Finite Group Databasebeta

← #22622476

Subgroups — #22622476

Order 9344.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989283C211yesmaximal, characteristic
2#17988993C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988915C211yesmaximal, characteristic, complemented
5#17988911C211yesmaximal, characteristic, complemented
6#17988911C211yesmaximal, characteristic, complemented
7#17988894C211yesmaximal, characteristic, complemented
8#17988874C211yesmaximal, characteristic, complemented
9#17988835C211yesmaximal, characteristic, complemented
10#17988818C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988630C211yesmaximal, characteristic, complemented
14#17988623C211yesmaximal, characteristic, complemented
15#556×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556586—21no—
20#14556583C2211yescharacteristic
21#14556573—21no—
22#14556565C2211yescharacteristic
23#14556565C2211yescharacteristic
24#14556563—21no—
25C4×D292C2211yescharacteristic
26#14556551—21no—
27#14556550C2211yescharacteristic
28C2×C4⋊Dic73C2211yescharacteristic
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556522C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556522C2211yescharacteristic
37#14556522C2211yescharacteristic
38C4⋊#10596831C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C4⋊Q8×C73C2211yescharacteristic
49#126×C73—21no—
50#126×C73—21no—
51#124×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53C22⋊Q8×C73C2211yescharacteristic
54C4×Q8×C73—21no—
55C4×Q8×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57#117×C73C2211yescharacteristic
58#117×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C2×C4×D73—21no—
64#11924015—22no—
65#11924012—22no—
66C2×#10596831—22no—
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81C4×Dic73—21no—
82C2×Q8×C73—21no—
83C2×Q8×C73C2311yescharacteristic
84C2×D4×C73D411yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C4⋊C4×C73—21no—
88C4⋊C4×C73—21no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73D411yescharacteristic
92C4⋊C4×C73C2311yescharacteristic
93C4⋊C4×C73C2311yescharacteristic
94C4⋊C4×C73C2311yescharacteristic
95C22⋊C4×C73—21no—
96C22⋊C4×C73—21no—
97C22⋊C4×C73—21no—
98C22⋊C4×C73—21no—
99C22⋊C4×C73D411yescharacteristic
100C22⋊C4×C73D411yescharacteristic
101C42×C73—21no—
102C42×C73—21no—
103C42×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73C2×D411yescharacteristic
106C23×C73C2×D411yescharacteristic
107C22×D73—21no—
108Q8×C73—21no—
109Q8×C73—21no—
110Q8×C73—42no—
111D4×C73—41no—
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—21no—
119C2×C4×C73—21no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—42no—
126C22⋊D73—81no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—81no—
131D292—21no—
132D292—21no—
133C4×D73—81no—
134#10596831—21no—
135#10596831—21no—
136#10596831—21no—
137#10596831#4112yes—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73C22×D411yescharacteristic
145C2×D73—41no—
146C2×D73—41no—
147C2×D73—41no—
148C4×C73—21no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73C2×#4111yescharacteristic
157C4×C732−1+411yescharacteristic
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161C2×C73—41no—
162C2×C73—41no—
163C2×C73#54711yescharacteristic
164C2×C73#57511yescharacteristic
165C2×C73#57711yescharacteristic
166D73—81no—
167#3350—731nomaximal, Sylow
168C73#335011yescharacteristic, complemented, Sylow
169#556D7311yescharacteristic, complemented
170#553—731no—
171#501—731no—
172#485—731no—
173#483—731no—
174#482—731no—
175#482—731no—
176#479—731no—
177#476—731no—
178#468—731no—
179#465—731no—
180#440—731no—
181#435—731no—
182#428—731no—
183#427—731no—
184C2×SD16—731no—
185C2×M16—731no—
186C22×C8—731no—
187C4⋊Q8C2×D7311yescharacteristic
188#126—21no—
189#126—21no—
190#126—1461no—
191#125—731no—
192#124—21no—
193#123—1461no—
194C22⋊Q8C2×D7311yescharacteristic
195C22⋊Q8C2×D7311yescharacteristic
196#121—731no—
197#121—731no—
198#121—1461no—
199C4×Q8—21no—
200C4×Q8C2×D7311yescharacteristic
201C4×D4—731no—
202C4×D4—1461no—
203C4×D4C2×D7311yescharacteristic
204#117—731no—
205#117C2×D7311yescharacteristic
206#117C2×D7311yescharacteristic
207C2×C4⋊C4—731no—
208#107—731no—
209#107—731no—
210#107—731no—
211#107—731no—
212#106—731no—
213#106—731no—
214#106—731no—
215#106—731no—
216#106—731no—
217C4⋊C8—731no—
218#103—731no—
219#103—731no—
220#103—731no—
221#102—731no—
222#102—731no—
223#102—731no—
224C22⋊C8—731no—
225C22⋊C8—731no—
226#97—731no—
227C2×Q8—21no—
228C2×Q8C22×D7311yescharacteristic
229C2×D4—731no—
230C2×D4—1461no—
231C2×D4—1461no—
232C2×D4C22⋊D7311yescharacteristic
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4C22×D7311yescharacteristic
236C22×C4C22×D7311yescharacteristic
237SD16—1462no—
238M16—1462no—
239C2×C8—731no—
240C2×C8—731no—
241C2×C8—731no—
242C2×C8—731no—
243C2×C8—1462no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—731no—
249C4⋊C4—731no—
250C4⋊C4—731no—
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—21no—
262C22⋊C4—1461no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4C22⋊D7311yescharacteristic
267C22⋊C4C22⋊D7311yescharacteristic
268C42—21no—
269C42—21no—
270C42—21no—
271C42—1461no—
272C42C22×D7311yescharacteristic
273C23—1461no—
274C23C2×C22⋊D7311yescharacteristic
275C23C2×C22⋊D7311yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—42no—
279D4—41no—
280D4—2922no—
281D4—5841no—
282D4—1461no—
283D4—1461no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—5841no—
293C2×C4—5841no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4C2×C22⋊D7311yescharacteristic
298C2×C4C2×C22⋊D7311yescharacteristic
299C2×C4C2×C22⋊D7311yescharacteristic
300C2×C4C2×C22⋊D7311yescharacteristic
301C2×C4C23×D7311yescharacteristic
302C8—732no—
303C8—1461no—
304C8—1461no—
305C8—1461no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—2921no—
313C22—2921no—
314C22—2921no—
315C22C22×C22⋊D7311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2921no—
325C4—2921no—
326C4—2921no—
327C4#41×D7311yescharacteristic
328C4#1455663811yescharacteristic
329C2—41no—
330C2—41no—
331C2—5841no—
332C2#1798923611yescharacteristic
333C2#1798938511yescharacteristic
334C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#556×C73C2
socleC22×C73C22×D4
hypercenter#556D73
hypocenterC73#3350
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #17988993C2semidirect
3. #17988925C2semidirect
4. #17988915C2semidirect
5. #17988911C2semidirect
6. #17988911C2semidirect
7. #17988894C2semidirect
8. #17988874C2semidirect
9. #17988835C2semidirect
10. #17988818C2semidirect
11. #17988685C2semidirect
12. #17988659C2semidirect
13. #17988630C2semidirect
14. #17988623C2semidirect
15. #556×C73C2semidirect
168. C73#3350semidirect
169. #556D73semidirect