Finite Group Databasebeta

← #22622818

Subgroups — #22622818

Order 9344.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#17989315C211yesmaximal, characteristic
2#17988990C211yesmaximal, characteristic
3#17988986C212yesmaximal
4#17988894C212yesmaximal
5#17988891C212yesmaximal
6#17988872C211yesmaximal, characteristic
7#17988869C211yesmaximal, characteristic
8Q8×#10596831C211yesmaximal, characteristic
9C4×#11924018C211yesmaximal, characteristic
10C4×#11924018C212yesmaximal
11#557×C73C211yesmaximal, characteristic
12C2×#11924018C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556589—21no—
15#14556583C2212yes—
16#14556581—22no—
17C4×Dic146C2211yescharacteristic
18C4×Dic146C2212yes—
19#14556556—21no—
20#14556524C2212yes—
21#14556524C2211yescharacteristic
22#14556524C2212yes—
23#14556522C2212yes—
24#14556522C2212yes—
25C4⋊#10596831C2211yescharacteristic
26C4⋊#10596831C2212yes—
27#14556515C2212yes—
28#14556515C2211yescharacteristic
29#14556514C2212yes—
30#14556514C2211yescharacteristic
31C4×#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73—21no—
34C4⋊Q8×C73C2211yescharacteristic
35#125×C73—22no—
36#125×C73C2212yes—
37C4×Q8×C73—21no—
38C4×Q8×C73C2211yescharacteristic
39C4×Q8×C73C2212yes—
40C4×Q8×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43#11924018Q814yescomplemented
44C2×#10596831C2312yes—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C4⋊Dic73—21no—
48C4⋊Dic73C2311yescharacteristic
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—21no—
52#11924007—22no—
53#11924007—22no—
54C4×Dic73—22no—
55C4×Dic73—21no—
56C2×Q8×C73—21no—
57C2×Q8×C73D411yescharacteristic
58C2×Q8×C73C2311yescharacteristic
59C4⋊C4×C73—22no—
60C4⋊C4×C73—21no—
61C4⋊C4×C73—22no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73D411yescharacteristic
65C4⋊C4×C73D412yes—
66C4⋊C4×C73C2311yescharacteristic
67C4⋊C4×C73C2312yes—
68C42×C73—22no—
69C42×C73—21no—
70C42×C73C2312yes—
71C42×C73C2311yescharacteristic
72Q8×C73—22no—
73Q8×C73—21no—
74Q8×C73—42no—
75Q8×C73C2×Q812yes—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D412yes—
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2411yescharacteristic
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—22no—
87Dic146—21no—
88Dic146—42no—
89Dic146C2×Q812yes—
90#10596831—22no—
91#10596831—21no—
92#10596831C2×Q812yes—
93C22×C73C22×D411yescharacteristic
94C4×C73—22no—
95C4×C73—22no—
96C4×C73—22no—
97C4×C73—21no—
98C4×C73—42no—
99C4×C73—41no—
100C4×C73#13512yes—
101C4×C73C22×Q811yescharacteristic
102C4×C732−1+411yescharacteristic
103Dic73—22no—
104Dic73—42no—
105Dic73—41no—
106C2×C73D4×Q811yescharacteristic
107C2×C73C2×#13511yescharacteristic
108C2×C73#57811yescharacteristic
109#3383—731nomaximal, Sylow
110C73#338311yescharacteristic, complemented, Sylow
111#557—731no—
112#557D7311yescharacteristic
113#500—731no—
114#499—732no—
115#479—732no—
116#479—732no—
117#475—731no—
118#475—731no—
119C8×Q8—731no—
120C4×Q16—732no—
121C4×Q16—731no—
122C2×Q16—731no—
123C4⋊Q8—21no—
124C4⋊Q8—731no—
125C4⋊Q8—1461no—
126C4⋊Q8C2×D7311yescharacteristic
127#125—22no—
128#125—732no—
129#125—1462no—
130#125C2×D7312yes—
131C4×Q8—21no—
132C4×Q8—731no—
133C4×Q8—732no—
134C4×Q8—1461no—
135C4×Q8C2×D7311yescharacteristic
136C4×Q8C2×D7312yes—
137C4×Q8C2×D7311yescharacteristic
138#107—731no—
139#107—732no—
140#107—732no—
141#106—732no—
142#106—732no—
143C4⋊C8—731no—
144C4⋊C8—732no—
145#103—732no—
146#103—731no—
147#103—732no—
148#103—731no—
149C4×C8—732no—
150C4×C8—731no—
151C2×Q8—21no—
152C2×Q8—731no—
153C2×Q8—1461no—
154C2×Q8C22⋊D7311yescharacteristic
155C2×Q8C22×D7311yescharacteristic
156Q16—734no—
157C2×C8—731no—
158C2×C8—732no—
159C2×C8—731no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—731no—
166C4⋊C4—732no—
167C4⋊C4—1461no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1461no—
172C4⋊C4C22⋊D7311yescharacteristic
173C4⋊C4C22⋊D7312yes—
174C4⋊C4C22×D7311yescharacteristic
175C4⋊C4C22×D7312yes—
176C42—22no—
177C42—21no—
178C42—1462no—
179C42—1461no—
180C42C22×D7312yes—
181C42C22×D7311yescharacteristic
182Q8—22no—
183Q8—21no—
184Q8—42no—
185Q8—2922no—
186Q8—732no—
187Q8—1461no—
188Q8Q8×D7312yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—1461no—
193C2×C4—1462no—
194C2×C4—1461no—
195C2×C4C2×C22⋊D7312yes—
196C2×C4C2×C22⋊D7311yescharacteristic
197C2×C4C2×C22⋊D7312yes—
198C2×C4C2×C22⋊D7311yescharacteristic
199C2×C4C23×D7311yescharacteristic
200C8—732no—
201C8—1462no—
202C8—1461no—
203C22C22×C22⋊D7311yescharacteristic
204C4—22no—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—41no—
209C4—42no—
210C4—2921no—
211C4—2922no—
212C4—1462no—
213C4#1455661112yes—
214C4C2×Q8×D7311yescharacteristic
215C4#1455663911yescharacteristic
216C2Q8×C22⋊D7311yescharacteristic
217C2C2×#1455661111yescharacteristic
218C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#557×C73C2
socleC22×C73C22×D4
hypercenter#557D73
hypocenterC73#3383
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
43. #11924018Q8semidirect
110. C73#3383semidirect