Finite Group Databasebeta

← #29570941

Subgroups — #29570941

Order 15616.

444 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 141 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#125×Dic61C211yesmaximal, characteristic
2#21445567C212yesmaximal
3C2×#16839504C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C2×C61×#330C211yesmaximal, characteristic
6C2×#14519688C2212yes—
7#16839661C412yes—
8#16839648—22no—
9#16839628C2211yescharacteristic
10C4⋊C4×Dic61—22no—
11C4⋊C4×Dic61C412yes—
12C42×Dic61C2211yescharacteristic
13#16839516—22no—
14#16839516—22no—
15#16839504C414yescomplemented
16C2×#125×C61C2211yescharacteristic
17C2×#97×C61C2212yes—
18C61×#330C414yescomplemented
19C22×#92418—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×C4×Dic61—22no—
23C2×C4×Dic61C2×C411yescharacteristic
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C2×C4×Dic61D412yes—
27#14519688—22no—
28#14519688C2×C414yes—
29#14519684—22no—
30#14519684—22no—
31#14519684—22no—
32C22×C8×C61—22no—
33#125×C61—22no—
34#125×C61C2×C412yes—
35#125×C61C2×C412yes—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61C2×C412yes—
38C2×C42×C61C2311yescharacteristic
39#97×C61—22no—
40#97×C61C2×C414yes—
41C22×C4×C61—22no—
42C22×C4×C61C22×C411yescharacteristic
43C22×C4×C61C2×D412yes—
44C22×Dic61—22no—
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C22⋊C412yes—
47C22×Dic61C22⋊C411yescharacteristic
48C2×C8×C61—24no—
49C2×C8×C61—42no—
50C2×C8×C61—42no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—24no—
53C4⋊C4×C61—24no—
54C4⋊C4×C61C4214yes—
55C42×C61C22×C411yescharacteristic
56C42×C61C22×C411yescharacteristic
57C42×C61#4112yes—
58C4⋊Dic61—44no—
59C4⋊Dic61—42no—
60C4×Dic61—22no—
61C4×Dic61—41no—
62C4×Dic61—42no—
63C4×Dic61—42no—
64C4×Dic61—44no—
65C2×#92418—24no—
66C2×#92418—42no—
67C2×#92418—42no—
68C23×C61C2×C22⋊C411yescharacteristic
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—24no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C4211yescharacteristic
77C2×C4×C61#11711yescharacteristic
78C2×C4×C61C4×D412yes—
79C2×C4×C61C4×D412yes—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61#10112yes—
90C8×C61—44no—
91#92418—44no—
92#8225—611nomaximal, Sylow
93C22×C61C4×C22⋊C411yescharacteristic
94C22×C61C2×#10111yescharacteristic
95C22×C61#41311yescharacteristic
96C22×C61#42112yes—
97C22×C61#42112yes—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—44no—
103Dic61—22no—
104Dic61—41no—
105Dic61—42no—
106Dic61—82no—
107C4×#125—611no—
108#1745—612no—
109C2×#330—611no—
110C2×#330D6111yescharacteristic
111#1295—612no—
112C2×C61#153411yescharacteristic
113C2×C61#153512yes—
114C2×C61#153711yescharacteristic
115C2×C61C4×#10111yescharacteristic
116C2×C61#175912yes—
117C2×#125C2×D6111yescharacteristic
118C2×#97—612no—
119C2×#97C2×D6112yes—
120#389—612no—
121#387—1222no—
122#382—611no—
123C4×C4⋊C4—612no—
124C4×C4⋊C4—1222no—
125C43—611no—
126#336—1222no—
127#336—1222no—
128#330—614no—
129#330Dic6114yescomplemented
130C61#822511yescharacteristic, complemented, Sylow
131C22×C8—22no—
132C22×C8—1222no—
133#125—22no—
134#125C4×D6112yes—
135#125C2×Dic6112yes—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—612no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4C4×D6112yes—
140C2×C42—611no—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—612no—
144C2×C42—1222no—
145C2×C42C22×D6111yescharacteristic
146#97—22no—
147#97—614no—
148#97—1222no—
149#97C2×Dic6114yes—
150#95—1222no—
151#95—1222no—
152#95—1222no—
153C22×C4—22no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—612no—
157C22×C4—1222no—
158C22×C4C2×C4×D6111yescharacteristic
159C22×C4D4×D6112yes—
160C2×C8—24no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—1224no—
164C2×C8—2442no—
165C2×C8—2442no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—24no—
169C4⋊C4—2442no—
170C4⋊C4—2444no—
171C4⋊C4C4×Dic6114yes—
172C42—1222no—
173C42—2441no—
174C42—2442no—
175C42—2442no—
176C42—2444no—
177C42C2×C4×D6111yescharacteristic
178C42#1175822412yes—
179C42C22×Dic6111yescharacteristic
180C23C22⋊C4×D6111yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—612no—
189C2×C4—1222no—
190C2×C4—1221no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4C2×C4×Dic6111yescharacteristic
199C2×C4#1451973311yescharacteristic
200C2×C4#1451973712yes—
201C2×C4D4×Dic6112yes—
202C8—44no—
203C8—2444no—
204C22C22⋊C4×Dic6111yescharacteristic
205C22#101×D6111yescharacteristic
206C22#1683974511yescharacteristic
207C22#1683977712yes—
208C22#1683977712yes—
209C4—21no—
210C4—21no—
211C4—22no—
212C4—22no—
213C4—44no—
214C4—1222no—
215C4—4882no—
216C4—2442no—
217C4—2441no—
218C2#2144444411yescharacteristic
219C2#2144444912yes—
220C2#2144445511yescharacteristic
221C2#101×Dic6111yescharacteristic
222C2#2144563112yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#8225
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
15. #16839504C4semidirect
18. C61×#330C4semidirect
129. #330Dic61semidirect
130. C61#8225semidirect

Maximal subgroups

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

subgroupindex
#125×Dic612
#214455672
C2×#168395042
#214437012
C2×C61×#3302
#822561