Finite Group Databasebeta

← #21450302

Subgroups — #21450302

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×#14519754C211yesmaximal, characteristic
2C22×#11758196C211yesmaximal, characteristic
3#16839704C212yesmaximal, complemented
4#16839703C212yesmaximal, complemented
5#16839666C212yesmaximal, complemented
6#16839626C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic
8#16839623C211yesmaximal, characteristic
9#16839623C211yesmaximal, characteristic
10C22⋊C4×Dic61C211yesmaximal, characteristic
11C61×#381C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15#14519754—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—24no—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C4×Dic61C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×Dic61—24no—
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61D414yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C2×Dic122—22no—
57C2×Dic122—24no—
58C22⋊C4×C61—22no—
59C22⋊C4×C61—22no—
60C22⋊Dic61—22no—
61C22⋊Dic61—22no—
62C4⋊Dic61—22no—
63#11758196—24no—
64#11758196—24no—
65#11758196—22no—
66#11758196—22no—
67C4×Dic61—24no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61C2×D412yes—
71C23×C61#4112yes—
72C23×C61#4112yes—
73C23×C61C2411yescharacteristic
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—44no—
85C2×Dic61—22no—
86C2×Dic61—28no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—44no—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×D412yes—
100C2×Dic61#4114yes—
101Dic122—44no—
102C22×C61—22no—
103C22×C61—22no—
104C22×C61—24no—
105C22×C61—24no—
106C22×C61#12414yes—
107C22×C61C22×D411yescharacteristic
108C22×C61C2×#4112yes—
109C22×C61C2×#4111yescharacteristic
110C22×C61C2×#4111yescharacteristic
111C22×C612−1+412yes—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—42no—
116Dic61—22no—
117Dic61—41no—
118Dic61—42no—
119Dic61—41no—
120Dic61—42no—
121Dic61#12314yes—
122#2503—611nomaximal, Sylow
123C2×C61—24no—
124C2×C61C2×#12311yescharacteristic
125C2×C61C2×#12411yescharacteristic
126C2×C61#53611yescharacteristic
127C2×C61#55212yes—
128C2×C61#55212yes—
129C2×C22⋊Q8—611no—
130C22×C4⋊C4—611no—
131#400—612no—
132#400—612no—
133#391—612no—
134#382—612no—
135#381—611no—
136#381—611no—
137#381—611no—
138#381D6111yescharacteristic
139C4×C22⋊C4—611no—
140C61#250311yescharacteristic, complemented, Sylow
141C22×Q8—611no—
142C23×C4—611no—
143C23×C4—611no—
144C23×C4C2×D6111yescharacteristic
145C22⋊Q8—1224no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—1224no—
152C2×C22⋊C4—611no—
153C2×C22⋊C4—611no—
154C2×C22⋊C4C2×D6111yescharacteristic
155C2×C22⋊C4C2×D6111yescharacteristic
156C2×C42—612no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95—612no—
162#95—612no—
163#95—612no—
164#95C2×D6112yes—
165#95C2×D6112yes—
166C24C22×D6111yescharacteristic
167C2×Q8—1222no—
168C2×Q8—1224no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—611no—
173C22×C4—614no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—612no—
179C22×C4—1224no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6111yescharacteristic
186C22×C4C22×D6112yes—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C42—1224no—
197C23—22no—
198C23—22no—
199C23#1175822212yes—
200C23D4×D6112yes—
201C23#1175822412yes—
202C23C23×D6111yescharacteristic
203Q8—2444no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—44no—
215C2×C4—612no—
216C2×C4—614no—
217C2×C4—612no—
218C2×C4—1228no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—2444no—
231C22—24no—
232C22—22no—
233C22—22no—
234C22—24no—
235C22#1451976314yes—
236C22C2×D4×D6111yescharacteristic
237C22#41×D6112yes—
238C22C2×#1175822411yescharacteristic
239C22C2×#1175822211yescharacteristic
240C22#1451982412yes—
241C4—42no—
242C4—41no—
243C4—42no—
244C4—41no—
245C4—614no—
246C4—1222no—
247C4—2441no—
248C4—2442no—
249C4—2441no—
250C4—2442no—
251C2—24no—
252C2#123×D6111yescharacteristic
253C2C2×#1451976311yescharacteristic
254C2#1684033411yescharacteristic
255C2#1684044512yes—
256C2#1684044912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#381C2
hypercenter#381D61
hypocenterC61#2503
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #16839704C2semidirect
4. #16839703C2semidirect
5. #16839666C2semidirect
6. #16839626C2semidirect
140. C61#2503semidirect