Finite Group Databasebeta

← #22611302

Subgroups — #22611302

Order 9344.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556522C211yesmaximal, characteristic, complemented
2C2×C4⋊#10596831C211yesmaximal, characteristic, complemented
3C2×#14556511C211yesmaximal, characteristic
4C2×#14556511C211yesmaximal, characteristic
5#17988489C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic, complemented
7#389×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924005—21no—
13C2×#11924005—21no—
14#14556522—22no—
15C4⋊#10596831—22no—
16#14556511—22no—
17#14556511—22no—
18C2×C4⋊C4×C73—21no—
19C2×C4⋊C4×C73C2211yescharacteristic
20C2×C4⋊C4×C73C2211yescharacteristic
21C2×C42×C73C2211yescharacteristic
22#95×C73—21no—
23C23×D73—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292Q812yes—
30C22×Dic73—21no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831D412yes—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39#11924005—42no—
40#11924005—42no—
41C22×C4×C73—21no—
42C22×C4×C73—21no—
43C22×C4×C73D411yescharacteristic
44C22×C4×C73D411yescharacteristic
45C22×C4×C73C2311yescharacteristic
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73—42no—
50C4⋊C4×C73D412yes—
51C42×C73—21no—
52C42×C73—21no—
53C23×C73C2×D411yescharacteristic
54C22×D73—22no—
55C22×D73—41no—
56C22×D73—41no—
57C22×D73—41no—
58C22×D73—41no—
59C22×D73—41no—
60C22×D73—41no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73SD1612yes—
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×Q811yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82D292—22no—
83D292—22no—
84D292—41no—
85D292—41no—
86#10596831—22no—
87#10596831—41no—
88C22×C73#12111yescharacteristic
89C22×C73#12111yescharacteristic
90C22×C73C22⋊Q811yescharacteristic
91C22×C73C2×SD1611yescharacteristic
92C22×C73#13511yescharacteristic
93C22×C73AGL(1,ℤ/8)11yescharacteristic
94C22×C73AGL(1,ℤ/8)11yescharacteristic
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73—81no—
99C2×D73—81no—
100C2×D73—81no—
101C2×D73—81no—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73—81no—
106C4×C73#12111yescharacteristic
107C4×C73C22⋊Q811yescharacteristic
108C4×C73C22⋊Q811yescharacteristic
109C4×C73#12611yescharacteristic
110Dic73—81no—
111C2×C73#39611yescharacteristic
112C2×C73#46011yescharacteristic
113C2×C73#46311yescharacteristic
114C2×C73#46511yescharacteristic
115C2×C73#46911yescharacteristic
116C2×C73#47611yescharacteristic
117C2×C73#47811yescharacteristic
118D73—82no—
119#2065—731nomaximal, Sylow
120C73#206511yescharacteristic, complemented, Sylow
121C2×#106—731no—
122C2×C4⋊C8—731no—
123C2×#102—731no—
124C2×#102—731no—
125#390—731no—
126#389D7311yescharacteristic, complemented
127#340—731no—
128C22×D4—731no—
129C22×C8—731no—
130C22×C8—731no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4C2×D7311yescharacteristic
134C2×C4⋊C4C2×D7311yescharacteristic
135C2×C22⋊C4—1461no—
136C2×C22⋊C4—1461no—
137C2×C42C2×D7311yescharacteristic
138#106—1462no—
139C4⋊C8—1462no—
140#102—1462no—
141#102—1462no—
142#95—21no—
143C24—1461no—
144C2×D4—732no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4—1461no—
148C2×D4—1461no—
149C2×D4—1461no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—1461no—
153C22×C4C22⋊D7311yescharacteristic
154C22×C4C22⋊D7311yescharacteristic
155C22×C4C22×D7311yescharacteristic
156C2×C8—732no—
157C2×C8—1461no—
158C2×C8—1461no—
159C2×C8—1461no—
160C2×C8—1461no—
161C2×C8—1461no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—42no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C4⋊C4D29212yes—
169C22⋊C4—2922no—
170C22⋊C4—2922no—
171C42—21no—
172C42—21no—
173C23—2921no—
174C23—2921no—
175C23—2921no—
176C23—2921no—
177C23—2921no—
178C23—2921no—
179C23—1462no—
180C23C2×C22⋊D7311yescharacteristic
181D4—2921no—
182D4—2921no—
183D4—1462no—
184D4—1462no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4#1192401512yes—
200C2×C4D4×D7311yescharacteristic
201C2×C4C2×D29211yescharacteristic
202C2×C4Q8×D7311yescharacteristic
203C2×C4#1192402711yescharacteristic
204C2×C4#1192402811yescharacteristic
205C2×C4#1192402911yescharacteristic
206C8—2921no—
207C8—1462no—
208C22—2922no—
209C22—2922no—
210C22—2922no—
211C22—5841no—
212C22—5841no—
213C22—5841no—
214C22—5841no—
215C22#1455656311yescharacteristic
216C22#1455656511yescharacteristic
217C22#1455656711yescharacteristic
218C22C2×#1192401511yescharacteristic
219C22#1455661111yescharacteristic
220C22#1455661611yescharacteristic
221C22#1455661711yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—5841no—
227C4#1455656611yescharacteristic
228C4#1455656911yescharacteristic
229C4#1455657111yescharacteristic
230C4#1455658611yescharacteristic
231C2—5842no—
232C2#1798850911yescharacteristic
233C2#1798878711yescharacteristic
234C2#1798880211yescharacteristic
235C2#1798881811yescharacteristic
236C2#1798883811yescharacteristic
237C2#1798887411yescharacteristic
238C2#1798888411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#389×C73C2
socleC23×C73C2×D4
hypercenter#389D73
hypocenterC73#2065
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14556522C2semidirect
2. C2×C4⋊#10596831C2semidirect
6. #17988349C2semidirect
7. #389×C73C2semidirect
120. C73#2065semidirect
126. #389D73semidirect