Finite Group Databasebeta

← #21461963

Subgroups — #21461963

Order 7808.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840765C211yesmaximal, characteristic, complemented
2C2×#14519838C212yesmaximal, complemented
3C2×#14519837C212yesmaximal
4C4×#11758217C211yesmaximal, characteristic, complemented
5C2×#14519763C211yesmaximal, characteristic
6C2×#11758217C2212yes—
7C2×#11758217C2212yes—
8#14519844—21no—
9C4⋊#92420—21no—
10#14519838—24no—
11#14519837—24no—
12#14519832—21no—
13C4×#92420—21no—
14C22×Dic122C2211yescharacteristic
15C22×C22⋊D61C2211yescharacteristic
16#14519763—21no—
17#14519763—21no—
18#14519763—21no—
19#14519763—21no—
20C2×C22⋊Dic61C411yescharacteristic
21C2×#11758198C411yescharacteristic
22C2×#11758198C411yescharacteristic
23C2×C4×Dic61C2211yescharacteristic
24C2×C22⋊C4×C61C411yescharacteristic
25C24×C61C2×C411yescharacteristic
26C23×D61C2×C411yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C2×C22⋊D61—22no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×C22⋊D61—22no—
33C22×Dic61C2×C411yescharacteristic
34C22×Dic61C2×C411yescharacteristic
35C22×Dic61C2311yescharacteristic
36C2×Dic122—22no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—22no—
40#11758217—22no—
41#11758217—22no—
42#11758217—22no—
43#11758217D414yes—
44C2×#92420—22no—
45C2×#92420—22no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—21no—
54C4×Dic61D411yescharacteristic
55C4×Dic61D411yescharacteristic
56C4×Dic61D411yescharacteristic
57C4×Dic61D411yescharacteristic
58C23×C61—21no—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61C22×C411yescharacteristic
63C22×D61—21no—
64C22×D61—22no—
65C22×D61—41no—
66C22×D61—41no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—41no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22⋊C411yescharacteristic
72C22⋊D61—42no—
73C22⋊D61—41no—
74C22⋊D61—41no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—41no—
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C22⋊C411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81C2×Dic61C2×D412yes—
82C2×Dic61C2×D411yescharacteristic
83C2×Dic61#4112yes—
84Dic122—42no—
85Dic122—41no—
86Dic122—41no—
87#92420—24no—
88#92420—42no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—82no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61C4×D412yes—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—82no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—41no—
104Dic61—21no—
105Dic61—21no—
106Dic61—41no—
107Dic61#12112yes—
108Dic61#12411yescharacteristic
109Dic61#12711yescharacteristic
110#1967—611nomaximal, Sylow
111C2×C61—22no—
112C2×C61—81no—
113C2×C61#39011yescharacteristic
114C2×C61#41311yescharacteristic
115C2×C61#41311yescharacteristic
116D61—81no—
117C2×#124—611no—
118#423—611no—
119C2×#101—612no—
120C2×#100—612no—
121C4×M16—611no—
122C61#196711yescharacteristic, complemented, Sylow
123C22×Q8—611no—
124C22×D4—611no—
125C2×M16—612no—
126C2×M16—612no—
127#124—1221no—
128#124—1221no—
129#124—1221no—
130#124—1221no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4—611no—
134C2×C22⋊C4#692311yescharacteristic
135C2×C42—611no—
136C4⋊C8—1221no—
137C4⋊C8—1221no—
138#101—1224no—
139#100—1224no—
140#97—1221no—
141C4×C8—1221no—
142C24—611no—
143C24C2×#692311yescharacteristic
144C2×Q8—1222no—
145C2×Q8—1221no—
146C2×Q8—1221no—
147C2×Q8—1222no—
148C2×D4—1222no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4—1222no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4C2×#692311yescharacteristic
156C22×C4C2×#692311yescharacteristic
157M16—614no—
158M16—1222no—
159M16—1222no—
160M16—1222no—
161C2×C8—1222no—
162C2×C8—1222no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C42—611no—
172C42—611no—
173C42—611no—
174C42—611no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—1222no—
180C23—1221no—
181C23—2441no—
182C23—2441no—
183C23C22×#692311yescharacteristic
184Q8—2442no—
185Q8—2441no—
186Q8—2441no—
187D4—2442no—
188D4—2441no—
189D4—2441no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—611no—
198C2×C4—611no—
199C2×C4—1221no—
200C2×C4—1222no—
201C2×C4—2441no—
202C2×C4C22⋊#692311yescharacteristic
203C2×C4C22⋊#692311yescharacteristic
204C8—1224no—
205C8—2442no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—4882no—
213C22—2441no—
214C22—2441no—
215C22—2441no—
216C22C2×C22⋊#692311yescharacteristic
217C22D4×#692312yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—612no—
222C4—611no—
223C4—611no—
224C4—1221no—
225C4—1221no—
226C4—2441no—
227C2—22no—
228C2—81no—
229C2—4881no—
230C2#1684071411yescharacteristic
231C2#1684074811yescharacteristic
232C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1967
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840765C2semidirect
2. C2×#14519838C2semidirect
4. C4×#11758217C2semidirect
122. C61#1967semidirect