Finite Group Databasebeta

← #21450844

Subgroups — #21450844

Order 7808.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14519776C212yesmaximal
2C2×#14519775C212yesmaximal
3#16839683C212yesmaximal
4#16839682C211yesmaximal, characteristic
5#16839659C212yesmaximal
6#16839657C212yesmaximal
7#16839631C211yesmaximal, characteristic
8#16839613C212yesmaximal
9C61×#395C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C22×Dic122C2212yes—
12#14519776—28no—
13#14519775—28no—
14C2×C4⋊Dic61C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C4×Dic61C2212yes—
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28C22×Q8×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2212yes—
30C2×C4⋊C4×C61C2211yescharacteristic
31#95×C61C2212yes—
32#95×C61C2211yescharacteristic
33C2×Q8×C61—24no—
34C2×Q8×C61—41no—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C2×Dic122—24no—
45C2×Dic122—24no—
46C2×Dic122—24no—
47C2×Dic122—41no—
48C2×Dic122—42no—
49C4⋊C4×C61—24no—
50C4⋊C4×C61—41no—
51C4⋊Dic61—24no—
52C4⋊Dic61—41no—
53#11758196—24no—
54#11758196—24no—
55#11758196—24no—
56#11758196—24no—
57#11758196D418yes—
58#11758196Q818yescomplemented
59C4×Dic61—24no—
60C4×Dic61—24no—
61C4×Dic61Q814yescomplemented
62C23×C61C2411yescharacteristic
63Q8×C61—44no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61C2×D414yes—
75C2×C4×C61C2×Q812yes—
76C2×C4×C61C2×Q814yes—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61C2×D414yes—
85C2×Dic61C2×D414yes—
86C2×Dic61C2×Q814yes—
87C2×Dic61C2×Q814yes—
88C2×Dic61C2×Q814yes—
89Dic122—44no—
90Dic122—48no—
91C22×C61C22×D412yes—
92C22×C61C22×Q811yescharacteristic
93C22×C61C22×Q812yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C612−1+411yescharacteristic
96C4×C61—22no—
97C4×C61—24no—
98C4×C61—24no—
99C4×C61—41no—
100C4×C61—41no—
101Dic61—24no—
102Dic61—24no—
103Dic61—42no—
104Dic61C4⋊Q818yescomplemented
105#2551—611nomaximal, Sylow
106C2×C61C2×C4⋊Q812yes—
107C2×C61#54411yescharacteristic
108C2×C61D4211yescharacteristic
109C2×C61D4×Q812yes—
110C2×C61Q8211yescharacteristic
111C2×C4⋊Q8—612no—
112C2×C4⋊Q8—612no—
113#395—611no—
114#395—612no—
115#395D6111yescharacteristic
116#389—612no—
117#389—612no—
118#384—611no—
119C4×C4⋊C4—612no—
120C61#255111yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C22×Q8—612no—
123C22×Q8C2×D6111yescharacteristic
124C4⋊Q8—1228no—
125C4⋊Q8—1228no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—612no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4C2×D6112yes—
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C42—611no—
137C2×C42—612no—
138C2×C42—612no—
139#95—612no—
140#95—611no—
141#95—612no—
142#95C2×D6112yes—
143#95C2×D6111yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—1224no—
147C2×Q8—1224no—
148C2×Q8—1224no—
149C2×Q8—2442no—
150C2×Q8—2441no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—612no—
154C22×C4—612no—
155C22×C4C22×D6111yescharacteristic
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6112yes—
158C22×C4C22×D6111yescharacteristic
159C22×C4C22×D6112yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—618no—
163C4⋊C4—618no—
164C4⋊C4—1224no—
165C4⋊C4—1224no—
166C4⋊C4—1224no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—2441no—
170C42—614no—
171C42—1224no—
172C42—1224no—
173C23C23×D6111yescharacteristic
174Q8—44no—
175Q8—2448no—
176Q8—2444no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—614no—
188C2×C4—614no—
189C2×C4—614no—
190C2×C4—614no—
191C2×C4—614no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4D4×D6114yes—
200C2×C4Q8×D6112yes—
201C2×C4Q8×D6114yes—
202C22C2×D4×D6112yes—
203C22C2×Q8×D6112yes—
204C22C2×Q8×D6111yescharacteristic
205C22#1451982211yescharacteristic
206C22#1451982411yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—618no—
213C4—1224no—
214C4—1224no—
215C4—2442no—
216C2C4⋊Q8×D6112yes—
217C2#1684039111yescharacteristic
218C2#1684039411yescharacteristic
219C2#1684042512yes—
220C2#1684049211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2551
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. #11758196Q8semidirect
61. C4×Dic61Q8semidirect
104. Dic61C4⋊Q8semidirect
120. C61#2551semidirect