Finite Group Databasebeta

← #21450299

Subgroups — #21450299

Order 7808.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519755C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839701C211yesmaximal, characteristic, complemented
5#16839700C211yesmaximal, characteristic, complemented
6#16839666C212yesmaximal, complemented
7#16839626C212yesmaximal, complemented
8#16839624C212yesmaximal
9#16839624C212yesmaximal
10#16839609C211yesmaximal, characteristic
11C61×#400C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C4×D61C2212yes—
14C22×C4×D61C2211yescharacteristic
15#14519755—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C4⋊C4×D61—24no—
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—24no—
49C2×C4×D61—24no—
50C2×C4×D61—28no—
51C2×C4×D61D414yes—
52C2×Dic122—22no—
53C2×Dic122—24no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56#11758198—22no—
57#11758198—22no—
58#11758198—24no—
59C4⋊Dic61—22no—
60#11758196—22no—
61#11758196—24no—
62#11758196—22no—
63C4×Dic61—24no—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61C2×D412yes—
69C22×D61#4114yes—
70C2×C4×C61—22no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—24no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—24no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61C2×D412yes—
93C2×Dic61#4114yes—
94C4×D61—28no—
95C4×D61—48no—
96Dic122—44no—
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4112yes—
99C22×C61C2×#4112yes—
100C22×C612−1+411yescharacteristic
101C22×C612−1+411yescharacteristic
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—24no—
105C2×D61—24no—
106C2×D61#12414yes—
107C4×C61—22no—
108C4×C61—41no—
109C4×C61—42no—
110C4×C61—41no—
111C4×C61—42no—
112Dic61—41no—
113Dic61—42no—
114Dic61—41no—
115Dic61—42no—
116Dic61#12314yes—
117#2503—611nomaximal, Sylow
118C2×C61C2×#12311yescharacteristic
119C2×C61C2×#12411yescharacteristic
120C2×C61#53611yescharacteristic
121C2×C61#55212yes—
122C2×C61#55212yes—
123D61—24no—
124C2×C22⋊Q8—611no—
125C22×C4⋊C4—611no—
126#400—611no—
127#400—611no—
128#400—611no—
129#400D6111yescharacteristic, complemented
130#391—612no—
131#382—612no—
132#381—612no—
133#381—612no—
134C4×C22⋊C4—611no—
135C61#250311yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C23×C4—611no—
138C23×C4—612no—
139C22⋊Q8—1224no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—1224no—
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C22⋊C4—611no—
148C2×C22⋊C4—611no—
149C2×C22⋊C4—612no—
150C2×C42—612no—
151#95—611no—
152#95—612no—
153#95—612no—
154#95—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95C2×D6111yescharacteristic
159#95C2×D6112yes—
160#95C2×D6112yes—
161C24—611no—
162C2×Q8—1222no—
163C2×Q8—1224no—
164C22×C4—611no—
165C22×C4—614no—
166C22×C4—612no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—612no—
170C22×C4—1224no—
171C22×C4—1224no—
172C22×C4—1228no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—1224no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C22⋊C4—1224no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C42—1224no—
188C23—612no—
189C23—614no—
190C23—1222no—
191C23—1221no—
192C23—1221no—
193C23C23×D6111yescharacteristic
194Q8—2444no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—612no—
207C2×C4—614no—
208C2×C4—1228no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1224no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—2448no—
220C2×C4D4×D6112yes—
221C22—614no—
222C22—1224no—
223C22—1222no—
224C22—1222no—
225C22—1224no—
226C22C2×D4×D6111yescharacteristic
227C22#41×D6112yes—
228C22#41×D6112yes—
229C22#1451982411yescharacteristic
230C22#1451982511yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—42no—
235C4—41no—
236C4—614no—
237C4—2441no—
238C4—2442no—
239C4—2441no—
240C4—2442no—
241C2—1224no—
242C2#123×D6111yescharacteristic
243C2#124×D6111yescharacteristic
244C2#1684033511yescharacteristic
245C2#1684044412yes—
246C2#1684044812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2503
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #16839702C2semidirect
4. #16839701C2semidirect
5. #16839700C2semidirect
6. #16839666C2semidirect
7. #16839626C2semidirect
11. C61×#400C2semidirect
129. #400D61semidirect
135. C61#2503semidirect