Finite Group Databasebeta

← #22621069

Subgroups — #22621069

Order 9344.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989144C211yesmaximal, characteristic, complemented
2#17989137C211yesmaximal, characteristic
3#17988992C211yesmaximal, characteristic, complemented
4#17988985C211yesmaximal, characteristic, complemented
5#17988934C211yesmaximal, characteristic, complemented
6#17988934C211yesmaximal, characteristic, complemented
7#17988912C214yesmaximal, complemented
8#17988888C214yesmaximal, complemented
9#431×C73C211yesmaximal, characteristic, complemented
10C2×#11924028—21no—
11#14556591C2211yescharacteristic
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556588C2211yescharacteristic
15#14556583C2212yes—
16#14556579—21no—
17#14556570—21no—
18#14556570—21no—
19#14556565—21no—
20#14556565C2212yes—
21C4×Dic146—21no—
22C4×Dic146—21no—
23C4×D292—21no—
24C4×D292C2212yes—
25#14556550C2212yes—
26#14556525C2214yes—
27#14556523C2214yes—
28#14556513C2214yes—
29#14556513C2214yes—
30C2×C42×C73C2211yescharacteristic
31C4⋊C8×C73C2212yes—
32C22⋊C8×C73C2212yes—
33C4×C8×C73C2211yescharacteristic
34C4×C8×C73C2211yescharacteristic
35#11924028—44no—
36C2×Dic146—21no—
37C2×Dic146—21no—
38C2×Dic146—21no—
39C2×D292—21no—
40C2×D292—21no—
41C2×D292C2312yes—
42C2×C22⋊D73—22no—
43C2×C4×D73—22no—
44C4⋊Dic73—21no—
45C4⋊Dic73—21no—
46C4⋊Dic73—21no—
47C4⋊Dic73C2312yes—
48C4⋊Dic73C2312yes—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52C22⋊Dic73—22no—
53#11924005—22no—
54#11924005—22no—
55C4×Dic73—22no—
56C22×C4×C73D411yescharacteristic
57C22×C4×C73D411yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C2×C8×C73C2312yes—
60C2×C8×C73C2312yes—
61C42×C73D411yescharacteristic
62C42×C73D411yescharacteristic
63C42×C73C2311yescharacteristic
64C42×C73C2311yescharacteristic
65C23×C73C2×D411yescharacteristic
66C22×D73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2411yescharacteristic
76C22⋊D73—44no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80D292—24no—
81D292—42no—
82D292—42no—
83C4×D73—44no—
84Dic146—42no—
85Dic146—42no—
86Dic146—42no—
87C8×C73—22no—
88C8×C73—22no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73C22×D411yescharacteristic
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—21no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73#13512yes—
100C4×C73AGL(1,ℤ/8)12yes—
101C4×C732−1+412yes—
102Dic73—42no—
103Dic73—42no—
104Dic73—42no—
105C2×C73—41no—
106C2×C73#53611yescharacteristic
107C2×C73C2×#13511yescharacteristic
108C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
109D73—82no—
110#3228—731nomaximal, Sylow
111C73#322811yescharacteristic, complemented, Sylow
112#533—731no—
113#532—731no—
114#500—731no—
115#498—731no—
116#486—731no—
117#486—731no—
118#482—734no—
119#478—734no—
120#431D7311yescharacteristic, complemented
121C2×#41—1461no—
122C4⋊Q8—731no—
123C4⋊Q8—731no—
124C4⋊Q8—731no—
125#127—731no—
126#125—732no—
127#124—1461no—
128C22⋊Q8—1461no—
129C22⋊Q8—1461no—
130#121—732no—
131#121—1461no—
132C4×Q8—1461no—
133C4×Q8—1461no—
134C4×D4—732no—
135C4×D4—1461no—
136#117—732no—
137C2×C42C2×D7311yescharacteristic
138#107—734no—
139#106—734no—
140C4⋊C8C2×D7312yes—
141#102—734no—
142#102—734no—
143C22⋊C8C2×D7312yes—
144C4×C8C2×D7311yescharacteristic
145C4×C8C2×D7311yescharacteristic
146#41—2924no—
147C2×Q8—1461no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×D4—732no—
151C2×D4—1462no—
152C2×D4—1461no—
153C2×D4—1461no—
154C22×C4—1462no—
155C22×C4D29211yescharacteristic
156C22×C4D29211yescharacteristic
157C22×C4C22×D7311yescharacteristic
158C2×C8C22×D7312yes—
159C2×C8C22×D7312yes—
160C4⋊C4—732no—
161C4⋊C4—732no—
162C4⋊C4—732no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C22⋊C4—1462no—
169C22⋊C4—1462no—
170C22⋊C4—1462no—
171C42—1462no—
172C42D29211yescharacteristic
173C42D29211yescharacteristic
174C42C22×D7311yescharacteristic
175C42C22×D7311yescharacteristic
176C23—1462no—
177C23C2×D29211yescharacteristic
178Q8—2922no—
179Q8—2922no—
180Q8—2922no—
181D4—2924no—
182D4—2922no—
183D4—2922no—
184D4—1464no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—2924no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4C2×D29211yescharacteristic
193C2×C4C2×D29211yescharacteristic
194C2×C4C2×D29211yescharacteristic
195C2×C4C2×D29211yescharacteristic
196C2×C4C2×D29211yescharacteristic
197C2×C4C23×D7311yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—2922no—
204C22—2922no—
205C22—2922no—
206C22C22×D29211yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—2922no—
211C4—2922no—
212C4—2922no—
213C4#1455661312yes—
214C4#1455661912yes—
215C4#1455663812yes—
216C2—41no—
217C2—5842no—
218C2#1798916311yescharacteristic
219C2C2×#1455661311yescharacteristic
220C2C2×#1455661911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#431×C73C2
socleC22×C73C22×D4
hypercenter#431D73
hypocenterC73#3228
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
3. #17988992C2semidirect
4. #17988985C2semidirect
5. #17988934C2semidirect
6. #17988934C2semidirect
7. #17988912C2semidirect
8. #17988888C2semidirect
9. #431×C73C2semidirect
111. C73#3228semidirect
120. #431D73semidirect