Finite Group Databasebeta

← #22621158

Subgroups — #22621158

Order 9344.

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

normal subgroups only

This group has 362 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
1C2×#14556591C211yesmaximal, characteristic, complemented
2#17988997C212yesmaximal, complemented
3#17988946C212yesmaximal, complemented
4#17988920C212yesmaximal, complemented
5#17988903C212yesmaximal
6#17988872C212yesmaximal, complemented
7#17988867C212yesmaximal, complemented
8#17988644C211yesmaximal, characteristic, complemented
9#529×C73C211yesmaximal, characteristic
10C22×Dic146—21no—
11#14556591—21no—
12#14556591—21no—
13#14556591C2212yes—
14#14556591C2212yes—
15C2×C4⋊Dic73—21no—
16C2×C4⋊Dic73C2212yes—
17#14556524C2214yes—
18#14556522C2214yes—
19C4⋊#10596831C2212yes—
20#14556515C2214yes—
21#14556512C2214yes—
22C22⋊#10596831C2212yes—
23#14556502C2212yes—
24#126×C73—21no—
25#125×C73C2211yescharacteristic
26#124×C73C2211yescharacteristic
27#123×C73—21no—
28C22⋊Q8×C73C2211yescharacteristic
29#121×C73C2211yescharacteristic
30C4×Q8×C73C2211yescharacteristic
31C4×D4×C73—21no—
32C4×D4×C73C2211yescharacteristic
33#117×C73—21no—
34C2×C42×C73C2211yescharacteristic
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146—44no—
38C22×Dic73—22no—
39C2×#10596831C2314yes—
40C4⋊Dic73—22no—
41C4⋊Dic73—22no—
42C4⋊Dic73—22no—
43C4⋊Dic73C2314yes—
44C2×Q8×C73C2311yescharacteristic
45C2×D4×C73—21no—
46C2×D4×C73C2311yescharacteristic
47C22×C4×C73—21no—
48C22×C4×C73D411yescharacteristic
49C22×C4×C73D411yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73C2311yescharacteristic
56C4⋊C4×C73C2311yescharacteristic
57C22⋊C4×C73—21no—
58C22⋊C4×C73—21no—
59C22⋊C4×C73—21no—
60C22⋊C4×C73—21no—
61C22⋊C4×C73—21no—
62C42×C73—21no—
63C42×C73D411yescharacteristic
64C42×C73D411yescharacteristic
65C42×C73C2311yescharacteristic
66C42×C73C2311yescharacteristic
67C23×C73—21no—
68C23×C73C2×D411yescharacteristic
69Q8×C73—22no—
70D4×C73—22no—
71D4×C73—42no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—42no—
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2411yescharacteristic
85C2×Dic73—24no—
86C2×Dic73—44no—
87Dic146—44no—
88Dic146—44no—
89#10596831—24no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73#13712yes—
96C22×C73C22×D411yescharacteristic
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—41no—
104C4×C73AGL(1,ℤ/8)12yes—
105C4×C732−1+412yes—
106Dic73—44no—
107C2×C73—22no—
108C2×C73—81no—
109C2×C73#53611yescharacteristic
110C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C73C2×#13711yescharacteristic
112#3239—731nomaximal, Sylow
113C73#323911yescharacteristic, complemented, Sylow
114C2×C4⋊Q8—731no—
115#529D7311yescharacteristic
116#501—732no—
117#489—732no—
118#484—732no—
119#481—732no—
120#475—732no—
121#474—732no—
122#432—731no—
123C22×Q8—1461no—
124C4⋊Q8—732no—
125C4⋊Q8—732no—
126C4⋊Q8—1461no—
127C4⋊Q8—1461no—
128#126—21no—
129#125C2×D7311yescharacteristic
130#124C2×D7311yescharacteristic
131#123—21no—
132C22⋊Q8C2×D7311yescharacteristic
133#121C2×D7311yescharacteristic
134C4×Q8C2×D7311yescharacteristic
135C4×D4—21no—
136C4×D4C2×D7311yescharacteristic
137#117—21no—
138C2×C4⋊C4—732no—
139C2×C4⋊C4—1461no—
140C2×C42C2×D7311yescharacteristic
141#107—734no—
142#106—734no—
143C4⋊C8—732no—
144#103—734no—
145#102—734no—
146C22⋊C8—732no—
147#97—732no—
148C2×Q8—2924no—
149C2×Q8—1462no—
150C2×Q8—1462no—
151C2×Q8C22×D7311yescharacteristic
152C2×D4—21no—
153C2×D4C22×D7311yescharacteristic
154C22×C4—21no—
155C22×C4—1462no—
156C22×C4C22⋊D7311yescharacteristic
157C22×C4C22⋊D7311yescharacteristic
158C22×C4C22×D7311yescharacteristic
159C2×C8—734no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—734no—
165C4⋊C4—1462no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4C22×D7311yescharacteristic
169C4⋊C4C22×D7311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C42—21no—
176C42C22⋊D7311yescharacteristic
177C42C22⋊D7311yescharacteristic
178C42C22×D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C23—21no—
181C23C2×C22⋊D7311yescharacteristic
182Q8—22no—
183Q8—2924no—
184Q8—2924no—
185D4—22no—
186D4—42no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—2924no—
195C2×C4—1464no—
196C2×C4C2×C22⋊D7311yescharacteristic
197C2×C4C2×C22⋊D7311yescharacteristic
198C2×C4C2×C22⋊D7311yescharacteristic
199C2×C4C2×C22⋊D7311yescharacteristic
200C2×C4C2×C22⋊D7311yescharacteristic
201C2×C4C23×D7311yescharacteristic
202C8—1464no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22#1455662112yes—
209C22C22×C22⋊D7311yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—2924no—
218C4#1455661612yes—
219C4#1455663812yes—
220C2—22no—
221C2—81no—
222C2#1798915811yescharacteristic
223C2C2×#1455661611yescharacteristic
224C2C2×#1455662111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#529×C73C2
socleC22×C73C22×D4
hypercenter#529D73
hypocenterC73#3239
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×#14556591C2semidirect
2. #17988997C2semidirect
3. #17988946C2semidirect
4. #17988920C2semidirect
6. #17988872C2semidirect
7. #17988867C2semidirect
8. #17988644C2semidirect
113. C73#3239semidirect