Finite Group Databasebeta

← #22622305

Subgroups — #22622305

Order 9344.

354 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#17989284C211yesmaximal, characteristic
2#17989271C211yesmaximal, characteristic, complemented
3#17988987C211yesmaximal, characteristic, complemented
4#17988925C211yesmaximal, characteristic, complemented
5#17988921C211yesmaximal, characteristic, complemented
6#17988908C211yesmaximal, characteristic, complemented
7#17988899C211yesmaximal, characteristic, complemented
8#17988896C211yesmaximal, characteristic, complemented
9#17988885C211yesmaximal, characteristic, complemented
10#17988813C211yesmaximal, characteristic, complemented
11SD16×Dic73C211yesmaximal, characteristic, complemented
12C8×C22⋊D73C211yesmaximal, characteristic, complemented
13#17988625C211yesmaximal, characteristic, complemented
14#106×D73C211yesmaximal, characteristic, complemented
15#465×C73C211yesmaximal, characteristic, complemented
16C2×C8×D73C2211yescharacteristic
17#14556584—21no—
18#14556584—21no—
19#14556582C2211yescharacteristic
20#14556582C2211yescharacteristic
21#14556581—21no—
22#14556573—21no—
23#14556572—21no—
24#14556567C2211yescharacteristic
25#14556562—21no—
26#14556562C2211yescharacteristic
27Q8×Dic73C2211yescharacteristic
28D4×Dic73C2211yescharacteristic
29C4×C22⋊D73C2211yescharacteristic
30#14556551—21no—
31#14556550C2211yescharacteristic
32#14556550C2211yescharacteristic
33#14556549—21no—
34C4⋊C4×D73C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36#14556525C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#106×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×C22⋊D73—21no—
60C2×C22⋊D73D411yescharacteristic
61C22×Dic73—21no—
62C2×C4×D73—21no—
63C2×C4×D73—21no—
64C2×C4×D73C2311yescharacteristic
65C2×#10596831C2311yescharacteristic
66C2×#10596831C2311yescharacteristic
67C8×D73—22no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007D411yescharacteristic
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73D411yescharacteristic
86#11924005—21no—
87#11924005D411yescharacteristic
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×D4×C73—21no—
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96SD16×C73—22no—
97C2×C8×C73—22no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C23×C73—21no—
106C23×C73C2×D411yescharacteristic
107C22×D73C2×D411yescharacteristic
108Q8×C73—21no—
109Q8×C73—21no—
110D4×C73—21no—
111D4×C73—21no—
112D4×C73—81no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—22no—
121C22⋊D73—42no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—81no—
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C4×D73—21no—
131C4×D73—21no—
132C4×D73—42no—
133C4×D73—81no—
134C8×C73—21no—
135C8×C73#4112yes—
136#10596831—21no—
137#10596831—21no—
138C22×C73—21no—
139C22×C73—21no—
140C22×C73—21no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73C22×D411yescharacteristic
145C2×D73—21no—
146C2×D73—21no—
147C2×D73#13512yes—
148C4×C73—21no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73C2×#4111yescharacteristic
153C4×C732−1+411yescharacteristic
154Dic73—21no—
155Dic73—21no—
156Dic73—21no—
157Dic73—41no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161C2×C73—41no—
162C2×C73—81no—
163C2×C73#54711yescharacteristic
164C2×C73C2×#13511yescharacteristic
165C2×C73#57711yescharacteristic
166D73—22no—
167#3337—731nomaximal, Sylow
168C73#333711yescharacteristic, complemented, Sylow
169#553—731no—
170#552—731no—
171#499—731no—
172#485—731no—
173#484—731no—
174#482—731no—
175#480—731no—
176#479—731no—
177#478—731no—
178#465—731no—
179#465D7311yescharacteristic, complemented
180C4×SD16—731no—
181C8×D4—731no—
182#427—731no—
183C2×#106—731no—
184C2×SD16C2×D7311yescharacteristic
185C22×C8—731no—
186C22×C8C2×D7311yescharacteristic
187#126—1461no—
188#126—1461no—
189#125—731no—
190#125—731no—
191#125—1461no—
192#123—1461no—
193#123—1461no—
194C22⋊Q8—731no—
195C22⋊Q8C2×D7311yescharacteristic
196#121—731no—
197#121—1461no—
198#121C2×D7311yescharacteristic
199C4×Q8—731no—
200C4×D4—731no—
201C4×D4—731no—
202C4×D4—1461no—
203#117—731no—
204#117—731no—
205#117—1461no—
206C2×C4⋊C4—731no—
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#106C2×D7311yescharacteristic
217C4⋊C8—731no—
218#103—731no—
219#103—731no—
220#103C2×D7311yescharacteristic
221#102—731no—
222#102—731no—
223#102C2×D7311yescharacteristic
224C22⋊C8—731no—
225C22⋊C8—731no—
226C4×C8—731no—
227C2×Q8C22×D7311yescharacteristic
228C2×D4—21no—
229C2×D4—731no—
230C2×D4—1461no—
231C2×D4C22×D7311yescharacteristic
232C22×C4—731no—
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4C22×D7311yescharacteristic
237SD16—22no—
238C2×C8—22no—
239C2×C8—731no—
240C2×C8—731no—
241C2×C8—1462no—
242C2×C8C22×D7311yescharacteristic
243C2×C8C22×D7311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—731no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—731no—
249C4⋊C4—731no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4C22×D7311yescharacteristic
259C4⋊C4C22×D7311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—731no—
263C22⋊C4—731no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C42—731no—
270C42—1461no—
271C42—1461no—
272C42—1461no—
273C23—21no—
274C23—731no—
275C23D4×D7311yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—21no—
279D4—21no—
280D4—81no—
281D4—2922no—
282D4—1462no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—2922no—
289C2×C4—5841no—
290C2×C4—5841no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4D4×D7311yescharacteristic
301C2×C4C23×D7311yescharacteristic
302C8—21no—
303C8—1461no—
304C8—1461no—
305C8#1192402712yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—732no—
313C22—1461no—
314C22—1461no—
315C22C2×D4×D7311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—2921no—
321C4—2921no—
322C4—2921no—
323C4—2921no—
324C4—1461no—
325C4—1461no—
326C4—1461no—
327C4C2×#1192402711yescharacteristic
328C4#1455663811yescharacteristic
329C2—41no—
330C2—81no—
331C2—1462no—
332C2#1798923711yescharacteristic
333C2#135×D7311yescharacteristic
334C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#465×C73C2
socleC22×C73C22×D4
hypercenter#465D73
hypocenterC73#3337
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
2. #17989271C2semidirect
3. #17988987C2semidirect
4. #17988925C2semidirect
5. #17988921C2semidirect
6. #17988908C2semidirect
7. #17988899C2semidirect
8. #17988896C2semidirect
9. #17988885C2semidirect
10. #17988813C2semidirect
11. SD16×Dic73C2semidirect
12. C8×C22⋊D73C2semidirect
13. #17988625C2semidirect
14. #106×D73C2semidirect
15. #465×C73C2semidirect
168. C73#3337semidirect
179. #465D73semidirect