Finite Group Databasebeta

← #22623756

Subgroups — #22623756

Order 9344.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989316C211yesmaximal, characteristic, complemented
2#17989313C211yesmaximal, characteristic, complemented
3#17989313C211yesmaximal, characteristic, complemented
4#17989298C213yesmaximal, complemented
5#17989297C213yesmaximal, complemented
6#17989293C213yesmaximal, complemented
7#17989293C213yesmaximal, complemented
8#17989217C213yesmaximal, complemented
9#17989214C213yesmaximal, complemented
10#17989141C213yesmaximal, complemented
11#125×D73C213yesmaximal, complemented
12#17989069C211yesmaximal, characteristic
13#17989069C211yesmaximal, characteristic
14C4×#11924029C211yesmaximal, characteristic
15#557×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17#14556591C2213yes—
18#14556590C2213yes—
19#14556590C2213yes—
20#14556590C2213yes—
21#14556589C2213yes—
22#14556583C2213yes—
23#14556583C2213yes—
24#14556582C2213yes—
25#14556582C2213yes—
26#14556582C2213yes—
27#14556582C2213yes—
28#14556581C2211yescharacteristic
29#14556581C2213yes—
30#14556581C2216yes—
31#14556571C2213yes—
32#14556571C2216yes—
33#14556569C2213yes—
34#14556569C2213yes—
35#14556569C2216yes—
36#14556569C2216yes—
37#14556567C2213yes—
38#14556567C2216yes—
39Q8×Dic73C2211yescharacteristic
40Q8×Dic73C2211yescharacteristic
41Q8×Dic73C2211yescharacteristic
42C4×Dic146C2213yes—
43C4×Dic146C2213yes—
44C4×Dic146C2213yes—
45C4×D292C2213yes—
46C4×D292C2213yes—
47C4×D292C2213yes—
48#14556553C2213yes—
49#14556553C2213yes—
50#14556553C2213yes—
51#14556549C2213yes—
52#14556548C2213yes—
53#14556548C2213yes—
54C4⋊C4×D73C2213yes—
55C4⋊C4×D73C2213yes—
56C4⋊C4×D73C2216yes—
57C4⋊C4×D73C2216yes—
58C42×D73C2213yes—
59C4⋊Q8×C73C2213yes—
60#125×C73C2213yes—
61#125×C73C2213yes—
62C4×Q8×C73C2213yes—
63C4×Q8×C73C2211yescharacteristic
64C4×Q8×C73C2211yescharacteristic
65C4×Q8×C73C2211yescharacteristic
66#11924029Q818yescomplemented
67C2×Dic146C2313yes—
68C2×Dic146C2313yes—
69C2×Dic146C2313yes—
70C2×D292C2313yes—
71C2×C4×D73C2313yes—
72C2×C4×D73C2313yes—
73C2×C4×D73C2316yes—
74C2×C4×D73C2316yes—
75C2×C4×D73C2313yes—
76C4⋊Dic73C2313yes—
77C4⋊Dic73C2313yes—
78C4⋊Dic73C2313yes—
79C4⋊Dic73C2316yes—
80C4⋊Dic73C2313yes—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2313yes—
83#11924007C2313yes—
84#11924007C2313yes—
85#11924007C2313yes—
86#11924007C2313yes—
87#11924007C2316yes—
88#11924007C2316yes—
89#11924007C2311yescharacteristic
90#11924007C2311yescharacteristic
91#11924007C2311yescharacteristic
92#11924007C2311yescharacteristic
93#11924007C2313yes—
94#11924007C2313yes—
95#11924005C2313yes—
96#11924005C2313yes—
97#11924005C2313yes—
98#11924005C2313yes—
99#11924005C2316yes—
100C4×Dic73C2311yescharacteristic
101C4×Dic73C2313yes—
102C4×Dic73C2313yes—
103C4×Dic73C2313yes—
104C4×Dic73C2313yes—
105C2×Q8×C73C2313yes—
106C2×Q8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2313yes—
109C4⋊C4×C73C2313yes—
110C4⋊C4×C73C2313yes—
111C4⋊C4×C73C2313yes—
112C4⋊C4×C73C2313yes—
113C4⋊C4×C73C2316yes—
114C42×C73C2313yes—
115C42×C73C2313yes—
116C42×C73C2313yes—
117C22×D73C2413yes—
118Q8×C73—43no—
119Q8×C73C2×Q814yes—
120C2×C4×C73C2411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C2×C4×C73C2413yes—
124C2×C4×C73C2413yes—
125C2×C4×C73C2413yes—
126C2×C4×C73C2413yes—
127C2×Dic73C2411yescharacteristic
128C2×Dic73C2411yescharacteristic
129C2×Dic73C2411yescharacteristic
130C2×Dic73C2413yes—
131C2×Dic73C2413yes—
132C2×Dic73C2413yes—
133C2×Dic73C2411yescharacteristic
134D292C2×Q8112yes—
135C4×D73—43no—
136C4×D73—46no—
137C4×D73—46no—
138C4×D73—43no—
139C4×D73C2×Q8112yes—
140Dic146—43no—
141Dic146—43no—
142Dic146—43no—
143C22×C73C2511yescharacteristic
144C2×D73—23no—
145C2×D73—23no—
146C2×D73C22×Q816yes—
147C4×C73—21no—
148C4×C73—23no—
149C4×C73—23no—
