420D412yes—
27C4⋊#92420D412yes—
28#14519841—44no—
29#14519834—22no—
30C22⋊#92420—24no—
31C4×#92420—22no—
32C2×#11758224D412yes—
33#14519777C2×C411yescharacteristic
34#14519764Q812yes—
35#14519748—22no—
36D4×Dic61—22no—
37C42×D61C2311yescharacteristic
38C4⋊#92418C2×C412yes—
39#14519689—22no—
40C8×Dic61—22no—
41#127×C61C2×C411yescharacteristic
42C4⋊C8×C61C2×C412yes—
43C22×#6923—41no—
44C2×D4×C61—22no—
45C2×D4×C61C4⋊C412yes—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—42no—
49#11758224—42no—
50C2×C4×D61C2×D411yescharacteristic
51C2×C4×D61#4112yes—
52C2×Dic122C4⋊C412yes—
53#11758217—82no—
54C2×#92420—22no—
55C2×#92420—22no—
56C2×#92420—41no—
57C2×#92420—82no—
58C4×#6923—22no—
59C4×#6923—24no—
60C4×#6923—42no—
61C4×#6923—41no—
62#11758213—42no—
63C2×C8×C61—22no—
64C42×C61C22×C411yescharacteristic
65C22⋊Dic61—24no—
66C4⋊Dic61—22no—
67C4×Dic61C2×D412yes—
68C4×Dic61C2×Q811yescharacteristic
69C2×#92418—22no—
70C23×C61—22no—
71C22×D61#12311yescharacteristic
72C2×#6923—42no—
73C2×#6923—44no—
74D4×C61—42no—
75D4×C61—42no—
76D4×C61—42no—
77C2×C4×C61C2×C4⋊C411yescharacteristic
78C2×C4×C61C4×D412yes—
79C22⋊D61—82no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61#12011yescharacteristic
84C2×Dic61C22⋊Q812yes—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—21no—
88C4×D61—21no—
89Dic122—42no—
90#92420—42no—
91#92420—42no—
92#92420—81no—
93C8×C61—42no—
94#92418—42no—
95#8934—611nomaximal, Sylow
96C22×C61—42no—
97C22×C61—44no—
98C22×C61#38511yescharacteristic
99C2×D61—21no—
100C2×D61—22no—
101#6923—44no—
102C4×C61—21no—
103C4×C61#44312yes—
104C4×C61#44412yes—
105Dic61—22no—
106Dic61—42no—
107Dic61#45311yescharacteristic
108Dic61#45511yescharacteristic
109#2979—611no—
110#1962—611no—
111#1574—612no—
112#1543—611no—
113#1276—612no—
114C2×C61—82no—
115C2×C61#185611yescharacteristic
116C2×C61#186612yes—
117D61—41no—
118#532—611no—
119#436—1222no—
120C8×D4—1222no—
121#431—612no—
122#431—612no—
123#423—611no—
124C2×#104—1222no—
125#408—1222no—
126C43—611no—
127#335—1222no—
128#334—1222no—
129#333—612no—
130#331—611no—
131#331#692311yescharacteristic, complemented
132C61#893411yescharacteristic, complemented, Sylow
133C2×#41—612no—
134C2×M16—1222no—
135C2×M16—1221no—
136C22×C8—1222no—
137C4⋊Q8—611no—
138#127C2×#692311yescharacteristic
139#124—612no—
140#121—1222no—
141C4×D4—1222no—
142C2×C42—611no—
143C2×C42—1222no—
144C2×C42—1221no—
145C4⋊C8—612no—
146C4⋊C8—612no—
147C4⋊C8—612no—
148C4⋊C8—1222no—
149C4⋊C8C2×#692312yes—
150#104—2444no—
151C22⋊C8—1222no—
152C22⋊C8—1222no—
153C22⋊C8—1224no—
154C4×C8—1222no—
155C4×C8—1222no—
156#41—2442no—
157#41—2442no—
158C2×Q8—612no—
159C2×D4—22no—
160C2×D4—1222no—
161C2×D4C4⋊#692312yes—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4—1222no—
165C22×C4—2441no—
166M16—4882no—
167M16—2442no—
168C2×C8—22no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—1222no—
172C2×C8—4882no—
173C2×C8—2441no—
174C4⋊C4—1222no—
175C22⋊C4—1224no—
176C42—611no—
177C42—612no—
178C42—1222no—
179C42—1224no—
180C42—2441no—
181C42—2442no—
182C42C22×#692311yescharacteristic
183C23—22no—
184C23—611no—
185Q8—2442no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—4882no—
190C2×C4—611no—
191C2×C4—612no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2444no—
201C2×C4C2×C4⋊#692311yescharacteristic
202C2×C4D4×#692312yes—
203C8—42no—
204C8—4881no—
205C8—2442no—
206C8—2442no—
207C8—2442no—
208C22—42no—
209C22—44no—
210C22—1221no—
211C22—1222no—
212C22#1684070911yescharacteristic
213C4—21no—
214C4—611no—
215C4—611no—
216C4—1222no—
217C4—2444no—
218C4—2442no—
219C4#1684080412yes—
220C4#1684080712yes—
221C2—82no—
222C2—2441no—
223C2#2146177411yescharacteristic
224C2#2146178612yes—
subgroupG/H
centerC22#16840709
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#331C4
socleC22×C61#385
prime radical#16840310C22
cosocleC42×D61C23
hypercenter#331#6923
hypocenterC61#8934
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #21461397C2semidirect
4. #21460646C2semidirect
17. #16839510C4semidirect
18. #16839506C4semidirect
19. C61×#331C4semidirect
131. #331#6923semidirect
132. C61#8934semidirect

Maximal subgroups

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

subgroupindex
#214627002
#214619532
#214613972
#214606462
#214444782
#893461