Finite Group Databasebeta

← #21446287

Subgroups — #21446287

Order 7808.

338 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519756C211yesmaximal, characteristic
2C2×#14519695C212yesmaximal, complemented
3#16839726C211yesmaximal, characteristic
4#16839530C212yesmaximal, complemented
5C22×M16×C61C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519756—21no—
9#14519756—21no—
10#14519756—21no—
11#14519756—21no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C412yes—
14C2×C22⋊Dic61C412yes—
15#14519695—24no—
16C22⋊#92418—21no—
17C22⋊#92418—21no—
18C23×C4×C61C2211yescharacteristic
19C2×M16×C61—21no—
20C2×M16×C61—24no—
21C2×M16×C61C2212yes—
22C22×C8×C61—21no—
23C24×C61C2×C411yescharacteristic
24C22×C4×C61—22no—
25C22×C4×C61—22no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×Dic61C2×C412yes—
33C22×Dic61C2×C412yes—
34C2×Dic122—22no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—22no—
38M16×C61—24no—
39M16×C61—22no—
40M16×C61D414yes—
41C2×C8×C61—24no—
42C2×C8×C61—22no—
43C22⋊Dic61—22no—
44C22⋊Dic61—22no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47#11758196—22no—
48#11758196—22no—
49#11758194—22no—
50#11758194—22no—
51C2×#92418—22no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61C22⋊C411yescharacteristic
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61#4112yes—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61—42no—
75Dic122—41no—
76Dic122—42no—
77Dic122—41no—
78C8×C61—24no—
79#92418—42no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—44no—
88C22×C61#10112yescomplemented
89C22×C61C2×C22⋊C411yescharacteristic
90C22×C61C4×D412yes—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61#12011yescharacteristic
94C4×C61#12112yes—
95C4×C61#12311yescharacteristic
96Dic61—42no—
97Dic61—42no—
98#1901—611nomaximal, Sylow
99C2×C61—22no—
100C2×C61—22no—
101C2×C61—41no—
102C2×C61#38611yescharacteristic
103C2×C61C2×#10111yescharacteristic
104C2×C61#41311yescharacteristic
105C22×M16D6111yescharacteristic
106C2×C22⋊Q8—611no—
107C2×#101—612no—
108#407—611no—
109#343—612no—
110C61#190111yescharacteristic, complemented, Sylow
111C22×Q8—611no—
112C23×C4C2×D6111yescharacteristic
113C2×M16—21no—
114C2×M16—24no—
115C2×M16—612no—
116C2×M16C2×D6112yes—
117C22×C8—21no—
118C22⋊Q8—1221no—
119C22⋊Q8—1221no—
120C22⋊Q8—1221no—
121C22⋊Q8—1221no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—611no—
124C2×C22⋊C4—612no—
125#101—1224no—
126C22⋊C8—1221no—
127C22⋊C8—1221no—
128C24C4×D6111yescharacteristic
129C2×Q8—1221no—
130C2×Q8—1222no—
131C2×Q8—1222no—
132C2×Q8—1221no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4C4×D6111yescharacteristic
138C22×C4D24411yescharacteristic
139C22×C4D24411yescharacteristic
140C22×C4C22⋊D6111yescharacteristic
141C22×C4C22⋊D6111yescharacteristic
142C22×C4C22×D6111yescharacteristic
143M16—24no—
144M16—22no—
145M16—1222no—
146M16—1222no—
147M16C22⋊D6114yes—
148C2×C8—24no—
149C2×C8—22no—
150C2×C8—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C22⋊C4—1222no—
156C22⋊C4—1222no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23#1175819811yescharacteristic
161C23#1175819811yescharacteristic
162C23C2×C4×D6111yescharacteristic
163Q8—2441no—
164Q8—2442no—
165Q8—2441no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1224no—
176C2×C4—2442no—
177C2×C4#1175819811yescharacteristic
178C2×C4#1175819811yescharacteristic
179C2×C4C2×D24411yescharacteristic
180C2×C4#1175822212yes—
181C2×C4C2×C22⋊D6112yes—
182C2×C4C2×C22⋊D6111yescharacteristic
183C8—24no—
184C8—2442no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#1451969512yescomplemented
194C22C2×#1175819811yescharacteristic
195C22C4×C22⋊D6112yes—
196C4—21no—
197C4—21no—
198C4—2442no—
199C4—2442no—
200C4#1451974611yescharacteristic
201C4#1451975112yes—
202C4#1451976011yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#1683964111yescharacteristic
207C2C2×#1451969511yescharacteristic
208C2#1683974411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC22×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC22×M16D61
hypocenterC61#1901
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#14519695C2semidirect
4. #16839530C2semidirect
88. C22×C61#101semidirect
110. C61#1901semidirect
193. C22#14519695semidirect