Finite Group Databasebeta

← #22608940

Subgroups — #22608940

Order 9344.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#17989216C211yesmaximal, characteristic
2#17988918C211yesmaximal, characteristic
3#17988915C211yesmaximal, characteristic
4#17988519C211yesmaximal, characteristic
5#17988323C211yesmaximal, characteristic
6#17988312C211yesmaximal, characteristic
7#328×C73C211yesmaximal, characteristic
8#14556590—21no—
9#14556589—21no—
10#14556581—21no—
11#14556581—21no—
12#14556570C2211yescharacteristic
13#14556568—21no—
14#14556547—21no—
15C2×C4⋊Dic73—21no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18#14556523—21no—
19#14556522—21no—
20#14556516—21no—
21#14556515—21no—
22C22⋊#10596831C2211yescharacteristic
23#14556498—21no—
24C22⋊Q8×C73C2211yescharacteristic
25C22⋊C8×C73C2211yescharacteristic
26#95×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×Dic146D411yescharacteristic
29C22×Dic73—21no—
30C22×Dic73D411yescharacteristic
31C22×Dic73D411yescharacteristic
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—42no—
37C4⋊Dic73D411yescharacteristic
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45C22⋊Dic73—21no—
46C4×Dic73—21no—
47C4×Dic73—21no—
48C2×Q8×C73D411yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73C2311yescharacteristic
51C2×C8×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73D411yescharacteristic
54C22⋊C4×C73—21no—
55C23×C73C2×D411yescharacteristic
56Q8×C73—41no—
57C2×C4×C73—22no—
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73—41no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74C2×Dic73SD1612yes—
75Dic146—41no—
76Dic146—81no—
77C8×C73—41no—
78#10596831—41no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73#12011yescharacteristic
82C22×C73C2×SD1611yescharacteristic
83C22×C73#13711yescharacteristic
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—42no—
87C4×C73—41no—
88C4×C73—41no—
89Dic73—22no—
90Dic73—41no—
91Dic73—41no—
92Dic73—41no—
93Dic73—81no—
94C2×C73—21no—
95C2×C73—21no—
96C2×C73#44811yescharacteristic
97C2×C73#45611yescharacteristic
98C2×C73#45811yescharacteristic
99#1611—731nomaximal, Sylow
100C73#161111yescharacteristic, complemented, Sylow
101#544—731no—
102#483—731no—
103#483—731no—
104#398—731no—
105#328—731no—
106#328D7311yescharacteristic
107#324—731no—
108C4⋊Q8—1461no—
109C4⋊Q8—1461no—
110#125—1461no—
111#125—1461no—
112C22⋊Q8—731no—
113C22⋊Q8—1461no—
114C22⋊Q8C2×D7311yescharacteristic
115#117—1461no—
116C2×C4⋊C4—731no—
117C2×C4⋊C4—731no—
118C2×C4⋊C4—1461no—
119#106—1461no—
120#106—1461no—
121#103—1461no—
122#103—1461no—
123C22⋊C8—731no—
124C22⋊C8C2×D7311yescharacteristic
125#95—1461no—
126#95C2×D7311yescharacteristic
127C2×Q8—731no—
128C2×Q8—1461no—
129C2×Q8D29211yescharacteristic
130C22×C4—21no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—1461no—
134C22×C4C22×D7311yescharacteristic
135C2×C8—21no—
136C2×C8—1461no—
137C4⋊C4—21no—
138C4⋊C4—2922no—
139C4⋊C4—731no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C4⋊C4—1461no—
148C4⋊C4—1461no—
149C4⋊C4—1461no—
150C4⋊C4D29211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1461no—
153C42—1461no—
154C42—1461no—
155C23D4×D7311yescharacteristic
156Q8—41no—
157Q8—2921no—
158Q8—5841no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—732no—
170C2×C4—1461no—
171C2×C4—1461no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4—1461no—
175C2×C4D4×D7311yescharacteristic
176C2×C4C2×D29211yescharacteristic
177C8—41no—
178C8—2921no—
179C22—21no—
180C22—21no—
181C22#1455656111yescharacteristic
182C22SD16×D7311yescharacteristic
183C22#1455662311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—2921no—
190C4—2921no—
191C4—2921no—
192C4—5841no—
193C4—1462no—
194C2—21no—
195C2—21no—
196C2#1798872711yescharacteristic
197C2#1798877111yescharacteristic
198C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#328×C73C2
socleC22×C73#120
hypercenter#328D73
hypocenterC73#1611
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
100. C73#1611semidirect