Finite Group Databasebeta

← #22626108

Subgroups — #22626108

Order 9344.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#11924038C211yesmaximal, characteristic
2C4×C4⋊#64408C211yesmaximal, characteristic
3#17989457C212yesmaximal
4#17989457C212yesmaximal
5#17989143C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×C4⋊#64408—21no—
8C2×C4×#64408C2212yes—
9#14556646—21no—
10C4×#10596833—21no—
11(C2×#64408)⋊C4—21no—
12#14556590C411yescharacteristic, complemented
13#14556590C411yescharacteristic, complemented
14#14556583C411yescharacteristic, complemented
15#14556569—21no—
16#14556569—21no—
17#14556556—21no—
18#14556556—21no—
19#14556549C2211yescharacteristic
20#14556549C2211yescharacteristic
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924038—22no—
25#11924038Q814yescomplemented
26C2×#10596833—22no—
27C4⋊#64408—24no—
28C4×#64408—24no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73C2311yescharacteristic
34C4⋊Dic73C2×C411yescharacteristic
35C4⋊Dic73C2×C411yescharacteristic
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924005—21no—
41#11924005—21no—
42C4×Dic73—21no—
43C4×Dic73—21no—
44C4×Dic73C2×C411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73D411yescharacteristic
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73C2×C411yescharacteristic
50C4⋊C4×C73C2×C411yescharacteristic
51C42×C73C2×C411yescharacteristic
52C22×D73C2×D411yescharacteristic
53C2×#64408—24no—
54C2×#64408—42no—
55C2×#64408—42no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22×C411yescharacteristic
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C2×D411yescharacteristic
66C4×D73—22no—
67C4×D73—41no—
68C4×D73C2×Q812yes—
69C4×D73#4112yes—
70Dic146—42no—
71Dic146—42no—
72#10596833—24no—
73C22×C73C2×C22⋊C411yescharacteristic
74C2×D73—21no—
75C2×D73—21no—
76C2×D73#12411yescharacteristic
77C2×D73C4⋊Q811yescharacteristic
78#64408—44no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73C4×Q812yes—
84Dic73—21no—
85Dic73—41no—
86Dic73—41no—
87Dic73#10412yes—
88Dic73C22⋊Q812yes—
89C2×C73#39111yescharacteristic
90C2×C73C2×#10411yescharacteristic
91C2×C73#42111yescharacteristic
92D73—21no—
93D73—21no—
94#1986—731nomaximal, Sylow
95C73#198611yescharacteristic, complemented, Sylow
96#533—731no—
97C4×M16—731no—
98C4×C4⋊C4—731no—
99#339—732no—
100#339—732no—
101C2×M16—732no—
102C4⋊Q8—731no—
103C4⋊Q8—731no—
104#125—731no—
105#125#6440811yescharacteristic, complemented
106C22⋊Q8—1461no—
107C22⋊Q8—1461no—
108C4×Q8—1461no—
109C4×Q8—1461no—
110#117—731no—
111#117—731no—
112C2×C4⋊C4—1461no—
113C2×C42—731no—
114C2×C42—732no—
115#97—1461no—
116C4×C8—1461no—
117#95—1461no—
118C2×Q8—1461no—
119C2×Q8—1461no—
120C22×C4—731no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—1462no—
124M16—734no—
125M16—1462no—
126C2×C8—1462no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—731no—
130C4⋊C4—731no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4—1464no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C4⋊C4C2×#6440811yescharacteristic
137C4⋊C4C2×#6440811yescharacteristic
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C42—731no—
141C42—731no—
142C42—731no—
143C42—1461no—
144C42—1461no—
145C42—1464no—
146C42C2×#6440811yescharacteristic
147C23—731no—
148Q8—2922no—
149Q8—2922no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2921no—
153C2×C4—2922no—
154C2×C4—2922no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—732no—
158C2×C4—732no—
159C2×C4—731no—
160C2×C4—1462no—
161C2×C4—1464no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4C22⋊#6440811yescharacteristic
165C2×C4C22⋊#6440811yescharacteristic
166C2×C4C22×#6440811yescharacteristic
167C8—1464no—
168C22—731no—
169C22—731no—
170C22—1461no—
171C22—1461no—
172C22C2×C22⋊#6440811yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—2924no—
178C4—2921no—
179C4—2921no—
180C4—732no—
181C4—732no—
182C4—1461no—
183C4Q8×#6440812yes—
184C2—1461no—
185C2—1461no—
186C2(C2×#64408)⋊Q811yescharacteristic
187C2D73⋊#10411yescharacteristic
188C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1986
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #14556590C4semidirect
13. #14556590C4semidirect
14. #14556583C4semidirect
22. #125×C73C4semidirect
25. #11924038Q8semidirect
95. C73#1986semidirect
105. #125#64408semidirect