Finite Group Databasebeta

← #22619852

Subgroups — #22619852

Order 9344.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989094C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988921C212yesmaximal, complemented
4#17988916C212yesmaximal, complemented
5#17988904C212yesmaximal, complemented
6#17988899C212yesmaximal, complemented
7#17988629C211yesmaximal, characteristic, complemented
8#17988627C211yesmaximal, characteristic, complemented
9#17988588C211yesmaximal, characteristic, complemented
10#17988550C211yesmaximal, characteristic, complemented
11#417×C73C211yesmaximal, characteristic, complemented
12C22×C4×D73—21no—
13C22×C4×D73C2211yescharacteristic
14C2×#11924012C2211yescharacteristic
15#14556572—21no—
16#14556567C2211yescharacteristic
17#14556567C2211yescharacteristic
18#14556562C2211yescharacteristic
19#14556562C2211yescharacteristic
20#14556559—21no—
21C4×C22⋊D73—21no—
22C4×C22⋊D73—21no—
23#14556550C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007—21no—
26C4⋊C4×D73—21no—
27C4⋊C4×D73—21no—
28C4⋊C4×D73C2212yes—
29C4⋊C4×D73C2212yes—
30#14556525C2212yescomplemented
31#14556524C2212yescomplemented
32#14556523C2212yescomplemented
33#14556522C2212yescomplemented
34#14556515C2212yescomplemented
35#14556512C2212yescomplemented
36#14556503C2212yes—
37#14556503C2212yes—
38C2×#41×C73C2211yescharacteristic
39C2×M16×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#103×C73C2212yescomplemented
42#102×C73C2212yescomplemented
43C23×D73D411yescharacteristic
44C2×C22⋊D73—21no—
45C2×C22⋊D73—21no—
46C22×Dic73—21no—
47C22×Dic73D411yescharacteristic
48C2×C4×D73—22no—
49C2×C4×D73—22no—
50C2×C4×D73—22no—
51C2×C4×D73—22no—
52C2×C4×D73—44no—
53C2×C4×D73D411yescharacteristic
54C2×C4×D73D411yescharacteristic
55C2×C4×D73C2311yescharacteristic
56C2×C4×D73C2311yescharacteristic
57#11924012—22no—
58C2×#10596831C2312yes—
59C4⋊Dic73—21no—
60C4⋊Dic73C2312yes—
61C4⋊Dic73C2311yescharacteristic
62C4⋊Dic73C2311yescharacteristic
63#11924007—22no—
64#11924007—22no—
65#11924007—21no—
66#11924007—21no—
67C22⋊Dic73—21no—
68C22⋊Dic73—21no—
69C22⋊Dic73—21no—
70#11924005—21no—
71#11924005—21no—
72C4×Dic73—21no—
73#41×C73—22no—
74#41×C73—22no—
75C2×Q8×C73C2311yescharacteristic
76C2×D4×C73—21no—
77C2×D4×C73C2311yescharacteristic
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73C2311yescharacteristic
81M16×C73—22no—
82C2×C8×C73C2312yes—
83C4⋊C4×C73—21no—
84C4⋊C4×C73C2312yes—
85C23×C73—21no—
86C23×C73C2×D411yescharacteristic
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73C2×D411yescharacteristic
91C22×D73C2×D411yescharacteristic
92Q8×C73—21no—
93Q8×C73—21no—
94D4×C73—21no—
95D4×C73—21no—
96D4×C73—42no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—42no—
100C2×C4×C73—42no—
101C2×C4×C73C2×D411yescharacteristic
102C2×C4×C73#4112yes—
103C2×C4×C73#4112yes—
104C2×C4×C73C2411yescharacteristic
105C22⋊D73—42no—
106C22⋊D73—42no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—21no—
110C2×Dic73—22no—
111C2×Dic73—42no—
112C2×Dic73C2×D411yescharacteristic
113C2×Dic73C2×D411yescharacteristic
114C4×D73—22no—
115C4×D73—22no—
116C4×D73—21no—
117C4×D73—21no—
118C4×D73—21no—
119C4×D73—21no—
120C4×D73—44no—
121C4×D73—44no—
122C8×C73—22no—
123#10596831—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—41no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73#12312yes—
130C22×C73C22×D411yescharacteristic
131C2×D73—28no—
132C2×D73—21no—
133C2×D73—21no—
134C2×D73—21no—
135C2×D73—21no—
136C2×D73AGL(1,ℤ/8)12yes—
137C2×D73#13712yes—
138C4×C73—41no—
139C4×C73—42no—
140C4×C73#12312yes—
141C4×C73C2×#4111yescharacteristic
142C4×C73C2×#4111yescharacteristic
143Dic73—21no—
144Dic73—21no—
145Dic73—42no—
146Dic73—41no—
