Finite Group Databasebeta

← #21446294

Subgroups — #21446294

Order 7808.

304 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 93 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#16840529C211yesmaximal, characteristic
2#16839779C211yesmaximal, characteristic
3#16839771C211yesmaximal, characteristic, complemented
4C2×#14519696C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C2×#137×C61C211yesmaximal, characteristic
8#14519784—22no—
9#14519784—22no—
10C2×#11758194—22no—
11C2×#11758194C2211yescharacteristic
12C2×#11758194C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519704—22no—
16#14519701—22no—
17#14519696—22no—
18C2×#41×C61C2211yescharacteristic
19C22×Q8×C61C2211yescharacteristic
20#137×C61—22no—
21#137×C61—22no—
22C2×Q16×C61C412yescomplemented
23C2×SD16×C61C412yescomplemented
24C2×M16×C61C2211yescharacteristic
25#41×C61—21no—
26#41×C61—21no—
27#41×C61D412yes—
28#41×C61D412yes—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61C2×C412yes—
35C2×Q8×C61C2×C411yescharacteristic
36C2×D4×C61—21no—
37C2×D4×C61C2×C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41Q16×C61—24no—
42SD16×C61—24no—
43M16×C61—21no—
44M16×C61—21no—
45C2×C8×C61C2×C412yes—
46C22⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4×Dic61—21no—
49#11758194—24no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194—21no—
55#11758194D412yes—
56C2×#92418—24no—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418D412yes—
60C23×C61—21no—
61C23×C61#4111yescharacteristic
62Q8×C61—21no—
63Q8×C61—22no—
64Q8×C61—22no—
65Q8×C61—41no—
66Q8×C61—41no—
67Q8×C61C22⋊C412yes—
68D4×C61—22no—
69D4×C61—22no—
70D4×C61—21no—
71D4×C61C22⋊C412yes—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C22×C411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×Dic61—41no—
85C8×C61—22no—
86#92418—22no—
87#92418—22no—
88#92418—41no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—81no—
92C22×C61C4×D411yescharacteristic
93C22×C61#12111yescharacteristic
94C22×C61#12311yescharacteristic
95C4×C61—22no—
96C4×C61—42no—
97C4×C61C2×C22⋊C411yescharacteristic
98C4×C61C4×D411yescharacteristic
99C4×C61#12011yescharacteristic
100C4×C61#12111yescharacteristic
101Dic61—81no—
102#1902—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—21no—
105C2×C61—21no—
106C2×C61—42no—
107C2×C61#38611yescharacteristic
108C2×#137D6111yescharacteristic
109#568—611no—
110#421—611no—
111#419—611no—
112C2×#101—611no—
113#344—611no—
114#338—611no—
115C61#190211yescharacteristic, complemented, Sylow
116C2×#41C2×D6111yescharacteristic
117C22×Q8C2×D6111yescharacteristic
118#137—22no—
119#137—22no—
120C2×Q16Dic6112yescomplemented
121C2×SD16Dic6112yescomplemented
122#131—1222no—
123#131—1222no—
124C2×M16—611no—
125C2×M16—611no—
126C2×M16—611no—
127C2×M16—1222no—
128C2×M16C2×D6111yescharacteristic
129#117—611no—
130#104—1222no—
131#103—1222no—
132#101—1222no—
133#41—21no—
134#41—21no—
135#41C22⋊D6112yes—
136#41C22⋊D6112yes—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic6112yes—
143C2×Q8C2×Dic6111yescharacteristic
144C2×D4—21no—
145C2×D4C2×Dic6111yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22×D6111yescharacteristic
149Q16—24no—
150SD16—24no—
151M16—21no—
152M16—21no—
153M16—612no—
154M16—1224no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16—1221no—
160C2×C8—612no—
161C2×C8—1224no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8C2×Dic6112yes—
165C4⋊C4—1221no—
166C22⋊C4—1221no—
167C42—1221no—
168C23—21no—
169C23#1175822411yescharacteristic
170Q8—21no—
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175Q8C22⋊Dic6112yes—
176D4—22no—
177D4—22no—
178D4—21no—
179D4C22⋊Dic6112yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2441no—
187C2×C4D4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C2×C4#1175822411yescharacteristic
190C2×C4C22×Dic6111yescharacteristic
191C2×C4C2×C22⋊D6111yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C8—22no—
194C8—1222no—
195C8—1222no—
196C8—2441no—
197C22—22no—
198C22—41no—
199C22—81no—
200C22D4×Dic6111yescharacteristic
201C22#1451974911yescharacteristic
202C22#1451975811yescharacteristic
203C4—22no—
204C4—42no—
205C4—4881no—
206C4C2×C22⋊Dic6111yescharacteristic
207C4D4×Dic6111yescharacteristic
208C4#1451974511yescharacteristic
209C4#1451974911yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2#1683964211yescharacteristic
subgroupG/H
centerC2#16839642
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#137×C61C2
socleC2×C61#386
hypercenterC2×#137D61
hypocenterC61#1902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
3. #16839771C2semidirect
4. C2×#14519696C2semidirect
5. #16839533C2semidirect
6. #16839520C2semidirect
22. C2×Q16×C61C4semidirect
23. C2×SD16×C61C4semidirect
115. C61#1902semidirect
120. C2×Q16Dic61semidirect
121. C2×SD16Dic61semidirect