Finite Group Databasebeta

← #22620076

Subgroups — #22620076

Order 9344.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4×#11924028C211yesmaximal, characteristic, complemented
2#17988908C212yesmaximal, complemented
3#17988869C211yesmaximal, characteristic, complemented
4#17988864C211yesmaximal, characteristic, complemented
5#17988784C211yesmaximal, characteristic, complemented
6#17988779C211yesmaximal, characteristic, complemented
7#17988730C212yesmaximal, complemented
8#17988697C212yesmaximal, complemented
9#17988687C212yesmaximal, complemented
10#17988644C211yesmaximal, characteristic, complemented
11#532×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924016C2212yes—
14C2×#11924013C2212yes—
15C4×Dic146C2211yescharacteristic
16C4×Dic146C2211yescharacteristic
17C4×D292C2211yescharacteristic
18C4×D292C2211yescharacteristic
19C4×C22⋊D73—21no—
20C4×C22⋊D73—21no—
21#14556550C2211yescharacteristic
22#14556548—21no—
23C42×D73—21no—
24#14556524C2212yes—
25#14556522C2212yes—
26C4⋊#10596831C2211yescharacteristic
27C4⋊#10596831C2211yescharacteristic
28#14556514C2212yes—
29#14556512C2212yes—
30#14556512C2212yes—
31#14556511C2212yes—
32C22⋊#10596831C2212yes—
33#14556502C2212yes—
34C2×#41×C73—21no—
35C4⋊Q8×C73C2211yescharacteristic
36#127×C73C2211yescharacteristic
37#124×C73—21no—
38#121×C73—21no—
39#121×C73C2212yes—
40C4×D4×C73—21no—
41C4×D4×C73C2212yes—
42C2×C42×C73C2211yescharacteristic
43#11924028—22no—
44#11924028—22no—
45C2×Dic146C2311yescharacteristic
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49C2×C4×D73—21no—
50C2×C4×D73—21no—
51#11924016—24no—
52#11924013—24no—
53C2×#10596831C2312yes—
54C2×#10596831C2312yes—
55C4⋊Dic73C2311yescharacteristic
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—21no—
59C22⋊Dic73—21no—
60#11924005—21no—
61#11924005—21no—
62C4×Dic73—21no—
63C4×Dic73—21no—
64C4×Dic73—21no—
65#41×C73—44no—
66C2×Q8×C73—21no—
67C2×D4×C73—22no—
68C2×D4×C73—21no—
69C2×D4×C73—21no—
70C2×D4×C73C2312yes—
71C22×C4×C73—22no—
72C22×C4×C73D411yescharacteristic
73C22×C4×C73D411yescharacteristic
74C22×C4×C73C2311yescharacteristic
75C4⋊C4×C73—21no—
76C4⋊C4×C73C2312yes—
77C22⋊C4×C73—22no—
78C22⋊C4×C73—22no—
79C42×C73D411yescharacteristic
80C42×C73D411yescharacteristic
81C42×C73C2311yescharacteristic
82C42×C73C2311yescharacteristic
83C23×C73—22no—
84C23×C73C2×D411yescharacteristic
85C22×D73—21no—
86Q8×C73—42no—
87D4×C73—22no—
88D4×C73—22no—
89D4×C73—42no—
90D4×C73—44no—
91D4×C73—42no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—41no—
97C2×C4×C73—44no—
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2×D411yescharacteristic
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2411yescharacteristic
104C22⋊D73—24no—
105C2×Dic73—21no—
106C2×Dic73—21no—
107C2×Dic73—21no—
108D292—21no—
109D292#4112yescomplemented
110C4×D73—24no—
111C4×D73—42no—
112C4×D73—42no—
113Dic146—21no—
114Dic146#4112yescomplemented
115#10596831—22no—
116#10596831—22no—
117C22×C73—21no—
118C22×C73—21no—
119C22×C73—21no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73C22×D411yescharacteristic
124C2×D73—22no—
125C2×D73—41no—
126C2×D73—41no—
127C4×C73—21no—
128C4×C73—21no—
129C4×C73—21no—
130C4×C73—21no—
131C4×C73—42no—
132C4×C73AGL(1,ℤ/8)12yes—
133C4×C73C2×#4111yescharacteristic
134C4×C73C2×#4111yescharacteristic
135Dic73—22no—
136Dic73—41no—
137Dic73—41no—
