Finite Group Databasebeta

← #22622463

Subgroups — #22622463

Order 9344.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989307C211yesmaximal, characteristic
2#17989277C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic, complemented
4#17988929C211yesmaximal, characteristic, complemented
5#17988929C211yesmaximal, characteristic, complemented
6#17988929C211yesmaximal, characteristic, complemented
7#17988923C211yesmaximal, characteristic, complemented
8#17988895C211yesmaximal, characteristic, complemented
9#17988883C211yesmaximal, characteristic, complemented
10#17988845C211yesmaximal, characteristic, complemented
11#17988828C211yesmaximal, characteristic, complemented
12#17988695C211yesmaximal, characteristic, complemented
13#17988629C211yesmaximal, characteristic, complemented
14#17988625C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic
16C2×Dic292C2211yescharacteristic
17#14556591C2211yescharacteristic
18#14556584—21no—
19#14556584—21no—
20#14556584—21no—
21#14556583C2211yescharacteristic
22#14556581—21no—
23#14556578—21no—
24#14556572—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27#14556570C2211yescharacteristic
28#14556570C2211yescharacteristic
29C4×Dic146C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31#14556556—21no—
32#14556550C2211yescharacteristic
33#14556550C2211yescharacteristic
34#14556550C2211yescharacteristic
35#14556547—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556525C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556523C2211yescharacteristic
45#14556523C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556516C2211yescharacteristic
50#14556516C2211yescharacteristic
51#14556516C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62C22×Dic73—21no—
63Dic292—22no—
64C4⋊Dic73—21no—
65C4⋊Dic73—21no—
66C4⋊Dic73C2311yescharacteristic
67C4⋊Dic73C2311yescharacteristic
68C4⋊Dic73C2311yescharacteristic
69C4⋊Dic73C2311yescharacteristic
70C4⋊Dic73C2311yescharacteristic
71C4⋊Dic73C2311yescharacteristic
72#11924007—21no—
73#11924007—21no—
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C2×D4×C73D411yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95M16×C73—22no—
96C2×C8×C73—22no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73D411yescharacteristic
102C22⋊C4×C73D411yescharacteristic
103C22⋊C4×C73D411yescharacteristic
104C42×C73C2311yescharacteristic
105C23×C73C2×D411yescharacteristic
106C23×C73C2×D411yescharacteristic
107D4×C73—41no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73C2×D411yescharacteristic
113C2×C4×C73C2×D411yescharacteristic
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—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—42no—
126Dic146—21no—
127Dic146—21no—
128Dic146—21no—
129Dic146—21no—
130Dic146—42no—
131C8×C73—21no—
132C8×C73—21no—
133C8×C73—21no—
134C8×C73#4112yes—
135C22×C73—21no—
136C22×C73—21no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73C22×D411yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73C2×#4111yescharacteristic
147C4×C732−1+411yescharacteristic
148Dic73—41no—
149Dic73—41no—
150Dic73—41no—
151Dic73—41no—
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73—41no—
156C2×C73—41no—
157C2×C73—41no—
158C2×C73#54711yescharacteristic
159C2×C73#57511yescharacteristic
160C2×C73#57811yescharacteristic
161#3349—731nomaximal, Sylow
162C73#334911yescharacteristic, complemented, Sylow
163#556—731no—
164#552—731no—
165#501—731no—
166#485—731no—
167#485—731no—
168#485—731no—
169#484—731no—
170#479—731no—
171#477—731no—
172#470—731no—
173#467—731no—
174#441—731no—
175#435D7311yescharacteristic
176#428—731no—
177#427—731no—
178C2×Q16—731no—
179C2×M16C2×D7311yescharacteristic
180C22×C8C2×D7311yescharacteristic
181C4⋊Q8—731no—
182#126—1461no—
183#126—1461no—
184#126—1461no—
185#125—731no—
186#125—1461no—
187#124—1461no—
188#123—1461no—
189C22⋊Q8—731no—
190C22⋊Q8—731no—
191C22⋊Q8—731no—
192C22⋊Q8—731no—
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—1461no—
196C4×D4C2×D7311yescharacteristic
197#117—731no—
198#117—731no—
199#117—731no—
200#117—1461no—
201C2×C4⋊C4—731no—
202#107—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
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218C22⋊C8C2×D7311yescharacteristic
219C22⋊C8C2×D7311yescharacteristic
220#97C2×D7311yescharacteristic
221C2×Q8—731no—
222C2×Q8—731no—
223C2×Q8—1461no—
224C2×D4D29211yescharacteristic
225C22×C4—1461no—
226C22×C4C22×D7311yescharacteristic
227C22×C4C22×D7311yescharacteristic
228Q16—1462no—
229M16—22no—
230C2×C8—22no—
231C2×C8C22×D7311yescharacteristic
232C2×C8C22×D7311yescharacteristic
233C2×C8C22×D7311yescharacteristic
234C2×C8C22×D7311yescharacteristic
235C4⋊C4—731no—
236C4⋊C4—731no—
237C4⋊C4—731no—
238C4⋊C4—731no—
239C4⋊C4—731no—
240C4⋊C4—731no—
241C4⋊C4—1461no—
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⋊C4D29211yescharacteristic
252C22⋊C4—1461no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C22⋊C4—1461no—
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C22⋊C4—1461no—
259C22⋊C4D29211yescharacteristic
260C22⋊C4D29211yescharacteristic
261C42—1461no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42—1461no—
266C42C22×D7311yescharacteristic
267C23C2×D29211yescharacteristic
268C23C2×D29211yescharacteristic
269Q8—2922no—
270Q8—1461no—
271Q8—1461no—
272Q8—1461no—
273Q8—1461no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—2922no—
280C2×C4—1461no—
281C2×C4—1461no—
282C2×C4—1461no—
283C2×C4—1461no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4C2×D29211yescharacteristic
289C2×C4C2×D29211yescharacteristic
290C2×C4C2×D29211yescharacteristic
291C2×C4C2×D29211yescharacteristic
292C2×C4C23×D7311yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8#1192402712yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×D29211yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—2921no—
309C4—2921no—
310C4—2921no—
311C4—2921no—
312C4—2921no—
313C4—2921no—
314C4—2921no—
315C4—2921no—
316C4C2×#1192402711yescharacteristic
317C4#1455663811yescharacteristic
318C2—41no—
319C2—41no—
320C2#1798924111yescharacteristic
321C2#1798938711yescharacteristic
322C2#1798940411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3349
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
3. #17988996C2semidirect
4. #17988929C2semidirect
5. #17988929C2semidirect
6. #17988929C2semidirect
7. #17988923C2semidirect
8. #17988895C2semidirect
9. #17988883C2semidirect
10. #17988845C2semidirect
11. #17988828C2semidirect
12. #17988695C2semidirect
13. #17988629C2semidirect
14. #17988625C2semidirect
162. C73#3349semidirect