Finite Group Databasebeta

← #21450461

Subgroups — #21450461

Order 7808.

412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#16839698C211yesmaximal, characteristic
2#16839690C212yesmaximal
3#16839649C212yesmaximal, complemented
4#16839644C212yesmaximal, complemented
5#16839643C212yesmaximal, complemented
6#16839634C211yesmaximal, characteristic
7#16839626C212yesmaximal, complemented
8C22⋊C4×Dic61C212yesmaximal
9C61×#397C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61C2212yes—
17C2×C4×Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—24no—
37C22×Dic61—41no—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C4⋊C4×C61—41no—
43C22⋊C4×C61—24no—
44C22⋊C4×C61—41no—
45C22⋊Dic61—22no—
46C22⋊Dic61—24no—
47C4⋊Dic61—41no—
48#11758196—24no—
49#11758196—24no—
50#11758196—24no—
51C4×Dic61—24no—
52C4×Dic61—42no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61#4112yes—
58C23×C61C2411yescharacteristic
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—44no—
80C2×Dic61#4114yes—
81C2×Dic61#4114yes—
82C22×C61—24no—
83C22×C61—22no—
84C22×C61—41no—
85C22×C61—42no—
86C22×C61—41no—
87C22×C61C2×#4112yes—
88C22×C61C2×#4112yes—
89C22×C61C2×#4111yescharacteristic
90C22×C61H(5,𝔽2)11yescharacteristic
91C22×C612−1+411yescharacteristic
92C4×C61—42no—
93C4×C61—42no—
94C4×C61—41no—
95C4×C61—41no—
96Dic61—24no—
97Dic61—24no—
98Dic61—42no—
99Dic61—42no—
100#2517—611nomaximal, Sylow
101C2×C61—42no—
102C2×C61#52912yes—
103C2×C61#53911yescharacteristic
104C2×C61#55111yescharacteristic
105C2×C61#55212yes—
106C2×C61#55911yescharacteristic
107#399—611no—
108#397—612no—
109#397D6111yescharacteristic
110#387—612no—
111#387—612no—
112#387—612no—
113#385—611no—
114#382—612no—
115C4×C22⋊C4—612no—
116C61#251711yescharacteristic, complemented, Sylow
117C23×C4—611no—
118C2×C4⋊C4—612no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—612no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4C2×D6111yescharacteristic
123C2×C22⋊C4—612no—
124C2×C22⋊C4—611no—
125C2×C22⋊C4C2×D6112yes—
126C2×C22⋊C4C2×D6111yescharacteristic
127C2×C42—612no—
128C2×C42—612no—
129#95—612no—
130#95—612no—
131#95—612no—
132#95—612no—
133#95—612no—
134#95—612no—
135#95—611no—
136#95C2×D6111yescharacteristic
137#95C2×D6112yes—
138C24C22×D6111yescharacteristic
139C22×C4—612no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4—612no—
143C22×C4—1224no—
144C22×C4—2441no—
145C22×C4C22×D6112yes—
146C22×C4C22×D6112yes—
147C22×C4C22×D6111yescharacteristic
148C22×C4C22×D6111yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—1224no—
151C4⋊C4—1224no—
152C4⋊C4—1224no—
153C4⋊C4—2441no—
154C22⋊C4—24no—
155C22⋊C4—41no—
156C22⋊C4—1224no—
157C22⋊C4—1222no—
158C42—1224no—
159C42—2442no—
160C23—22no—
161C23—22no—
162C23—21no—
163C23—21no—
164C23#1175822412yes—
165C23C23×D6111yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—614no—
177C2×C4—614no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—2444no—
189C22—24no—
190C22—22no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22#41×D6112yes—
195C22#41×D6112yes—
196C22C2×#1175822411yescharacteristic
197C22#1451982211yescharacteristic
198C22#1451982411yescharacteristic
199C4—41no—
200C4—42no—
201C4—42no—
202C4—41no—
203C4—1224no—
204C4—1224no—
205C4—2442no—
206C4—2442no—
207C2—42no—
208C2#1684028912yes—
209C2#1684035711yescharacteristic
210C2#1684044211yescharacteristic
211C2#1684044812yes—
212C2#1684049611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2517
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #16839649C2semidirect
4. #16839644C2semidirect
5. #16839643C2semidirect
7. #16839626C2semidirect
116. C61#2517semidirect