Finite Group Databasebeta

← #21445741

Subgroups — #21445741

Order 7808.

564 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×Q8×D61C211yesmaximal, characteristic
2C2×#14519696C211yesmaximal, characteristic, complemented
3C2×#14519695C212yesmaximal, complemented
4#16839725C212yesmaximal
5C2×#101×C61C211yesmaximal, characteristic, complemented
6C22×Dic122C412yes—
7C22×Dic122C2211yescharacteristic
8C2×Q8×D61—22no—
9C2×Q8×D61—22no—
10C2×Q8×D61—24no—
11C2×Q8×D61—24no—
12C22×C4×D61C412yes—
13C22×C4×D61C2211yescharacteristic
14C2×#11758194C2212yes—
15#14519696—22no—
16#14519695—24no—
17#14519689—24no—
18C22×Q8×C61C2211yescharacteristic
19C2×M16×C61C2212yes—
20#101×C61—22no—
21C23×D61C2×C411yescharacteristic
22C2×Q8×C61—22no—
23C2×Q8×C61—22no—
24C2×Q8×C61D412yes—
25C2×Q8×C61D412yes—
26C22×C4×C61C2×C412yes—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61C2×C412yes—
29C22×Dic61C2×C411yescharacteristic
30Q8×D61—216no—
31Q8×D61—216no—
32C2×C4×D61—24no—
33C2×C4×D61—24no—
34C2×C4×D61—21no—
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37C2×C4×D61—24no—
38C2×C4×D61D414yes—
39C2×Dic122—24no—
40C2×Dic122—21no—
41C2×Dic122—22no—
42C2×Dic122—21no—
43C2×Dic122—24no—
44C2×Dic122—24no—
45C2×Dic122D414yes—
46M16×C61—22no—
47M16×C61—22no—
48C2×C8×C61—22no—
49#11758194—22no—
50#11758194—22no—
51C2×#92418—22no—
52C23×C61C22×C411yescharacteristic
53C22×D61—21no—
54C22×D61—21no—
55C22×D61—24no—
56C22×D61C22⋊C412yes—
57Q8×C61—24no—
58Q8×C61—24no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61C22⋊C414yes—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D411yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—22no—
70C2×Dic61C22⋊C412yes—
71C2×Dic61C22⋊C414yes—
72C4×D61—216no—
73C4×D61—24no—
74C4×D61—24no—
75Dic122—216no—
76Dic122—24no—
77Dic122—24no—
78C8×C61—42no—
79#92418—42no—
80C22×C61—22no—
81C22×C61C2×C22⋊C411yescharacteristic
82C22×C61C2×C22⋊C411yescharacteristic
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—24no—
85C2×D61—24no—
86C2×D61—22no—
87C2×D61—22no—
88C2×D61#10114yescomplemented
89C4×C61—24no—
90C4×C61#12012yes—
91C4×C61#12012yes—
92Dic61—22no—
93Dic61—24no—
94#1784—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#37911yescharacteristic
98C2×C61C2×#10112yes—
99D61—24no—
100C23×Q8—611no—
101C2×#101—611no—
102C2×#101—612no—
103C2×#101D6111yescharacteristic, complemented
104#407—612no—
105C61#178411yescharacteristic, complemented, Sylow
106C22×Q8—612no—
107C22×Q8—611no—
108C22×Q8—1224no—
109C22×Q8—1224no—
110C22×Q8—1222no—
111C22×Q8—1222no—
112C22×Q8C2×D6111yescharacteristic
113C23×C4—611no—
114C23×C4—612no—
115C2×M16—612no—
116C2×M16C2×D6112yes—
117#101—22no—
118#101—1224no—
119#101—1222no—
120C22⋊C8—1224no—
121C24—611no—
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—614no—
125C2×Q8—1224no—
126C2×Q8—1224no—
127C2×Q8—12216no—
128C2×Q8—12216no—
129C2×Q8—1224no—
130C2×Q8—1221no—
131C2×Q8—1222no—
132C2×Q8—1221no—
133C2×Q8D24412yes—
134C2×Q8C22⋊D6112yes—
135C22×C4—612no—
136C22×C4—611no—
137C22×C4—614no—
138C22×C4—1224no—
139C22×C4—1224no—
140C22×C4—1224no—
141C22×C4—1221no—
142C22×C4—1222no—
143C22×C4—1221no—
144C22×C4C4×D6112yes—
145C22×C4C22×D6111yescharacteristic
146M16—22no—
147M16—22no—
148M16—1222no—
149M16—1222no—
150C2×C8—22no—
151C2×C8—1222no—
152C23—612no—
153C23—1224no—
154C23—1221no—
155C23—1221no—
156C23C2×C4×D6111yescharacteristic
157Q8—24no—
158Q8—24no—
159Q8—12216no—
160Q8—1224no—
161Q8—1224no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—614no—
165C2×C4—612no—
166C2×C4—12216no—
167C2×C4—1221no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1221no—
171C2×C4—1224no—
172C2×C4—1224no—
173C2×C4#1175819814yes—
174C2×C4C2×D24411yescharacteristic
175C2×C4D4×D6112yes—
176C2×C4D4×D6112yes—
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—42no—
179C8—2442no—
180C22—22no—
181C22—614no—
182C22—1224no—
183C22—1224no—
184C22—1222no—
185C22—1222no—
186C22C22⋊C4×D6111yescharacteristic
187C22C22⋊C4×D6111yescharacteristic
188C22C2×#1175819811yescharacteristic
189C4—24no—
190C4—1224no—
191C4—1222no—
192C4#1451974512yes—
193C4#1451974712yes—
194C2—21no—
195C2—21no—
196C2—1224no—
197C2#1683961711yescharacteristic
198C2#101×D6112yes—
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#101D61
hypocenterC61#1784
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14519696C2semidirect
3. C2×#14519695C2semidirect
5. C2×#101×C61C2semidirect
88. C2×D61#101semidirect
103. C2×#101D61semidirect
105. C61#1784semidirect