Finite Group Databasebeta

← #21446868

Subgroups — #21446868

Order 7808.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519810C212yesmaximal, complemented
2#16840343C211yesmaximal, characteristic
3C2×#14519703C212yesmaximal, complemented
4#16839667C211yesmaximal, characteristic, complemented
5C61×#343C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7C22×Dic122C2211yescharacteristic
8#14519810—24no—
9#14519810—24no—
10C2×Dic244—22no—
11C2×#11758190—22no—
12#14519757—22no—
13#14519752—22no—
14#14519751—22no—
15C2×C4×Dic61C2211yescharacteristic
16#14519703—24no—
17#14519684—22no—
18C2×M16×C61C2212yes—
19C2×C4⋊C4×C61C2211yescharacteristic
20C22×C4×C61D412yes—
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—22no—
23C22×Dic61—21no—
24C22×Dic61—21no—
25#11758222—22no—
26#11758222—22no—
27#11758222—22no—
28#11758222—22no—
29C2×D244—22no—
30C2×D244D412yes—
31C2×C4×D61—22no—
32C2×Dic122—22no—
33C2×Dic122—22no—
34C2×Dic122—21no—
35C2×Dic122D412yes—
36C2×Dic122D412yescomplemented
37M16×C61—22no—
38M16×C61D414yescomplemented
39C2×C8×C61—22no—
40C4⋊C4×C61—22no—
41#11758198—24no—
42C4⋊Dic61—22no—
43C4×Dic61—22no—
44Dic244—28no—
45#11758190—28no—
46C23×C61C2×D411yescharacteristic
47C22×D61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—42no—
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D412yes—
52C2×C4×C61C2×D412yes—
53C2×C4×C61#4111yescharacteristic
54C22⋊D61—42no—
55C22⋊D61—42no—
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61—22no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63D244—22no—
64D244—22no—
65D244—82no—
66C4×D61—42no—
67C4×D61—42no—
68Dic122—24no—
69Dic122—22no—
70Dic122—22no—
71Dic122—42no—
72C8×C61—24no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#12011yescharacteristic
76C22×C61#12111yescharacteristic
77C22×C61#12711yescharacteristic
78C2×D61—42no—
79C2×D61—42no—
80C2×D61—42no—
81C4×C61—42no—
82C4×C61#12012yes—
83C4×C61#12112yes—
84Dic61—42no—
85Dic61—42no—
86Dic61—42no—
87#2007—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—21no—
90C2×C61#39211yescharacteristic
91C2×C61#45511yescharacteristic
92C2×C61#45611yescharacteristic
93D61—82no—
94C2×#137—612no—
95#537—611no—
96C2×#104—612no—
97#391—611no—
98#343D6111yescharacteristic, complemented
99C61#200711yescharacteristic, complemented, Sylow
100C2×#41—612no—
101C22×Q8—611no—
102#137—1224no—
103#137—1224no—
104C2×Q16—1222no—
105C2×SD16—1222no—
106C2×M16C2×D6112yes—
107C22⋊Q8—1222no—
108#121—1222no—
109#121—1222no—
110C2×C4⋊C4C2×D6111yescharacteristic
111C2×C42—611no—
112#104—1224no—
113#95—1222no—
114#41—1222no—
115#41—1222no—
116#41—1222no—
117#41—1222no—
118C2×Q8—612no—
119C2×Q8—612no—
120C2×Q8—1221no—
121C2×Q8—1222no—
122C2×Q8—1222no—
123C2×D4—612no—
124C2×D4—1222no—
125C2×D4—1222no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4—1222no—
129C22×C4D24412yes—
130C22×C4C22×D6111yescharacteristic
131Q16—1228no—
132SD16—1228no—
133M16—22no—
134M16D24414yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—1222no—
138C22⋊C4—1224no—
139C42—1222no—
140C23—1222no—
141C23C2×D24411yescharacteristic
142Q8—1224no—
143Q8—1222no—
144Q8—1222no—
145Q8—2442no—
146D4—1222no—
147D4—1222no—
148D4—4882no—
149D4—2442no—
150D4—2442no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—1222no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2442no—
161C2×C4—2442no—
162C2×C4C2×D24412yes—
163C2×C4D4×D6111yescharacteristic
164C2×C4D4×D6112yes—
165C2×C4#1175822611yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—2442no—
170C22—2442no—
171C22—2442no—
172C22#1451974711yescharacteristic
173C22#1451975211yescharacteristic
174C22#1451977411yescharacteristic
175C4—42no—
176C4—2442no—
177C4—2442no—
178C4—2442no—
179C4#1451974712yes—
180C4#1451975212yes—
181C2—21no—
182C2—21no—
183C2—4882no—
184C2#1683967211yescharacteristic
185C2#1683994211yescharacteristic
186C2#1683994711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#120
hypercenter#343D61
hypocenterC61#2007
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
3. C2×#14519703C2semidirect
4. #16839667C2semidirect
5. C61×#343C2semidirect
36. C2×Dic122D4semidirect
38. M16×C61D4semidirect
98. #343D61semidirect
99. C61#2007semidirect
134. M16D244semidirect