Finite Group Databasebeta

← #21450796

Subgroups — #21450796

Order 7808.

576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519766C211yesmaximal, characteristic
2C2×#14519766C211yesmaximal, characteristic
3C2×Q8×Dic61C211yesmaximal, characteristic, complemented
4#16839684C214yesmaximal, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic
7#16839652C214yesmaximal, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11#14519766—24no—
12#14519766—24no—
13Q8×Dic61—24no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2214yes—
19C2×#11758198C2214yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2212yes—
22C2×C4×Dic61C2211yescharacteristic
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2214yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C22×Q8×C61C2211yescharacteristic
28C4⋊Q8×C61—24no—
29C2×C4⋊C4×C61C2214yes—
30C2×C42×C61C2211yescharacteristic
31C23×D61C2312yes—
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61D414yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C2×D244—22no—
47C2×D244—22no—
48C2×D244—22no—
49C4⋊C4×C61—28no—
50C42×C61—22no—
51#11758198—28no—
52#11758198—28no—
53#11758198—24no—
54#11758198—24no—
55C4⋊Dic61—22no—
56C4⋊Dic61—24no—
57#11758196—24no—
58C4×Dic61—22no—
59C4×Dic61—24no—
60C4×Dic61D414yes—
61C23×C61C2411yescharacteristic
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—24no—
65C22×D61—22no—
66C22×D61—24no—
67Q8×C61—28no—
68Q8×C61—44no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D414yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61#4114yes—
80C2×C4×C61#4112yes—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90D244—44no—
91C22×C61C22×D411yescharacteristic
92C22×C61C22×D411yescharacteristic
93C22×C61C2×#4111yescharacteristic
94C22×C61C2×#4112yes—
95C22×C612−1+412yes—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—44no—
100C2×D61—44no—
101C4×C61—24no—
102C4×C61—24no—
103C4×C61—42no—
104C4×C61#12114yes—
105Dic61—22no—
106Dic61—22no—
107Dic61—42no—
108Dic61—42no—
109#2545—611nomaximal, Sylow
110C2×C61C2×#12111yescharacteristic
111C2×C61#53211yescharacteristic
112C2×C61#53611yescharacteristic
113C2×C61#54812yes—
114C2×C61#55612yes—
115D61—82no—
116C2×C4⋊Q8D6111yescharacteristic, complemented
117C2×#124—611no—
118C2×#124—611no—
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×Q8C2×D6111yescharacteristic
127C22×Q8C2×D6111yescharacteristic
128C22×D4—611no—
129C4⋊Q8—24no—
130#124—1224no—
131#124—1224no—
132C4×Q8—1224no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4C2×D6114yes—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—614no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4—614no—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—611no—
144C2×C42C2×D6111yescharacteristic
145#95—612no—
146#95—614no—
147C24—612no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8C22⋊D6114yes—
154C2×D4—1222no—
155C2×D4—1222no—
156C2×D4—1222no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4C22×D6112yes—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C4⋊C4—28no—
166C4⋊C4—1224no—
167C4⋊C4—1222no—
168C4⋊C4—1224no—
169C22⋊C4—1224no—
170C22⋊C4—1224no—
171C22⋊C4—1228no—
172C22⋊C4—1228no—
173C42—22no—
174C42—614no—
175C42—1224no—
176C42—1222no—
177C23—1222no—
178C23—1222no—
179C23—1222no—
180C23—1224no—
181C23—1224no—
182C23C23×D6111yescharacteristic
183Q8—28no—
184Q8—44no—
185D4—2444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—612no—
194C2×C4—612no—
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×C4#1175822614yes—
205C2×C4C2×C22⋊D6114yes—
206C2×C4C2×C22⋊D6112yes—
207C22—2444no—
208C22—2442no—
209C22—2442no—
210C22—2442no—
211C22—2444no—
212C22C2×D4×D6111yescharacteristic
213C22C22×C22⋊D6111yescharacteristic
214C22C2×#1175822411yescharacteristic
215C22C2×#1175822612yes—
216C22#1451982512yes—
217C4—24no—
218C4—24no—
219C4—42no—
220C4—1222no—
221C4—1222no—
222C4—2442no—
223C4—2442no—
224C4#1451974914yes—
225C2—4882no—
226C2C2×#1451974911yescharacteristic
227C2#1684031311yescharacteristic
228C2#1684033711yescharacteristic
229C2#1684042312yes—
230C2#1684048612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2545
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8×Dic61C2semidirect
4. #16839684C2semidirect
5. #16839669C2semidirect
7. #16839652C2semidirect
8. C4×#11758196C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
116. C2×C4⋊Q8D61semidirect
125. C61#2545semidirect