Finite Group Databasebeta

← #22608945

Subgroups — #22608945

Order 9344.

232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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#17988915C211yesmaximal, characteristic, complemented
2#17988898C211yesmaximal, characteristic, complemented
3#17988512C211yesmaximal, characteristic, complemented
4#17988324C211yesmaximal, characteristic, complemented
5#17988321C211yesmaximal, characteristic, complemented
6#17988311C211yesmaximal, characteristic, complemented
7#538×C73C211yesmaximal, characteristic
8C2×C4⋊Dic73C2211yescharacteristic
9C2×C22⋊Dic73—21no—
10#14556524—21no—
11#14556522—21no—
12#14556515—21no—
13#14556512—21no—
14C22⋊#10596831C2211yescharacteristic
15C22⋊#10596831C2211yescharacteristic
16#14556498—21no—
17#14556498C2211yescharacteristic
18#126×C73—21no—
19#124×C73—21no—
20#123×C73—21no—
21C22⋊Q8×C73C2211yescharacteristic
22#121×C73—21no—
23#121×C73C2211yescharacteristic
24#120×C73—21no—
25C4×D4×C73—21no—
26C2×C22⋊C4×C73C2211yescharacteristic
27C22×Dic73—21no—
28C22×Dic73—21no—
29C2×#10596831—21no—
30C2×#10596831—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C22⋊Dic73—42no—
34C24×C73D411yescharacteristic
35C2×Q8×C73D411yescharacteristic
36C2×D4×C73—21no—
37C2×D4×C73—21no—
38C2×D4×C73—21no—
39C2×D4×C73D411yescharacteristic
40C22×C4×C73—21no—
41C22×C4×C73D411yescharacteristic
42C22×C4×C73C2311yescharacteristic
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73D411yescharacteristic
46C4⋊C4×C73D411yescharacteristic
47C22⋊C4×C73—21no—
48C22⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C22⋊C4×C73—21no—
51C22⋊C4×C73—21no—
52C22⋊C4×C73—21no—
53C22⋊C4×C73—21no—
54C42×C73—21no—
55C23×C73—21no—
56C23×C73—21no—
57C23×C73—21no—
58C23×C73—21no—
59C23×C73—41no—
60C23×C73—41no—
61C23×C73C2×D411yescharacteristic
62Q8×C73—41no—
63D4×C73—41no—
64D4×C73—41no—
65D4×C73—41no—
66D4×C73—81no—
67D4×C73—81no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73—81no—
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83#10596831—41no—
84#10596831—41no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—42no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—81no—
95C22×C73#12011yescharacteristic
96C22×C73#13511yescharacteristic
97C22×C73AGL(1,ℤ/8)11yescharacteristic
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—41no—
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—41no—
104Dic73—81no—
105Dic73—81no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73—81no—
109C2×C73—81no—
110C2×C73#44911yescharacteristic
111C2×C73#45511yescharacteristic
112C2×C73#45811yescharacteristic
113#1612—731nomaximal, Sylow
114C73#161211yescharacteristic, complemented, Sylow
115#538D7311yescharacteristic
116#483—731no—
117#480—731no—
118#397—731no—
119#328—731no—
120#327—731no—
121#323—731no—
122#126—21no—
123#124—21no—
124#123—21no—
125C22⋊Q8C2×D7311yescharacteristic
126#121—21no—
127#121C2×D7311yescharacteristic
128#120—21no—
129C4×D4—21no—
130C2×C4⋊C4—731no—
131C2×C22⋊C4—1461no—
132C2×C22⋊C4C2×D7311yescharacteristic
133#107—1461no—
134#106—1461no—
135#103—1461no—
136#102—1461no—
137C22⋊C8—731no—
138C22⋊C8—731no—
139#95—731no—
140#95—1461no—
141C24C22⋊D7311yescharacteristic
142C2×Q8C22⋊D7311yescharacteristic
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D7311yescharacteristic
147C22×C4—21no—
148C22×C4—1461no—
149C22×C4—1461no—
150C22×C4C22⋊D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C2×C8—1461no—
153C2×C8—1461no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4C22⋊D7311yescharacteristic
159C4⋊C4C22⋊D7311yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—2922no—
168C42—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊D7311yescharacteristic
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4C2×C22⋊D7311yescharacteristic
196C2×C4C2×C22⋊D7311yescharacteristic
197C8—2921no—
198C8—2921no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22#1455656011yescharacteristic
210C22#1455661111yescharacteristic
211C22#1455661611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—5841no—
219C4—5841no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—81no—
224C2#1798873211yescharacteristic
225C2#1798876511yescharacteristic
226C2#1798877711yescharacteristic
subgroupG/H
centerC22#14556560
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#538×C73C2
socleC22×C73#120
hypercenter#538D73
hypocenterC73#1612
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #17988915C2semidirect
2. #17988898C2semidirect
3. #17988512C2semidirect
4. #17988324C2semidirect
5. #17988321C2semidirect
6. #17988311C2semidirect
114. C73#1612semidirect