Finite Group Databasebeta

← #22611233

Subgroups — #22611233

Order 9344.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14556624C211yesmaximal, characteristic
2C2×#14556526C211yesmaximal, characteristic, complemented
3#17988586C211yesmaximal, characteristic
4C2×#14556514C211yesmaximal, characteristic, complemented
5C2×#14556509C211yesmaximal, characteristic, complemented
6#17988555C211yesmaximal, characteristic
7#343×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×Dic146C2211yescharacteristic
10#14556624—22no—
11#14556624—22no—
12C2×Dic292—21no—
13C2×#11924017—21no—
14C2×#11924012C2211yescharacteristic
15C22×#10596831C2211yescharacteristic
16#14556526—22no—
17#14556514—21no—
18#14556514—22no—
19#14556511—21no—
20#14556509—22no—
21#14556503—22no—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24C2×C4⋊C4×C73C2211yescharacteristic
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—21no—
34C2×Dic146D412yes—
35C2×Dic146D411yescharacteristic
36C2×D292D411yescharacteristic
37C2×C22⋊D73—21no—
38C22×Dic73—21no—
39C2×C4×D73—21no—
40Dic292—24no—
41#11924017—24no—
42#11924012—21no—
43#11924012—21no—
44C2×#10596831—21no—
45C2×#10596831—21no—
46C2×#10596831—21no—
47C2×#10596831D412yes—
48C22×C4×C73—21no—
49C22×C4×C73C2311yescharacteristic
50M16×C73—21no—
51M16×C73—21no—
52M16×C73—21no—
53M16×C73D412yes—
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C4⋊C4×C73—21no—
57C4⋊C4×C73—21no—
58C23×C73#4111yescharacteristic
59C22×D73—21no—
60C2×C4×C73—41no—
61C2×C4×C73—81no—
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73#4111yescharacteristic
67C2×C4×C73#4111yescharacteristic
68C22⋊D73—41no—
69C22⋊D73—41no—
70C2×Dic73—21no—
71C2×Dic73—22no—
72C2×Dic73—41no—
73C2×Dic73—41no—
74D292—21no—
75D292—21no—
76C4×D73—41no—
77C4×D73—41no—
78Dic146—22no—
79Dic146—21no—
80Dic146—22no—
81Dic146—21no—
82Dic146—41no—
83Dic146—41no—
84C8×C73—22no—
85C8×C73—41no—
86#10596831—22no—
87#10596831—41no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73#12111yescharacteristic
91C22×C73#12311yescharacteristic
92C22×C73#12411yescharacteristic
93C2×D73—41no—
94C2×D73—41no—
95C2×D73—41no—
96C4×C73—81no—
97C4×C73#12011yescharacteristic
98C4×C73#12111yescharacteristic
99C4×C73#12111yescharacteristic
100C4×C73#12311yescharacteristic
101Dic73—42no—
102Dic73—41no—
103C2×C73—21no—
104C2×C73—21no—
105C2×C73#39411yescharacteristic
106C2×C73#47111yescharacteristic
107C2×C73#47311yescharacteristic
108D73—81no—
109#2052—731nomaximal, Sylow
110C73#205211yescharacteristic, complemented, Sylow
111C2×#137—731no—
112C2×#108—731no—
113#417—731no—
114C2×#103—731no—
115C2×#101—731no—
116#408—731no—
117#343D7311yescharacteristic, complemented
118C2×#41—731no—
119C22×Q8—731no—
120#137—1462no—
121#137—1462no—
122C2×Q16—1461no—
123C2×SD16—1461no—
124C2×M16—731no—
125C2×M16C2×D7311yescharacteristic
126C2×M16C2×D7311yescharacteristic
127C22×C8—731no—
128C2×C4⋊C4C2×D7311yescharacteristic
129#108—1462no—
130#103—1462no—
131#103—1461no—
132#102—1461no—
133#101—1462no—
134C22⋊C8—1462no—
135#41—1461no—
136#41—1461no—
137#41—1461no—
138#41—1461no—
139C2×Q8—732no—
140C2×Q8—731no—
141C2×Q8—1461no—
142C2×Q8—1461no—
143C2×Q8—1461no—
144C2×Q8—1461no—
145C2×Q8—1461no—
146C2×D4—731no—
147C2×D4—1461no—
148C22×C4—21no—
149C22×C4—1461no—
150C22×C4—1461no—
151C22×C4C22×D7311yescharacteristic
152Q16—1464no—
153SD16—1464no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—1461no—
158M16—1461no—
159M16D29212yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—732no—
163C2×C8—1461no—
164C2×C8—1461no—
165C2×C8—1461no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—1461no—
169C23#1192402811yescharacteristic
170Q8—2921no—
171Q8—2921no—
172Q8—1462no—
173Q8—1461no—
174Q8—1462no—
175Q8—1461no—
176D4—2921no—
177D4—2921no—
178D4—1461no—
179D4—1461no—
180C2×C4—41no—
181C2×C4—81no—
182C2×C4—2921no—
183C2×C4—2921no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—1461no—
187C2×C4—1462no—
188C2×C4D4×D7311yescharacteristic
189C2×C4D4×D7311yescharacteristic
190C2×C4D4×D7311yescharacteristic
191C2×C4C2×D29211yescharacteristic
192C2×C4#1192402811yescharacteristic
193C2×C4#1192402911yescharacteristic
194C8—22no—
195C8—41no—
196C8—2921no—
197C8—1462no—
198C22—21no—
199C22—21no—
200C22—2921no—
201C22—2921no—
202C22—2921no—
203C22#1455656411yescharacteristic
204C22#1455657611yescharacteristic
205C22#1455657911yescharacteristic
206C4—81no—
207C4—2921no—
208C4—2922no—
209C4#1455656111yescharacteristic
210C4#1455656411yescharacteristic
211C4#1455656611yescharacteristic
212C4#1455657611yescharacteristic
213C2—21no—
214C2—21no—
215C2—5841no—
216C2#1798850511yescharacteristic
217C2#1798884911yescharacteristic
218C2#1798886111yescharacteristic
subgroupG/H
centerC22#14556564
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#343×C73C2
socleC22×C73#121
hypercenter#343D73
hypocenterC73#2052
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#14556526C2semidirect
4. C2×#14556514C2semidirect
5. C2×#14556509C2semidirect
7. #343×C73C2semidirect
110. C73#2052semidirect
117. #343D73semidirect