147Dic73—41no—
148C2×C73—22no—
149C2×C73—81no—
150C2×C73C2×#12311yescharacteristic
151C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C73C2×#13711yescharacteristic
153D73—22no—
154D73—22no—
155#3092—731nomaximal, Sylow
156C73#309211yescharacteristic, complemented, Sylow
157#525—731no—
158C22×C4⋊C4—731no—
159#484—732no—
160#483—732no—
161#481—732no—
162#480—732no—
163#428—731no—
164#428—731no—
165#417—731no—
166#417D7311yescharacteristic, complemented
167#407—731no—
168C2×#41C2×D7311yescharacteristic
169C23×C4—731no—
170C23×C4—1461no—
171C2×M16—731no—
172C2×M16C2×D7311yescharacteristic
173#123—1461no—
174C22⋊Q8—731no—
175C22⋊Q8—731no—
176#121—731no—
177#121—731no—
178#120—1461no—
179C4×D4—1461no—
180C4×D4—1461no—
181#117—731no—
182C2×C4⋊C4—731no—
183C2×C4⋊C4—732no—
184C2×C4⋊C4—732no—
185C2×C4⋊C4—1461no—
186C2×C4⋊C4—1461no—
187C2×C4⋊C4—1461no—
188C2×C4⋊C4C2×D7311yescharacteristic
189#107—732no—
190#107—732no—
191#106—732no—
192#106—732no—
193#103—732no—
194#103C2×D7312yescomplemented
195#102—732no—
196#102C2×D7312yescomplemented
197C22⋊C8—732no—
198C22⋊C8—732no—
199C24—731no—
200#41—22no—
201#41—22no—
202C2×Q8C22×D7311yescharacteristic
203C2×D4—21no—
204C2×D4—1461no—
205C2×D4—1461no—
206C2×D4C22×D7311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—2924no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4—731no—
213C22×C4—731no—
214C22×C4—731no—
215C22×C4—1462no—
216C22×C4—1462no—
217C22×C4—1461no—
218C22×C4—1462no—
219C22×C4—1462no—
220C22×C4C22×D7311yescharacteristic
221M16—22no—
222M16—1462no—
223C2×C8—732no—
224C2×C8C22×D7312yes—
225C4⋊C4—21no—
226C4⋊C4—732no—
227C4⋊C4—731no—
228C4⋊C4—731no—
229C4⋊C4—1462no—
230C4⋊C4—1462no—
231C4⋊C4—1461no—
232C4⋊C4—1461no—
233C4⋊C4—1461no—
234C4⋊C4C22×D7312yes—
235C22⋊C4—1461no—
236C22⋊C4—1461no—
237C22⋊C4—1461no—
238C22⋊C4—1461no—
239C22⋊C4—1461no—
240C42—1461no—
241C23—21no—
242C23—731no—
243C23—731no—
244C23—1462no—
245C23—1462no—
246C23—1462no—
247C23D4×D7311yescharacteristic
248Q8—21no—
249Q8—21no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—2922no—
254D4—2922no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—2924no—
260C2×C4—2924no—
261C2×C4—2922no—
262C2×C4—731no—
263C2×C4—731no—
264C2×C4—1461no—
265C2×C4—1461no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1461no—
271C2×C4—1461no—
272C2×C4—1461no—
273C2×C4—1461no—
274C2×C4D4×D7311yescharacteristic
275C2×C4#1192402712yes—
276C2×C4#1192402812yes—
277C2×C4C23×D7311yescharacteristic
278C8—22no—
279C8—1462no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—732no—
286C22—732no—
287C22—1468no—
288C22—1461no—
289C22—1461no—
290C22—1461no—
291C22—1461no—
292C22#1455657312yes—
293C22C2×D4×D7311yescharacteristic
294C4—41no—
295C4—42no—
296C4—2921no—
297C4—2922no—
298C4—2921no—
299C4—1461no—
300C4—1461no—
301C4#1455657312yes—
302C4C2×#1192402711yescharacteristic
303C4C2×#1192402811yescharacteristic
304C2—22no—
305C2—81no—
306C2—1462no—
307C2—1462no—
308C2C2×#1455657311yescharacteristic
309C2AGL(1,ℤ/8)×D7311yescharacteristic
310C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3092
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988921C2semidirect
4. #17988916C2semidirect
5. #17988904C2semidirect
6. #17988899C2semidirect
7. #17988629C2semidirect
8. #17988627C2semidirect
9. #17988588C2semidirect
10. #17988550C2semidirect
11. #417×C73C2semidirect
30. #14556525C22semidirect
31. #14556524C22semidirect
32. #14556523C22semidirect
33. #14556522C22semidirect
34. #14556515C22semidirect
35. #14556512C22semidirect
41. #103×C73C22semidirect
42. #102×C73C22semidirect
156. C73#3092semidirect
166. #417D73semidirect
194. #103C2×D73semidirect
196. #102C2×D73semidirect