Finite Group Databasebeta

← #21451608

Subgroups — #21451608

Order 7808.

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

normal subgroups only

This group has 548 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×#14519751C211yesmaximal, characteristic
2#16839697C212yesmaximal, complemented
3#16839688C212yesmaximal, complemented
4#16839677C214yesmaximal, complemented
5#16839664C212yesmaximal, complemented
6#16839660C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8C2×#117×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2212yes—
11#14519751—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2214yes—
15C2×C22⋊Dic61C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2214yes—
18C2×#11758198C2214yes—
19#14519684C2212yes—
20#14519684C2214yes—
21C23×C4×C61C2211yescharacteristic
22#117×C61—24no—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61C2212yes—
26C2×C42×C61C2212yes—
27C24×C61C2311yescharacteristic
28C23×D61C2312yes—
29C22×C4×C61—24no—
30C22×C4×C61D414yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—24no—
36C2×C22⋊D61—44no—
37C22×Dic61C2312yes—
38C22×Dic61C2314yes—
39C2×D244—22no—
40C2×D244—24no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—22no—
43C22⋊C4×C61—24no—
44C42×C61—24no—
45C22⋊Dic61—42no—
46#11758198—24no—
47#11758198—44no—
48#11758198—44no—
49C4⋊Dic61—22no—
50C4⋊Dic61—24no—
51#11758196—44no—
52C23×C61—22no—
53C23×C61—21no—
54C23×C61—22no—
55C23×C61—21no—
56C23×C61C2×D412yes—
57C23×C61C2411yescharacteristic
58C22×D61—22no—
59C22×D61—24no—
60C22×D61—22no—
61C22×D61—24no—
62C22×D61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—28no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61#4114yes—
74C22⋊D61—48no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80D244—44no—
81C22×C61—22no—
82C22×C61—22no—
83C22×C61—22no—
84C22×C61—42no—
85C22×C61—42no—
86C22×C61C22×D411yescharacteristic
87C22×C61C2×#4112yes—
88C22×C61H(5,𝔽2)12yes—
89C22×C61H(5,𝔽2)11yescharacteristic
90C22×C612−1+411yescharacteristic
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—44no—
95C2×D61—44no—
96C4×C61—22no—
97C4×C61—42no—
98C4×C61—42no—
99C4×C61#12314yes—
100Dic61—42no—
101Dic61—44no—
102#2624—611nomaximal, Sylow
103C2×C61—42no—
104C2×C61C2×#12311yescharacteristic
105C2×C61#53511yescharacteristic
106C2×C61#53711yescharacteristic
107C2×C61#54012yes—
108C2×C61#54212yes—
109D61—82no—
110C2×#121—611no—
111C2×#117D6111yescharacteristic, complemented
112#399—612no—
113#397—612no—
114#394—614no—
115#390—612no—
116#389—612no—
117#380—611no—
118C61#262411yescharacteristic, complemented, Sylow
119C22×D4—612no—
120C22×D4—611no—
121C23×C4C2×D6111yescharacteristic
122#121—1224no—
123#117—24no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—614no—
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C22⋊C4—612no—
130C2×C22⋊C4—612no—
131C2×C22⋊C4—614no—
132C2×C22⋊C4—614no—
133C2×C22⋊C4C2×D6112yes—
134C2×C42C2×D6112yes—
135#95—612no—
136#95—614no—
137C24—612no—
138C24C22×D6111yescharacteristic
139C2×D4—1224no—
140C2×D4—1224no—
141C2×D4—1222no—
142C2×D4—2444no—
143C22×C4—24no—
144C22×C4—614no—
145C22×C4—612no—
146C22×C4C22⋊D6114yes—
147C22×C4C22×D6112yes—
148C22×C4C22×D6112yes—
149C22×C4C22×D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—1224no—
154C4⋊C4—1222no—
155C4⋊C4—2444no—
156C22⋊C4—24no—
157C22⋊C4—1224no—
158C22⋊C4—2444no—
159C22⋊C4—2444no—
160C22⋊C4—2442no—
161C42—24no—
162C23—22no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—1222no—
167C23—1224no—
168C23—1222no—
169C23—1224no—
170C23—1222no—
171C23C2×C22⋊D6112yes—
172C23C23×D6111yescharacteristic
173D4—2448no—
174D4—2444no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4—1224no—
187C2×C4—1224no—
188C2×C4#1175822214yes—
189C2×C4C2×C22⋊D6112yes—
190C2×C4C2×C22⋊D6112yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—2442no—
197C22—2442no—
198C22—2442no—
199C22—2444no—
200C22—2444no—
201C22C22×C22⋊D6111yescharacteristic
202C22C2×#1175822212yes—
203C22#1451982312yes—
204C22#1451982311yescharacteristic
205C22#1451982411yescharacteristic
206C4—22no—
207C4—42no—
208C4—42no—
209C4—2442no—
210C4—2444no—
211C4#1451976014yes—
212C2—42no—
213C2—4882no—
214C2C2×#1451976011yescharacteristic
215C2#1684032611yescharacteristic
216C2#1684034011yescharacteristic
217C2#1684036712yes—
218C2#1684038312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#117×C61C2
hypercenterC2×#117D61
hypocenterC61#2624
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16839697C2semidirect
3. #16839688C2semidirect
4. #16839677C2semidirect
5. #16839664C2semidirect
6. #16839660C2semidirect
7. #16839622C2semidirect
8. C2×#117×C61C2semidirect
111. C2×#117D61semidirect
118. C61#2624semidirect