Finite Group Databasebeta

← #21452193

Subgroups — #21452193

Order 7808.

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

normal subgroups only

This group has 592 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×#14519755C212yesmaximal, complemented
2C2×#14519753C212yesmaximal, complemented
3#16839686C212yesmaximal, complemented
4#16839684C212yesmaximal, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839663C211yesmaximal, characteristic
7#16839659C212yesmaximal, complemented
8#16839640C212yesmaximal
9C61×#395C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519755—28no—
14#14519753—28no—
15C2×C4⋊Dic61C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28C22×Q8×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2212yes—
30C2×C4⋊C4×C61C2211yescharacteristic
31#95×C61C2211yescharacteristic
32#95×C61C2212yes—
33C23×D61C2312yes—
34C2×Q8×C61—24no—
35C2×Q8×C61—41no—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C2×D244—41no—
45C2×D244—41no—
46C2×D244Q814yescomplemented
47C2×C4×D61—24no—
48C2×C4×D61—24no—
49C2×C4×D61—42no—
50C2×Dic122—24no—
51C2×Dic122—41no—
52C4⋊C4×C61—24no—
53C4⋊C4×C61—41no—
54#11758198—24no—
55#11758198—24no—
56#11758198—24no—
57#11758198—24no—
58#11758198—42no—
59C4⋊Dic61—24no—
60#11758196—24no—
61#11758196—24no—
62#11758196—42no—
63#11758196D418yescomplemented
64C4×Dic61—41no—
65C23×C61C2411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61C2×Q814yes—
73Q8×C61—44no—
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—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D414yes—
86C2×C4×C61C2×Q812yes—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61C2×D414yes—
95C2×Dic61C2×D414yes—
96D244—44no—
97C4×D61—48no—
98Dic122—44no—
99C22×C61C22×D412yes—
100C22×C61C22×Q811yescharacteristic
101C22×C61H(5,𝔽2)11yescharacteristic
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C612−1+412yes—
104C2×D61—24no—
105C2×D61—24no—
106C2×D61—24no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C4×C61—22no—
112C4×C61—24no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—41no—
116Dic61—24no—
117Dic61—24no—
118Dic61—42no—
119#2683—611nomaximal, Sylow
120C2×C61#53712yes—
121C2×C61#54311yescharacteristic
122C2×C61D4211yescharacteristic
123C2×C61D4×Q812yes—
124C2×C61#56311yescharacteristic
125D61—44no—
126C2×C22⋊Q8—612no—
127C2×C22⋊Q8—612no—
128#396—612no—
129#396—612no—
130#395—611no—
131#395D6111yescharacteristic, complemented
132#390—611no—
133#389—612no—
134#386—612no—
135C61#268311yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×Q8C2×D6111yescharacteristic
138C22×D4—611no—
139C23×C4—612no—
140C22⋊Q8—1228no—
141C22⋊Q8—1228no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4C2×D6112yes—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154C2×C42—611no—
155#95—612no—
156#95—611no—
157#95C2×D6112yes—
158#95C2×D6111yescharacteristic
159C24—612no—
160C2×Q8—24no—
161C2×Q8—41no—
162C2×Q8—1224no—
163C2×Q8—2441no—
164C2×D4—614no—
165C2×D4—2441no—
166C2×D4—2441no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—1224no—
171C22×C4—1224no—
172C22×C4—2442no—
173C22×C4C22×D6111yescharacteristic
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—41no—
180C4⋊C4—618no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1224no—
184C4⋊C4—2442no—
185C22⋊C4—1224no—
186C22⋊C4—1224no—
187C22⋊C4—1224no—
188C22⋊C4—1224no—
189C22⋊C4—2442no—
190C42—2441no—
191C23—614no—
192C23—1222no—
193C23—1222no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23—1222no—
198C23C23×D6111yescharacteristic
199Q8—44no—
200Q8—2444no—
201D4—2444no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—614no—
214C2×C4—614no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—2448no—
223C2×C4D4×D6114yes—
224C2×C4Q8×D6112yes—
225C22—1224no—
226C22—1224no—
227C22—1224no—
228C22—2442no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22C2×D4×D6112yes—
233C22C2×Q8×D6111yescharacteristic
234C22#1451982211yescharacteristic
235C22#1451982311yescharacteristic
236C22#1451982512yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—1224no—
243C4—1224no—
244C4—2442no—
245C2—2444no—
246C2#1684034212yes—
247C2#1684038711yescharacteristic
248C2#1684039411yescharacteristic
249C2#1684042712yes—
250C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2683
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
2. C2×#14519753C2semidirect
3. #16839686C2semidirect
4. #16839684C2semidirect
5. #16839682C2semidirect
7. #16839659C2semidirect
9. C61×#395C2semidirect
46. C2×D244Q8semidirect
63. #11758196D4semidirect
131. #395D61semidirect
135. C61#2683semidirect