Finite Group Databasebeta

← #22621135

Subgroups — #22621135

Order 9344.

324 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989141C211yesmaximal, characteristic
2#125×D73C211yesmaximal, characteristic
3#17988995C211yesmaximal, characteristic, complemented
4#17988994C211yesmaximal, characteristic, complemented
5#17988954C211yesmaximal, characteristic, complemented
6#17988954C211yesmaximal, characteristic, complemented
7#17988924C211yesmaximal, characteristic
8#17988921C211yesmaximal, characteristic
9#17988919C211yesmaximal, characteristic
10#17988916C211yesmaximal, characteristic
11#17988895C211yesmaximal, characteristic, complemented
12#17988894C211yesmaximal, characteristic, complemented
13#17988891C211yesmaximal, characteristic, complemented
14#17988643C211yesmaximal, characteristic
15#479×C73C211yesmaximal, characteristic, complemented
16#14556590C2211yescharacteristic
17#14556589C2211yescharacteristic
18#14556583C2211yescharacteristic
19#14556582C2211yescharacteristic
20#14556582C2211yescharacteristic
21#14556581—21no—
22#14556581—21no—
23#14556581—21no—
24#14556571C2211yescharacteristic
25#14556569—21no—
26#14556567C2211yescharacteristic
27C4×Dic146—21no—
28C4×Dic146C2211yescharacteristic
29#14556548—21no—
30C4⋊C4×D73—21no—
31C4⋊C4×D73—21no—
32C4⋊C4×D73C2211yescharacteristic
33C4⋊C4×D73C2211yescharacteristic
34C42×D73C2211yescharacteristic
35#14556525C2211yescharacteristic
36#14556524C2211yescharacteristic
37#14556524C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic
51#14556501C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×C4×D73—21no—
62C2×C4×D73—21no—
63C2×C4×D73D411yescharacteristic
64C2×C4×D73D411yescharacteristic
65C2×C4×D73C2311yescharacteristic
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924005—21no—
86#11924005—21no—
87C4×Dic73—21no—
88C4×Dic73D411yescharacteristic
89C4×Dic73D411yescharacteristic
90C4×Dic73C2311yescharacteristic
91C2×Q8×C73C2311yescharacteristic
92C2×C8×C73C2311yescharacteristic
93C2×C8×C73C2311yescharacteristic
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73C2311yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C42×C73—21no—
101C42×C73C2311yescharacteristic
102C22×D73C2×D411yescharacteristic
103Q8×C73—21no—
104Q8×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73C2×D411yescharacteristic
110C2×C4×C73C2×D411yescharacteristic
111C2×C4×C73C2411yescharacteristic
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73C2×D411yescharacteristic
117C2×Dic73C2×D411yescharacteristic
118C2×Dic73C2×D411yescharacteristic
119C4×D73—22no—
120C4×D73—21no—
121C4×D73—21no—
122C4×D73—41no—
123C4×D73—42no—
124C4×D73—42no—
125Dic146—21no—
126Dic146—21no—
127Dic146—42no—
128C8×C73—21no—
129C8×C73—21no—
130#10596831—21no—
131#10596831—21no—
132C22×C73C22×D411yescharacteristic
133C2×D73—21no—
134C2×D73—21no—
135C2×D73#13712yes—
136C4×C73—21no—
137C4×C73—21no—
138C4×C73—41no—
139C4×C73—41no—
140C4×C73—41no—
141C4×C73—41no—
142C4×C732−1+411yescharacteristic
143C4×C732−1+411yescharacteristic
144Dic73—21no—
145Dic73—21no—
146Dic73—21no—
147Dic73—41no—
148Dic73—41no—
149Dic73—41no—
150Dic73—41no—
151C2×C73#53611yescharacteristic
152C2×C73C2×#13711yescharacteristic
