Finite Group Databasebeta

← #22625937

Subgroups — #22625937

Order 9344.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989655C211yesmaximal, characteristic
2#17989580C212yesmaximal
3D73⋊#101C211yesmaximal, characteristic
4#17989458C212yesmaximal
5C4⋊Q8×D73C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7Q8×#64408—24no—
8#14556670—22no—
9#14556670C2212yes—
10#14556654—24no—
11#14556652—22no—
12C2×Q8×D73C2211yescharacteristic
13C2×Q8×D73C2211yescharacteristic
14#14556591C411yescharacteristic, complemented
15#14556590—22no—
16#14556589C411yescharacteristic, complemented
17#14556589C411yescharacteristic, complemented
18C4⋊C4×D73—22no—
19C42×D73C2211yescharacteristic
20C4⋊Q8×C73C411yescharacteristic, complemented
21#11924038—22no—
22#11924037—22no—
23#11924036—22no—
24C4⋊#64408—24no—
25C4⋊#64408D414yes—
26C22⋊#64408—22no—
27C4×#64408—24no—
28C4×#64408—22no—
29C2×Dic146—21no—
30C2×Dic146C2×C411yescharacteristic
31C2×Dic146C2×C411yescharacteristic
32C2×Dic146D412yes—
33Q8×D73—22no—
34Q8×D73—22no—
35Q8×D73—22no—
36Q8×D73—22no—
37C2×C4×D73—21no—
38C2×C4×D73—21no—
39C2×C4×D73D412yes—
40C2×C4×D73C2311yescharacteristic
41C4⋊Dic73—22no—
42#11924007—22no—
43#11924007—22no—
44C4×Dic73—21no—
45C4×Dic73C2×C411yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×Q8×C73C2×C411yescharacteristic
48C4⋊C4×C73—22no—
49C42×C73C2×C411yescharacteristic
50C22×D73C2×D411yescharacteristic
51C2×#64408—24no—
52Q8×C73—22no—
53Q8×C73—22no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73C22⋊C412yes—
57C2×C4×C73C22×C411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73C22⋊C412yes—
61C2×Dic73C2×D411yescharacteristic
62C4×D73—24no—
63C4×D73—22no—
64C4×D73—22no—
65C4×D73—41no—
66C4×D73—41no—
67C4×D73C2×D412yes—
68C4×D73#4112yes—
69Dic146—22no—
70Dic146—24no—
71Dic146—22no—
72Dic146—42no—
73#10596833—42no—
74C22×C73C2×C22⋊C411yescharacteristic
75C2×D73—22no—
76C2×D73#12011yescharacteristic
77C2×D73#12311yescharacteristic
78#64408—44no—
79C4×C73—22no—
80C4×C73—22no—
81C4×C73—41no—
82C4×C73C4×D412yes—
83Dic73—22no—
84Dic73—22no—
85Dic73—41no—
86Dic73#12112yes—
87C2×C73—21no—
88C2×C73#38611yescharacteristic
89D73—21no—
90D73#45612yes—
91#1886—731nomaximal, Sylow
92C73#188611yescharacteristic, complemented, Sylow
93C2×C4⋊Q8—731no—
94#519—731no—
95#419—732no—
96C2×#101—731no—
97#339—732no—
98C22×Q8—731no—
99C22×Q8—731no—
100C2×M16—732no—
101C4⋊Q8—731no—
102C4⋊Q8—731no—
103C4⋊Q8—731no—
104C4⋊Q8—1462no—
105C4⋊Q8#6440811yescharacteristic, complemented
106C4×Q8—1464no—
107#117—732no—
108#117—1462no—
109C2×C4⋊C4—1462no—
110C2×C42—731no—
111#103—1464no—
112#101—1462no—
113C2×Q8—732no—
114C2×Q8—731no—
115C2×Q8—731no—
116C2×Q8—1461no—
117C2×Q8—1462no—
118C2×Q8—1462no—
119C2×Q8—1462no—
120C2×Q8—1462no—
121C2×Q8C2×#6440811yescharacteristic
122C2×Q8C2×#6440811yescharacteristic
123C22×C4—731no—
124C22×C4—732no—
125C22×C4—1461no—
126C22×C4—1461no—
127M16—1462no—
128M16—1462no—
129C2×C8—1462no—
130C4⋊C4—22no—
131C4⋊C4—734no—
132C4⋊C4—1462no—
133C4⋊C4—1462no—
134C4⋊C4—1464no—
135C4⋊C4—1462no—
136C22⋊C4—1462no—
137C42—731no—
138C42—1461no—
139C42—1462no—
140C42—1464no—
141C42C2×#6440811yescharacteristic
142C23—731no—
143Q8—22no—
144Q8—22no—
145Q8—2922no—
146Q8—1464no—
147Q8—1462no—
148Q8—1462no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—2921no—
152C2×C4—2921no—
153C2×C4—731no—
154C2×C4—732no—
155C2×C4—732no—
156C2×C4—732no—
157C2×C4—1462no—
158C2×C4—1462no—
159C2×C4—1464no—
160C2×C4—1464no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4C22⋊#6440812yes—
164C2×C4C22×#6440811yescharacteristic
165C8—2922no—
166C22—731no—
167C22—731no—
168C22—1462no—
169C22C2×C22⋊#6440811yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—2924no—
174C4—2921no—
175C4—732no—
176C4—1462no—
177C4—1462no—
178C4D4×#6440812yes—
179C2—21no—
180C2—732no—
181C2—1461no—
182C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊Q8×C73C4
socleC2×C73#386
hypercenterC4⋊Q8#64408
hypocenterC73#1886
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. #14556591C4semidirect
16. #14556589C4semidirect
17. #14556589C4semidirect
20. C4⋊Q8×C73C4semidirect
92. C73#1886semidirect
105. C4⋊Q8#64408semidirect