Finite Group Databasebeta

← #22627052

Subgroups — #22627052

Order 9344.

248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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#17989700C211yesmaximal, characteristic
2#17989700C211yesmaximal, characteristic
3Q8⋊#10596842C214yesmaximal, complemented
4C2×Q8×#64408C211yesmaximal, characteristic
5C4⋊#10596842—21no—
6C4⋊#10596842C2212yes—
7C22⋊#10596842—21no—
8C22⋊#10596842—21no—
9C4×#10596842—21no—
10C4×#10596842C2212yes—
11Q8×#64408—21no—
12Q8×#64408—21no—
13Q8×#64408C412yes—
14Q8×#64408C2212yes—
15C2×C4⋊#64408—21no—
16C2×C4⋊#64408C411yescharacteristic
17C2×C4×#64408—21no—
18C2×C4×#64408C2211yescharacteristic
19C2×Q8×D73C411yescharacteristic
20C2×#10596842—22no—
21C2×#10596842—22no—
22C22×#64408—21no—
23C22×#64408D411yescharacteristic
24C22×#64408D411yescharacteristic
25C4⋊#64408—22no—
26C4⋊#64408—22no—
27C4⋊#64408—21no—
28C4⋊#64408C2×C412yes—
29C4×#64408—22no—
30C4×#64408—22no—
31C4×#64408C2×C411yescharacteristic
32C4×#64408D411yescharacteristic
33C4×#64408D411yescharacteristic
34C4×#64408C2311yescharacteristic
35C2×Dic146—21no—
36C2×Dic146C811yescharacteristic, complemented
37Q8×D73—21no—
38Q8×D73—21no—
39Q8×D73C812yescomplemented
40Q8×D73C2×C412yes—
41C2×C4×D73—21no—
42C2×C4×D73C2×C411yescharacteristic
43C2×Q8×C73C811yescharacteristic, complemented
44C22×D73C22⋊C411yescharacteristic
45C2×#64408—22no—
46C2×#64408—22no—
47C2×#64408—41no—
48C2×#64408—42no—
49C2×#64408C22⋊C411yescharacteristic
50C2×#64408C22⋊C411yescharacteristic
51C2×#64408C2×D411yescharacteristic
52C2×#64408C2×D411yescharacteristic
53#10596842—42no—
54#10596842—42no—
55Q8×C73—21no—
56Q8×C73C2×C812yes—
57C2×C4×C73—21no—
58C2×C4×C73C2×C811yescharacteristic
59C2×Dic73—21no—
60C2×Dic73M1611yescharacteristic
61C4×D73—22no—
62C4×D73—22no—
63C4×D73C22⋊C411yescharacteristic
64C4×D73C2×C811yescharacteristic
65C4×D73M1611yescharacteristic
66C4×D73C22×C411yescharacteristic
67Dic146—21no—
68Dic146—22no—
69Dic146—22no—
70Dic146C2×C812yes—
71C22×C73C22⋊C811yescharacteristic
72C2×D73—21no—
73C2×D73—21no—
74C2×D73C22⋊C811yescharacteristic
75C2×D73C2×C22⋊C411yescharacteristic
76#64408—21no—
77#64408—21no—
78#64408—21no—
79#64408—42no—
80#64408#13712yes—
81C4×C73—22no—
82C4×C73C22⋊C811yescharacteristic
83C4×C73C22×C811yescharacteristic
84Dic73—22no—
85Dic73C22⋊C811yescharacteristic
86Dic73C2×M1611yescharacteristic
87C2×C73—21no—
88C2×C73C2×C22⋊C811yescharacteristic
89D73—21no—
90D73#41911yescharacteristic
91D73#42111yescharacteristic
92#1479—731nomaximal, Sylow
93C73#147911yescharacteristic, complemented, Sylow
94C2×C4×Q8—731no—
95#431—731no—
96#431—731no—
97Q8⋊C8—734no—
98C22×Q8—731no—
99C4×Q8—732no—
100C4×Q8—732no—
101C4×Q8—1461no—
102C4×Q8—1461no—
103C2×C4⋊C4—731no—
104C2×C4⋊C4—1461no—
105C2×C42—731no—
106C2×C42—1461no—
107C4⋊C8—732no—
108C4⋊C8—1461no—
109C22⋊C8—1461no—
110C22⋊C8—1461no—
111C4×C8—732no—
112C4×C8—1461no—
113C2×Q8—732no—
114C2×Q8—732no—
115C2×Q8—731no—
116C2×Q8—1461no—
117C2×Q8—1461no—
118C2×Q8—1461no—
119C2×Q8#1059684211yescharacteristic, complemented
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—1461no—
124C22×C4—1461no—
125C2×C8—1462no—
126C2×C8—1462no—
127C4⋊C4—732no—
128C4⋊C4—1461no—
129C4⋊C4—1462no—
130C4⋊C4—1462no—
131C42—731no—
132C42—731no—
133C42—731no—
134C42—731no—
135C42—1462no—
136C42—1462no—
137C23—731no—
138Q8—21no—
139Q8—732no—
140Q8—1462no—
141Q8—1462no—
142Q8—1461no—
143Q8C2×#1059684212yes—
144C2×C4—21no—
145C2×C4—2922no—
146C2×C4—2921no—
147C2×C4—731no—
148C2×C4—731no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—731no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—1462no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1462no—
160C2×C4—1461no—
161C2×C4C2×#1059684211yescharacteristic
162C8—2922no—
163C8—2922no—
164C22—731no—
165C22—731no—
166C22—1461no—
167C22—1461no—
168C22C22⋊#1059684211yescharacteristic
169C4—22no—
170C4—2922no—
171C4—732no—
172C4—731no—
173C4—731no—
174C4—1461no—
175C4—1461no—
176C4—1461no—
177C4—1462no—
178C4C22⋊#1059684211yescharacteristic
179C4C22×#1059684211yescharacteristic
180C2—21no—
181C2—731no—
182C2—731no—
183C2—1461no—
184C2C2×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10596842
commutatorC4×C73C22×C8
FrattiniC4C22×#10596842
FittingC2×Q8×C73C8
socleC2×C73C2×C22⋊C8
hypercenterC2×Q8#10596842
hypocenterC73#1479
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. Q8⋊#10596842C2semidirect
36. C2×Dic146C8semidirect
39. Q8×D73C8semidirect
43. C2×Q8×C73C8semidirect
93. C73#1479semidirect
119. C2×Q8#10596842semidirect