Finite Group Databasebeta

← #22617637

Subgroups — #22617637

Order 9344.

428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988507C211yesmaximal, characteristic, complemented
2#17988505C212yesmaximal
3#17988504C211yesmaximal, characteristic
4#17988500C212yesmaximal, complemented
5#17988478C212yesmaximal, complemented
6#17988477C212yesmaximal, complemented
7#17988476C212yesmaximal, complemented
8#17988451C212yesmaximal, complemented
9#382×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C2×#11924007C2212yes—
13C2×#11924007C2212yes—
14C2×#11924005C2212yes—
15C2×#11924005C2212yes—
16C2×#11924005C2212yes—
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×C4×Dic73C2212yes—
21#14556498C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2211yescharacteristic
25#14556498C2212yes—
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C42×C73C2211yescharacteristic
29#95×C73C2212yes—
30#95×C73C2212yes—
31C23×D73C2312yes—
32C2×Dic146—41no—
33C2×Dic146—42no—
34C2×D292—41no—
35C2×D292—42no—
36C22×Dic73C2312yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39#11924007—42no—
40#11924007—42no—
41#11924005—24no—
42#11924005—24no—
43#11924005—24no—
44#11924005—42no—
45#11924005—42no—
46#11924005—42no—
47C4×Dic73—24no—
48C22×C4×C73C2312yes—
49C22×C4×C73C2312yes—
50C22×C4×C73C2311yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—41no—
54C4⋊C4×C73—41no—
55C42×C73—22no—
56C23×C73C2411yescharacteristic
57C22×D73—22no—
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73#4112yes—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73#4114yes—
86D292—44no—
87Dic146—44no—
88C22×C73C2×#4112yes—
89C22×C73C2×#4111yescharacteristic
90C22×C73H(5,𝔽2)11yescharacteristic
91C22×C73H(5,𝔽2)12yes—
92C22×C732−1+411yescharacteristic
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—42no—
100C4×C73—22no—
101C4×C73—42no—
102C4×C73—42no—
103C4×C73—41no—
104C4×C73—41no—
105Dic73—24no—
106Dic73—42no—
107Dic73—42no—
108C2×C73#53911yescharacteristic
109C2×C73#53912yes—
110C2×C73#55511yescharacteristic
111C2×C73#55512yes—
112C2×C73H(3,𝔽4)11yescharacteristic
113D73—82no—
114#2785—731nomaximal, Sylow
115C73#278511yescharacteristic, complemented, Sylow
116#395—731no—
117#394—731no—
118#394—732no—
119#393—732no—
120#388—732no—
121#388—732no—
122#388—732no—
123#382—732no—
124#382D7311yescharacteristic, complemented
125C22×Q8—731no—
126C22×D4—731no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4C2×D7311yescharacteristic
130C2×C4⋊C4C2×D7311yescharacteristic
131C2×C22⋊C4—732no—
132C2×C22⋊C4—732no—
133C2×C22⋊C4—732no—
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C22⋊C4—732no—
137C2×C42—732no—
138C2×C42C2×D7311yescharacteristic
139#95—731no—
140#95—732no—
141#95—732no—
142#95—731no—
143#95—732no—
144#95C2×D7312yes—
145#95C2×D7312yes—
146C24—732no—
147C2×Q8—2921no—
148C2×Q8—2922no—
149C2×D4—2921no—
150C2×D4—2922no—
151C22×C4—732no—
152C22×C4—732no—
153C22×C4—732no—
154C22×C4C22×D7312yes—
155C22×C4C22×D7312yes—
156C22×C4C22×D7311yescharacteristic
157C22×C4C22×D7311yescharacteristic
158C22×C4C22×D7311yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—2922no—
162C4⋊C4—2922no—
163C22⋊C4—2922no—
164C22⋊C4—2922no—
165C22⋊C4—2922no—
166C22⋊C4—1464no—
167C22⋊C4—1464no—
168C22⋊C4—1464no—
169C42—22no—
170C42—1464no—
171C23—1462no—
172C23—1462no—
173C23—1462no—
174C23—1462no—
175C23—1462no—
176C23—1462no—
177C23—1462no—
178C23C23×D7311yescharacteristic
179Q8—2924no—
180D4—2924no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—734no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4#1192402812yes—
203C22—2922no—
204C22—2922no—
205C22—2922no—
206C22—2922no—
207C22—2922no—
208C22—2922no—
209C22—2922no—
210C22#41×D7312yes—
211C22C2×#1192402811yescharacteristic
212C22#1455663611yescharacteristic
213C22#1455663712yes—
214C22#1455663911yescharacteristic
215C4—22no—
216C4—42no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—2922no—
221C4—2922no—
222C4—1464no—
223C2—5842no—
224C2#1798918411yescharacteristic
225C2#1798918512yes—
226C2#1798929911yescharacteristic
227C2#1798930012yes—
228C2#1798932911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#382×C73C2
hypercenter#382D73
hypocenterC73#2785
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #17988507C2semidirect
4. #17988500C2semidirect
5. #17988478C2semidirect
6. #17988477C2semidirect
7. #17988476C2semidirect
8. #17988451C2semidirect
9. #382×C73C2semidirect
115. C73#2785semidirect
124. #382D73semidirect