Finite Group Databasebeta

← #22622293

Subgroups — #22622293

Order 9344.

342 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#17989277C211yesmaximal, characteristic
2#17988986C211yesmaximal, characteristic, complemented
3#17988928C211yesmaximal, characteristic, complemented
4#17988925C211yesmaximal, characteristic, complemented
5#17988917C211yesmaximal, characteristic, complemented
6#17988915C211yesmaximal, characteristic, complemented
7#17988894C211yesmaximal, characteristic, complemented
8#17988891C211yesmaximal, characteristic, complemented
9#17988826C211yesmaximal, characteristic, complemented
10#17988826C211yesmaximal, characteristic, complemented
11C4×#11924018C211yesmaximal, characteristic, complemented
12D4×#10596831C211yesmaximal, characteristic
13#17988623C211yesmaximal, characteristic, complemented
14C2×#14556524C211yesmaximal, characteristic, complemented
15#552×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic
17C22×#10596831C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556584—21no—
20#14556583C2211yescharacteristic
21#14556581—21no—
22#14556572—21no—
23#14556570C2211yescharacteristic
24#14556570C2211yescharacteristic
25C4×Dic146C2211yescharacteristic
26#14556550C2211yescharacteristic
27#14556547—21no—
28C2×C4⋊Dic73C2211yescharacteristic
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556522C2211yescharacteristic
37#14556522C2211yescharacteristic
38C4⋊#10596831C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556514C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48#126×C73—21no—
49#125×C73—21no—
50#125×C73C2211yescharacteristic
51#123×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53C22⋊Q8×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic
56#117×C73—21no—
57#117×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C22×Dic73—21no—
61#11924018—22no—
62C2×#10596831—22no—
63C2×#10596831—22no—
64C2×#10596831C2311yescharacteristic
65C2×#10596831C2311yescharacteristic
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C4⋊Dic73—21no—
69C4⋊Dic73C2311yescharacteristic
70C4⋊Dic73C2311yescharacteristic
71C4⋊Dic73C2311yescharacteristic
72#11924007—21no—
73#11924007—21no—
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78C22⋊Dic73—21no—
79C22⋊Dic73—21no—
80C4×Dic73—21no—
81C4×Dic73—21no—
82C2×Q8×C73C2311yescharacteristic
83C2×D4×C73D411yescharacteristic
84C22×C4×C73—21no—
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C4⋊C4×C73—21no—
88C4⋊C4×C73—21no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73D411yescharacteristic
94C4⋊C4×C73C2311yescharacteristic
95C4⋊C4×C73C2311yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C22⋊C4×C73—21no—
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73D411yescharacteristic
101C22⋊C4×C73D411yescharacteristic
102C42×C73—21no—
103C42×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73C2×D411yescharacteristic
106C23×C73C2×D411yescharacteristic
107Q8×C73—21no—
108Q8×C73—21no—
109D4×C73—22no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—42no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—42no—
129Dic146—21no—
130Dic146—21no—
131#10596831—21no—
132#10596831—21no—
133#10596831—21no—
134#10596831#4112yes—
135C22×C73—21no—
136C22×C73—21no—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73#13512yes—
141C22×C73C22×D411yescharacteristic
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73C2×#4111yescharacteristic
151C4×C732−1+411yescharacteristic
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73—41no—
156C2×C73—22no—
157C2×C73—41no—
158C2×C73#54711yescharacteristic
159C2×C73C2×#13511yescharacteristic
160C2×C73#57811yescharacteristic
161#3336—731nomaximal, Sylow
162C73#333611yescharacteristic, complemented, Sylow
163#552—731no—
164#552D7311yescharacteristic
165#499—731no—
166#485—731no—
167#485—731no—
168#483—731no—
169#483—731no—
170#479—731no—
171#479—731no—
172#467—731no—
173#467—731no—
174C4×Q16—731no—
175C8×D4—731no—
176#427—731no—
177C2×#107—731no—
178C2×Q16—731no—
179C22×C8—731no—
180C22×C8—731no—
181#126—21no—
182#126—1461no—
183#125—21no—
184#125—731no—
185#125—1461no—
186#125C2×D7311yescharacteristic
187#123—21no—
188#123—1461no—
189C22⋊Q8—731no—
190C22⋊Q8—731no—
191C22⋊Q8C2×D7311yescharacteristic
192C22⋊Q8C2×D7311yescharacteristic
193C4×Q8—731no—
194C4×Q8C2×D7311yescharacteristic
195C4×D4C2×D7311yescharacteristic
196#117—21no—
197#117—731no—
198#117—1461no—
199#117C2×D7311yescharacteristic
200C2×C4⋊C4—731no—
201C2×C4⋊C4C2×D7311yescharacteristic
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⋊C8—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218C22⋊C8—731no—
219C22⋊C8—731no—
220C4×C8—731no—
221C2×Q8—731no—
222C2×Q8C22×D7311yescharacteristic
223C2×D4C22⋊D7311yescharacteristic
224C22×C4—21no—
225C22×C4—1461no—
226C22×C4C22×D7311yescharacteristic
227C22×C4C22×D7311yescharacteristic
228Q16—1462no—
229C2×C8—731no—
230C2×C8—731no—
231C2×C8—731no—
232C2×C8—731no—
233C2×C8—1462no—
234C2×C8—1462no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—731no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4C22⋊D7311yescharacteristic
251C4⋊C4C22×D7311yescharacteristic
252C4⋊C4C22×D7311yescharacteristic
253C4⋊C4C22×D7311yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—1461no—
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C22⋊C4C22⋊D7311yescharacteristic
261C22⋊C4C22⋊D7311yescharacteristic
262C42—21no—
263C42—21no—
264C42—1461no—
265C42—1461no—
266C42C22×D7311yescharacteristic
267C23C2×C22⋊D7311yescharacteristic
268C23C2×C22⋊D7311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—1461no—
272Q8—1461no—
273D4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—2922no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4C2×C22⋊D7311yescharacteristic
289C2×C4C2×C22⋊D7311yescharacteristic
290C2×C4C2×C22⋊D7311yescharacteristic
291C2×C4C2×C22⋊D7311yescharacteristic
292C2×C4C23×D7311yescharacteristic
293C8—732no—
294C8—1461no—
295C8—1461no—
296C8—1461no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22#1455661112yes—
303C22C22×C22⋊D7311yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—2921no—
313C4—2921no—
314C4—2921no—
315C4—2921no—
316C4#41×D7311yescharacteristic
317C4#1455663811yescharacteristic
318C2—22no—
319C2—41no—
320C2#1798923611yescharacteristic
321C2C2×#1455661111yescharacteristic
322C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#552×C73C2
socleC22×C73C22×D4
hypercenter#552D73
hypocenterC73#3336
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #17988986C2semidirect
3. #17988928C2semidirect
4. #17988925C2semidirect
5. #17988917C2semidirect
6. #17988915C2semidirect
7. #17988894C2semidirect
8. #17988891C2semidirect
9. #17988826C2semidirect
10. #17988826C2semidirect
11. C4×#11924018C2semidirect
13. #17988623C2semidirect
14. C2×#14556524C2semidirect
162. C73#3336semidirect