Finite Group Databasebeta

← #22608366

Subgroups — #22608366

Order 9344.

246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C4×#11924028C211yesmaximal, characteristic
2#17988644C211yesmaximal, characteristic, complemented
3#17988319C212yesmaximal, complemented
4#17988316C212yesmaximal, complemented
5#431×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C411yescharacteristic
7C4×Dic146C411yescharacteristic
8C4×Dic146C2211yescharacteristic
9C4×D292C411yescharacteristic
10C4×D292C2211yescharacteristic
11C4×C22⋊D73—21no—
12C4×C22⋊D73—21no—
13#14556550C411yescharacteristic
14#14556548—21no—
15C42×D73—21no—
16C4⋊#10596831C2212yes—
17C22⋊#10596831—21no—
18#14556502—21no—
19C2×C42×C73C2211yescharacteristic
20C4⋊C8×C73—21no—
21C22⋊C8×C73—21no—
22C4×C8×C73C2212yes—
23#11924028—22no—
24#11924028—22no—
25C2×Dic146C2×C411yescharacteristic
26C2×D292C2×C411yescharacteristic
27C2×C22⋊D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×#10596831—22no—
32C4⋊Dic73C2×C411yescharacteristic
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36C22⋊Dic73—21no—
37#11924005—21no—
38#11924005—21no—
39C4×Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C22×C4×C73C2×C411yescharacteristic
43C22×C4×C73D411yescharacteristic
44C22×C4×C73D411yescharacteristic
45C2×C8×C73—22no—
46C42×C73C2×C411yescharacteristic
47C42×C73D411yescharacteristic
48C42×C73D411yescharacteristic
49C42×C73C2311yescharacteristic
50C23×C73C22⋊C411yescharacteristic
51C22×D73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—22no—
55C2×C4×C73—41no—
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C22⋊D73—24no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66D292—21no—
67D292M1612yes—
68C4×D73—24no—
69C4×D73—42no—
70C4×D73—42no—
71Dic146—21no—
72Dic146M1612yes—
73C8×C73—42no—
74#10596831—42no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73—21no—
78C22×C73C2×C22⋊C411yescharacteristic
79C2×D73—22no—
80C2×D73—41no—
81C2×D73—41no—
82C4×C73—21no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73C2×M1611yescharacteristic
87C4×C73C2×M1611yescharacteristic
88C4×C73#13512yes—
89Dic73—22no—
90Dic73—41no—
91Dic73—41no—
92C2×C73—41no—
93C2×C73#40711yescharacteristic
94C2×C73#41611yescharacteristic
95C2×C73#42111yescharacteristic
96D73—42no—
97#1488—731nomaximal, Sylow
98C73#148811yescharacteristic, complemented, Sylow
99C4×#41—731no—
100#432—731no—
101#431D7311yescharacteristic, complemented
102Q8⋊C8—732no—
103D4⋊C8—732no—
104C2×#41—731no—
105C4×Q8—731no—
106C4×Q8—731no—
107C4×D4—731no—
108C4×D4—731no—
109C4×D4—1461no—
110C4×D4—1461no—
111#117—731no—
112#117—1461no—
113C2×C42—1461no—
114C2×C42C2×D7311yescharacteristic
115C4⋊C8—21no—
116C4⋊C8—732no—
117C22⋊C8—21no—
118C22⋊C8—1461no—
119#97—1461no—
120C4×C8C2×D7312yes—
121#41—1462no—
122#41—1462no—
123C2×Q8—731no—
124C2×D4—731no—
125C2×D4—1461no—
126C22×C4—1461no—
127C22×C4—1461no—
128C22×C4—1461no—
129C22×C4C4×D7311yescharacteristic
130C22×C4D29211yescharacteristic
131C22×C4C22⋊D7311yescharacteristic
132C2×C8—22no—
133C2×C8—1462no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C4⋊C4—1461no—
137C4⋊C4—1461no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C22⋊C4—1461no—
141C42—1461no—
142C42—1461no—
143C42—1461no—
144C42C4×D7311yescharacteristic
145C42D29211yescharacteristic
146C42C22⋊D7311yescharacteristic
147C42C22×D7311yescharacteristic
148C23—1461no—
149C23#1192400511yescharacteristic
150Q8—732no—
151Q8—1461no—
152D4—732no—
153D4—1464no—
154D4—1461no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—2922no—
160C2×C4—2922no—
161C2×C4—1464no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4#1192400511yescharacteristic
166C2×C4#1192400511yescharacteristic
167C2×C4#1192400511yescharacteristic
168C2×C4C2×C4×D7311yescharacteristic
169C2×C4C2×C22⋊D7311yescharacteristic
170C2×C4C2×D29211yescharacteristic
171C8—42no—
172C8—2922no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—2921no—
177C22—2921no—
178C22—1462no—
179C22C2×#1192400511yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—2921no—
185C4—2921no—
186C4—1462no—
187C4M16×D7311yescharacteristic
188C4M16×D7311yescharacteristic
189C4#1455661312yes—
190C2—41no—
191C2—2922no—
192C2#1798855011yescharacteristic
193C2#1798858411yescharacteristic
194C2#1798860511yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1488
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #17988644C2semidirect
3. #17988319C2semidirect
4. #17988316C2semidirect
5. #431×C73C2semidirect
98. C73#1488semidirect
101. #431D73semidirect