Finite Group Databasebeta

← #21450800

Subgroups — #21450800

Order 7808.

576 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic
3C2×C4×Dic122C211yesmaximal, characteristic, complemented
4#16839685C214yesmaximal, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839665C211yesmaximal, characteristic
7#16839650C214yesmaximal, complemented
8C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
9C2×#124×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519775—24no—
12#14519764—24no—
13C4×Dic122—24no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2214yes—
18C2×C22⋊Dic61C2214yes—
19C2×C22⋊Dic61C2214yes—
20C2×C4×Dic61C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2214yes—
24#14519684C2212yes—
25C22×Q8×C61C2211yescharacteristic
26C22×D4×C61C2211yescharacteristic
27#124×C61—24no—
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30C2×C42×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C2×D4×C61—22no—
36C2×D4×C61—22no—
37C2×D4×C61—22no—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122D414yes—
49C22⋊C4×C61—24no—
50C22⋊C4×C61—24no—
51C42×C61D414yes—
52C22⋊Dic61—28no—
53C22⋊Dic61—28no—
54C4⋊Dic61—22no—
55C4⋊Dic61—24no—
56#11758196—24no—
57#11758196—28no—
58C4×Dic61—24no—
59C4×Dic61—22no—
60C4×Dic61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—24no—
64C23×C61—22no—
65C23×C61—24no—
66C23×C61C2411yescharacteristic
67Q8×C61—44no—
68D4×C61—44no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61#4112yes—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61C2×D414yes—
89C2×Dic61#4114yes—
90Dic122—28no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—44no—
96C22×C61C22×D411yescharacteristic
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4112yes—
99C22×C61C2×#4111yescharacteristic
100C22×C612−1+412yes—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—42no—
104C4×C61#12114yes—
105Dic61—24no—
106Dic61—24no—
107Dic61—42no—
108Dic61—42no—
109#2545—611nomaximal, Sylow
110C2×C61—82no—
111C2×C61C2×#12111yescharacteristic
112C2×C61#53211yescharacteristic
113C2×C61#53611yescharacteristic
114C2×C61#54812yes—
115C2×C61#55612yes—
116C2×C4⋊Q8—611no—
117C2×#124—611no—
118C2×#124D6111yescharacteristic
119C2×C4×Q8—611no—
120#396—614no—
121#391—611no—
122#390—611no—
123#388—614no—
124C4×C4⋊C4—611no—
125C61#254511yescharacteristic, complemented, Sylow
126C22×Q8—611no—
127C22×Q8C2×D6111yescharacteristic
128C22×D4C2×D6111yescharacteristic
129C4⋊Q8—1224no—
130#124—24no—
131#124—1224no—
132C4×Q8—1224no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—614no—
136C2×C4⋊C4—612no—
137C2×C22⋊C4—614no—
138C2×C22⋊C4—614no—
139C2×C22⋊C4C2×D6112yes—
140C2×C22⋊C4C2×D6112yes—
141C2×C42—612no—
142C2×C42—611no—
143C2×C42—611no—
144C2×C42C2×D6111yescharacteristic
145#95—612no—
146#95—614no—
147C24C22×D6112yes—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—614no—
152C2×Q8—1222no—
153C2×Q8—1222no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4C22×D6112yes—
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6111yescharacteristic
165C4⋊C4—1228no—
166C4⋊C4—1224no—
167C4⋊C4—1224no—
168C4⋊C4—1222no—
169C22⋊C4—24no—
170C22⋊C4—24no—
171C22⋊C4—1228no—
172C22⋊C4—1228no—
173C42—1222no—
174C42—1222no—
175C42—1224no—
176C42C22⋊D6114yes—
177C23—22no—
178C23—22no—
179C23—24no—
180C23—22no—
181C23—24no—
182C23C23×D6111yescharacteristic
183Q8—44no—
184Q8—1228no—
185D4—44no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—614no—
192C2×C4—614no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1224no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4D4×D6112yes—
203C2×C4#1175822412yes—
204C2×C4C2×C22⋊D6112yes—
205C2×C4C2×C22⋊D6112yes—
206C2×C4C2×C22⋊D6112yes—
207C22—44no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—44no—
212C22C2×D4×D6111yescharacteristic
213C22C22×C22⋊D6111yescharacteristic
214C22#41×D6112yes—
215C22C2×#1175822411yescharacteristic
216C22#1451982412yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—1224no—
221C4—1224no—
222C4—2442no—
223C4—2442no—
224C4#1451974814yes—
225C2—82no—
226C2C2×#1451974811yescharacteristic
227C2#1684030811yescharacteristic
228C2#1684033311yescharacteristic
229C2#1684042012yes—
230C2#1684048112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2545
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
3. C2×C4×Dic122C2semidirect
4. #16839685C2semidirect
5. #16839669C2semidirect
7. #16839650C2semidirect
8. C4×C4⋊Dic61C2semidirect
125. C61#2545semidirect