Finite Group Databasebeta

← #22611622

Subgroups — #22611622

Order 9344.

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

normal subgroups only

This group has 262 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#17988571C211yesmaximal, characteristic, complemented
3#17988383C214yesmaximal, complemented
4#413×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic
6C2×#11924012—21no—
7#14556587C412yes—
8#14556580C2212yes—
9#14556565—21no—
10#14556565—21no—
11#14556559—21no—
12#14556559—21no—
13#14556550C411yescharacteristic
14#14556510C2212yescomplemented
15#14556508—21no—
16C2×#41×C73C2211yescharacteristic
17C2×M16×C73—21no—
18#101×C73C2212yescomplemented
19#100×C73—21no—
20C23×D73—21no—
21C2×D292—21no—
22C2×D292—41no—
23C2×D292—41no—
24C2×D292C2×C412yes—
25C2×C22⋊D73—22no—
26C2×C22⋊D73—22no—
27#11924012—22no—
28#11924012—41no—
29C2×#10596831—41no—
30C4⋊Dic73—21no—
31C22⋊Dic73—21no—
32#11924005—22no—
33#11924005—22no—
34C4×Dic73C2×C412yes—
35#41×C73—41no—
36#41×C73—41no—
37C2×Q8×C73C2311yescharacteristic
38C2×D4×C73C2×C411yescharacteristic
39C2×D4×C73D411yescharacteristic
40C2×D4×C73D411yescharacteristic
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44M16×C73—22no—
45M16×C73—41no—
46C2×C8×C73—41no—
47C23×C73C22⋊C411yescharacteristic
48C23×C73C22⋊C411yescharacteristic
49C23×C73C22⋊C411yescharacteristic
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×C73C22⋊C411yescharacteristic
64C2×C4×C73C22×C411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C22⋊D73—82no—
68C22⋊D73—82no—
69C2×Dic73—22no—
70D292—42no—
71D292—41no—
72D292—41no—
73C8×C73—42no—
74#10596831—42no—
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#9911yescharacteristic
90C4×C73#9911yescharacteristic
91Dic73—42no—
92C2×C73—21no—
93C2×C73—41no—
94C2×C73—41no—
95C2×C73—41no—
96C2×C73C2×#9911yescharacteristic
97D73—82no—
98#2134—731nomaximal, Sylow
99C73#213411yescharacteristic, complemented, Sylow
100#535—731no—
101#413—731no—
102#413D7311yescharacteristic, complemented
103#355—734no—
104C2×#41C2×D7311yescharacteristic
105C22×D4—731no—
106C2×M16—21no—
107C2×M16—1461no—
108#127—732no—
109#124—732no—
110#121—1461no—
111#121—1461no—
112#120—1461no—
113#120—1461no—
114#117—731no—
115#101—732no—
116#101C2×D7312yescomplemented
117#100—21no—
118#100—1461no—
119C24—1461no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D7311yescharacteristic
123C2×D4—2921no—
124C2×D4—2921no—
125C2×D4—732no—
126C2×D4—1462no—
127C2×D4—1462no—
128C2×D4—1461no—
129C2×D4C4×D7311yescharacteristic
130C2×D4D29211yescharacteristic
131C2×D4C22⋊D7311yescharacteristic
132C22×C4C4×D7311yescharacteristic
133C22×C4D29211yescharacteristic
134C22×C4C22⋊D7311yescharacteristic
135M16—22no—
136M16—41no—
137M16—2921no—
138M16—1462no—
139C2×C8—41no—
140C2×C8—2921no—
141C4⋊C4—1461no—
142C22⋊C4—1461no—
143C22⋊C4—1462no—
144C22⋊C4—1462no—
145C42—732no—
146C23—2922no—
147C23—5842no—
148C23—1462no—
149C23#1192400511yescharacteristic
150C23#1192400511yescharacteristic
151C23#1192400511yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2922no—
157D4—2921no—
158D4—2921no—
159D4—5842no—
160D4—5842no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—1462no—
168C2×C4#1192400511yescharacteristic
169C2×C4C2×C4×D7311yescharacteristic
170C2×C4C2×C22⋊D7311yescharacteristic
171C2×C4C2×D29211yescharacteristic
172C8—42no—
173C8—2922no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—2922no—
181C22—2922no—
182C22—2922no—
183C22—5844no—
184C22C2×#1192400511yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—2922no—
189C4#1455650511yescharacteristic
190C4#1455650511yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—5842no—
196C2C2×#1455650511yescharacteristic
subgroupG/H
centerC2C2×#14556505
commutatorC2×C4×C73C22×C4
FrattiniC2×Q8C22×D73
Fitting#413×C73C2
socleC2×C73C2×#99
hypercenter#413D73
hypocenterC73#2134
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #17988571C2semidirect
3. #17988383C2semidirect
4. #413×C73C2semidirect
14. #14556510C22semidirect
18. #101×C73C22semidirect
99. C73#2134semidirect
102. #413D73semidirect
116. #101C2×D73semidirect