Finite Group Databasebeta

← #22625933

Subgroups — #22625933

Order 9344.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#17989667C211yesmaximal, characteristic, complemented
2#17989586C212yesmaximal, complemented
3#17989568C211yesmaximal, characteristic, complemented
4#17989458C212yesmaximal, complemented
5#17989138C211yesmaximal, characteristic
6#14556679—24no—
7D73⋊M16—22no—
8D73⋊M16C2212yes—
9#14556670C2212yes—
10#14556656—24no—
11#14556650—22no—
12C2×#11924029C2211yescharacteristic
13C2×#11924029C2211yescharacteristic
14#14556588C411yescharacteristic, complemented
15#14556580C411yescharacteristic, complemented
16#14556580C411yescharacteristic, complemented
17#14556566—22no—
18#14556553—22no—
19C42×D73C2211yescharacteristic
20C4⋊Q8×C73C411yescharacteristic, complemented
21#11924038—24no—
22#11924038D414yescomplemented
23#11924037—22no—
24#11924036—24no—
25#11924036—22no—
26C4⋊#64408—22no—
27C22⋊#64408—22no—
28C4×#64408—22no—
29#11924029—22no—
30#11924029—22no—
31#11924029—22no—
32#11924029—22no—
33C2×D292—22no—
34C2×D292—21no—
35C2×D292C2×C411yescharacteristic
36C2×D292C2×C411yescharacteristic
37C2×D292D412yes—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73D412yes—
41C2×C4×D73C2311yescharacteristic
42#11924005—22no—
43#11924005—22no—
44C4×Dic73—21no—
45C4×Dic73C2×C411yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×Q8×C73C2×C411yescharacteristic
48C4⋊C4×C73—22no—
49C42×C73C2×C411yescharacteristic
50C22×D73—21no—
51C22×D73C22⋊C412yes—
52C22×D73C2×D411yescharacteristic
53C2×#64408—42no—
54Q8×C73—22no—
55Q8×C73—22no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C22⋊C412yes—
59C2×C4×C73C22×C411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73C2×D411yescharacteristic
62D292—24no—
63D292—22no—
64D292—22no—
65D292—44no—
66D292—42no—
67C4×D73—22no—
68C4×D73—22no—
69C4×D73—42no—
70C4×D73—41no—
71C4×D73—41no—
72C4×D73C2×D412yes—
73C4×D73#4112yes—
74#10596833—24no—
75C22×C73C2×C22⋊C411yescharacteristic
76C2×D73—22no—
77C2×D73—41no—
78C2×D73—42no—
79C2×D73—42no—
80C2×D73—41no—
81C2×D73#12112yes—
82#64408—82no—
83C4×C73—22no—
84C4×C73—22no—
85C4×C73—41no—
86C4×C73C4×D412yes—
87Dic73—41no—
88Dic73#12011yescharacteristic
89Dic73#12311yescharacteristic
90C2×C73—21no—
91C2×C73#38611yescharacteristic
92D73—22no—
93D73—42no—
94D73—81no—
95#1884—731nomaximal, Sylow
96C73#188411yescharacteristic, complemented, Sylow
97#568—731no—
98#532—731no—
99#421—732no—
100#410—731no—
101#339—732no—
102C2×#41—731no—
103C2×#41—731no—
104#131—1464no—
105C2×M16—732no—
106C2×M16—1462no—
107C4⋊Q8#6440811yescharacteristic, complemented
108#127—731no—
109#124—731no—
110#124—731no—
111#121—1462no—
112C4×D4—1462no—
113#117—732no—
114C2×C42—731no—
115#104—1464no—
116#99—1462no—
117#41—1462no—
118#41—1462no—
119#41—1462no—
120#41—1462no—
121C2×Q8C2×#6440811yescharacteristic
122C2×Q8C2×#6440811yescharacteristic
123C2×D4—732no—
124C2×D4—731no—
125C2×D4—731no—
126C2×D4—1462no—
127C2×D4—1461no—
128C22×C4—731no—
129C22×C4—732no—
130C22×C4—1461no—
131C22×C4—1461no—
132M16—734no—
133M16—1462no—
134M16—1464no—
135C2×C8—1462no—
136C2×C8—1464no—
137C4⋊C4—22no—
138C4⋊C4—1462no—
139C22⋊C4—1462no—
140C22⋊C4—1462no—
141C22⋊C4—1462no—
142C42—731no—
143C42—1461no—
144C42—1462no—
145C42C2×#6440811yescharacteristic
146C23—731no—
147C23—732no—
148C23—1461no—
149Q8—22no—
150Q8—22no—
151D4—2924no—
152D4—2922no—
153D4—1464no—
154D4—1462no—
155D4—1462no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—2922no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4—2922no—
162C2×C4—731no—
163C2×C4—732no—
164C2×C4—732no—
165C2×C4—1462no—
166C2×C4—1462no—
167C2×C4—1461no—
168C2×C4C22⋊#6440812yes—
169C2×C4C22×#6440811yescharacteristic
170C8—1464no—
171C22—2922no—
172C22—2922no—
173C22—2921no—
174C22—2921no—
175C22—732no—
176C22—1462no—
177C22C2×C22⋊#6440811yescharacteristic
178C4—22no—
179C4—22no—
180C4—41no—
181C4—2921no—
182C4—5842no—
183C4—731no—
184C4—731no—
185C4D4×#6440812yes—
186C2—21no—
187C2—2922no—
188C2—5841no—
189C2—1462no—
190C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊Q8×C73C4
socleC2×C73#386
hypercenterC4⋊Q8#64408
hypocenterC73#1884
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
1. #17989667C2semidirect
2. #17989586C2semidirect
3. #17989568C2semidirect
4. #17989458C2semidirect
14. #14556588C4semidirect
15. #14556580C4semidirect
16. #14556580C4semidirect
20. C4⋊Q8×C73C4semidirect
22. #11924038D4semidirect
96. C73#1884semidirect
107. C4⋊Q8#64408semidirect