Finite Group Databasebeta

← #22622386

Subgroups — #22622386

Order 9344.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989294C211yesmaximal, characteristic
2#17988997C211yesmaximal, characteristic, complemented
3#17988928C211yesmaximal, characteristic, complemented
4#17988920C211yesmaximal, characteristic, complemented
5#17988917C211yesmaximal, characteristic, complemented
6#17988915C211yesmaximal, characteristic, complemented
7#17988891C211yesmaximal, characteristic, complemented
8#17988872C211yesmaximal, characteristic, complemented
9#17988843C211yesmaximal, characteristic, complemented
10#17988826C211yesmaximal, characteristic, complemented
11#17988692C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic
13#17988630C211yesmaximal, characteristic, complemented
14C2×#14556522C211yesmaximal, characteristic, complemented
15#552×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556582—21no—
21#14556570C2211yescharacteristic
22#14556570C2211yescharacteristic
23#14556568—21no—
24#14556568—21no—
25C4×Dic146C2211yescharacteristic
26D4×Dic73—21no—
27C2×C4⋊Dic73C2211yescharacteristic
28C2×C4⋊Dic73C2211yescharacteristic
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
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
47#14556502C2211yescharacteristic
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×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C22×Dic73—21no—
62C22×Dic73—21no—
63#11924018—22no—
64#11924012—22no—
65C2×#10596831—22no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80C22⋊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—81no—
129C2×Dic73—81no—
130Dic146—21no—
131Dic146—21no—
132Dic146—81no—
133#10596831—21no—
134#10596831—21no—
135#10596831—21no—
136#10596831#4112yes—
137C22×C73—21no—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73#13712yes—
143C22×C73C22×D411yescharacteristic
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73C2×#4111yescharacteristic
153C4×C732−1+411yescharacteristic
154Dic73—41no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158C2×C73—22no—
159C2×C73—41no—
160C2×C73#54711yescharacteristic
161C2×C73C2×#13711yescharacteristic
162C2×C73#57711yescharacteristic
163#3344—731nomaximal, Sylow
164C73#334411yescharacteristic, complemented, Sylow
165#554—731no—
166#552D7311yescharacteristic
167#501—731no—
168#485—731no—
169#484—731no—
170#483—731no—
171#483—731no—
172#479—731no—
173#475—731no—
174#470—731no—
175#467—731no—
176#441—731no—
177#435—731no—
178#428—731no—
179C2×#106—731no—
180C2×Q16—731no—
181C2×M16—731no—
182C22×C8—731no—
183C4⋊Q8—731no—
184#126—21no—
185#125—21no—
186#125—1461no—
187#125C2×D7311yescharacteristic
188#123—21no—
189C22⋊Q8—731no—
190C22⋊Q8—731no—
191C22⋊Q8—1461no—
192C22⋊Q8—1461no—
193C22⋊Q8C2×D7311yescharacteristic
194C22⋊Q8C2×D7311yescharacteristic
195C4×Q8—731no—
196C4×Q8C2×D7311yescharacteristic
197C4×D4—1461no—
198C4×D4C2×D7311yescharacteristic
199#117—21no—
200#117C2×D7311yescharacteristic
201C2×C4⋊C4—731no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4C2×D7311yescharacteristic
204#107—731no—
205#107—731no—
206#107—731no—
207#106—731no—
208#106—731no—
209#106—731no—
210#106—731no—
211#106—731no—
212#106—731no—
213C4⋊C8—731no—
214#103—731no—
215#103—731no—
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220C22⋊C8—731no—
221C22⋊C8—731no—
222#97—731no—
223C2×Q8—731no—
224C2×Q8—1461no—
225C2×Q8C22×D7311yescharacteristic
226C2×D4C22⋊D7311yescharacteristic
227C22×C4—21no—
228C22×C4—1461no—
229C22×C4—1461no—
230C22×C4C22×D7311yescharacteristic
231C22×C4C22×D7311yescharacteristic
232Q16—1462no—
233M16—1462no—
234C2×C8—731no—
235C2×C8—731no—
236C2×C8—731no—
237C2×C8—731no—
238C2×C8—1462no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
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⋊C4C22⋊D7311yescharacteristic
255C4⋊C4C22×D7311yescharacteristic
256C4⋊C4C22×D7311yescharacteristic
257C4⋊C4C22×D7311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C22⋊C4C22⋊D7311yescharacteristic
264C22⋊C4C22⋊D7311yescharacteristic
265C42—21no—
266C42—21no—
267C42—1461no—
268C42C22×D7311yescharacteristic
269C23C2×C22⋊D7311yescharacteristic
270C23C2×C22⋊D7311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—5841no—
274Q8—1461no—
275Q8—1461no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—5841no—
287C2×C4—5841no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4C2×C22⋊D7311yescharacteristic
293C2×C4C2×C22⋊D7311yescharacteristic
294C2×C4C2×C22⋊D7311yescharacteristic
295C2×C4C2×C22⋊D7311yescharacteristic
296C2×C4C23×D7311yescharacteristic
297C8—732no—
298C8—1461no—
299C8—1461no—
300C8—1461no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1455662112yes—
307C22C22×C22⋊D7311yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—2921no—
317C4—2921no—
318C4—2921no—
319C4—2921no—
320C4#41×D7311yescharacteristic
321C4#1455663811yescharacteristic
322C2—22no—
323C2—41no—
324C2#1798923611yescharacteristic
325C2C2×#1455662111yescharacteristic
326C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#552×C73C2
socleC22×C73C22×D4
hypercenter#552D73
hypocenterC73#3344
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. #17988997C2semidirect
3. #17988928C2semidirect
4. #17988920C2semidirect
5. #17988917C2semidirect
6. #17988915C2semidirect
7. #17988891C2semidirect
8. #17988872C2semidirect
9. #17988843C2semidirect
10. #17988826C2semidirect
11. #17988692C2semidirect
13. #17988630C2semidirect
14. C2×#14556522C2semidirect
164. C73#3344semidirect