Finite Group Databasebeta

← #22621154

Subgroups — #22621154

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#17989121C211yesmaximal, characteristic
3#17988996C212yesmaximal, complemented
4#17988947C212yesmaximal, complemented
5#17988918C212yesmaximal, complemented
6#17988901C212yesmaximal
7#17988883C212yesmaximal, complemented
8#17988878C212yesmaximal, complemented
9#432×C73C211yesmaximal, characteristic, complemented
10C22×Dic146—21no—
11#14556591—21no—
12#14556591—21no—
13#14556591C2212yes—
14#14556591C2212yes—
15#14556585—21no—
16#14556583C2211yescharacteristic
17#14556579C2211yescharacteristic
18#14556574—21no—
19#14556570C2211yescharacteristic
20#14556565C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22C4×D292C2211yescharacteristic
23C4×C22⋊D73—21no—
24#14556548—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2212yes—
27#14556525C2214yes—
28#14556523C2214yes—
29#14556516C2214yes—
30#14556513C2214yes—
31C2×C42×C73C2211yescharacteristic
32C4⋊C8×C73C2212yes—
33C22⋊C8×C73C2212yes—
34#97×C73C2212yes—
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146—44no—
38C2×Dic146C2311yescharacteristic
39C2×D292C2311yescharacteristic
40C2×C22⋊D73—21no—
41C22×Dic73—22no—
42C2×C4×D73—21no—
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45C4⋊Dic73—22no—
46C4⋊Dic73C2314yes—
47C4⋊Dic73C2311yescharacteristic
48C4⋊Dic73C2311yescharacteristic
49#11924007—21no—
50#11924007—21no—
51#11924007—21no—
52#11924007—21no—
53C22⋊Dic73—21no—
54#11924005—21no—
55#11924005—21no—
56#11924005—21no—
57#11924005—21no—
58C4×Dic73—21no—
59C22×C4×C73D411yescharacteristic
60C22×C4×C73D411yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C2×C8×C73C2314yes—
63C42×C73D411yescharacteristic
64C42×C73D411yescharacteristic
65C42×C73C2311yescharacteristic
66C42×C73C2311yescharacteristic
67C23×C73C2×D411yescharacteristic
68C22×D73—21no—
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
78C22⋊D73—42no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—24no—
83C2×Dic73—44no—
84D292—22no—
85C4×D73—42no—
86Dic146—22no—
87Dic146—44no—
88Dic146—44no—
89C8×C73—24no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73AGL(1,ℤ/8)12yes—
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#13712yes—
102C4×C732−1+412yes—
103Dic73—41no—
104Dic73—44no—
105Dic73—41no—
106Dic73—41no—
107C2×C73—22no—
108C2×C73#53611yescharacteristic
109C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C73C2×#13711yescharacteristic
111D73—81no—
112#3238—731nomaximal, Sylow
113C73#323811yescharacteristic, complemented, Sylow
114C2×C4⋊Q8—731no—
115#529—731no—
116#501—732no—
117#489—732no—
118#483—732no—
119#480—732no—
120#477—732no—
121#476—732no—
122#432D7311yescharacteristic, complemented
123C22×Q8—1461no—
124C4⋊Q8—732no—
125C4⋊Q8—732no—
126C4⋊Q8—1461no—
127C4⋊Q8—1461no—
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—732no—
139C2×C4⋊C4—1461no—
140C2×C42C2×D7311yescharacteristic
141#107—734no—
142#106—734no—
143C4⋊C8C2×D7312yes—
144#103—734no—
145#102—734no—
146C22⋊C8C2×D7312yes—
147#97C2×D7312yes—
148C2×Q8—2924no—
149C2×Q8—731no—
150C2×Q8—1462no—
151C2×Q8—1462no—
152C2×D4—731no—
153C2×D4—1461no—
154C22×C4—1462no—
155C22×C4—1461no—
156C22×C4D29211yescharacteristic
157C22×C4D29211yescharacteristic
158C22×C4C22×D7311yescharacteristic
159C2×C8C22×D7314yes—
160C4⋊C4—734no—
161C4⋊C4—731no—
162C4⋊C4—731no—
163C4⋊C4—1461no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C22⋊C4—1461no—
175C42—1461no—
176C42D29211yescharacteristic
177C42D29211yescharacteristic
178C42C22×D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C23—1461no—
181C23C2×D29211yescharacteristic
182Q8—2924no—
183Q8—2924no—
184Q8—1462no—
185D4—2922no—
186D4—1462no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—2924no—
191C2×C4—2922no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4—1464no—
196C2×C4C2×D29211yescharacteristic
197C2×C4C2×D29211yescharacteristic
198C2×C4C2×D29211yescharacteristic
199C2×C4C2×D29211yescharacteristic
200C2×C4C2×D29211yescharacteristic
201C2×C4C23×D7311yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—2921no—
206C22—2921no—
207C22—2921no—
208C22#1455661912yes—
209C22C22×D29211yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—2924no—
215C4—2921no—
216C4—2921no—
217C4—2921no—
218C4#1455662412yes—
219C4#1455663812yes—
220C2—22no—
221C2—5841no—
222C2#1798916311yescharacteristic
223C2C2×#1455661911yescharacteristic
224C2C2×#1455662411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3238
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#14556591C2semidirect
3. #17988996C2semidirect
4. #17988947C2semidirect
5. #17988918C2semidirect
7. #17988883C2semidirect
8. #17988878C2semidirect
9. #432×C73C2semidirect
113. C73#3238semidirect
122. #432D73semidirect