Finite Group Databasebeta

← #22620935

Subgroups — #22620935

Order 9344.

400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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#17989142C211yesmaximal, characteristic, complemented
2#124×D73C211yesmaximal, characteristic
3#17988982C211yesmaximal, characteristic, complemented
4#17988981C211yesmaximal, characteristic, complemented
5#17988949C211yesmaximal, characteristic, complemented
6#17988812C212yesmaximal, complemented
7#17988808C212yesmaximal, complemented
8#17988744C212yesmaximal, complemented
9#17988739C212yesmaximal
10#17988642C211yesmaximal, characteristic, complemented
11#489×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14C2×Dic292C2212yescomplemented
15C2×#11924018C2212yescomplemented
16C2×#11924017C2212yes—
17C2×#11924016C2212yes—
18#14556591C2211yescharacteristic, complemented
19#14556582—21no—
20#14556580C2211yescharacteristic
21#14556579C2211yescharacteristic
22#14556578C2211yescharacteristic
23#14556577—21no—
24#14556577—21no—
25#14556571C2212yes—
26#14556567—21no—
27Q8×Dic73—21no—
28#14556556C2212yescomplemented
29#14556549—21no—
30C22⋊C4×D73—21no—
31C22⋊C4×D73—21no—
32C42×D73C2211yescharacteristic
33#14556520C2212yescomplemented
34#14556514C2212yescomplemented
35#14556511C2212yes—
36#14556503C2212yes—
37#14556502C2211yescharacteristic, complemented
38C4⋊Q8×C73C2211yescharacteristic, complemented
39#124×C73C2211yescharacteristic
40#103×C73C2212yescomplemented
41#102×C73C2212yes—
42#97×C73C2211yescharacteristic, complemented
43C23×D73—21no—
44C2×Dic146—21no—
45C2×Dic146C2311yescharacteristic
46C2×Dic146C2312yes—
47Q8×D73—42no—
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50D4×D73—42no—
51C2×C4×D73—21no—
52C2×C4×D73D411yescharacteristic
53C2×C4×D73D411yescharacteristic
54C2×C4×D73C2311yescharacteristic
55Dic292—42no—
56#11924018—42no—
57#11924017—42no—
58#11924016—42no—
59C2×#10596831C2312yes—
60C4⋊Dic73—21no—
61C4⋊Dic73—21no—
62C4⋊Dic73—22no—
63#11924007—22no—
64C22⋊Dic73—21no—
65C22⋊Dic73—21no—
66#11924005—22no—
67#11924005—21no—
68#11924005—21no—
69#11924005—21no—
70#11924005—21no—
71C4×Dic73—22no—
72C4×Dic73D411yescharacteristic
73C4×Dic73D411yescharacteristic
74C4×Dic73C2311yescharacteristic
75C2×Q8×C73—21no—
76C2×Q8×C73C2311yescharacteristic
77C2×D4×C73C2311yescharacteristic
78C2×C8×C73C2312yes—
79C4⋊C4×C73—21no—
80C4⋊C4×C73C2312yes—
81C22⋊C4×C73—21no—
82C22⋊C4×C73—21no—
83C42×C73C2311yescharacteristic
84C23×C73—21no—
85C22×D73—21no—
86C22×D73—42no—
87C22×D73—42no—
88C22×D73—42no—
89C22×D73C2×D411yescharacteristic
90Q8×C73—22no—
91Q8×C73—42no—
92D4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73C2411yescharacteristic
98C22⋊D73—42no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73C2×D411yescharacteristic
102C2×Dic73C2×D411yescharacteristic
103C2×Dic73C2×D411yescharacteristic
104D292—22no—
105C4×D73—22no—
106C4×D73—22no—
107C4×D73—41no—
108C4×D73—42no—
109Dic146—22no—
110Dic146—22no—
111Dic146—22no—
112Dic146—42no—
113C8×C73—22no—
114#10596831—22no—
115C22×C73—41no—
116C22×C73—41no—
117C22×C73—41no—
118C22×C73C22×D411yescharacteristic
119C2×D73—21no—
120C2×D73—21no—
121C2×D73—41no—
122C2×D73—41no—
123C2×D73—41no—
124C2×D73—84no—
125C2×D73#13712yes—
126C4×C73—21no—
127C4×C73—21no—
128C4×C73—41no—
129C4×C73—42no—
130C4×C73H(5,𝔽2)12yes—
131Dic73—21no—
132Dic73—21no—
133Dic73—21no—
134Dic73—41no—
135Dic73—42no—
136C2×C73—81no—