138C2×C73—41no—
139C2×C73—82no—
140C2×C73#52511yescharacteristic
141C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C73#57511yescharacteristic
143D73—42no—
144#3115—731nomaximal, Sylow
145C73#311511yescharacteristic, complemented, Sylow
146#532D7311yescharacteristic, complemented
147C4×#41—731no—
148#482—732no—
149#475—731no—
150#474—731no—
151#460—731no—
152#459—731no—
153#449—732no—
154#442—732no—
155#440—732no—
156#432—731no—
157C2×#41—21no—
158C2×#41—731no—
159C2×SD16—732no—
160C2×D8—732no—
161C4⋊Q8C2×D7311yescharacteristic
162#127C2×D7311yescharacteristic
163#124—21no—
164#121—21no—
165#121C2×D7312yes—
166C4×Q8—731no—
167C4×Q8—731no—
168C4×D4—21no—
169C4×D4—731no—
170C4×D4—731no—
171C4×D4—1461no—
172C4×D4—1461no—
173C4×D4C2×D7312yes—
174#117—731no—
175#117—1461no—
176C2×C42—1461no—
177C2×C42C2×D7311yescharacteristic
178#107—732no—
179#106—732no—
180C4⋊C8—731no—
181C4⋊C8—731no—
182#103—732no—
183#102—732no—
184#102—732no—
185#102—732no—
186C22⋊C8—732no—
187#97—732no—
188#41—44no—
189#41—1462no—
190#41—1462no—
191C2×Q8—21no—
192C2×Q8—731no—
193C2×D4—22no—
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—731no—
197C2×D4—1461no—
198C2×D4C22×D7312yes—
199C22×C4—22no—
200C22×C4—1461no—
201C22×C4—1461no—
202C22×C4—1461no—
203C22×C4C22⋊D7311yescharacteristic
204C22×C4C22⋊D7311yescharacteristic
205C22×C4C22×D7311yescharacteristic
206SD16—1464no—
207D8—1464no—
208C2×C8—732no—
209C2×C8—732no—
210C4⋊C4—21no—
211C4⋊C4—731no—
212C4⋊C4—731no—
213C4⋊C4—1461no—
214C4⋊C4—1461no—
215C4⋊C4C22×D7312yes—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—1461no—
219C22⋊C4—1461no—
220C22⋊C4—1461no—
221C42—1461no—
222C42—1461no—
223C42—1461no—
224C42C22⋊D7311yescharacteristic
225C42C22⋊D7311yescharacteristic
226C42C22×D7311yescharacteristic
227C42C22×D7311yescharacteristic
228C23—22no—
229C23—1461no—
230C23C2×C22⋊D7311yescharacteristic
231Q8—42no—
232Q8—732no—
233Q8—1461no—
234D4—22no—
235D4—22no—
236D4—42no—
237D4—44no—
238D4—42no—
239D4—732no—
240D4—1464no—
241D4—1461no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—44no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—1464no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4—1461no—
254C2×C4C2×C22⋊D7311yescharacteristic
255C2×C4C2×C22⋊D7311yescharacteristic
256C2×C4C2×C22⋊D7311yescharacteristic
257C2×C4C2×C22⋊D7311yescharacteristic
258C2×C4C2×C22⋊D7311yescharacteristic
259C2×C4C23×D7311yescharacteristic
260C8—1462no—
261C8—1462no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—2921no—
269C22—2921no—
270C22—1462no—
271C22C22×C22⋊D7311yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—2921no—
278C4—2921no—
279C4—1462no—
280C4#1455661712yes—
281C4#41×D7311yescharacteristic
282C4#41×D7311yescharacteristic
283C2—41no—
284C2—82no—
285C2—2922no—
286C2#1798909411yescharacteristic
287C2C2×#1455661711yescharacteristic
288C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3115
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C4×#11924028C2semidirect
2. #17988908C2semidirect
3. #17988869C2semidirect
4. #17988864C2semidirect
5. #17988784C2semidirect
6. #17988779C2semidirect
7. #17988730C2semidirect
8. #17988697C2semidirect
9. #17988687C2semidirect
10. #17988644C2semidirect
11. #532×C73C2semidirect
109. D292#41semidirect
114. Dic146#41semidirect
145. C73#3115semidirect
146. #532D73semidirect