Finite Group Databasebeta

← #22621161

Subgroups — #22621161

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
1#17989121C211yesmaximal, characteristic
2#17988993C212yesmaximal, complemented
3#17988949C212yesmaximal, complemented
4#17988922C212yesmaximal, complemented
5#17988905C212yesmaximal
6#17988869C212yesmaximal, complemented
7#17988864C212yesmaximal, complemented
8#17988644C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
10#14556585—21no—
11#14556583C2211yescharacteristic
12#14556579C2211yescharacteristic
13#14556574—21no—
14#14556570C2211yescharacteristic
15#14556565C2211yescharacteristic
16C4×Dic146C2211yescharacteristic
17C4×D292C2211yescharacteristic
18C4×C22⋊D73—21no—
19#14556548—21no—
20#14556524C2214yes—
21#14556522C2214yes—
22C4⋊#10596831C2212yes—
23#14556514C2214yes—
24#14556511C2214yes—
25C22⋊#10596831C2212yes—
26#14556502C2212yes—
27C22×Q8×C73—21no—
28C4⋊Q8×C73—21no—
29C4⋊Q8×C73—21no—
30C4⋊Q8×C73C2212yes—
31C4⋊Q8×C73C2212yes—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73C2212yes—
34C2×C42×C73C2211yescharacteristic
35C2×Dic146C2311yescharacteristic
36C2×D292C2311yescharacteristic
37C2×C22⋊D73—21no—
38C2×C4×D73—21no—
39C2×#10596831C2314yes—
40C4⋊Dic73C2311yescharacteristic
41C4⋊Dic73C2311yescharacteristic
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45#11924007—21no—
46C22⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49#11924005—21no—
50#11924005—21no—
51C4×Dic73—21no—
52C2×Q8×C73—22no—
53C2×Q8×C73—22no—
54C2×Q8×C73—44no—
55C22×C4×C73—22no—
56C22×C4×C73D411yescharacteristic
57C22×C4×C73D411yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C4⋊C4×C73—22no—
60C4⋊C4×C73—22no—
61C4⋊C4×C73—22no—
62C4⋊C4×C73C2314yes—
63C42×C73D411yescharacteristic
64C42×C73D411yescharacteristic
65C42×C73C2311yescharacteristic
66C42×C73C2311yescharacteristic
67C23×C73C2×D411yescharacteristic
68C22×D73—21no—
69Q8×C73—44no—
70Q8×C73—44no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—24no—
75C2×C4×C73—44no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2411yescharacteristic
82C22⋊D73—42no—
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86D292—22no—
87C4×D73—42no—
88Dic146—22no—
89#10596831—24no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73#13712yes—
93C22×C73C22×D411yescharacteristic
94C2×D73—41no—
95C2×D73—41no—
96C2×D73—41no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—44no—
102C4×C73AGL(1,ℤ/8)12yes—
103C4×C732−1+412yes—
104Dic73—41no—
105Dic73—41no—
106Dic73—41no—
107C2×C73—22no—
108C2×C73#53611yescharacteristic
109C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C73C2×#13711yescharacteristic
111D73—81no—
112#3239—731nomaximal, Sylow
113C73#323911yescharacteristic, complemented, Sylow
114C2×C4⋊Q8D7311yescharacteristic, complemented
115#529—731no—
116#501—732no—
117#489—732no—
118#484—732no—
119#481—732no—
120#475—732no—
121#474—732no—
122#432—731no—
123C22×Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8C2×D7312yes—
127C4⋊Q8C2×D7312yes—
128#126—1461no—
129#125—731no—
130#124—731no—
131#123—1461no—
132C22⋊Q8—731no—
133#121—731no—
134C4×Q8—731no—
135C4×D4—731no—
136C4×D4—1461no—
137#117—1461no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×D7312yes—
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—22no—
149C2×Q8—22no—
150C2×Q8—44no—
151C2×Q8—731no—
152C2×D4—731no—
153C2×D4—1461no—
154C22×C4—22no—
155C22×C4—1461no—
156C22×C4C22⋊D7311yescharacteristic
157C22×C4C22⋊D7311yescharacteristic
158C22×C4C22×D7311yescharacteristic
159C2×C8—734no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—731no—
164C4⋊C4—731no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C4⋊C4—1461no—
169C4⋊C4C22×D7314yes—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C22⋊C4—1461no—
175C42—1461no—
176C42C22⋊D7311yescharacteristic
177C42C22⋊D7311yescharacteristic
178C42C22×D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C23—1461no—
181C23C2×C22⋊D7311yescharacteristic
182Q8—44no—
183Q8—44no—
184Q8—1462no—
185D4—2922no—
186D4—1462no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—44no—
192C2×C4—2922no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4—1461no—
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—2921no—
206C22—2921no—
207C22—2921no—
208C22#1455662212yes—
209C22C22×C22⋊D7311yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—44no—
215C4—2921no—
216C4—2921no—
217C4—2921no—
218C4#1455661712yes—
219C4#1455663912yes—
220C2—22no—
221C2—5841no—
222C2#1798916111yescharacteristic
223C2C2×#1455661711yescharacteristic
224C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4⋊Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4⋊Q8D73
hypocenterC73#3239
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988993C2semidirect
3. #17988949C2semidirect
4. #17988922C2semidirect
6. #17988869C2semidirect
7. #17988864C2semidirect
8. #17988644C2semidirect
9. C2×C4⋊Q8×C73C2semidirect
113. C73#3239semidirect
114. C2×C4⋊Q8D73semidirect