150C4×C73—21no—
151C4×C73—23no—
152C4×C73—21no—
153C4×C73C22×Q816yes—
154Dic73—21no—
155Dic73—21no—
156Dic73—23no—
157Dic73—23no—
158Dic73—23no—
159Dic73—21no—
160Dic73C22×Q812yes—
161C2×C73C23×Q811yescharacteristic
162C2×C73#58511yescharacteristic
163C2×C73#58511yescharacteristic
164D73—26no—
165#3504—731nomaximal, Sylow
166C73#350411yescharacteristic, complemented, Sylow
167#557—731no—
168#557—731no—
169#557—731no—
170#557D7311yescharacteristic, complemented
171#554—733no—
172#554—733no—
173#554—733no—
174#554—733no—
175#544—733no—
176#544—733no—
177#533—733no—
178C2×#125—733no—
179#520—731no—
180#520—731no—
181C4×#41—731no—
182C2×#41—731no—
183C4⋊Q8—733no—
184C4⋊Q8—733no—
185C4⋊Q8—733no—
186C4⋊Q8—733no—
187C4⋊Q8—733no—
188C4⋊Q8C2×D7313yes—
189#125—733no—
190#125—736no—
191#125—733no—
192#125—733no—
193#125—731no—
194#125—733no—
195#125—733no—
196#125—733no—
197#125—733no—
198#125C2×D7313yes—
199#125C2×D7313yes—
200C22⋊Q8—733no—
201C22⋊Q8—736no—
202C22⋊Q8—733no—
203C22⋊Q8—733no—
204C22⋊Q8—733no—
205C22⋊Q8—736no—
206C22⋊Q8—736no—
207C22⋊Q8—736no—
208C4×Q8—731no—
209C4×Q8—731no—
210C4×Q8—731no—
211C4×Q8—733no—
212C4×Q8—733no—
213C4×Q8—733no—
214C4×Q8C2×D7311yescharacteristic
215C4×Q8C2×D7311yescharacteristic
216C4×Q8C2×D7311yescharacteristic
217C4×Q8C2×D7313yes—
218C4×D4—733no—
219C4×D4—733no—
220C4×D4—733no—
221C4×D4—733no—
222C4×D4—733no—
223C4×D4—733no—
224#117—733no—
225#117—733no—
226#117—733no—
227C2×C4⋊C4—733no—
228C2×C4⋊C4—733no—
229C2×C4⋊C4—736no—
230C2×C4⋊C4—736no—
231C2×C42—733no—
232#41—738no—
233C2×Q8—733no—
234C2×Q8—733no—
235C2×Q8—733no—
236C2×Q8C22×D7313yes—
237C2×Q8C22×D7311yescharacteristic
238C2×D4—733no—
239C22×C4—733no—
240C22×C4—733no—
241C22×C4—736no—
242C22×C4—736no—
243C22×C4—733no—
244C4⋊C4—733no—
245C4⋊C4—733no—
246C4⋊C4—733no—
247C4⋊C4—733no—
248C4⋊C4—736no—
249C4⋊C4—736no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—731no—
253C4⋊C4—731no—
254C4⋊C4—733no—
255C4⋊C4—733no—
256C4⋊C4—733no—
257C4⋊C4—733no—
258C4⋊C4—733no—
259C4⋊C4—736no—
260C4⋊C4—733no—
261C4⋊C4—731no—
262C4⋊C4—733no—
263C4⋊C4C22×D7313yes—
264C4⋊C4C22×D7313yes—
265C4⋊C4C22×D7313yes—
266C4⋊C4C22×D7316yes—
267C4⋊C4C22×D7313yes—
268C4⋊C4C22×D7311yescharacteristic
269C4⋊C4C22×D7313yes—
270C22⋊C4—733no—
271C22⋊C4—733no—
272C22⋊C4—736no—
273C22⋊C4—733no—
274C22⋊C4—733no—
275C42—731no—
276C42—733no—
277C42—733no—
278C42—733no—
279C42—733no—
280C42C22×D7313yes—
281C42C22×D7313yes—
282C42C22×D7313yes—
283C23—733no—
284Q8—43no—
285Q8—2923no—
286Q8—2923no—
287Q8—2923no—
288Q8Q8×D7314yes—
289D4—7312no—
290C2×C4—2926no—
291C2×C4—2923no—
292C2×C4—2923no—
293C2×C4—2926no—
294C2×C4—731no—
295C2×C4—7312no—
296C2×C4—731no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—733no—
300C2×C4—733no—
301C2×C4—733no—
302C2×C4C23×D7311yescharacteristic
303C2×C4C23×D7313yes—
304C2×C4C23×D7311yescharacteristic
305C2×C4C23×D7311yescharacteristic
306C2×C4C23×D7313yes—
307C2×C4C23×D7313yes—
308C2×C4C23×D7313yes—
309C22—736no—
310C22—1463no—
311C22—1463no—
312C22C24×D7311yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—732no—
320C4—1461no—
321C4—1463no—
322C4—1461no—
323C4—1463no—
324C4—1463no—
325C4—1461no—
326C4C2×Q8×D7316yes—
327C2—1466no—
328C2C22×Q8×D7311yescharacteristic
329C2#1798942311yescharacteristic
330C2#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#557×C73C2
hypercenter#557D73
hypocenterC73#3504
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #17989316C2semidirect
2. #17989313C2semidirect
3. #17989313C2semidirect
4. #17989298C2semidirect
5. #17989297C2semidirect
6. #17989293C2semidirect
7. #17989293C2semidirect
8. #17989217C2semidirect
9. #17989214C2semidirect
10. #17989141C2semidirect
11. #125×D73C2semidirect
15. #557×C73C2semidirect
66. #11924029Q8semidirect
166. C73#3504semidirect
170. #557D73semidirect