Finite Group Databasebeta

← #22622694

Subgroups — #22622694

Order 9344.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989323C211yesmaximal, characteristic
2#17989314C211yesmaximal, characteristic, complemented
3#17988945C211yesmaximal, characteristic, complemented
4#17988940C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988889C211yesmaximal, characteristic, complemented
7#17988875C211yesmaximal, characteristic, complemented
8#17988808C211yesmaximal, characteristic, complemented
9#17988808C211yesmaximal, characteristic, complemented
10#17988784C211yesmaximal, characteristic
11#17988715C211yesmaximal, characteristic, complemented
12#17988695C211yesmaximal, characteristic, complemented
13#17988684C211yesmaximal, characteristic, complemented
14#17988678C211yesmaximal, characteristic, complemented
15#490×C73C211yesmaximal, characteristic
16C2×Dic292C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556590—21no—
20#14556590C2211yescharacteristic
21#14556582C2211yescharacteristic
22#14556581—21no—
23#14556581—21no—
24#14556578—21no—
25#14556578C2211yescharacteristic
26#14556578C2211yescharacteristic
27#14556572—21no—
28#14556572—21no—
29C4×Dic146C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31C4×Dic146C2211yescharacteristic
32#14556556—21no—
33#14556556C2211yescharacteristic
34#14556556C2211yescharacteristic
35D4×Dic73—21no—
36D4×Dic73C2211yescharacteristic
37D4×Dic73C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#127×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic
54#102×C73C2211yescharacteristic
55#102×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146D411yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63C22×Dic73—21no—
64C22×Dic73—21no—
65Dic292—22no—
66#11924016—22no—
67#11924016—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73D411yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007D411yescharacteristic
81#11924007D411yescharacteristic
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106C23×C73—21no—
107D4×C73—21no—
108D4×C73—21no—
109D4×C73—21no—
110D4×C73—21no—
111D4×C73—42no—
112D4×C73—81no—
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×Dic73—81no—
123C2×Dic73—81no—
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128Dic146—21no—
129Dic146—21no—
130Dic146—21no—
131Dic146—41no—
132Dic146—42no—
133Dic146#4112yes—
134C8×C73—21no—
135C8×C73—21no—
136#10596831—21no—
137#10596831—21no—
138C22×C73—41no—
139C22×C73—41no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73C22×D411yescharacteristic
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73C2×#4111yescharacteristic
150C4×C732−1+411yescharacteristic
151Dic73—22no—
152Dic73—21no—
153Dic73—21no—
154Dic73—21no—
155Dic73—21no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159C2×C73—81no—
160C2×C73—81no—
161C2×C73#54811yescharacteristic
162C2×C73#57511yescharacteristic
163C2×C73#57711yescharacteristic
164#3371—731nomaximal, Sylow
165C73#337111yescharacteristic, complemented, Sylow
166#559—731no—
167#557—731no—
168#490D7311yescharacteristic
169#489—731no—
170#488—731no—
171#479—731no—
172#478—731no—
173#476—731no—
174#464—731no—
175#464—731no—
176#460—731no—
177#446—731no—
178#441—731no—
179#440—731no—
180C4×SD16—731no—
181C2×Q16—731no—
182C2×SD16—731no—
183C2×SD16—731no—
184C4⋊Q8—731no—
185C4⋊Q8—1461no—
186#127C2×D7311yescharacteristic
187#125—731no—
188#125—1461no—
189#125—1461no—
190#125C2×D7311yescharacteristic
191#124—731no—
192#124—731no—
193#124—1461no—
194#123—1461no—
195#123—1461no—
196C4×Q8—731no—
197C4×Q8—731no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—1461no—
202C4×D4—731no—
203C4×D4—731no—
204C4×D4—1461no—
205#107—731no—
206#106—731no—
207#106—731no—
208C4⋊C8—731no—
209C4⋊C8—731no—
210C4⋊C8—731no—
211#103—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#102—731no—
216#102—731no—
217#102C2×D7311yescharacteristic
218#102C2×D7311yescharacteristic
219#102C2×D7311yescharacteristic
220#102C2×D7311yescharacteristic
221#97—731no—
222#97C2×D7311yescharacteristic
223C4×C8—731no—
224C2×Q8—731no—
225C2×Q8—731no—
226C2×Q8—731no—
227C2×Q8—1461no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D7311yescharacteristic
231C2×D4C22×D7311yescharacteristic
232C22×C4—1461no—
233C22×C4—1461no—
234Q16—1462no—
235SD16—1462no—
236SD16—1462no—
237C2×C8—731no—
238C2×C8—731no—
239C2×C8C22×D7311yescharacteristic
240C2×C8C22×D7311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—731no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4C22×D7311yescharacteristic
256C4⋊C4C22×D7311yescharacteristic
257C22⋊C4—1461no—
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C22⋊C4—1461no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C42—731no—
264C42—731no—
265C42—1461no—
266C42—1461no—
267C42—1461no—
268C42—1461no—
269C42C22×D7311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—2921no—
273Q8—2922no—
274Q8—732no—
275Q8—1461no—
276Q8—1461no—
277Q8—1461no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—5841no—
287C2×C4—5841no—
288C2×C4—731no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4D4×D7311yescharacteristic
297C2×C4D4×D7311yescharacteristic
298C2×C4C23×D7311yescharacteristic
299C8—21no—
300C8—21no—
301C8—1461no—
302C8—1461no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D7311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—2921no—
315C4—2921no—
316C4—2921no—
317C4—1461no—
318C4—1461no—
319C4—1461no—
320C4—1461no—
321C4—1462no—
322C4#41×D7311yescharacteristic
323C4#1455663811yescharacteristic
324C2—81no—
325C2—81no—
326C2#1798924511yescharacteristic
327C2#1798938311yescharacteristic
328C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3371
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #17989314C2semidirect
3. #17988945C2semidirect
4. #17988940C2semidirect
5. #17988891C2semidirect
6. #17988889C2semidirect
7. #17988875C2semidirect
8. #17988808C2semidirect
9. #17988808C2semidirect
11. #17988715C2semidirect
12. #17988695C2semidirect
13. #17988684C2semidirect
14. #17988678C2semidirect
165. C73#3371semidirect