Finite Group Databasebeta

← #22621186

Subgroups — #22621186

Order 9344.

332 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#17989215C211yesmaximal, characteristic, complemented
2#17989192C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic, complemented
4#17988989C211yesmaximal, characteristic, complemented
5#17988952C211yesmaximal, characteristic, complemented
6#17988934C211yesmaximal, characteristic, complemented
7#17988912C211yesmaximal, characteristic, complemented
8#17988912C211yesmaximal, characteristic, complemented
9#17988906C211yesmaximal, characteristic, complemented
10#17988901C211yesmaximal, characteristic, complemented
11#17988888C211yesmaximal, characteristic, complemented
12#17988888C211yesmaximal, characteristic, complemented
13#17988878C211yesmaximal, characteristic, complemented
14#17988868C211yesmaximal, characteristic, complemented
15#433×C73C211yesmaximal, characteristic, complemented
16#14556591C2211yescharacteristic
17#14556591C2211yescharacteristic
18#14556590—21no—
19#14556588C2211yescharacteristic
20#14556583C2211yescharacteristic
21#14556583C2211yescharacteristic
22#14556583C2211yescharacteristic
23#14556582—21no—
24#14556576—21no—
25#14556576—21no—
26#14556568—21no—
27#14556568—21no—
28#14556565C2211yescharacteristic
29#14556565C2211yescharacteristic
30#14556564—21no—
31#14556564—21no—
32C4×D292C2211yescharacteristic
33C4×D292C2211yescharacteristic
34#14556550C2211yescharacteristic
35C2×C4⋊Dic73C2211yescharacteristic
36#14556525C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52#117×C73C2211yescharacteristic
53C4⋊C8×C73C2211yescharacteristic
54C4⋊C8×C73C2211yescharacteristic
55C22⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57#97×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C22×C4×C73C2311yescharacteristic
92C2×C8×C73C2311yescharacteristic
93C2×C8×C73C2311yescharacteristic
94C2×C8×C73C2311yescharacteristic
95C2×C8×C73C2311yescharacteristic
96C4⋊C4×C73D411yescharacteristic
97C4⋊C4×C73D411yescharacteristic
98C22⋊C4×C73D411yescharacteristic
99C22⋊C4×C73D411yescharacteristic
100C42×C73C2311yescharacteristic
101C42×C73C2311yescharacteristic
102C23×C73C2×D411yescharacteristic
103C22×D73—21no—
104C22×D73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73C2×D411yescharacteristic
108C2×C4×C73C2×D411yescharacteristic
109C2×C4×C73C2×D411yescharacteristic
110C2×C4×C73C2×D411yescharacteristic
111C2×C4×C73C2×D411yescharacteristic
112C2×C4×C73C2411yescharacteristic
113C22⋊D73—81no—
114C22⋊D73—81no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—81no—
122D292—21no—
123D292—21no—
124D292—21no—
125D292—21no—
126D292—81no—
127D292—81no—
128C4×D73—81no—
129C4×D73—81no—
130Dic146—81no—
131Dic146—81no—
132C8×C73—21no—
133C8×C73—21no—
134C8×C73—21no—
135C8×C73—21no—
136C22×C73—21no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73C22×D411yescharacteristic
140C2×D73—41no—
141C2×D73—41no—
142C2×D73—41no—
143C2×D73—41no—
144C2×D73—41no—
145C2×D73—41no—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C732−1+411yescharacteristic
152C4×C732−1+411yescharacteristic
153Dic73—41no—
154Dic73—41no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159C2×C73—41no—
160C2×C73#53611yescharacteristic
161C2×C73#57611yescharacteristic
162C2×C73#57711yescharacteristic
163D73—81no—
164D73—81no—
165#3241—731nomaximal, Sylow
166C73#324111yescharacteristic, complemented, Sylow
167#544—731no—
168#540—731no—
