Finite Group Databasebeta

← #22625324

Subgroups — #22625324

Order 9344.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989610C211yesmaximal, characteristic
2#17989523C211yesmaximal, characteristic
3#17989441C212yesmaximal
4#17989440C212yesmaximal
5#17989141C211yesmaximal, characteristic
6C2×C4×#64408—21no—
7#14556658—21no—
8#14556648C2212yes—
9#14556646—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556590C411yescharacteristic, complemented
13#14556589C411yescharacteristic, complemented
14#14556581—21no—
15#14556571C2211yescharacteristic
16#14556569—21no—
17#14556567C2211yescharacteristic
18C4×Dic146—21no—
19C4×Dic146C411yescharacteristic, complemented
20#14556548—21no—
21C42×D73C2211yescharacteristic
22C4×Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4×#64408—24no—
26C2×Dic146—21no—
27C2×Dic146C2×C411yescharacteristic
28C2×C4×D73D411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73C2311yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C411yescharacteristic
33#11924007—21no—
34#11924007—21no—
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C2×Q8×C73C2×C411yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C42×C73—21no—
48C42×C73C2×C411yescharacteristic
49C22×D73C2×D411yescharacteristic
50C2×#64408—24no—
51C2×#64408—42no—
52C2×#64408—42no—
53Q8×C73—41no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22×C411yescharacteristic
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73C22⋊C411yescharacteristic
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C2×D411yescharacteristic
64C4×D73—22no—
65C4×D73—22no—
66C4×D73—41no—
67Dic146—42no—
68Dic146—41no—
69#10596833—42no—
70C22×C73C2×C22⋊C411yescharacteristic
71C2×D73—21no—
72C2×D73—21no—
73C2×D73#13712yes—
74#64408—44no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79C4×C73—41no—
80Dic73—21no—
81Dic73—21no—
82Dic73—41no—
83Dic73—41no—
84Dic73#10412yes—
85C2×C73#41011yescharacteristic
86C2×C73#41911yescharacteristic
87C2×C73C2×#10411yescharacteristic
88D73—22no—
89#1506—731nomaximal, Sylow
90C73#150611yescharacteristic, complemented, Sylow
91#533—731no—
92#432—731no—
93#376—731no—
94#328—732no—
95#328—732no—
96C4⋊Q8—731no—
97C4⋊Q8—731no—
98#125—1461no—
99C22⋊Q8—731no—
100C22⋊Q8—731no—
101C22⋊Q8—1461no—
102C4×Q8—731no—
103C4×Q8—1461no—
104C4×Q8#6440811yescharacteristic, complemented
105#117—1461no—
106C2×C42—731no—
107C2×C42—1461no—
108C4⋊C8—1461no—
109C22⋊C8—732no—
110#97—1461no—
111#95—732no—
112#95—1461no—
113C2×Q8—731no—
114C2×Q8—1461no—
115C2×Q8C2×#6440811yescharacteristic
116C22×C4—731no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—1462no—
120C2×C8—1462no—
121C4⋊C4—21no—
122C4⋊C4—731no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C2×#6440811yescharacteristic
130C22⋊C4—1461no—
131C22⋊C4—1461no—
132C42—21no—
133C42—731no—
134C42—731no—
135C42—731no—
136C42—1464no—
137C42—1461no—
138C42C2×#6440811yescharacteristic
139C23—731no—
140Q8—41no—
141Q8—2921no—
142Q8—2922no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2921no—
146C2×C4—2922no—
147C2×C4—2922no—
148C2×C4—731no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—1462no—
152C2×C4—1462no—
153C2×C4—1464no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4C22⋊#6440811yescharacteristic
157C2×C4C22⋊#6440811yescharacteristic
158C2×C4C22×#6440811yescharacteristic
159C8—2922no—
160C22—732no—
161C22—1461no—
162C22—1461no—
163C22C2×C22⋊#6440811yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—2924no—
170C4—2921no—
171C4—2921no—
172C4—732no—
173C4—1461no—
174C4—1461no—
175C2—1462no—
176C2#1798956611yescharacteristic
177C2#1798958011yescharacteristic
178C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1506
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #14556590C4semidirect
13. #14556589C4semidirect
19. C4×Dic146C4semidirect
22. C4×Q8×C73C4semidirect
90. C73#1506semidirect
104. C4×Q8#64408semidirect