Finite Group Databasebeta

← #22621117

Subgroups — #22621117

Order 9344.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#14556583C211yesmaximal, characteristic, complemented
2#17988993C212yesmaximal, complemented
3#17988951C212yesmaximal, complemented
4#17988903C212yesmaximal, complemented
5#17988898C212yesmaximal, complemented
6#17988887C214yesmaximal, complemented
7#17988644C211yesmaximal, characteristic, complemented
8#532×C73C211yesmaximal, characteristic
9#14556583—21no—
10#14556583—21no—
11#14556583C2212yes—
12#14556583C2212yes—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007—21no—
16C2×#11924007—21no—
17#14556524C2214yes—
18#14556522C2214yes—
19C4⋊#10596831C2212yes—
20#14556512C2214yes—
21#14556512C2214yes—
22C22⋊#10596831C2212yes—
23#14556502C2212yes—
24C2×#41×C73—21no—
25C4⋊Q8×C73C2211yescharacteristic
26#127×C73C2211yescharacteristic
27#124×C73—21no—
28#121×C73—21no—
29#121×C73C2212yes—
30C4×D4×C73—21no—
31C4×D4×C73C2212yes—
32C2×C42×C73C2211yescharacteristic
33C22×Dic73—21no—
34C22×Dic73—21no—
35C2×#10596831C2314yes—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73C2312yes—
39C4⋊Dic73C2312yes—
40#11924007—22no—
41#11924007—22no—
42#11924007—22no—
43#11924007—22no—
44#41×C73—44no—
45C2×Q8×C73—21no—
46C2×D4×C73—22no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73C2312yes—
50C22×C4×C73—22no—
51C22×C4×C73D411yescharacteristic
52C22×C4×C73D411yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73—21no—
55C4⋊C4×C73C2312yes—
56C22⋊C4×C73—22no—
57C22⋊C4×C73—22no—
58C42×C73D411yescharacteristic
59C42×C73D411yescharacteristic
60C42×C73C2311yescharacteristic
61C42×C73C2311yescharacteristic
62C23×C73—22no—
63C23×C73C2×D411yescharacteristic
64Q8×C73—42no—
65D4×C73—24no—
66D4×C73—42no—
67D4×C73—42no—
68D4×C73—44no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—41no—
73C2×C4×C73—44no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84#10596831—24no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73AGL(1,ℤ/8)12yes—
91C22×C73C22×D411yescharacteristic
92C4×C73—21no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—21no—
97C4×C73—42no—
98C4×C732−1+412yes—
99Dic73—42no—
100Dic73—42no—
101C2×C73—22no—
102C2×C73—82no—
103C2×C73#53611yescharacteristic
104C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C73#57511yescharacteristic
106#3234—731nomaximal, Sylow
107C73#323411yescharacteristic, complemented, Sylow
108#532D7311yescharacteristic
109C2×#125—731no—
110#501—732no—
111#490—732no—
112#481—732no—
113#480—732no—
114#478—734no—
115#432—731no—
116C2×#41—21no—
117C4⋊Q8C2×D7311yescharacteristic
118#127C2×D7311yescharacteristic
119#125—732no—
120#125—732no—
121#125—1461no—
122#125—1461no—
123#124—21no—
124#121—21no—
125#121C2×D7312yes—
126C4×D4—21no—
127C4×D4C2×D7312yes—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—731no—
130C2×C4⋊C4—1461no—
131C2×C4⋊C4—1461no—
132C2×C42C2×D7311yescharacteristic
133#107—734no—
134#106—734no—
135C4⋊C8—732no—
136#102—734no—
137#102—734no—
138C22⋊C8—732no—
139#97—732no—
140#41—44no—
141C2×Q8—21no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4C22×D7312yes—
146C22×C4—22no—
147C22×C4—1461no—
148C22×C4—1461no—
149C22×C4C22⋊D7311yescharacteristic
150C22×C4C22⋊D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C2×C8—734no—
153C4⋊C4—21no—
154C4⋊C4—732no—
155C4⋊C4—732no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1461no—
161C4⋊C4—1461no—
162C4⋊C4C22×D7312yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C42C22⋊D7311yescharacteristic
166C42C22⋊D7311yescharacteristic
167C42C22×D7311yescharacteristic
168C42C22×D7311yescharacteristic
169C23—22no—
170C23C2×C22⋊D7311yescharacteristic
171Q8—42no—
172D4—24no—
173D4—42no—
174D4—42no—
175D4—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—41no—
180C2×C4—44no—
181C2×C4—2922no—
182C2×C4—2922no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4C2×C22⋊D7311yescharacteristic
186C2×C4C2×C22⋊D7311yescharacteristic
187C2×C4C2×C22⋊D7311yescharacteristic
188C2×C4C2×C22⋊D7311yescharacteristic
189C2×C4C2×C22⋊D7311yescharacteristic
190C2×C4C23×D7311yescharacteristic
191C8—1464no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22#1455661712yes—
198C22C22×C22⋊D7311yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—42no—
205C4—2922no—
206C4—2922no—
207C4#1455663812yes—
208C2—22no—
209C2—82no—
210C2#1798915811yescharacteristic
211C2C2×#1455661711yescharacteristic
212C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3234
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14556583C2semidirect
2. #17988993C2semidirect
3. #17988951C2semidirect
4. #17988903C2semidirect
5. #17988898C2semidirect
6. #17988887C2semidirect
7. #17988644C2semidirect
107. C73#3234semidirect