137C2×C73#53511yescharacteristic
138C2×C73C2×#13711yescharacteristic
139C2×C73#57511yescharacteristic
140D73—22no—
141D73—81no—
142#3215—731nomaximal, Sylow
143C73#321511yescharacteristic, complemented, Sylow
144#533—731no—
145C2×#124—731no—
146#497—731no—
147#497—731no—
148#489—731no—
149#489D7311yescharacteristic, complemented
150#464—732no—
151#464—732no—
152#451—732no—
153#450—732no—
154#432—731no—
155C22×Q8—731no—
156C22×D4—731no—
157C2×Q16—732no—
158C2×Q16—732no—
159C2×SD16—732no—
160C2×SD16—732no—
161C4⋊Q8—731no—
162C4⋊Q8C2×D7311yescharacteristic, complemented
163#125—1461no—
164#124—731no—
165#124—731no—
166#124—731no—
167#124—1461no—
168#124—1461no—
169#124C2×D7311yescharacteristic
170C22⋊Q8—732no—
171C22⋊Q8—1461no—
172C4×Q8—732no—
173C4×Q8—1461no—
174#117—1461no—
175C2×C22⋊C4—1461no—
176C2×C22⋊C4—1461no—
177C2×C42—731no—
178C4⋊C8—732no—
179#103—732no—
180#103C2×D7312yescomplemented
181#102—732no—
182#102C2×D7312yes—
183C22⋊C8—732no—
184#97—731no—
185#97C2×D7311yescharacteristic, complemented
186C24—1461no—
187C2×Q8—21no—
188C2×Q8—2922no—
189C2×Q8—731no—
190C2×Q8—732no—
191C2×Q8—1461no—
192C2×Q8C22×D7311yescharacteristic
193C2×D4—2922no—
194C2×D4—731no—
195C2×D4—1461no—
196C2×D4C22×D7311yescharacteristic
197C22×C4—731no—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—1461no—
201Q16—2922no—
202Q16—2922no—
203SD16—2922no—
204SD16—2922no—
205C2×C8—732no—
206C2×C8C22×D7312yes—
207C4⋊C4—21no—
208C4⋊C4—1462no—
209C4⋊C4—1462no—
210C4⋊C4—1461no—
211C4⋊C4—1461no—
212C4⋊C4C22×D7312yes—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—1461no—
216C22⋊C4—1461no—
217C22⋊C4—1462no—
218C22⋊C4—1461no—
219C22⋊C4—1461no—
220C22⋊C4—1461no—
221C22⋊C4—1461no—
222C42—731no—
223C42—731no—
224C42—731no—
225C42—1462no—
226C42C22×D7311yescharacteristic
227C23—21no—
228C23—2922no—
229C23—2922no—
230C23—2922no—
231C23—731no—
232C23—1461no—
233Q8—22no—
234Q8—42no—
235Q8—2922no—
236Q8—1462no—
237Q8—1462no—
238Q8—1462no—
239D4—22no—
240D4—2922no—
241D4—1462no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—2921no—
245C2×C4—2922no—
246C2×C4—731no—
247C2×C4—731no—
248C2×C4—731no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4D4×D7311yescharacteristic
254C2×C4D4×D7311yescharacteristic
255C2×C4C23×D7311yescharacteristic
256C8—22no—
257C8—1462no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—2921no—
262C22—2921no—
263C22—2921no—
264C22—5844no—
265C22—732no—
266C22—1461no—
267C22—1461no—
268C22C2×D4×D7311yescharacteristic
269C4—21no—
270C4—21no—
271C4—42no—
272C4—41no—
273C4—2921no—
274C4—2922no—
275C4—1461no—
276C4—1461no—
277C4—1461no—
278C4#1455663712yes—
279C2—81no—
280C2—5841no—
281C2—1462no—
282C2#1798915511yescharacteristic
283C2#137×D7311yescharacteristic
284C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3215
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988982C2semidirect
4. #17988981C2semidirect
5. #17988949C2semidirect
6. #17988812C2semidirect
7. #17988808C2semidirect
8. #17988744C2semidirect
10. #17988642C2semidirect
11. #489×C73C2semidirect
14. C2×Dic292C22semidirect
15. C2×#11924018C22semidirect
18. #14556591C22semidirect
28. #14556556C22semidirect
33. #14556520C22semidirect
34. #14556514C22semidirect
37. #14556502C22semidirect
38. C4⋊Q8×C73C22semidirect
40. #103×C73C22semidirect
42. #97×C73C22semidirect
143. C73#3215semidirect
149. #489D73semidirect
162. C4⋊Q8C2×D73semidirect
180. #103C2×D73semidirect
185. #97C2×D73semidirect