Finite Group Databasebeta

← #21462072

Subgroups — #21462072

Order 7808.

264 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 54 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#16840748C211yesmaximal, characteristic, complemented
2#16840741C211yesmaximal, characteristic, complemented
3#16840665C212yesmaximal, complemented
4#16840663C212yesmaximal, complemented
5#16840274C211yesmaximal, characteristic
6D61⋊M16—21no—
7#14519856—21no—
8#14519838—21no—
9#14519837C2212yes—
10#14519836—21no—
11#14519835C2212yes—
12C2×#11758222C2211yescharacteristic
13C22×C4×D61C411yescharacteristic, complemented
14#14519761C411yescharacteristic, complemented
15#14519761C2211yescharacteristic
16#14519757—21no—
17#14519752—21no—
18#14519747C411yescharacteristic, complemented
19#14519747C2211yescharacteristic
20C4×D244—21no—
21C4×D244—21no—
22#117×C61C411yescharacteristic, complemented
23C23×D61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61C2×C411yescharacteristic
26C2×C22⋊D61C2311yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28#11758222—41no—
29#11758222—41no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244D411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61—41no—
36C2×C4×D61—41no—
37C2×C4×D61D411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×Dic122D411yescharacteristic
40C22⋊#6923—22no—
41#11758217—22no—
42C4⋊#6923—41no—
43C4×#6923—41no—
44#11758213—41no—
45D61⋊C8—41no—
46C4⋊C4×C61—21no—
47C22⋊C4×C61C2×C411yescharacteristic
48C22⋊C4×C61C2×C411yescharacteristic
49C42×C61—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C23×C61C22×C411yescharacteristic
57C22×D61—21no—
58C22×D61—42no—
59C22×D61—41no—
60C22×D61C22⋊C411yescharacteristic
61C22×D61C2×D411yescharacteristic
62C2×#6923—42no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C22⋊D61—41no—
70C22⋊D61—41no—
71C2×Dic61—21no—
72C2×Dic61—41no—
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C2×D411yescharacteristic
75D244—41no—
76D244—42no—
77D244—42no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—42no—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—41no—
86#92420—42no—
87C22×C61—21no—
88C22×C61—41no—
89C22×C61C2×C22⋊C411yescharacteristic
90C2×D61—22no—
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—41no—
94C2×D61—42no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—42no—
99#6923—82no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—41no—
103C4×C61#9911yescharacteristic
104C4×C61#9911yescharacteristic
105Dic61—21no—
106Dic61—21no—
107Dic61—41no—
108#2120—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—41no—
111C2×C61C2×#9911yescharacteristic
112D61—41no—
113D61—41no—
114D61—42no—
115#525—611no—
116#413—611no—
117#410—611no—
118#352—612no—
119AΣL(1,𝔽16)—612no—
120C61#212011yescharacteristic, complemented, Sylow
121C2×#41—611no—
122C23×C4—611no—
123C2×M16—1221no—
124#123—611no—
125#123—611no—
126C22⋊Q8—1221no—
127#121—1221no—
128#120—611no—
129#120—611no—
130C4×D4—1221no—
131C4×D4—1221no—
132#117—1221no—
133#117#692311yescharacteristic, complemented
134#101—1221no—
135#100—612no—
136#99—612no—
137#99—1221no—
138C24—611no—
139#41—2441no—
140#41—2441no—
141C2×Q8—611no—
142C2×D4—611no—
143C2×D4—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C2×D4—1221no—
147C22×C4—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4—2441no—
153C22×C4—2441no—
154C22×C4C2×#692311yescharacteristic
155M16—1222no—
156M16—2441no—
157C2×C8—2441no—
158C4⋊C4—21no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—2441no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1222no—
167C22⋊C4C2×#692311yescharacteristic
168C22⋊C4C2×#692311yescharacteristic
169C42—21no—
170C42—2441no—
171C23—611no—
172C23—611no—
173C23—1221no—
174C23—2441no—
175C23—2442no—
176C23C22×#692311yescharacteristic
177Q8—2441no—
178D4—2441no—
179D4—2442no—
180D4—2442no—
181D4—2441no—
182D4—2441no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4C22⋊#692311yescharacteristic
200C2×C4C22⋊#692311yescharacteristic
201C8—2442no—
202C22—21no—
203C22—41no—
204C22—1222no—
205C22—1221no—
206C22—1221no—
207C22—2441no—
208C22—2441no—
209C22—2441no—
210C22—2442no—
211C22—2442no—
212C22—2441no—
213C22C2×C22⋊#692311yescharacteristic
214C4—21no—
215C4—41no—
216C4—41no—
217C4—1221no—
218C4—1221no—
219C4—4882no—
220C4—2441no—
221C4#1451983611yescharacteristic
222C4#1451983611yescharacteristic
223C2—21no—
224C2—41no—
225C2—2441no—
226C2—2442no—
227C2—2441no—
228C2C2×#1451983611yescharacteristic
subgroupG/H
centerC4#14519836
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#117×C61C4
socleC2×C61C2×#99
hypercenter#117#6923
hypocenterC61#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #16840748C2semidirect
2. #16840741C2semidirect
3. #16840665C2semidirect
4. #16840663C2semidirect
13. C22×C4×D61C4semidirect
14. #14519761C4semidirect
18. #14519747C4semidirect
22. #117×C61C4semidirect
120. C61#2120semidirect
133. #117#6923semidirect