Finite Group Databasebeta

← #22608290

Subgroups — #22608290

Order 9344.

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

normal subgroups only

This group has 322 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
1C2×#14556565C211yesmaximal, characteristic
2#17988551C211yesmaximal, characteristic, complemented
3#17988310C214yesmaximal, complemented
4C2×C22⋊C8×C73C211yesmaximal, characteristic, complemented
5C22×D292C411yescharacteristic
6C22×C22⋊D73C412yes—
7C2×#11924012—21no—
8#14556565—21no—
9#14556565—21no—
10#14556565—21no—
11#14556565—21no—
12C2×C4⋊Dic73C411yescharacteristic
13C2×#11924005C2212yes—
14C22⋊#10596831—21no—
15C22⋊#10596831C2212yes—
16C23×C4×C73C2211yescharacteristic
17C22×C8×C73—21no—
18C22⋊C8×C73—21no—
19C22⋊C8×C73C2212yes—
20C23×D73C2×C412yes—
21C2×D292—21no—
22C2×D292—21no—
23C2×D292—42no—
24C2×C22⋊D73—22no—
25C2×C22⋊D73—22no—
26C2×C22⋊D73—44no—
27C22×Dic73C2×C412yes—
28#11924012—42no—
29C2×#10596831—22no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32#11924005—22no—
33#11924005—22no—
34C24×C73C2×C411yescharacteristic
35C22×C4×C73—42no—
36C22×C4×C73C2×C411yescharacteristic
37C22×C4×C73D411yescharacteristic
38C22×C4×C73D411yescharacteristic
39C22×C4×C73D411yescharacteristic
40C22×C4×C73D411yescharacteristic
41C22×C4×C73C2311yescharacteristic
42C2×C8×C73—22no—
43C2×C8×C73—42no—
44C23×C73—22no—
45C23×C73—22no—
46C23×C73—41no—
47C23×C73C22⋊C411yescharacteristic
48C23×C73C22⋊C411yescharacteristic
49C23×C73C22×C411yescharacteristic
50C22×D73—22no—
51C22×D73—24no—
52C22×D73—42no—
53C22×D73—42no—
54C2×C4×C73—22no—
55C2×C4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C22⋊D73—44no—
65C22⋊D73—44no—
66C2×Dic73—22no—
67C2×Dic73—42no—
68D292—42no—
69D292—42no—
70C8×C73—42no—
71#10596831—42no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73—44no—
80C22×C73#10012yes—
81C22×C73C2×C22⋊C411yescharacteristic
82C22×C73#13112yes—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73—42no—
86C2×D73—84no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—21no—
90C4×C73#9912yes—
91Dic73—42no—
92C2×C73—22no—
93C2×C73—22no—
94C2×C73—41no—
95C2×C73#40811yescharacteristic
96C2×C73C2×#9911yescharacteristic
97C2×C73C2×#10011yescharacteristic
98D73—82no—
99#1471—731nomaximal, Sylow
100C73#147111yescharacteristic, complemented, Sylow
101C2×#121—731no—
102#407—731no—
103C2×C22⋊C8D7311yescharacteristic, complemented
104#323—734no—
105C22×D4—732no—
106C22×D4—731no—
107C23×C4C2×D7311yescharacteristic
108C2×M16—1461no—
109C22×C8—21no—
110#121—1461no—
111#121—1461no—
112#121—1461no—
113#121—1461no—
114C2×C4⋊C4—731no—
115C2×C22⋊C4—732no—
116C22⋊C8—21no—
117C22⋊C8—732no—
118C22⋊C8—1461no—
119C22⋊C8C2×D7312yes—
120C24—732no—
121C24C4×D7311yescharacteristic
122C2×D4—2922no—
123C2×D4—2924no—
124C2×D4—1462no—
125C2×D4—1462no—
126C2×D4—1461no—
127C2×D4—1461no—
128C22×C4—42no—
129C22×C4—732no—
130C22×C4C4×D7311yescharacteristic
131C22×C4D29211yescharacteristic
132C22×C4D29211yescharacteristic
133C22×C4C22⋊D7311yescharacteristic
134C22×C4C22⋊D7311yescharacteristic
135C22×C4C22×D7311yescharacteristic
136M16—2922no—
137C2×C8—22no—
138C2×C8—42no—
139C2×C8—1462no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C22⋊C4—1462no—
143C22⋊C4—1462no—
144C23—22no—
145C23—22no—
146C23—41no—
147C23—2922no—
148C23—2922no—
149C23—1462no—
150C23—1464no—
151C23#1192400511yescharacteristic
152C23#1192400511yescharacteristic
153C23C2×C4×D7311yescharacteristic
154D4—2922no—
155D4—2924no—
156D4—2924no—
157D4—2922no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—2922no—
165C2×C4—1462no—
166C2×C4#1192400511yescharacteristic
167C2×C4#1192400511yescharacteristic
168C2×C4C2×C22⋊D7311yescharacteristic
169C2×C4C2×D29211yescharacteristic
170C8—42no—
171C8—2922no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—44no—
180C22—2922no—
181C22—2922no—
182C22—2922no—
183C22—5844no—
184C22#1455650712yes—
185C22C2×#1192400511yescharacteristic
186C22#1455659712yes—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—2922no—
191C4#1455650512yes—
192C2—22no—
193C2—22no—
194C2—41no—
195C2—5842no—
196C2#1798855311yescharacteristic
197C2C2×#1455650511yescharacteristic
198C2C2×#1455650711yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×C22⋊C8×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C8D73
hypocenterC73#1471
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988551C2semidirect
3. #17988310C2semidirect
4. C2×C22⋊C8×C73C2semidirect
100. C73#1471semidirect
103. C2×C22⋊C8D73semidirect