Finite Group Databasebeta

← #22625250

Subgroups — #22625250

Order 9344.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989603C211yesmaximal, characteristic, complemented
2C4×#11924037C211yesmaximal, characteristic, complemented
3#17989435C212yesmaximal, complemented
4D4⋊#10596833C212yesmaximal, complemented
5#17989132C211yesmaximal, characteristic
6C2×#11924037—21no—
7C4⋊#10596833C2212yes—
8C22⋊#10596833—21no—
9#14556646—21no—
10C4×#10596833—21no—
11C4×#10596833C2212yes—
12C2×#11924027—21no—
13#14556590C411yescharacteristic
14#14556587C411yescharacteristic
15#14556577—21no—
16#14556565C411yescharacteristic
17#14556563—21no—
18D4×Dic73C2211yescharacteristic
19#14556553C2211yescharacteristic
20#14556551—21no—
21C2×C4×Dic73C2211yescharacteristic
22#121×C73C411yescharacteristic
23#11924037—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26#11924027—44no—
27C2×Dic146—21no—
28C2×D292C2×C411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C22×Dic73—21no—
33C22×Dic73D411yescharacteristic
34C22×Dic73D411yescharacteristic
35C2×C4×D73—21no—
36C4⋊Dic73C2×C411yescharacteristic
37#11924007—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45C2×D4×C73—21no—
46C2×D4×C73C2×C411yescharacteristic
47C22×C4×C73C2×C411yescharacteristic
48C4⋊C4×C73C2×C411yescharacteristic
49C22⋊C4×C73—21no—
50C23×C73—21no—
51C23×C73C22⋊C411yescharacteristic
52C22×D73—21no—
53D4×C73—22no—
54D4×C73—42no—
55C2×C4×C73—22no—
56C2×C4×C73—21no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22×C411yescharacteristic
59C22⋊D73—42no—
60C22⋊D73—42no—
61C22⋊D73—42no—
62C2×Dic73—22no—
63C2×Dic73—22no—
64C2×Dic73—21no—
65C2×Dic73—42no—
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C2×D411yescharacteristic
69C2×Dic73C2×D411yescharacteristic
70D292—22no—
71C4×D73—42no—
72Dic146—42no—
73#10596833—24no—
74#10596833—42no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73—21no—
78C22×C73—41no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73C2×C22⋊C411yescharacteristic
82C2×D73—41no—
83C2×D73—41no—
84C2×D73—41no—
85C4×C73—21no—
86C4×C73—41no—
87C4×C73#13112yes—
88Dic73—21no—
89Dic73—21no—
90Dic73—41no—
91Dic73#10412yes—
92Dic73AGL(1,ℤ/8)12yes—
93C2×C73—41no—
94C2×C73—81no—
95C2×C73#40811yescharacteristic
96C2×C73#41811yescharacteristic
97C2×C73C2×#10411yescharacteristic
98D73—81no—
99#1484—731nomaximal, Sylow
100C73#148411yescharacteristic, complemented, Sylow
101#532—731no—
102#431—731no—
103C4×M16—731no—
104D4⋊C8—732no—
105D4⋊C8—732no—
106C2×#41—1461no—
107C2×M16—1461no—
108C4⋊Q8—731no—
109#127—731no—
110#124—1461no—
111#121—731no—
112#121—1461no—
113#121#6440811yescharacteristic
114C4×D4—731no—
115C4×D4—731no—
116C4×D4—1461no—
117C2×C42—731no—
118C4⋊C8—732no—
119C22⋊C8—1461no—
120#97—1461no—
121C4×C8—732no—
122C4×C8—1461no—
123#41—2924no—
124C2×Q8—1461no—
125C2×D4—21no—
126C2×D4—731no—
127C2×D4—1461no—
128C2×D4—1461no—
129C2×D4—1461no—
130C2×D4C2×#6440811yescharacteristic
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—1461no—
134C22×C4—1461no—
135C22×C4C2×#6440811yescharacteristic
136M16—1464no—
137C2×C8—1462no—
138C2×C8—1462no—
139C4⋊C4—731no—
140C4⋊C4—1461no—
141C4⋊C4C2×#6440811yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—1461no—
144C22⋊C4—1461no—
145C22⋊C4—1461no—
146C42—731no—
147C42—731no—
148C42—731no—
149C42—731no—
150C23—21no—
151C23—1461no—
152C23C22⋊#6440811yescharacteristic
153Q8—2922no—
154D4—22no—
155D4—42no—
156D4—2922no—
157D4—2922no—
158D4—2922no—
159D4—1462no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—2922no—
163C2×C4—2922no—
164C2×C4—731no—
165C2×C4—731no—
166C2×C4—731no—
167C2×C4—731no—
168C2×C4—1461no—
169C2×C4—1462no—
170C2×C4—1462no—
171C2×C4C22⋊#6440811yescharacteristic
172C2×C4C22×#6440811yescharacteristic
173C8—2922no—
174C8—1464no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2921no—
182C22—2921no—
183C22—2921no—
184C22C2×C22⋊#6440811yescharacteristic
185C4—21no—
186C4—41no—
187C4—2921no—
188C4—732no—
189C4—732no—
190C4—1461no—
191C4—1461no—
192C4#1455667812yes—
193C2—41no—
194C2—81no—
195C2—5841no—
196C2#1798956011yescharacteristic
197C2#1798957911yescharacteristic
198C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1484
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989603C2semidirect
2. C4×#11924037C2semidirect
3. #17989435C2semidirect
4. D4⋊#10596833C2semidirect
100. C73#1484semidirect