Finite Group Databasebeta

← #22619764

Subgroups — #22619764

Order 9344.

398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989215C211yesmaximal, characteristic, complemented
2#17989062C211yesmaximal, characteristic
3#17988889C212yesmaximal, complemented
4#17988885C212yesmaximal, complemented
5#17988875C212yesmaximal, complemented
6#17988865C212yesmaximal, complemented
7#17988629C211yesmaximal, characteristic, complemented
8#17988623C211yesmaximal, characteristic, complemented
9#17988615C211yesmaximal, characteristic, complemented
10C2×#14556512C211yesmaximal, characteristic
11#418×C73C211yesmaximal, characteristic
12C22×#10596831C2211yescharacteristic
13#14556591—21no—
14#14556590C2212yescomplemented
15#14556583—21no—
16#14556582C2212yescomplemented
17#14556568—22no—
18D4×Dic73—21no—
19D4×Dic73—21no—
20D4×Dic73C2212yes—
21D4×Dic73C2212yes—
22#14556550C2211yescharacteristic
23#14556550C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73—22no—
26#14556525C2212yescomplemented
27#14556524C2211yescharacteristic, complemented
28#14556524C2211yescharacteristic, complemented
29#14556523C2212yescomplemented
30#14556522C2211yescharacteristic, complemented
31#14556522C2211yescharacteristic, complemented
32#14556520C2212yescomplemented
33#14556520C2212yescomplemented
34#14556512C2212yes—
35#14556512C2212yes—
36C22×D4×C73C2211yescharacteristic
37C2×M16×C73C2211yescharacteristic
38#117×C73C2211yescharacteristic
39#102×C73C2212yes—
40#102×C73C2212yes—
41C2×Dic146—22no—
42C22×Dic73—21no—
43C22×Dic73—22no—
44C22×Dic73—22no—
45C2×#10596831—22no—
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73—22no—
50C4⋊Dic73D411yescharacteristic
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—22no—
56#11924007—22no—
57C22⋊Dic73—21no—
58C22⋊Dic73—22no—
59C22⋊Dic73—22no—
60C22⋊Dic73D412yes—
61C4×Dic73—21no—
62C4×Dic73C2312yes—
63C24×C73—21no—
64C2×D4×C73—21no—
65C2×D4×C73—22no—
66C2×D4×C73Q814yescomplemented
67C2×D4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69M16×C73—22no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C42×C73—21no—
75C23×C73—22no—
76C23×C73—24no—
77C23×C73—81no—
78C23×C73—81no—
79C23×C73C2×D411yescharacteristic
80D4×C73—24no—
81D4×C73—22no—
82D4×C73C2×Q814yes—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×Q812yes—
87C2×C4×C73#4112yes—
88C2×C4×C73C2411yescharacteristic
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—82no—
93C2×Dic73—82no—
94C2×Dic73—81no—
95C2×Dic73C2×D412yes—
96C2×Dic73C2×D412yes—
97Dic146—82no—
98C8×C73—22no—
99#10596831—21no—
100#10596831—21no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73—24no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73—84no—
107C22×C73C22⋊Q812yes—
108C22×C73C22×D411yescharacteristic
109C4×C73—41no—
110C4×C73—41no—
111C4×C73C22⋊Q812yes—
112C4×C73C22×Q811yescharacteristic
113C4×C73C2×#4111yescharacteristic
114Dic73—22no—
115Dic73—22no—
116Dic73—42no—
117Dic73—41no—
118Dic73—41no—
119C2×C73—22no—
120C2×C73—44no—
121C2×C73C2×C22⋊Q811yescharacteristic
122C2×C73#57611yescharacteristic
123C2×C73#57711yescharacteristic
124#3081—731nomaximal, Sylow
125C73#308111yescharacteristic, complemented, Sylow
126#544—731no—
127#518—731no—
128#478—732no—
129#478—732no—
130#476—732no—
131#474—732no—
132#428—731no—
133#427—731no—
134#424—731no—
135#418D7311yescharacteristic
136C2×#102—731no—
137C22×D4C2×D7311yescharacteristic
138C2×M16C2×D7311yescharacteristic
139C22×C8—731no—
140C4⋊Q8—732no—
141C4⋊Q8—1461no—
142#125—732no—
143#125—1461no—
144C22⋊Q8—1462no—
145C4×D4—732no—
146C4×D4—732no—
147C4×D4—1461no—
148C4×D4—1461no—
149#117—731no—
150#117—731no—
151#117C2×D7311yescharacteristic
152C2×C4⋊C4—731no—
153C2×C22⋊C4—1462no—
154#107—732no—
155#107—731no—
156#107—731no—
157#106—732no—
158#106—731no—
159#106—731no—
160C4⋊C8—732no—
161C4⋊C8—732no—
162#102—732no—
163#102—732no—
164#102C2×D7312yes—
165#102C2×D7312yes—
166C24—21no—
167C2×Q8—1462no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4Dic14614yescomplemented
171C2×D4C22×D7312yes—
172C22×C4—1462no—
173C22×C4—1462no—
174C22×C4—1461no—
175C22×C4C22×D7311yescharacteristic
176M16—22no—
177C2×C8—731no—
178C2×C8—731no—
179C2×C8—1462no—
180C2×C8C22×D7312yes—
181C4⋊C4—731no—
182C4⋊C4—731no—
183C4⋊C4—732no—
184C4⋊C4—731no—
185C4⋊C4—731no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1461no—
190C4⋊C4C22×D7311yescharacteristic
191C4⋊C4C22×D7311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—732no—
194C22⋊C4—1462no—
195C22⋊C4—1462no—
196C22⋊C4—1461no—
197C42—21no—
198C42—732no—
199C42—1461no—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23D4×D7311yescharacteristic
205Q8—5842no—
206D4—24no—
207D4—22no—
208D4C2×Dic14614yes—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—5841no—
212C2×C4—5842no—
213C2×C4—5842no—
214C2×C4—732no—
215C2×C4—732no—
216C2×C4—1461no—
217C2×C4—1461no—
218C2×C4—1462no—
219C2×C4D4×D7311yescharacteristic
220C2×C4C2×Dic14612yes—
221C2×C4#1192402712yes—
222C2×C4C23×D7311yescharacteristic
223C8—22no—
224C8—1461no—
225C8—1461no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1455656812yes—
233C22C2×D4×D7311yescharacteristic
234C4—41no—
235C4—41no—
236C4—2921no—
237C4—2922no—
238C4—2921no—
239C4—1462no—
240C4—1462no—
241C4#1455656812yes—
242C4C22×Dic14611yescharacteristic
243C4C2×#1192402711yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1455656811yescharacteristic
247C2#1798939111yescharacteristic
248C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3081
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
3. #17988889C2semidirect
4. #17988885C2semidirect
5. #17988875C2semidirect
6. #17988865C2semidirect
7. #17988629C2semidirect
8. #17988623C2semidirect
9. #17988615C2semidirect
14. #14556590C22semidirect
16. #14556582C22semidirect
26. #14556525C22semidirect
27. #14556524C22semidirect
28. #14556524C22semidirect
29. #14556523C22semidirect
30. #14556522C22semidirect
31. #14556522C22semidirect
32. #14556520C22semidirect
33. #14556520C22semidirect
66. C2×D4×C73Q8semidirect
125. C73#3081semidirect
170. C2×D4Dic146semidirect