Finite Group Databasebeta

← #22620316

Subgroups — #22620316

Order 9344.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#17988949C211yesmaximal, characteristic, complemented
4#17988947C211yesmaximal, characteristic, complemented
5#17988946C211yesmaximal, characteristic, complemented
6#17988943C212yesmaximal, complemented
7#17988940C212yesmaximal, complemented
8#17988594C212yesmaximal, complemented
9#17988590C212yesmaximal
10#17988539C211yesmaximal, characteristic, complemented
11#489×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14C2×#11924011C2212yes—
15#14556591C2211yescharacteristic, complemented
16#14556582C2212yescomplemented
17#14556580C2211yescharacteristic
18#14556579C2211yescharacteristic
19#14556578C2211yescharacteristic
20#14556577—21no—
21#14556577—21no—
22#14556571—21no—
23#14556567—21no—
24Q8×Dic73—21no—
25#14556556—21no—
26#14556549C2212yes—
27C22⋊C4×D73—21no—
28C22⋊C4×D73—21no—
29C42×D73C2211yescharacteristic
30#14556516C2212yescomplemented
31#14556515C2212yescomplemented
32#14556514C2212yescomplemented
33#14556513C2212yes—
34#14556512C2212yes—
35#14556511C2212yes—
36#14556502C2211yescharacteristic, complemented
37C8×Dic73C2212yescomplemented
38C4⋊Q8×C73C2211yescharacteristic, complemented
39#124×C73C2211yescharacteristic
40#103×C73C2212yescomplemented
41#102×C73C2212yes—
42#97×C73C2211yescharacteristic, complemented
43C23×D73—21no—
44C2×Dic146—21no—
45C2×Dic146—21no—
46C2×Dic146C2311yescharacteristic
47Q8×D73—24no—
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50D4×D73—24no—
51C2×C4×D73—21no—
52C2×C4×D73D411yescharacteristic
53C2×C4×D73D411yescharacteristic
54C2×C4×D73C2311yescharacteristic
55#11924011—24no—
56C2×#10596831C2312yes—
57C4⋊Dic73—21no—
58C4⋊Dic73—22no—
59C4⋊Dic73C2312yes—
60#11924007—22no—
61C22⋊Dic73—21no—
62C22⋊Dic73—21no—
63#11924005—22no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67#11924005—21no—
68C4×Dic73—22no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73—21no—
73C2×Q8×C73C2311yescharacteristic
74C2×D4×C73C2311yescharacteristic
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2312yes—
78C22⋊C4×C73—21no—
79C22⋊C4×C73—21no—
80C42×C73C2311yescharacteristic
81C23×C73—21no—
82C22×D73—21no—
83C22×D73—42no—
84C22×D73—42no—
85C22×D73—42no—
86C22×D73C2×D411yescharacteristic
87Q8×C73—22no—
88Q8×C73—42no—
89D4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2411yescharacteristic
95C22⋊D73—42no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101D292—22no—
102C4×D73—41no—
103C4×D73—41no—
104C4×D73—42no—
105C4×D73#4114yes—
106Dic146—22no—
107Dic146—42no—
108Dic146—42no—
109C8×C73—22no—
110#10596831—22no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73C22×D411yescharacteristic
115C2×D73—21no—
116C2×D73—21no—
117C2×D73—41no—
118C2×D73—41no—
119C2×D73—41no—
120C2×D73—84no—
121C2×D73#12412yes—
122C4×C73—21no—
123C4×C73—21no—
124C4×C73—41no—
125C4×C73—42no—
126C4×C73C2×#4112yes—
127Dic73—21no—
128Dic73—21no—
129Dic73—41no—
130Dic73—42no—
131Dic73#12412yes—
132C2×C73—81no—
133C2×C73C2×#12411yescharacteristic
134C2×C73#57511yescharacteristic
135C2×C73#57511yescharacteristic
136D73—22no—
137D73—81no—
138#3140—731nomaximal, Sylow
