Finite Group Databasebeta

← #22611065

Subgroups — #22611065

Order 9344.

326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556512C211yesmaximal, characteristic
3#17988490C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic
8C22×Dic146—21no—
9C22×#10596831C2211yescharacteristic
10#14556590—22no—
11#14556590—22no—
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007—21no—
15C2×C22⋊Dic73—21no—
16C2×C22⋊Dic73—21no—
17C2×C4×Dic73C2211yescharacteristic
18#14556512—22no—
19C22×D4×C73C2211yescharacteristic
20C22×C8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22#102×C73—22no—
23C2×Dic146—24no—
24C2×Dic146—42no—
25C2×Dic146—42no—
26C22×Dic73—21no—
27C22×Dic73—21no—
28C22×Dic73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C2×#10596831—21no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D412yes—
37#11924007—24no—
38C22⋊Dic73—42no—
39C22⋊Dic73—42no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C24×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73Q812yescomplemented
49C22×C4×C73—21no—
50C22×C4×C73C2311yescharacteristic
51C2×C8×C73—21no—
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73D412yes—
56C23×C73—22no—
57C23×C73—41no—
58C23×C73—41no—
59C23×C73—41no—
60C23×C73—41no—
61C23×C73—41no—
62C23×C73—41no—
63C23×C73C2×D411yescharacteristic
64D4×C73—22no—
65D4×C73—22no—
66D4×C73—41no—
67D4×C73—41no—
68C2×C4×C73—22no—
69C2×C4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×Q811yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—22no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86C2×Dic73—41no—
87C2×Dic73D812yes—
88C2×Dic73SD1612yes—
89Dic146—48no—
90C8×C73—41no—
91#10596831—41no—
92C22×C73—42no—
93C22×C73—42no—
94C22×C73—42no—
95C22×C73—81no—
96C22×C73—81no—
97C22×C73—81no—
98C22×C73—81no—
99C22×C73#12011yescharacteristic
100C22×C73C22⋊Q811yescharacteristic
101C22×C73#12411yescharacteristic
102C22×C73C2×D811yescharacteristic
103C22×C73C2×SD1611yescharacteristic
104C22×C73AGL(1,ℤ/8)11yescharacteristic
105C22×C73#13711yescharacteristic
106C4×C73—42no—
107C4×C73C22⋊Q811yescharacteristic
108C4×C73C22⋊Q811yescharacteristic
109C4×C73#12411yescharacteristic
110C4×C73#12411yescharacteristic
111Dic73—22no—
112Dic73—22no—
113Dic73—42no—
114Dic73—81no—
115C2×C73—82no—
116C2×C73#39311yescharacteristic
117C2×C73#44711yescharacteristic
118C2×C73#44811yescharacteristic
119C2×C73#47411yescharacteristic
120C2×C73#47611yescharacteristic
121C2×C73#48611yescharacteristic
122C2×C73#48911yescharacteristic
123#2023—731nomaximal, Sylow
124C73#202311yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—731no—
126C2×#102—731no—
127C2×#102D7311yescharacteristic
128#390—731no—
129#340—731no—
130#340—731no—
131#336—731no—
132C22×Q8—1461no—
133C22×D4C2×D7311yescharacteristic
134C22×C8—731no—
135C22×C8C2×D7311yescharacteristic
136C4⋊Q8—1462no—
137C4⋊Q8—1462no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—731no—
140C2×C4⋊C4—1461no—
141C2×C4⋊C4C2×D7311yescharacteristic
142C2×C22⋊C4—1461no—
143C2×C22⋊C4—1461no—
144C2×C42—731no—
145#102—22no—
146#102—1462no—
147C24—21no—
148C2×Q8—2922no—
149C2×Q8—2922no—
150C2×Q8—1464no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4Dic14612yescomplemented
157C22×C4—21no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—1461no—
161C22×C4—1461no—
162C22×C4C22×D7311yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1461no—
167C2×C8—1461no—
168C2×C8—1461no—
169C4⋊C4—21no—
170C4⋊C4—732no—
171C4⋊C4—1464no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C4⋊C4—1461no—
175C4⋊C4C22⋊D7312yes—
176C22⋊C4—2922no—
177C22⋊C4—2922no—
178C42—1461no—
179C42—1461no—
180C23—22no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23D4×D7311yescharacteristic
188Q8—2928no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—2921no—
200C2×C4—2921no—
201C2×C4—732no—
202C2×C4—732no—
203C2×C4—1462no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4D4×D7311yescharacteristic
209C2×C4C2×C22⋊D7311yescharacteristic
210C2×C4C2×Dic14611yescharacteristic
211C2×C4#1192402711yescharacteristic
212C2×C4#1192402711yescharacteristic
213C2×C4#1192402811yescharacteristic
214C8—41no—
215C8—2921no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—81no—
220C22—81no—
221C22—81no—
222C22—81no—
223C22#1455655911yescharacteristic
224C22#1455656811yescharacteristic
225C22#1455657711yescharacteristic
226C22D8×D7311yescharacteristic
227C22SD16×D7311yescharacteristic
228C22#1455661511yescharacteristic
229C22#1455662011yescharacteristic
230C4—42no—
231C4—2922no—
232C4—5841no—
233C4—1462no—
234C4—1462no—
235C4#1455656811yescharacteristic
236C4#1455657011yescharacteristic
237C4#1455657711yescharacteristic
238C4#1455657811yescharacteristic
239C2—82no—
240C2#1798849911yescharacteristic
241C2#1798871911yescharacteristic
242C2#1798872411yescharacteristic
243C2#1798886511yescharacteristic
244C2#1798887511yescharacteristic
245C2#1798893211yescharacteristic
246C2#1798894511yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2023
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
4. #17988350C2semidirect
5. #17988349C2semidirect
6. #17988341C2semidirect
48. C2×D4×C73Q8semidirect
124. C73#2023semidirect
156. C2×D4Dic146semidirect