Finite Group Databasebeta

← #22620233

Subgroups — #22620233

Order 9344.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989200C211yesmaximal, characteristic
2#17989063C211yesmaximal, characteristic
3#17988931C211yesmaximal, characteristic
4#17988930C211yesmaximal, characteristic
5#17988891C211yesmaximal, characteristic, complemented
6#17988798C211yesmaximal, characteristic, complemented
7#17988797C211yesmaximal, characteristic, complemented
8#17988744C211yesmaximal, characteristic
9#17988744C211yesmaximal, characteristic
10#17988693C211yesmaximal, characteristic, complemented
11#17988691C211yesmaximal, characteristic, complemented
12#17988681C211yesmaximal, characteristic, complemented
13#17988679C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic
15#479×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×#11924018C2211yescharacteristic
20C2×#11924018C2211yescharacteristic
21#14556591C2211yescharacteristic
22#14556586—21no—
23#14556586—21no—
24#14556582—21no—
25#14556582—21no—
26#14556571C2211yescharacteristic
27#14556571C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29C4×Dic146—21no—
30C4×Dic146C2211yescharacteristic
31#14556556—21no—
32#14556556C2211yescharacteristic
33#14556556C2211yescharacteristic
34#14556556C2211yescharacteristic
35#14556549—21no—
36#14556549C2211yescharacteristic
37#14556548—21no—
38#14556548C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
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×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—22no—
65C2×C4×D73—21no—
66C2×C4×D73C2311yescharacteristic
67Dic292—22no—
68Dic292—22no—
69#11924018—22no—
70#11924018—22no—
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005D411yescharacteristic
89#11924005D411yescharacteristic
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C22×D73C2×D411yescharacteristic
109Q8×C73—21no—
110Q8×C73#4112yes—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2411yescharacteristic
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125C4×D73—24no—
126C4×D73—21no—
127C4×D73—21no—
128Dic146—24no—
129Dic146—21no—
130Dic146—21no—
131Dic146—21no—
132Dic146—21no—
133Dic146—21no—
134Dic146#4112yes—
135C8×C73—21no—
136C8×C73—21no—
137#10596831—21no—
138#10596831—21no—
139C22×C73C22×D411yescharacteristic
140C2×D73—21no—
141C2×D73—21no—
142C2×D73—21no—
143C4×C73—22no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73C2×#4111yescharacteristic
150C4×C73C2×#4111yescharacteristic
151Dic73—21no—
152Dic73—22no—
153Dic73—21no—
154Dic73—21no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158C2×C73#52511yescharacteristic
159C2×C73#57811yescharacteristic
160C2×C73#57811yescharacteristic
161D73—41no—
162#3127—731nomaximal, Sylow
163C73#312711yescharacteristic, complemented, Sylow
164#541—731no—
165#519—731no—
166#485—731no—
167#485—731no—
168#479—731no—
169#479D7311yescharacteristic, complemented
170#462—731no—
171#462—731no—
172#451—731no—
173#451—731no—
174#441—731no—
175#441—731no—
176C4×Q16—731no—
177C4×Q16—731no—
178#433—731no—
179C22×Q8—731no—
180C2×Q16—731no—
181C2×Q16—731no—
182C2×Q16—731no—
183C2×Q16—731no—
184C4⋊Q8—731no—
185#126—1461no—
186#126—1461no—
187#125—1461no—
188#125—1461no—
189#125C2×D7311yescharacteristic
190C22⋊Q8—731no—
191C22⋊Q8—731no—
192C4×Q8—731no—
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—731no—
196C4×Q8—731no—
197C4×Q8—1461no—
198C4×Q8—1461no—
199C4×Q8C2×D7311yescharacteristic
200#117—731no—
201#117—731no—
202#117—1461no—
203#117—1461no—
204#107—731no—
205#107C2×D7311yescharacteristic
206#106—731no—
207#106C2×D7311yescharacteristic
208C4⋊C8—731no—
209C4⋊C8C2×D7311yescharacteristic
210#103—731no—
211#103—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103C2×D7311yescharacteristic
217#103C2×D7311yescharacteristic
218C22⋊C8—731no—
219C22⋊C8—731no—
220#97—731no—
221C4×C8—731no—
222C2×Q8—731no—
223C2×Q8—731no—
224C2×Q8—731no—
225C2×Q8—1461no—
226C2×Q8—1462no—
227C2×Q8—1462no—
228C2×Q8C22×D7311yescharacteristic
229C22×C4—731no—
230C22×C4—1461no—
231Q16—1462no—
232Q16—1462no—
233Q16—1462no—
234Q16—1462no—
235C2×C8—731no—
236C2×C8—731no—
237C2×C8C22×D7311yescharacteristic
238C2×C8C22×D7311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4C22×D7311yescharacteristic
255C4⋊C4C22×D7311yescharacteristic
256C4⋊C4C22×D7311yescharacteristic
257C22⋊C4—731no—
258C22⋊C4—731no—
259C22⋊C4—1461no—
260C22⋊C4—1461no—
261C22⋊C4—1461no—
262C42—21no—
263C42—731no—
264C42—1461no—
265C42—1461no—
266C42—1461no—
267C42—1461no—
268C42—1461no—
269C42—1461no—
270C42C22×D7311yescharacteristic
271C23—731no—
272Q8—21no—
273Q8—732no—
274Q8—1464no—
275Q8—1461no—
276Q8—1461no—
277Q8—1461no—
278Q8—1461no—
279Q8—1461no—
280Q8#1192402912yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—731no—
286C2×C4—731no—
287C2×C4—731no—
288C2×C4—1464no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4D4×D7311yescharacteristic
296C2×C4D4×D7311yescharacteristic
297C2×C4C23×D7311yescharacteristic
298C8—21no—
299C8—21no—
300C8—1461no—
301C8—1461no—
302C22—1461no—
303C22—1461no—
304C22—1461no—
305C22C2×D4×D7311yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—2921no—
313C4—2921no—
314C4—2921no—
315C4—1461no—
316C4—1461no—
317C4—1461no—
318C4—1462no—
319C4#41×D7311yescharacteristic
320C4C2×#1192402911yescharacteristic
321C2—2921no—
322C2#1798910011yescharacteristic
323C2#1798940111yescharacteristic
324C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3127
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
5. #17988891C2semidirect
6. #17988798C2semidirect
7. #17988797C2semidirect
10. #17988693C2semidirect
11. #17988691C2semidirect
12. #17988681C2semidirect
13. #17988679C2semidirect
15. #479×C73C2semidirect
163. C73#3127semidirect
169. #479D73semidirect