Finite Group Databasebeta

← #22611166

Subgroups — #22611166

Order 9344.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14556588C211yesmaximal, characteristic
2C2×#14556513C212yesmaximal, complemented
3C2×#14556513C212yesmaximal, complemented
4#17988485C211yesmaximal, characteristic, complemented
5#336×C73C211yesmaximal, characteristic, complemented
6C22×D292—21no—
7C22×D292—21no—
8C22×D292C2212yes—
9#14556588—24no—
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556513—24no—
14#14556513—24no—
15#14556498—21no—
16C22×C8×C73C2212yes—
17C2×C42×C73C2211yescharacteristic
18C23×D73—22no—
19C2×D292—22no—
20C2×D292—22no—
21C2×D292—22no—
22C2×D292—22no—
23C2×D292—24no—
24C2×D292—24no—
25C2×D292—22no—
26C2×D292—42no—
27C2×D292—42no—
28C2×D292—42no—
29C2×D292—42no—
30C2×D292D414yes—
31C22×Dic73—21no—
32C22×Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—22no—
35C4⋊Dic73D412yescomplemented
36#11924007—42no—
37C22×C4×C73D411yescharacteristic
38C22×C4×C73D411yescharacteristic
39C22×C4×C73C2311yescharacteristic
40C2×C8×C73—22no—
41C2×C8×C73—22no—
42C2×C8×C73—22no—
43C42×C73—22no—
44C23×C73C2×D411yescharacteristic
45C22×D73—24no—
46C22×D73—42no—
47C22×D73—42no—
48C22×D73—42no—
49C22×D73—42no—
50C22×D73—42no—
51C22×D73—42no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73D812yes—
57C2×C4×C73SD1612yes—
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D412yes—
60C2×C4×C73#4112yes—
61C2×C4×C73#4111yescharacteristic
62C2×Dic73—22no—
63C2×Dic73—41no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73—41no—
67C2×Dic73—41no—
68D292—24no—
69D292—24no—
70D292—48no—
71D292—48no—
72D292—42no—
73D292—42no—
74C8×C73—42no—
75C22×C73#12011yescharacteristic
76C22×C73#12111yescharacteristic
77C22×C73#12411yescharacteristic
78C22×C73C2×D811yescharacteristic
79C22×C73C2×SD1611yescharacteristic
80C22×C73AGL(1,ℤ/8)11yescharacteristic
81C22×C73AGL(1,ℤ/8)11yescharacteristic
82C2×D73—44no—
83C2×D73—44no—
84C2×D73—44no—
85C2×D73—82no—
86C2×D73—82no—
87C2×D73—82no—
88C2×D73—82no—
89C4×C73—22no—
90C4×C73—22no—
91C4×C73#12112yes—
92C4×C73#12312yes—
93Dic73—42no—
94Dic73—81no—
95C2×C73#39411yescharacteristic
96C2×C73#44711yescharacteristic
97C2×C73#45011yescharacteristic
98C2×C73#45911yescharacteristic
99C2×C73#46011yescharacteristic
100C2×C73#48611yescharacteristic
101C2×C73#49011yescharacteristic
102D73—84no—
103#2041—731nomaximal, Sylow
104C73#204111yescharacteristic, complemented, Sylow
105C2×#127—731no—
106C2×#102—732no—
107C2×#102—732no—
108#389—731no—
109#336D7311yescharacteristic, complemented
110C22×D4—732no—
111C22×D4—1461no—
112C22×D4—1461no—
113C22×C8C2×D7312yes—
114#127—1464no—
115C2×C4⋊C4—731no—
116C2×C4⋊C4—731no—
117C2×C4⋊C4—1461no—
118C2×C42C2×D7311yescharacteristic
119#102—1464no—
120#102—1464no—
121#95—1461no—
122C24—1462no—
123C2×D4—2922no—
124C2×D4—2922no—
125C2×D4—2922no—
126C2×D4—2922no—
127C2×D4—734no—
128C2×D4—1464no—
129C2×D4—1464no—
130C2×D4—1462no—
131C2×D4—1462no—
132C2×D4—1462no—
133C2×D4—1462no—
134C2×D4—1462no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4D29211yescharacteristic
138C22×C4D29211yescharacteristic
139C22×C4C22×D7311yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C4⋊C4—2922no—
144C4⋊C4—732no—
145C4⋊C4—1462no—
146C4⋊C4—1461no—
147C42—22no—
148C23—2922no—
149C23—2922no—
150C23—2922no—
151C23—2922no—
152C23—2922no—
153C23—2922no—
154C23—1464no—
155C23C2×D29211yescharacteristic
156D4—2928no—
157D4—2928no—
158D4—2922no—
159D4—2922no—
160D4—1464no—
161D4—1464no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—1462no—
172C2×C4D58412yes—
173C2×C4#1192401712yes—
174C2×C4D4×D7311yescharacteristic
175C2×C4D4×D7312yes—
176C2×C4#1192402812yes—
177C2×C4#1192402911yescharacteristic
178C8—42no—
179C22—2924no—
180C22—2924no—
181C22—2924no—
182C22—5842no—
183C22—5842no—
184C22—5842no—
185C22—5842no—
186C22#1455656111yescharacteristic
187C22#1455656611yescharacteristic
188C22#1455657911yescharacteristic
189C22C2×D58411yescharacteristic
190C22C2×#1192401711yescharacteristic
191C22#1455661911yescharacteristic
192C22#1455661911yescharacteristic
193C4—22no—
194C4—22no—
195C4—2922no—
196C4—5841no—
197C4#1455656412yes—
198C4#1455657612yes—
199C2—5844no—
200C2#1798850511yescharacteristic
201C2#1798872311yescharacteristic
202C2#1798874011yescharacteristic
203C2#1798878311yescharacteristic
204C2#1798878811yescharacteristic
205C2#1798893411yescharacteristic
206C2#1798895211yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#336×C73C2
socleC23×C73C2×D4
hypercenter#336D73
hypocenterC73#2041
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×#14556513C2semidirect
3. C2×#14556513C2semidirect
4. #17988485C2semidirect
5. #336×C73C2semidirect
35. C4⋊Dic73D4semidirect
104. C73#2041semidirect
109. #336D73semidirect