153C2×C73#57511yescharacteristic
154D73—22no—
155#3236—731nomaximal, Sylow
156C73#323611yescharacteristic, complemented, Sylow
157#533—731no—
158C2×#125—731no—
159#501—731no—
160#501—731no—
161#491—731no—
162#491—731no—
163#484—731no—
164#484—731no—
165#483—731no—
166#483—731no—
167#479—731no—
168#479—731no—
169#479—731no—
170#479D7311yescharacteristic, complemented
171#432—731no—
172C4⋊Q8—731no—
173C4⋊Q8—731no—
174#125—731no—
175#125—731no—
176#125—731no—
177#125—1461no—
178#125—1461no—
179#125—1461no—
180#125C2×D7311yescharacteristic
181C22⋊Q8—731no—
182C22⋊Q8—731no—
183C22⋊Q8—1461no—
184C4×Q8—731no—
185C4×Q8—1461no—
186C4×Q8C2×D7311yescharacteristic
187#117—1461no—
188C2×C4⋊C4—731no—
189C2×C4⋊C4—731no—
190C2×C4⋊C4—1461no—
191C2×C4⋊C4—1461no—
192C2×C42—731no—
193#107—731no—
194#107—731no—
195#107—731no—
196#107C2×D7311yescharacteristic
197#106—731no—
198#106—731no—
199#106—731no—
200#106C2×D7311yescharacteristic
201C4⋊C8—731no—
202C4⋊C8C2×D7311yescharacteristic
203#103—731no—
204#103—731no—
205#103—731no—
206#103—731no—
207#103—731no—
208#103—731no—
209#103C2×D7311yescharacteristic
210#103C2×D7311yescharacteristic
211C22⋊C8—731no—
212C22⋊C8—731no—
213#97—731no—
214#97—731no—
215C2×Q8—731no—
216C2×Q8—1461no—
217C2×Q8C22×D7311yescharacteristic
218C22×C4—731no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—1461no—
222C22×C4—1461no—
223C2×C8—731no—
224C2×C8—731no—
225C2×C8C22×D7311yescharacteristic
226C2×C8C22×D7311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—731no—
231C4⋊C4—731no—
232C4⋊C4—731no—
233C4⋊C4—1461no—
234C4⋊C4—1461no—
235C4⋊C4—1461no—
236C4⋊C4—1461no—
237C4⋊C4—1461no—
238C4⋊C4—1461no—
239C4⋊C4—1461no—
240C4⋊C4—1461no—
241C4⋊C4—1461no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4C22×D7311yescharacteristic
248C4⋊C4C22×D7311yescharacteristic
249C4⋊C4C22×D7311yescharacteristic
250C22⋊C4—1461no—
251C22⋊C4—1461no—
252C42—21no—
253C42—731no—
254C42—731no—
255C42—731no—
256C42—1461no—
257C42C22×D7311yescharacteristic
258C23—731no—
259Q8—21no—
260Q8—21no—
261Q8—2922no—
262Q8—1461no—
263Q8—1461no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—2921no—
269C2×C4—2922no—
270C2×C4—2922no—
271C2×C4—731no—
272C2×C4—731no—
273C2×C4—731no—
274C2×C4—1462no—
275C2×C4—1461no—
276C2×C4—1461no—
277C2×C4—1461no—
278C2×C4—1461no—
279C2×C4—1461no—
280C2×C4—1461no—
281C2×C4D4×D7311yescharacteristic
282C2×C4D4×D7311yescharacteristic
283C2×C4C23×D7311yescharacteristic
284C8—21no—
285C8—21no—
286C8—1461no—
287C8—1461no—
288C22—732no—
289C22—1461no—
290C22—1461no—
291C22C2×D4×D7311yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—2921no—
299C4—2921no—
300C4—2921no—
301C4—2921no—
302C4—1461no—
303C4—1461no—
304C4—1461no—
305C4#1455663811yescharacteristic
306C4#1455663911yescharacteristic
307C2—1462no—
308C2#1798916011yescharacteristic
309C2#137×D7311yescharacteristic
310C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3236
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #17988995C2semidirect
4. #17988994C2semidirect
5. #17988954C2semidirect
6. #17988954C2semidirect
11. #17988895C2semidirect
12. #17988894C2semidirect
13. #17988891C2semidirect
15. #479×C73C2semidirect
156. C73#3236semidirect
170. #479D73semidirect