Finite Group Databasebeta

← #21450301

Subgroups — #21450301

Order 7808.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519757C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839704C214yesmaximal, complemented
4#16839668C211yesmaximal, characteristic, complemented
5#16839667C211yesmaximal, characteristic, complemented
6#16839627C211yesmaximal, characteristic, complemented
7#16839624C214yesmaximal
8C4×#11758198C211yesmaximal, characteristic
9C61×#382C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×C4×D61C2212yes—
12C22×C4×D61C2211yescharacteristic
13#14519757—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2212yes—
16C2×#11758196C2212yes—
17C4⋊C4×D61—24no—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×C4×Dic61C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2214yes—
23#14519684C2214yes—
24#14519684C2214yes—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#95×C61C2214yes—
29C23×D61C2311yescharacteristic
30C22×C4×C61C2312yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61C2312yes—
35C22×Dic61C2312yes—
36C22×Dic61C2312yes—
37C22×Dic61C2311yescharacteristic
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61—24no—
41C2×C4×D61—28no—
42C2×C4×D61D414yes—
43C2×Dic122—22no—
44C2×Dic122—22no—
45C2×Dic122—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—22no—
48C42×C61—22no—
49#11758198—24no—
50#11758198—24no—
51C4⋊Dic61—22no—
52C4⋊Dic61—24no—
53#11758196—24no—
54C4×Dic61—22no—
55C23×C61C2411yescharacteristic
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—22no—
59C22×D61C2×D412yes—
60C22×D61#4114yes—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—24no—
66C2×C4×C61—24no—
67C2×C4×C61—22no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61#4112yes—
70C2×C4×C61#4112yes—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61—22no—
81C2×Dic61C2×D412yes—
82C4×D61—28no—
83C4×D61—48no—
84Dic122—44no—
85C22×C61C22×D411yescharacteristic
86C22×C61C2×#4112yes—
87C22×C61C2×#4111yescharacteristic
88C22×C61C2×#4111yescharacteristic
89C22×C612−1+412yes—
90C2×D61—22no—
91C2×D61—22no—
92C2×D61—24no—
93C2×D61—24no—
94C2×D61#12414yes—
95C4×C61—42no—
96C4×C61—42no—
97C4×C61—42no—
98C4×C61#12314yes—
99Dic61—22no—
100Dic61—42no—
101Dic61—42no—
102Dic61—42no—
103#2503—611nomaximal, Sylow
104C2×C61C2×#12311yescharacteristic
105C2×C61C2×#12411yescharacteristic
106C2×C61#53611yescharacteristic
107C2×C61#55212yes—
108C2×C61#55212yes—
109D61—24no—
110C2×C22⋊Q8—611no—
111C22×C4⋊C4—611no—
112#400—614no—
113#391—611no—
114#391—611no—
115#382—611no—
116#382D6111yescharacteristic, complemented
117#381—614no—
118C4×C22⋊C4—611no—
119C61#250311yescharacteristic, complemented, Sylow
120C22×Q8—611no—
121C23×C4—611no—
122C23×C4—612no—
123C22⋊Q8—1224no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—1224no—
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C4⋊C4C2×D6111yescharacteristic
130C2×C22⋊C4—612no—
131C2×C22⋊C4—612no—
132C2×C42—611no—
133C2×C42C2×D6111yescharacteristic
134#95—612no—
135#95—614no—
136#95—614no—
137#95—614no—
138#95C2×D6114yes—
139C24—611no—
140C2×Q8—1222no—
141C2×Q8—1222no—
142C2×Q8—1222no—
143C22×C4—611no—
144C22×C4—614no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—1224no—
149C22×C4—1228no—
150C22×C4—1222no—
151C22×C4—1222no—
152C22×C4C22×D6112yes—
153C22×C4C22×D6112yes—
154C22×C4C22×D6112yes—
155C22×C4C22×D6111yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—1224no—
159C4⋊C4—1224no—
160C4⋊C4—1222no—
161C22⋊C4—1224no—
162C22⋊C4—1224no—
163C42—22no—
164C42—1222no—
165C23—612no—
166C23—614no—
167C23—1221no—
168C23—1221no—
169C23—1222no—
170C23C23×D6111yescharacteristic
171Q8—2444no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—612no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1228no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1224no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—2448no—
192C2×C4#1175822212yes—
193C2×C4D4×D6112yes—
194C2×C4#1175822612yes—
195C22—614no—
196C22—1224no—
197C22—1224no—
198C22—1222no—
199C22—1222no—
200C22C2×D4×D6111yescharacteristic
201C22#41×D6112yes—
202C22C2×#1175822211yescharacteristic
203C22C2×#1175822611yescharacteristic
204C22#1451982412yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—1222no—
209C4—2442no—
210C4—2442no—
211C4—2442no—
212C4#1451976214yes—
213C2—1224no—
214C2C2×#1451976211yescharacteristic
215C2#124×D6111yescharacteristic
216C2#1684033211yescharacteristic
217C2#1684045012yes—
218C2#1684045112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#382C2
hypercenter#382D61
hypocenterC61#2503
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #16839704C2semidirect
4. #16839668C2semidirect
5. #16839667C2semidirect
6. #16839627C2semidirect
9. C61×#382C2semidirect
116. #382D61semidirect
119. C61#2503semidirect