Finite Group Databasebeta

← #22621086

Subgroups — #22621086

Order 9344.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989144C211yesmaximal, characteristic
2#17988990C211yesmaximal, characteristic, complemented
3#17988983C211yesmaximal, characteristic, complemented
4#17988937C211yesmaximal, characteristic, complemented
5#17988937C211yesmaximal, characteristic, complemented
6#17988925C214yesmaximal
7#17988894C214yesmaximal, complemented
8#17988640C211yesmaximal, characteristic
9#533×C73C211yesmaximal, characteristic
10#14556591C2211yescharacteristic
11#14556591C2211yescharacteristic
12#14556583C2212yes—
13#14556570—21no—
14#14556570—21no—
15C4×Dic146—21no—
16C4×Dic146—21no—
17#14556550C2212yes—
18#14556524C2214yes—
19#14556522C2214yes—
20C4⋊#10596831C2212yes—
21#14556515C2214yes—
22#14556515C2214yes—
23C22⋊#10596831C2212yes—
24C4×#10596831C2211yescharacteristic
25C4×#10596831C2211yescharacteristic
26C4⋊Q8×C73C2211yescharacteristic
27C4⋊Q8×C73C2211yescharacteristic
28#125×C73—21no—
29C22⋊Q8×C73—21no—
30C22⋊Q8×C73C2212yes—
31C4×Q8×C73—21no—
32C4×Q8×C73C2212yes—
33#117×C73—21no—
34C2×C42×C73C2211yescharacteristic
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×#10596831C2312yes—
38C2×#10596831C2312yes—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73C2312yes—
42C4⋊Dic73C2312yes—
43#11924007—22no—
44#11924007—22no—
45C22⋊Dic73—22no—
46C4×Dic73—22no—
47C2×Q8×C73—21no—
48C2×Q8×C73C2312yes—
49C22×C4×C73D411yescharacteristic
50C22×C4×C73D411yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—22no—
57C4⋊C4×C73C2312yes—
58C22⋊C4×C73—22no—
59C42×C73—22no—
60C42×C73D411yescharacteristic
61C42×C73D411yescharacteristic
62C42×C73C2311yescharacteristic
63C42×C73C2311yescharacteristic
64C23×C73C2×D411yescharacteristic
65Q8×C73—24no—
66Q8×C73—42no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2411yescharacteristic
78C2×Dic73—22no—
79C2×Dic73—22no—
80Dic146—42no—
81Dic146—42no—
82#10596831—22no—
83#10596831—22no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73C22×D411yescharacteristic
88C4×C73—21no—
89C4×C73—21no—
90C4×C73—21no—
91C4×C73—42no—
92C4×C73—42no—
93C4×C73#13512yes—
94C4×C73#13712yes—
95C4×C732−1+412yes—
96Dic73—42no—
97Dic73—42no—
98C2×C73—41no—
99C2×C73#53611yescharacteristic
100C2×C73C2×#13511yescharacteristic
101C2×C73C2×#13711yescharacteristic
102#3231—731nomaximal, Sylow
103C73#323111yescharacteristic, complemented, Sylow
104#533—731no—
105#533D7311yescharacteristic
106#500—731no—
107#498—731no—
108#487—731no—
109#487—731no—
110#485—734no—
111#479—734no—
112#431—731no—
113C4⋊Q8—731no—
114C4⋊Q8—731no—
115C4⋊Q8C2×D7311yescharacteristic
116C4⋊Q8C2×D7311yescharacteristic
117#125—21no—
118#125—732no—
119C22⋊Q8—21no—
120C22⋊Q8—1461no—
121C22⋊Q8—1461no—
122C22⋊Q8C2×D7312yes—
123C4×Q8—21no—
124C4×Q8—1461no—
125C4×Q8—1461no—
126C4×Q8C2×D7312yes—
127#117—21no—
128#117—732no—
129C2×C42C2×D7311yescharacteristic
130#107—734no—
131#106—734no—
132C4⋊C8—732no—
133#103—734no—
134#103—734no—
135C22⋊C8—732no—
136C4×C8—731no—
137C4×C8—731no—
138C2×Q8—21no—
139C2×Q8—1461no—
140C2×Q8—1461no—
141C2×Q8C22×D7312yes—
142C22×C4C22⋊D7311yescharacteristic
143C22×C4C22⋊D7311yescharacteristic
144C22×C4C22×D7311yescharacteristic
145C2×C8—732no—
146C2×C8—732no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—732no—
153C4⋊C4—732no—
154C4⋊C4—1462no—
155C4⋊C4—1462no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4C22×D7312yes—
159C22⋊C4—22no—
160C22⋊C4—1462no—
161C42—22no—
162C42—1462no—
163C42C22⋊D7311yescharacteristic
164C42C22⋊D7311yescharacteristic
165C42C22×D7311yescharacteristic
166C42C22×D7311yescharacteristic
167C23C2×C22⋊D7311yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—2922no—
171Q8—2922no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—1462no—
178C2×C4—1462no—
179C2×C4C2×C22⋊D7311yescharacteristic
180C2×C4C2×C22⋊D7311yescharacteristic
181C2×C4C2×C22⋊D7311yescharacteristic
182C2×C4C2×C22⋊D7311yescharacteristic
183C2×C4C2×C22⋊D7311yescharacteristic
184C2×C4C23×D7311yescharacteristic
185C8—1462no—
186C8—1462no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D7311yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—2922no—
197C4—2922no—
198C4#1455661112yes—
199C4#1455662212yes—
200C4#1455663812yes—
201C2—41no—
202C2#1798915811yescharacteristic
203C2C2×#1455661111yescharacteristic
204C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3231
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988990C2semidirect
3. #17988983C2semidirect
4. #17988937C2semidirect
5. #17988937C2semidirect
7. #17988894C2semidirect
103. C73#3231semidirect