Finite Group Databasebeta

← #22622668

Subgroups — #22622668

Order 9344.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989317C211yesmaximal, characteristic, complemented
2#17989306C211yesmaximal, characteristic
3#17988945C211yesmaximal, characteristic
4#17988936C211yesmaximal, characteristic, complemented
5#17988875C211yesmaximal, characteristic
6#17988870C211yesmaximal, characteristic, complemented
7#17988869C211yesmaximal, characteristic, complemented
8#17988808C211yesmaximal, characteristic
9#17988806C211yesmaximal, characteristic
10#17988796C211yesmaximal, characteristic, complemented
11#17988715C211yesmaximal, characteristic, complemented
12#17988695C211yesmaximal, characteristic, complemented
13#17988691C211yesmaximal, characteristic, complemented
14#17988678C211yesmaximal, characteristic
15#489×C73C211yesmaximal, characteristic
16C2×Dic292C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556590—21no—
20#14556590C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556589—21no—
23#14556589—21no—
24#14556589C2211yescharacteristic
25#14556584—21no—
26#14556584—21no—
27#14556578C2211yescharacteristic
28#14556568—21no—
29Q8×Dic73C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31C4×Dic146C2211yescharacteristic
32C4×Dic146C2211yescharacteristic
33#14556556—21no—
34#14556556C2211yescharacteristic
35#14556556C2211yescharacteristic
36D4×Dic73C2211yescharacteristic
37#14556547—21no—
38#14556523C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53#124×C73C2211yescharacteristic
54#103×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146D411yescharacteristic
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C22×Dic73—21no—
65Dic292—22no—
66#11924018—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#11924007—21no—
81#11924007—21no—
82#11924007D411yescharacteristic
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×Q8×C73—21no—
95C2×Q8×C73C2311yescharacteristic
96C2×D4×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C22⋊C4×C73—21no—
103C22⋊C4×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106Q8×C73—21no—
107Q8×C73—21no—
108Q8×C73—81no—
109D4×C73—21no—
110D4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2411yescharacteristic
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—42no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126Dic146—21no—
127Dic146—22no—
128Dic146—21no—
129Dic146—21no—
130Dic146—81no—
131Dic146—81no—
132Dic146#4112yes—
133C8×C73—21no—
134C8×C73—21no—
135#10596831—21no—
136#10596831—21no—
137C22×C73—41no—
138C22×C73—41no—
139C22×C73—41no—
140C22×C73C22×D411yescharacteristic
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C73—41no—
146C4×C73C2×#4111yescharacteristic
147C4×C732−1+411yescharacteristic
148Dic73—22no—
149Dic73—21no—
150Dic73—21no—
151Dic73—21no—
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73#13712yes—
156C2×C73—81no—
157C2×C73#54811yescharacteristic
158C2×C73C2×#13711yescharacteristic
159C2×C73#57711yescharacteristic
160#3369—731nomaximal, Sylow
161C73#336911yescharacteristic, complemented, Sylow
162Q82—731no—
163#556—731no—
164#489—731no—
165#489D7311yescharacteristic
166#487—731no—
167#476—731no—
168#475—731no—
169#475—731no—
170#464—731no—
171#464—731no—
172#462—731no—
173#446—731no—
174#441—731no—
175#441—731no—
176C4×SD16—731no—
177C2×Q16—731no—
178C2×Q16—731no—
179C2×SD16—731no—
180C4⋊Q8—731no—
181C4⋊Q8—731no—
182C4⋊Q8—731no—
183C4⋊Q8—1461no—
184C4⋊Q8—1461no—
185C4⋊Q8—1461no—
186C4⋊Q8C2×D7311yescharacteristic
187#126—1461no—
188#126—1461no—
189#124—731no—
190#124C2×D7311yescharacteristic
191C22⋊Q8—1461no—
192C4×Q8—731no—
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—731no—
196C4×Q8—731no—
197C4×Q8—731no—
198C4×Q8—1461no—
199C4×D4—731no—
200#117—1461no—
201#106—731no—
202#106—731no—
203#106—731no—
204C4⋊C8—731no—
205C4⋊C8—731no—
206C4⋊C8—731no—
207#103—731no—
208#103—731no—
209#103—731no—
210#103—731no—
211#103—731no—
212#103C2×D7311yescharacteristic
213#103C2×D7311yescharacteristic
214#102—731no—
215#102C2×D7311yescharacteristic
216#102C2×D7311yescharacteristic
217#97—731no—
218#97C2×D7311yescharacteristic
219C4×C8—731no—
220C2×Q8—21no—
221C2×Q8—731no—
222C2×Q8—731no—
223C2×Q8—731no—
224C2×Q8—1461no—
225C2×Q8—1461no—
226C2×Q8C22×D7311yescharacteristic
227C2×D4C22×D7311yescharacteristic
228C22×C4—1461no—
229Q16—1462no—
230Q16—1462no—
231SD16—1462no—
232C2×C8—731no—
233C2×C8—731no—
234C2×C8C22×D7311yescharacteristic
235C2×C8C22×D7311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—731no—
238C4⋊C4—731no—
239C4⋊C4—731no—
240C4⋊C4—731no—
241C4⋊C4—731no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4C22×D7311yescharacteristic
252C4⋊C4C22×D7311yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—1461no—
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C42—731no—
259C42—731no—
260C42—1461no—
261C42—1461no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42C22×D7311yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—5841no—
271Q8—5841no—
272Q8—732no—
273Q8—1462no—
274Q8—1461no—
275Q8—1461no—
276Q8—1461no—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—2922no—
283C2×C4—731no—
284C2×C4—731no—
285C2×C4—731no—
286C2×C4—731no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4D4×D7311yescharacteristic
292C2×C4D4×D7311yescharacteristic
293C2×C4C23×D7311yescharacteristic
294C8—21no—
295C8—21no—
296C8—1461no—
297C8—1461no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D7311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—2921no—
308C4—2921no—
309C4—2921no—
310C4—732no—
311C4—1461no—
312C4—1461no—
313C4—1461no—
314C4—1462no—
315C4#41×D7311yescharacteristic
316C4#1455663811yescharacteristic
317C2—81no—
318C2#1798924511yescharacteristic
319C2#137×D7311yescharacteristic
320C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3369
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989317C2semidirect
4. #17988936C2semidirect
6. #17988870C2semidirect
7. #17988869C2semidirect
10. #17988796C2semidirect
11. #17988715C2semidirect
12. #17988695C2semidirect
13. #17988691C2semidirect
161. C73#3369semidirect