Finite Group Databasebeta

← #30597858

Subgroups — #30597858

Order 15616.

436 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 104 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#21462541C211yesmaximal, characteristic
2#21461274C211yesmaximal, characteristic
3#21461031C212yesmaximal, complemented
4#21460705C212yesmaximal, complemented
5#21444478C211yesmaximal, characteristic
6C2×#14519864C412yes—
7#16840797—22no—
8D4×#92420—22no—
9#16840766C2211yescharacteristic
10#16840736C412yes—
11C4×#11758213C2212yes—
12C4×D61⋊C8C2211yescharacteristic
13#16840617C414yes—
14#92420⋊C8—22no—
15#16840603—22no—
16#16840310C2211yescharacteristic
17#16839814C2212yes—
18#16839510C412yes—
19#16839506C411yescharacteristic
20C61×#331C411yescharacteristic
21#14519864—44no—
22C2×#11758213—22no—
23C2×#11758213C2×C412yes—
24C2×#11758217—22no—
25C2×D61⋊C8C2×C411yescharacteristic
26C2×D61⋊C8C2×C411yescharacteristic
27C22×#92420—22no—
28C4⋊#92420—22no—
29C22⋊#92420—24no—
30#14519832C2×C414yes—
31C4×#92420—22no—
32C4×#92420D412yes—
33C4×#92420D412yes—
34C2×#11758224C2×C412yes—
35#14519777C2×C411yescharacteristic
36#14519764C2×C412yes—
37#14519748—22no—
38D4×Dic61—22no—
39C42×D61C2311yescharacteristic
40C4⋊#92418C2×C412yes—
41#14519689—22no—
42C8×Dic61—22no—
43#127×C61C2×C411yescharacteristic
44C4⋊C8×C61C2×C412yes—
45C2×D4×C61—22no—
46C2×D4×C61C4212yes—
47C2×C22⋊D61—22no—
48C22×Dic61—22no—
49#11758224—42no—
50#11758224—42no—
51C2×C4×D61C22×C411yescharacteristic
52C2×C4×D61#4112yes—
53C2×Dic122C4212yes—
54#11758217—44no—
55C2×#92420—22no—
56C2×#92420—24no—
57C2×#92420—44no—
58C2×#92420C22⋊C412yes—
59C2×#92420C22⋊C411yescharacteristic
60C2×#92420C22⋊C411yescharacteristic
61#11758213—42no—
62#11758213—42no—
63#11758213—42no—
64D61⋊C8—22no—
65D61⋊C8—41no—
66C2×C8×C61—22no—
67C42×C61C22×C411yescharacteristic
68C22⋊Dic61—24no—
69C4⋊Dic61—22no—
70C4×Dic61C22×C411yescharacteristic
71C4×Dic61C2×D412yes—
72C2×#92418—22no—
73C23×C61—22no—
74C22×D61#11711yescharacteristic
75D4×C61—42no—
76D4×C61—42no—
77D4×C61—42no—
78C2×C4×C61C2×C4211yescharacteristic
79C2×C4×C61C4×D412yes—
80C22⋊D61—44no—
81C2×Dic61—22no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61C2×C22⋊C411yescharacteristic
85C2×Dic61C4×D412yes—
86C4×D61—22no—
87C4×D61—22no—
88C4×D61—21no—
89C4×D61—21no—
90Dic122—42no—
91#92420—21no—
92#92420—22no—
93#92420—44no—
94#92420—42no—
95#92420#10012yes—
96C8×C61—42no—
97#92418—42no—
98#8243—611nomaximal, Sylow
99C22×C61—42no—
100C22×C61—44no—
101C22×C61C4×C22⋊C411yescharacteristic
102C2×D61—21no—
103C2×D61—22no—
104C4×C61—21no—
105C4×C61#44412yes—
106C4×C61#44412yes—
107Dic61—22no—
108Dic61—42no—
109Dic61C2×#10011yescharacteristic
110Dic61#41311yescharacteristic
111#2931—611no—
112#1543—611no—
113#1525—611no—
114#1451—612no—
115#1299—612no—
116C2×C61—82no—
117C2×C61C4×#10011yescharacteristic
118C2×C61#176512yes—
119D61—41no—
120C2×#131—612no—
121#532—611no—
122#436—1222no—
123C8×D4—1222no—
124#431—612no—
125#423—611no—
126#408—612no—
127C4×M16—612no—
128C2×C4×C8—611no—
129#333—612no—
130#331—611no—
131#331#692311yescharacteristic
132#329—614no—
133#322—1222no—
134#322—1222no—
135C61#824311yescharacteristic, complemented, Sylow
136C2×#41—612no—
137#131—2444no—
138C2×M16—612no—
139C2×M16—1222no—
140C2×M16—1222no—
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—1222no—
144C4⋊Q8—611no—
145#127C2×#692311yescharacteristic
146#124—612no—
147#121—1222no—
148C4×D4—1222no—
149C2×C42—611no—
150C4⋊C8—612no—
151C4⋊C8—1222no—
152C4⋊C8C2×#692312yes—
153C22⋊C8—1222no—
154C22⋊C8—1224no—
155#97—614no—
156C4×C8—612no—
157C4×C8—612no—
158C4×C8—1222no—
159C4×C8—1222no—
160#41—2442no—
161#41—2442no—
162C2×Q8—612no—
163C2×D4—22no—
164C2×D4—1222no—
165C2×D4C4×#692312yes—
166C22×C4—611no—
167C22×C4—612no—
168C22×C4—1222no—
169M16—2444no—
170M16—2442no—
171M16—2442no—
172M16—2442no—
173C2×C8—22no—
174C2×C8—611no—
175C2×C8—612no—
176C2×C8—611no—
177C2×C8—1222no—
178C2×C8—1224no—
179C2×C8—1222no—
180C2×C8—1222no—
181C2×C8—2444no—
182C2×C8—2441no—
183C4⋊C4—1222no—
184C22⋊C4—1224no—
185C42—611no—
186C42—612no—
187C42C22×#692311yescharacteristic
188C23—22no—
189C23—611no—
190Q8—2442no—
191D4—42no—
192D4—42no—
193D4—42no—
194D4—2444no—
195C2×C4—611no—
196C2×C4—612no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4C2×C4×#692311yescharacteristic
205C2×C4D4×#692312yes—
206C8—42no—
207C8—612no—
208C8—1221no—
209C8—1222no—
210C8—2442no—
211C8—2444no—
212C8—2442no—
213C22—42no—
214C22—44no—
215C22—1221no—
216C22—1222no—
217C22C22⋊C4×#692311yescharacteristic
218C4—21no—
219C4—611no—
220C4—611no—
221C4—1222no—
222C4—2442no—
223C4#1684080712yes—
224C4#1684080912yes—
225C2—82no—
226C2—2441no—
227C2#100×#692311yescharacteristic
228C2#2146159812yes—
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#331C4
socleC22×C61C4×C22⋊C4
prime radical#16840310C22
cosocleC42×D61C23
hypercenter#331#6923
hypocenterC61#8243
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #21461031C2semidirect
4. #21460705C2semidirect
135. C61#8243semidirect

Maximal subgroups

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

subgroupindex
#214625412
#214612742
#214610312
#214607052
#214444782
#824361