Finite Group Databasebeta

← #22611602

Subgroups — #22611602

Order 9344.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#17989151C211yesmaximal, characteristic
2#17988561C211yesmaximal, characteristic, complemented
3#17988379C214yesmaximal, complemented
4#410×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic, complemented
6#14556587C2212yes—
7#14556580C412yescomplemented
8#14556565—21no—
9#14556565—21no—
10#14556559—21no—
11#14556559—21no—
12#14556550—21no—
13#14556550C411yescharacteristic, complemented
14#14556506—21no—
15#14556506C2212yescomplemented
16C2×#41×C73C2211yescharacteristic
17#117×C73—21no—
18#99×C73—21no—
19#99×C73C2212yescomplemented
20C23×D73—21no—
21C2×D292—21no—
22C2×D292—41no—
23C2×D292—41no—
24C2×D292C2×C412yes—
25C2×C22⋊D73—22no—
26C2×C22⋊D73—22no—
27C4⋊Dic73—21no—
28C4⋊Dic73—41no—
29C22⋊Dic73—21no—
30C22⋊Dic73—22no—
31#11924005—22no—
32#11924005—22no—
33C4×Dic73—41no—
34C4×Dic73C2×C412yes—
35#41×C73—41no—
36#41×C73—41no—
37C2×Q8×C73C2×C411yescharacteristic
38C2×D4×C73D411yescharacteristic
39C2×D4×C73D411yescharacteristic
40C2×D4×C73C2311yescharacteristic
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44C4⋊C4×C73—41no—
45C22⋊C4×C73—22no—
46C42×C73—41no—
47C23×C73C22⋊C411yescharacteristic
48C23×C73C2×D411yescharacteristic
49C23×C73C2×D411yescharacteristic
50C22×D73—22no—
51C22×D73—42no—
52C22×D73—82no—
53Q8×C73—41no—
54D4×C73—41no—
55D4×C73—41no—
56D4×C73—41no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—42no—
64C2×C4×C73C22⋊C411yescharacteristic
65C2×C4×C73C22⋊C411yescharacteristic
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C22×C411yescharacteristic
68C22⋊D73—82no—
69C22⋊D73—82no—
70C2×Dic73—22no—
71C2×Dic73—42no—
72D292—42no—
73D292—41no—
74D292—41no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73—21no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73C2×C22⋊C411yescharacteristic
82C2×D73—42no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—84no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—82no—
90C4×C73#9911yescharacteristic
91C4×C73#9911yescharacteristic
92Dic73—42no—
93Dic73—82no—
94C2×C73—21no—
95C2×C73—41no—
96C2×C73—41no—
97C2×C73—41no—
98C2×C73C2×#9911yescharacteristic
99D73—82no—
100#2128—731nomaximal, Sylow
101C73#212811yescharacteristic, complemented, Sylow
102#535—731no—
103#410—731no—
104#410D7311yescharacteristic, complemented
105#353—734no—
106C2×#41C2×D7311yescharacteristic
107C22×D4—731no—
108#127—732no—
109#124—732no—
110#121—1461no—
111#121—1461no—
112#120—1461no—
113#120—1461no—
114#117—21no—
115#117—731no—
116#117—1461no—
117#99—21no—
118#99—732no—
119#99—1461no—
120#99C2×D7312yescomplemented
121C24—1461no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D7311yescharacteristic
125C2×D4—2921no—
126C2×D4—2921no—
127C2×D4—732no—
128C2×D4—1462no—
129C2×D4—1462no—
130C2×D4—1461no—
131C2×D4D29211yescharacteristic
132C2×D4C22⋊D7311yescharacteristic
133C2×D4C22×D7311yescharacteristic
134C22×C4C4×D7311yescharacteristic
135C22×C4D29211yescharacteristic
136C22×C4C22⋊D7311yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—2921no—
139C4⋊C4—1461no—
140C22⋊C4—22no—
141C22⋊C4—1462no—
142C22⋊C4—1461no—
143C22⋊C4—1462no—
144C22⋊C4—1462no—
145C42—41no—
146C42—2921no—
147C42—732no—
148C23—2922no—
149C23—5842no—
150C23—1462no—
151C23#1192400511yescharacteristic
152C23C2×C22⋊D7311yescharacteristic
153C23C2×D29211yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—2922no—
159D4—2921no—
160D4—2921no—
161D4—5842no—
162D4—5842no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—2922no—
171C2×C4—1462no—
172C2×C4#1192400511yescharacteristic
173C2×C4#1192400511yescharacteristic
174C2×C4#1192400511yescharacteristic
175C2×C4C2×C4×D7311yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—2922no—
183C22—2922no—
184C22—2922no—
185C22—5844no—
186C22C2×#1192400511yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—2922no—
192C4—5842no—
193C4#1455650511yescharacteristic
194C4#1455650511yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—5842no—
200C2C2×#1455650511yescharacteristic
subgroupG/H
centerC2C2×#14556505
commutatorC2×C4×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#410×C73C2
socleC2×C73C2×#99
hypercenter#410D73
hypocenterC73#2128
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #17988561C2semidirect
3. #17988379C2semidirect
4. #410×C73C2semidirect
5. C22×D292C4semidirect
7. #14556580C4semidirect
13. #14556550C4semidirect
15. #14556506C22semidirect
19. #99×C73C22semidirect
101. C73#2128semidirect
104. #410D73semidirect
120. #99C2×D73semidirect