Finite Group Databasebeta

← #22625400

Subgroups — #22625400

Order 9344.

256 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989607C211yesmaximal, characteristic, complemented
2C2×#14556646C211yesmaximal, characteristic, complemented
3#17989443C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#17989133C211yesmaximal, characteristic
6C22×#10596833—21no—
7#14556658—21no—
8C22⋊#10596833—21no—
9#14556646—21no—
10#14556646C2212yes—
11#14556646C2212yes—
12C2×#11924028C411yescharacteristic
13#14556589C411yescharacteristic
14#14556587C411yescharacteristic
15#14556580C2211yescharacteristic
16#14556578C2211yescharacteristic
17#14556563—21no—
18#14556563—21no—
19C4×C22⋊D73—21no—
20C4×C22⋊D73—21no—
21C2×C4×Dic73C2211yescharacteristic
22C2×#41×C73C411yescharacteristic
23C2×#10596833—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26#11924028—42no—
27C2×Dic146C2×C411yescharacteristic
28C2×D292C2×C411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C22×Dic73D411yescharacteristic
33C22×Dic73D411yescharacteristic
34C2×C4×D73—21no—
35#11924007—21no—
36#11924007—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45#41×C73—42no—
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73—21no—
48C2×D4×C73C2×C411yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73C2×C411yescharacteristic
51C23×C73—21no—
52C23×C73C22⋊C411yescharacteristic
53C22×D73—21no—
54Q8×C73—41no—
55D4×C73—41no—
56D4×C73—42no—
57C2×C4×C73—22no—
58C2×C4×C73—21no—
59C2×C4×C73—42no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22×C411yescharacteristic
62C22⋊D73—42no—
63C22⋊D73—42no—
64C22⋊D73—42no—
65C2×Dic73—22no—
66C2×Dic73—21no—
67C2×Dic73—41no—
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71C2×Dic73C2×D411yescharacteristic
72D292—41no—
73C4×D73—42no—
74Dic146—41no—
75#10596833—24no—
76#10596833—42no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73#10012yes—
83C22×C73C2×C22⋊C411yescharacteristic
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—41no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73—41no—
90Dic73—21no—
91Dic73—21no—
92Dic73—21no—
93Dic73—41no—
94Dic73#10412yes—
95C2×C73—22no—
96C2×C73—81no—
97C2×C73C2×#10011yescharacteristic
98C2×C73C2×#10411yescharacteristic
99C2×C73#42111yescharacteristic
100D73—81no—
101#1530—731nomaximal, Sylow
102C73#153011yescharacteristic, complemented, Sylow
103#532—731no—
104#432—731no—
105C2×#97—731no—
106#329—732no—
107#329—732no—
108C2×#41—731no—
109C2×#41#6440811yescharacteristic
110C22×C8—1461no—
111C4⋊Q8—731no—
112#127—731no—
113#124—731no—
114#124—731no—
115#121—1461no—
116#121—1461no—
117C4×D4—1461no—
118C4×D4—1461no—
119C2×C42—731no—
120C4⋊C8—1461no—
121C22⋊C8—1461no—
122#97—732no—
123#97—732no—
124#97—1461no—
125#41—42no—
126#41—2922no—
127C2×Q8—731no—
128C2×Q8C2×#6440811yescharacteristic
129C2×D4—21no—
130C2×D4—731no—
131C2×D4—1461no—
132C2×D4—1461no—
133C2×D4—1461no—
134C2×D4C2×#6440811yescharacteristic
135C22×C4—21no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—1461no—
139C22×C4C2×#6440811yescharacteristic
140C2×C8—1462no—
141C2×C8—1462no—
142C2×C8—1464no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C22⋊C4—1461no—
149C42—731no—
150C42—731no—
151C42—731no—
152C42—731no—
153C23—21no—
154C23—1461no—
155C23C22⋊#6440811yescharacteristic
156Q8—41no—
157Q8—2921no—
158D4—41no—
159D4—42no—
160D4—2921no—
161D4—2922no—
162D4—2922no—
163D4—2922no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—42no—
167C2×C4—2922no—
168C2×C4—2921no—
169C2×C4—731no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—1461no—
174C2×C4—1462no—
175C2×C4C22⋊#6440811yescharacteristic
176C2×C4C22×#6440811yescharacteristic
177C8—2922no—
178C8—1464no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—2921no—
185C22—2921no—
186C22—2921no—
187C22#1455665112yes—
188C22C2×C22⋊#6440811yescharacteristic
189C4—21no—
190C4—21no—
191C4—41no—
192C4—2921no—
193C4—732no—
194C4—1461no—
195C4—1461no—
196C4—1461no—
197C2—22no—
198C2—81no—
199C2—5841no—
200C2C2×#1455665111yescharacteristic
201C2D73⋊#10411yescharacteristic
202C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×#41×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73#1530
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #17989607C2semidirect
2. C2×#14556646C2semidirect
3. #17989443C2semidirect
4. #17989442C2semidirect
102. C73#1530semidirect