139C73#314011yescharacteristic, complemented, Sylow
140#533—731no—
141C2×#124—731no—
142#489—731no—
143#489—731no—
144#489—731no—
145#489D7311yescharacteristic, complemented
146#488—732no—
147#488—732no—
148#419—732no—
149#418—732no—
150C4×M16—731no—
151C22×Q8—731no—
152C22×D4—731no—
153C2×M16—732no—
154C4⋊Q8—731no—
155C4⋊Q8C2×D7311yescharacteristic, complemented
156#125—732no—
157#124—731no—
158#124—731no—
159#124—731no—
160#124—1461no—
161#124—1461no—
162#124C2×D7311yescharacteristic
163C22⋊Q8—1461no—
164C22⋊Q8—1461no—
165C4×Q8—1461no—
166C4×Q8—1461no—
167#117—732no—
168C2×C22⋊C4—1461no—
169C2×C22⋊C4—1461no—
170C2×C42—731no—
171#103—732no—
172#103—732no—
173#103—732no—
174#103C2×D7312yescomplemented
175#102—732no—
176#102—732no—
177#102—732no—
178#102C2×D7312yes—
179#97—731no—
180#97C2×D7311yescharacteristic, complemented
181C4×C8—732no—
182C24—1461no—
183C2×Q8—21no—
184C2×Q8—731no—
185C2×Q8—1461no—
186C2×Q8—1464no—
187C2×Q8—1461no—
188C2×Q8C22×D7311yescharacteristic
189C2×D4—731no—
190C2×D4—1464no—
191C2×D4—1461no—
192C2×D4C22×D7311yescharacteristic
193C22×C4—731no—
194C22×C4—731no—
195C22×C4—731no—
196C22×C4—1461no—
197M16—1464no—
198C2×C8—732no—
199C2×C8C22×D7312yes—
200C4⋊C4—21no—
201C4⋊C4—732no—
202C4⋊C4—1462no—
203C4⋊C4—1462no—
204C4⋊C4—1461no—
205C4⋊C4C22×D7312yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—1461no—
209C22⋊C4—1461no—
210C22⋊C4—1462no—
211C22⋊C4—1461no—
212C22⋊C4—1461no—
213C22⋊C4—1461no—
214C22⋊C4—1461no—
215C42—731no—
216C42—731no—
217C42—731no—
218C42—1462no—
219C42C22×D7311yescharacteristic
220C23—21no—
221C23—2922no—
222C23—2922no—
223C23—2922no—
224C23—731no—
225C23—1461no—
226Q8—22no—
227Q8—42no—
228Q8—2922no—
229Q8—2922no—
230Q8—1462no—
231D4—22no—
232D4—2922no—
233D4—1462no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—2921no—
237C2×C4—2921no—
238C2×C4—2922no—
239C2×C4—731no—
240C2×C4—734no—
241C2×C4—731no—
242C2×C4—731no—
243C2×C4—1462no—
244C2×C4—1461no—
245C2×C4D4×D7311yescharacteristic
246C2×C4D4×D7311yescharacteristic
247C2×C4C23×D7311yescharacteristic
248C8—22no—
249C8—1462no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—2921no—
254C22—2921no—
255C22—2921no—
256C22—5844no—
257C22—732no—
258C22—1461no—
259C22—1461no—
260C22C2×D4×D7311yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—2922no—
266C4—2921no—
267C4—732no—
268C4—1461no—
269C4—1461no—
270C4#41×D7312yes—
271C2—81no—
272C2—5841no—
273C2—1462no—
274C2#124×D7311yescharacteristic
275C2#1798938311yescharacteristic
276C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3140
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. #17988949C2semidirect
4. #17988947C2semidirect
5. #17988946C2semidirect
6. #17988943C2semidirect
7. #17988940C2semidirect
8. #17988594C2semidirect
10. #17988539C2semidirect
11. #489×C73C2semidirect
15. #14556591C22semidirect
16. #14556582C22semidirect
30. #14556516C22semidirect
31. #14556515C22semidirect
32. #14556514C22semidirect
36. #14556502C22semidirect
37. C8×Dic73C22semidirect
38. C4⋊Q8×C73C22semidirect
40. #103×C73C22semidirect
42. #97×C73C22semidirect
139. C73#3140semidirect
145. #489D73semidirect
155. C4⋊Q8C2×D73semidirect
174. #103C2×D73semidirect
180. #97C2×D73semidirect