Finite Group Databasebeta

← #22611108

Subgroups — #22611108

Order 9344.

278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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#17989213C211yesmaximal, characteristic, complemented
2C2×#14556506C211yesmaximal, characteristic
3C2×#14556506C211yesmaximal, characteristic
4#17988354C211yesmaximal, characteristic, complemented
5#17988353C211yesmaximal, characteristic, complemented
6#17988353C211yesmaximal, characteristic, complemented
7C2×#99×C73C211yesmaximal, characteristic
8#14556570—22no—
9#14556568—22no—
10#14556568—22no—
11C2×C22⋊Dic73C2211yescharacteristic
12C2×C22⋊Dic73C2211yescharacteristic
13C2×C22⋊Dic73C2211yescharacteristic
14C2×C22⋊Dic73C2211yescharacteristic
15#14556506—22no—
16#14556506—22no—
17C22×D4×C73C2211yescharacteristic
18C2×C22⋊C4×C73C2211yescharacteristic
19C2×C22⋊C4×C73C2211yescharacteristic
20#99×C73—22no—
21C2×Dic146—22no—
22C22×Dic73—21no—
23C22×Dic73—21no—
24C22×Dic73—21no—
25C22×Dic73—21no—
26C4⋊Dic73—22no—
27#11924007—24no—
28C22⋊Dic73—21no—
29C22⋊Dic73—21no—
30C22⋊Dic73—21no—
31C22⋊Dic73—21no—
32C22⋊Dic73—21no—
33C22⋊Dic73—21no—
34C22⋊Dic73D412yes—
35C22⋊Dic73D412yes—
36C24×C73Q811yescharacteristic, complemented
37C24×C73C2311yescharacteristic
38C2×D4×C73—21no—
39C2×D4×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73Q811yescharacteristic, complemented
47C22⋊C4×C73—21no—
48C22⋊C4×C73—21no—
49C22⋊C4×C73—21no—
50C22⋊C4×C73D412yes—
51C23×C73—21no—
52C23×C73—21no—
53C23×C73—21no—
54C23×C73—81no—
55C23×C73—81no—
56C23×C73C2×D411yescharacteristic
57C23×C73C2×D411yescharacteristic
58C23×C73C2×D411yescharacteristic
59C23×C73C2×Q811yescharacteristic
60C23×C73#4111yescharacteristic
61C23×C73#4111yescharacteristic
62C23×C73#4111yescharacteristic
63D4×C73—41no—
64D4×C73—41no—
65D4×C73—41no—
66D4×C73—41no—
67C2×C4×C73—22no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73—81no—
73C2×C4×C73—81no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—41no—
77C2×Dic73—41no—
78C2×Dic73—81no—
79C2×Dic73—81no—
80C2×Dic73—81no—
81C2×Dic73—81no—
82Dic146—82no—
83C22×C73—41no—
84C22×C73—41no—
85C22×C73—41no—
86C22×C73—41no—
87C22×C73—41no—
88C22×C73—41no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73—81no—
94C22×C73#12011yescharacteristic
95C22×C73C22⋊Q811yescharacteristic
96C22×C73C22⋊Q811yescharacteristic
97C22×C73C22⋊Q811yescharacteristic
98C22×C73#12411yescharacteristic
99C22×C73#12411yescharacteristic
100C22×C73#12411yescharacteristic
101C4×C73—42no—
102C4×C73—41no—
103C4×C73—81no—
104Dic73—42no—
105Dic73—42no—
106Dic73—81no—
107Dic73—81no—
108C2×C73—21no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73—21no—
112C2×C73—21no—
113C2×C73—21no—
114C2×C73—21no—
115C2×C73—81no—
116C2×C73#39311yescharacteristic
117#2032—731nomaximal, Sylow
118C73#203211yescharacteristic, complemented, Sylow
119#543—731no—
120C2×#99—731no—
121C2×#99—731no—
122C2×#99D7311yescharacteristic
123#342—731no—
124#342—731no—
125#342—731no—
126C22×D4C2×D7311yescharacteristic
127C22⋊Q8—1462no—
128C22⋊Q8—1462no—
129C22⋊Q8—1462no—
130C2×C22⋊C4—731no—
131C2×C22⋊C4—731no—
132C2×C22⋊C4—731no—
133C2×C22⋊C4—731no—
134C2×C22⋊C4C2×D7311yescharacteristic
135C2×C22⋊C4C2×D7311yescharacteristic
136#99—22no—
137#99—1462no—
138#99—1462no—
139C24Dic14611yescharacteristic, complemented
140C24C22×D7311yescharacteristic
141C2×Q8—1462no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1461no—
151C22×C4—1461no—
152C22×C4—1461no—
153C22×C4—1461no—
154C22×C4Dic14611yescharacteristic, complemented
155C4⋊C4—1464no—
156C4⋊C4—1462no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—732no—
161C22⋊C4—732no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C22⋊C4—1461no—
166C22⋊C4—1461no—
167C22⋊C4—1461no—
168C22⋊C4C22⋊D7312yes—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—81no—
173C23—81no—
174C23D4×D7311yescharacteristic
175C23D4×D7311yescharacteristic
176C23C2×C22⋊D7311yescharacteristic
177C23C2×Dic14611yescharacteristic
178C23#1192402711yescharacteristic
179C23#1192402711yescharacteristic
180C23#1192402811yescharacteristic
181Q8—5842no—
182D4—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—5841no—
196C2×C4—5841no—
197C2×C4—5841no—
198C2×C4—5841no—
199C2×C4—1462no—
200C2×C4—1462no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22#1455655911yescharacteristic
213C22#1455656811yescharacteristic
214C22#1455656811yescharacteristic
215C22#1455657011yescharacteristic
216C22#1455657711yescharacteristic
217C22#1455657711yescharacteristic
218C22#1455657811yescharacteristic
219C4—42no—
220C4—41no—
221C4—81no—
222C4—2922no—
223C4—2922no—
224C4—5841no—
225C4—5841no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#1798849911yescharacteristic
subgroupG/H
centerC2#17988499
commutatorC24×C73C23
FrattiniC24C22×D73
FittingC2×#99×C73C2
socleC2×C73#393
hypercenterC2×#99D73
hypocenterC73#2032
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #17989213C2semidirect
4. #17988354C2semidirect
5. #17988353C2semidirect
6. #17988353C2semidirect
36. C24×C73Q8semidirect
46. C22×C4×C73Q8semidirect
118. C73#2032semidirect
139. C24Dic146semidirect
154. C22×C4Dic146semidirect