Finite Group Databasebeta

← #21451019

Subgroups — #21451019

Order 7808.

548 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519769C211yesmaximal, characteristic, complemented
2C2×C4×D244C211yesmaximal, characteristic
3#16839684C214yesmaximal, complemented
4#16839664C211yesmaximal, characteristic
5#16839664C211yesmaximal, characteristic
6#16839636C214yesmaximal, complemented
7#16839632C211yesmaximal, characteristic, complemented
8#16839628C211yesmaximal, characteristic, complemented
9C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C4×D61C2212yes—
12#14519769—24no—
13C4×D244—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2214yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2214yes—
23#14519684C2214yes—
24C2×C4⋊C4×C61C2212yes—
25C2×C42×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#95×C61C2212yes—
29C23×D61C2312yes—
30C22×C4×C61C2312yes—
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2312yes—
36C22×Dic61C2312yes—
37C22×Dic61C2312yes—
38C2×D244—22no—
39C2×D244—22no—
40C2×D244Q814yes—
41C2×C4×D61—24no—
42C2×C4×D61—44no—
43C4⋊C4×C61—24no—
44C42×C61—22no—
45C42×C61—22no—
46C42×C61D414yes—
47#11758198—24no—
48#11758198—28no—
49#11758198—44no—
50C4⋊Dic61—22no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—44no—
54#11758196—24no—
55#11758196—24no—
56C23×C61C2411yescharacteristic
57C22×D61—22no—
58C22×D61—24no—
59C22×D61—22no—
60C22×D61—24no—
61C22×D61C2×Q814yes—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×Q812yes—
73C2×C4×C61#4114yes—
74C2×C4×C61#4112yes—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—24no—
79C2×Dic61—24no—
80C2×Dic61—24no—
81D244—28no—
82C4×D61—48no—
83C22×C61C22×D411yescharacteristic
84C22×C61C22×Q811yescharacteristic
85C22×C61C2×#4111yescharacteristic
86C22×C61C2×#4112yes—
87C22×C61H(5,𝔽2)12yes—
88C2×D61—24no—
89C2×D61—28no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—44no—
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—24no—
96C4×C61—42no—
97C4×C61C22⋊Q814yes—
98Dic61—42no—
99Dic61—42no—
100Dic61—42no—
101#2566—611nomaximal, Sylow
102C2×C61C2×C22⋊Q811yescharacteristic
103C2×C61#53211yescharacteristic
104C2×C61#53511yescharacteristic
105C2×C61#55312yes—
106C2×C61#55412yes—
107D61—44no—
108C2×#125—611no—
109C2×C4×D4—611no—
110#396—614no—
111#390—611no—
112#390—611no—
113#385—614no—
114#384—611no—
115#382—611no—
116C4×C4⋊C4D6111yescharacteristic, complemented
117C61#256611yescharacteristic, complemented, Sylow
118C22×D4—611no—
119C23×C4—612no—
120#125—1224no—
121C4×D4—1224no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—614no—
128C2×C4⋊C4C2×D6112yes—
129C2×C22⋊C4—612no—
130C2×C22⋊C4—614no—
131C2×C22⋊C4—614no—
132C2×C42C2×D6111yescharacteristic
133C2×C42C2×D6111yescharacteristic
134C2×C42C2×D6111yescharacteristic
135#95—614no—
136#95C2×D6112yes—
137C24—612no—
138C2×D4—614no—
139C2×D4—1222no—
140C2×D4—1222no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—612no—
144C22×C4—1224no—
145C22×C4—2444no—
146C22×C4C22×D6112yes—
147C22×C4C22×D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—24no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—2444no—
158C22⋊C4—1224no—
159C22⋊C4—1228no—
160C22⋊C4—2444no—
161C42—22no—
162C42—22no—
163C42D24414yes—
164C23—614no—
165C23—1222no—
166C23—1222no—
167C23—1224no—
168C23—1224no—
169C23C23×D6111yescharacteristic
170D4—1228no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1224no—
182C2×C4—1224no—
183C2×C4—1224no—
184C2×C4—2448no—
185C2×C4C2×D24412yes—
186C2×C4C2×D24412yes—
187C2×C4C2×D24412yes—
188C2×C4#1175822214yes—
189C2×C4#1175822412yes—
190C2×C4Q8×D6112yes—
191C22—1228no—
192C22—1224no—
193C22—2444no—
194C22—2442no—
195C22—2442no—
196C22C22×D24411yescharacteristic
197C22C2×Q8×D6111yescharacteristic
198C22C2×#1175822411yescharacteristic
199C22C2×#1175822212yes—
200C22#1451982312yes—
201C4—24no—
202C4—22no—
203C4—22no—
204C4—42no—
205C4—2442no—
206C4—2442no—
207C4—2442no—
208C4#1451975714yes—
209C2—2444no—
210C2C2×#1451975711yescharacteristic
211C2#1684031211yescharacteristic
212C2#1684033111yescharacteristic
213C2#1684045812yes—
214C2#1684047212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C4⋊C4×C61C2
hypercenterC4×C4⋊C4D61
hypocenterC61#2566
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519769C2semidirect
3. #16839684C2semidirect
6. #16839636C2semidirect
7. #16839632C2semidirect
8. #16839628C2semidirect
9. C4×C4⋊C4×C61C2semidirect
116. C4×C4⋊C4D61semidirect
117. C61#2566semidirect