Finite Group Databasebeta

← #21461987

Subgroups — #21461987

Order 7808.

344 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#14519840C212yesmaximal, complemented
3C2×#14519839C212yesmaximal
4C4×C4⋊#6923C211yesmaximal, characteristic, complemented
5#124×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8C2×C4×#6923—21no—
9#14519844—21no—
10C4⋊#92420—21no—
11#14519840—24no—
12#14519839—24no—
13(C2×#6923)⋊C4—21no—
14C2×Q8×D61C2211yescharacteristic
15C2×D4×D61C2211yescharacteristic
16#14519766C411yescharacteristic, complemented
17#14519765C411yescharacteristic, complemented
18#14519764C411yescharacteristic, complemented
19#14519763—21no—
20#14519763—21no—
21C22⋊C4×D61—21no—
22C22⋊C4×D61—21no—
23C42×D61C2211yescharacteristic
24#124×C61C411yescharacteristic, complemented
25C23×D61—21no—
26C22×#6923—22no—
27C2×Q8×C61C2×C411yescharacteristic
28C2×D4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30Q8×D61—22no—
31Q8×D61—22no—
32D4×D61—22no—
33D4×D61—22no—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C4×D61C2311yescharacteristic
39C2×Dic122—21no—
40C2×Dic122C2×C411yescharacteristic
41C2×#92420—22no—
42C4⋊#6923—22no—
43C4⋊#6923D414yes—
44C4×#6923—42no—
45D61⋊C8—22no—
46D61⋊C8—22no—
47C22⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C42×C61C2×C411yescharacteristic
50C22⋊Dic61—21no—
51C22⋊Dic61—21no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—21no—
56C4×Dic61C2×C411yescharacteristic
57C4×Dic61D411yescharacteristic
58C4×Dic61D411yescharacteristic
59C23×C61—21no—
60C22×D61—21no—
61C22×D61—42no—
62C22×D61—42no—
63C22×D61—41no—
64C22×D61—41no—
65C22×D61C2×D411yescharacteristic
66C2×#6923—24no—
67C2×#6923—42no—
68C2×#6923—42no—
69Q8×C61—22no—
70D4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22×C411yescharacteristic
75C22⋊D61—41no—
76C22⋊D61—41no—
77C2×Dic61—21no—
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C22⋊C411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81D244—22no—
82C4×D61—22no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—42no—
86C4×D61C2×D412yes—
87C4×D61#4112yes—
88Dic122—22no—
89Dic122—41no—
90Dic122—41no—
91#92420—42no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61C2×C22⋊C411yescharacteristic
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—82no—
100C2×D61—82no—
101C2×D61#12112yes—
102C2×D61#13512yes—
103C2×D61AGL(1,ℤ/8)11yescharacteristic
104C2×D61#13711yescharacteristic
105#6923—44no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61C4×D412yes—
110Dic61—21no—
111Dic61—21no—
112Dic61—41no—
113Dic61#12411yescharacteristic
114Dic61#12711yescharacteristic
115#1983—611nomaximal, Sylow
116C2×C61—81no—
117C2×C61#39011yescharacteristic
118C2×C61#41611yescharacteristic
119C2×C61#41711yescharacteristic
120D61—81no—
121D61#46312yes—
122D61#46412yes—
123C2×#124—611no—
124C2×C4⋊C8—611no—
125C2×#103—612no—
126C2×#102—612no—
127C4×C4⋊C4—611no—
128C61#198311yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C22×D4—611no—
131C22×C8—612no—
132#124—611no—
133#124—611no—
134#124—611no—
135#124—1221no—
136#124—1221no—
137#124#692311yescharacteristic, complemented
138C2×C4⋊C4—612no—
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141C2×C42—611no—
142C2×C42—1221no—
143C4⋊C8—1221no—
144C4⋊C8—1221no—
145#103—1224no—
146#102—1224no—
147#95—1221no—
148C24—1221no—
149C2×Q8—611no—
150C2×Q8—1221no—
151C2×Q8—1222no—
152C2×Q8—1222no—
153C2×Q8C2×#692311yescharacteristic
154C2×D4—611no—
155C2×D4—1222no—
156C2×D4—1222no—
157C2×D4—1221no—
158C2×D4C2×#692311yescharacteristic
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—1221no—
163C22×C4—1222no—
164C2×C8—1222no—
165C2×C8—1222no—
166C2×C8—1222no—
167C4⋊C4—614no—
168C4⋊C4—1222no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C42—611no—
178C42—611no—
179C42—611no—
180C42—2442no—
181C42C2×#692311yescharacteristic
182C23—21no—
183C23—611no—
184C23—1221no—
185C23—2442no—
186C23—2442no—
187C23—2441no—
188C23—2441no—
189Q8—22no—
190Q8—1222no—
191Q8—2441no—
192Q8—2441no—
193D4—22no—
194D4—1222no—
195D4—2441no—
196D4—2441no—
197C2×C4—21no—
198C2×C4—611no—
199C2×C4—612no—
200C2×C4—612no—
201C2×C4—611no—
202C2×C4—611no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4—1221no—
206C2×C4—1224no—
207C2×C4—1221no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4C22⋊#692311yescharacteristic
212C2×C4C22⋊#692311yescharacteristic
213C2×C4C22×#692311yescharacteristic
214C8—2442no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—612no—
219C22—612no—
220C22—611no—
221C22—611no—
222C22—4882no—
223C22—4882no—
224C22—2441no—
225C22—2441no—
226C22—2441no—
227C22C2×C22⋊#692311yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—611no—
232C4—611no—
233C4—1221no—
234C4—1221no—
235C4—2444no—
236C4—2441no—
237C4D4×#692312yes—
238C2—81no—
239C2—612no—
240C2—612no—
241C2—4881no—
242C2#1684071411yescharacteristic
243C2#1684075211yescharacteristic
244C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D61⋊(C4⋊C8)C2semidirect
2. C2×#14519840C2semidirect
4. C4×C4⋊#6923C2semidirect
16. #14519766C4semidirect
17. #14519765C4semidirect
18. #14519764C4semidirect
24. #124×C61C4semidirect
128. C61#1983semidirect
137. #124#6923semidirect