Finite Group Databasebeta

← #22616093

Subgroups — #22616093

Order 9344.

434 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556583C211yesmaximal, characteristic, complemented
2#17988526C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic
4#17988520C212yesmaximal, complemented
5#17988517C211yesmaximal, characteristic, complemented
6#17988512C211yesmaximal, characteristic
7#17988510C212yesmaximal
8#17988482C212yesmaximal, complemented
9#17988481C212yesmaximal
10C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
11C2×#126×C73C211yesmaximal, characteristic
12#14556583—24no—
13C2×C4⋊Dic73C2212yes—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C4×Dic73C2212yes—
23#14556498C2211yescharacteristic
24#14556498C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#126×C73—24no—
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C4⋊C4×C73C2211yescharacteristic
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36C2×C42×C73C2211yescharacteristic
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2312yes—
41C4⋊Dic73—22no—
42C4⋊Dic73—22no—
43C4⋊Dic73—24no—
44#11924007—24no—
45#11924007—24no—
46#11924007—24no—
47#11924007—42no—
48C22⋊Dic73—24no—
49C22⋊Dic73—42no—
50C4×Dic73—42no—
51C24×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C4⋊C4×C73—22no—
59C4⋊C4×C73—22no—
60C4⋊C4×C73—22no—
61C22⋊C4×C73—22no—
62C22⋊C4×C73—22no—
63C22⋊C4×C73—22no—
64C42×C73D414yes—
65C23×C73—21no—
66C23×C73—22no—
67C23×C73—21no—
68C23×C73—22no—
69C23×C73—21no—
70C23×C73C2411yescharacteristic
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D412yes—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73#4114yes—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73C22×D411yescharacteristic
103C22×C73C2×#4112yes—
104C22×C73H(5,𝔽2)11yescharacteristic
105C22×C732−1+412yes—
106C22×C732−1+411yescharacteristic
107C4×C73—22no—
108C4×C73—22no—
109C4×C73—22no—
110C4×C73—41no—
111C4×C73—41no—
112C4×C73—41no—
113Dic73—24no—
114Dic73—42no—
115Dic73—42no—
116Dic73—42no—
117C2×C73—81no—
118C2×C73#53211yescharacteristic
119C2×C73#53611yescharacteristic
120C2×C73#53711yescharacteristic
121C2×C73#53912yes—
122C2×C73#54112yes—
123#2664—731nomaximal, Sylow
124C73#266411yescharacteristic, complemented, Sylow
125C2×#126D7311yescharacteristic
126C2×#125—731no—
127#400—731no—
128#399—731no—
129#398—731no—
130#398—732no—
131#397—731no—
132#396—732no—
133#389—732no—
134#388—732no—
135C4×C4⋊C4—731no—
136#126—24no—
137#125—1464no—
138C2×C4⋊C4—732no—
139C2×C4⋊C4—732no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—732no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C22⋊C4—732no—
149C2×C22⋊C4—732no—
150C2×C22⋊C4C2×D7311yescharacteristic
151C2×C22⋊C4C2×D7311yescharacteristic
152C2×C22⋊C4C2×D7311yescharacteristic
153C2×C42—732no—
154C2×C42C2×D7311yescharacteristic
155#95—731no—
156#95—731no—
157#95—732no—
158#95—732no—
159#95—732no—
160#95—732no—
161C24C22×D7311yescharacteristic
162C22×C4—732no—
163C22×C4—732no—
164C22×C4—732no—
165C22×C4—732no—
166C22×C4C22×D7311yescharacteristic
167C22×C4C22×D7311yescharacteristic
168C22×C4C22×D7311yescharacteristic
169C22×C4C22×D7311yescharacteristic
170C22×C4C22×D7311yescharacteristic
171C22×C4C22×D7311yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—2922no—
176C4⋊C4—1464no—
177C4⋊C4—1464no—
178C4⋊C4—1464no—
179C4⋊C4—1464no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—2922no—
186C22⋊C4—1464no—
187C42—2922no—
188C42C22⋊D7314yes—
189C23—21no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23C23×D7311yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—734no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4C2×C22⋊D7312yes—
219C2×C4C2×C22⋊D7312yes—
220C2×C4C2×C22⋊D7312yes—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22C22×C22⋊D7311yescharacteristic
227C22#41×D7312yes—
228C22#1455663711yescharacteristic
229C22#1455663812yes—
230C22#1455663811yescharacteristic
231C4—22no—
232C4—22no—
233C4—22no—
234C4—41no—
235C4—41no—
236C4—41no—
237C4—2922no—
238C4—2922no—
239C4—2922no—
240C4—1464no—
241C2—81no—
242C2#1798913311yescharacteristic
243C2#1798915811yescharacteristic
244C2#1798916511yescharacteristic
245C2#1798917812yes—
246C2#1798919412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#126×C73C2
hypercenterC2×#126D73
hypocenterC73#2664
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#14556583C2semidirect
2. #17988526C2semidirect
4. #17988520C2semidirect
5. #17988517C2semidirect
8. #17988482C2semidirect
10. C4×C4⋊Dic73C2semidirect
124. C73#2664semidirect