169#501—731no—
170#499—731no—
171#490—731no—
172#486—731no—
173#482—731no—
174#482—731no—
175#481—731no—
176#480—731no—
177#478—731no—
178#478—731no—
179#476—731no—
180#474—731no—
181#433D7311yescharacteristic, complemented
182C4⋊Q8—731no—
183C4⋊Q8—731no—
184C4⋊Q8—1461no—
185#127—731no—
186#125—731no—
187#125—731no—
188#125—731no—
189#125—1461no—
190#123—1461no—
191#123—1461no—
192C22⋊Q8—1461no—
193C22⋊Q8—1461no—
194#121—731no—
195#121—731no—
196#121—1461no—
197#121—1461no—
198C4×D4—731no—
199C4×D4—731no—
200#117—731no—
201#117C2×D7311yescharacteristic
202C2×C4⋊C4—731no—
203#107—731no—
204#107—731no—
205#107—731no—
206#107—731no—
207#106—731no—
208#106—731no—
209#106—731no—
210#106—731no—
211C4⋊C8C2×D7311yescharacteristic
212C4⋊C8C2×D7311yescharacteristic
213#102—731no—
214#102—731no—
215#102—731no—
216#102—731no—
217#102—731no—
218#102—731no—
219#102—731no—
220#102—731no—
221C22⋊C8C2×D7311yescharacteristic
222C22⋊C8C2×D7311yescharacteristic
223#97C2×D7311yescharacteristic
224C4×C8C2×D7311yescharacteristic
225C2×Q8—1461no—
226C2×Q8—1461no—
227C2×D4—731no—
228C2×D4—731no—
229C2×D4—1461no—
230C2×D4—1461no—
231C2×D4—1461no—
232C2×D4—1461no—
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4C22×D7311yescharacteristic
237C2×C8C22×D7311yescharacteristic
238C2×C8C22×D7311yescharacteristic
239C2×C8C22×D7311yescharacteristic
240C2×C8C22×D7311yescharacteristic
241C4⋊C4—731no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—731no—
246C4⋊C4—731no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4D29211yescharacteristic
257C4⋊C4D29211yescharacteristic
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C22⋊C4—1461no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C22⋊C4D29211yescharacteristic
264C22⋊C4D29211yescharacteristic
265C42—1461no—
266C42C22×D7311yescharacteristic
267C42C22×D7311yescharacteristic
268C23—1461no—
269C23—1461no—
270C23C2×D29211yescharacteristic
271Q8—5841no—
272Q8—5841no—
273D4—5841no—
274D4—5841no—
275D4—5841no—
276D4—5841no—
277D4—1461no—
278D4—1461no—
279D4—1461no—
280D4—1461no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—5841no—
284C2×C4—5841no—
285C2×C4—5841no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4C2×D29211yescharacteristic
293C2×C4C2×D29211yescharacteristic
294C2×C4C2×D29211yescharacteristic
295C2×C4C2×D29211yescharacteristic
296C2×C4C2×D29211yescharacteristic
297C2×C4C23×D7311yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—2921no—
306C22—2921no—
307C22—2921no—
308C22—2921no—
309C22—2921no—
310C22—2921no—
311C22C22×D29211yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—2921no—
318C4—2921no—
319C4—2921no—
320C4—2921no—
321C4—2921no—
322C4—2921no—
323C4#1455663811yescharacteristic
324C4#1455663811yescharacteristic
325C2—41no—
326C2—5841no—
327C2—5841no—
328C2#1798916311yescharacteristic
329C2#1798939211yescharacteristic
330C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#433×C73C2
socleC22×C73C22×D4
hypercenter#433D73
hypocenterC73#3241
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
3. #17988996C2semidirect
4. #17988989C2semidirect
5. #17988952C2semidirect
6. #17988934C2semidirect
7. #17988912C2semidirect
8. #17988912C2semidirect
9. #17988906C2semidirect
10. #17988901C2semidirect
11. #17988888C2semidirect
12. #17988888C2semidirect
13. #17988878C2semidirect
14. #17988868C2semidirect
15. #433×C73C2semidirect
166. C73#3241semidirect
181. #433D73semidirect