Finite Group Databasebeta

← #22619790

Subgroups — #22619790

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989214C211yesmaximal, characteristic, complemented
2#17989069C211yesmaximal, characteristic
3#17988896C211yesmaximal, characteristic, complemented
4#17988894C211yesmaximal, characteristic, complemented
5#17988888C211yesmaximal, characteristic, complemented
6#17988886C211yesmaximal, characteristic, complemented
7#17988876C211yesmaximal, characteristic, complemented
8#17988874C211yesmaximal, characteristic, complemented
9#17988870C211yesmaximal, characteristic, complemented
10#17988626C211yesmaximal, characteristic, complemented
11#106×D73C211yesmaximal, characteristic, complemented
12#17988612C211yesmaximal, characteristic, complemented
13#17988587C211yesmaximal, characteristic
14#17988582C211yesmaximal, characteristic
15#475×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18C2×C8×D73C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556589—21no—
21#14556583C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556581—21no—
24#14556569—21no—
25#14556567—21no—
26Q8×Dic73C2211yescharacteristic
27C4×D292—21no—
28C4×D292C2211yescharacteristic
29#14556553—21no—
30#14556553C2211yescharacteristic
31#14556549C2211yescharacteristic
32#14556548—21no—
33#14556548C2211yescharacteristic
34C4⋊C4×D73—21no—
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43C4⋊#10596831C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556511C2211yescharacteristic
51#14556511C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54#106×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59#11924029—22no—
60#11924029Q814yescomplemented
61C2×Dic146—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×C4×D73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73C2311yescharacteristic
70#11924011—22no—
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C8×D73—22no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86#11924007D411yescharacteristic
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005D411yescharacteristic
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73—21no—
96C2×Q8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C42×C73—21no—
105C42×C73C2311yescharacteristic
106C22×D73—21no—
107C22×D73C2×D411yescharacteristic
108Q8×C73—21no—
109Q8×C73—81no—
110Q8×C73C2×Q812yes—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2411yescharacteristic
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124D292—24no—
125D292—21no—
126D292C2×Q812yes—
127C4×D73—24no—
128C4×D73—81no—
129C4×D73—81no—
130C4×D73—81no—
131C4×D73—81no—
132C4×D73C2×Q812yes—
133C4×D73#4112yes—
134Dic146—81no—
135C8×C73—21no—
136C8×C73—21no—
137#10596831—21no—
138#10596831—21no—
139C22×C73C22×D411yescharacteristic
140C2×D73—21no—
141C2×D73—21no—
142C2×D73—22no—
143C2×D73—41no—
144C2×D73—41no—
145C2×D73C22⋊Q812yes—
146C4×C73—22no—
147C4×C73—21no—
148C4×C73—21no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73—41no—
152C4×C73C22×Q811yescharacteristic
153C4×C73C2×#4111yescharacteristic
154Dic73—21no—
155Dic73—21no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159Dic73C22⋊Q812yes—
160C2×C73C2×C22⋊Q811yescharacteristic
161C2×C73#57711yescharacteristic
162C2×C73#57711yescharacteristic
163D73—22no—
164D73—42no—
165#3084—731nomaximal, Sylow
166C73#308411yescharacteristic, complemented, Sylow
167#544—731no—
168#520—731no—
169#479—731no—
170#479—731no—
171#478—731no—
172#478—731no—
173#476—731no—
174#476—731no—
175#475—731no—
176#475D7311yescharacteristic, complemented
177#428—731no—
178C2×#106—731no—
179#424—731no—
180#417—731no—
181#416—731no—
182C2×#41—731no—
183C2×M16—731no—
184C22×C8—731no—
185C4⋊Q8—731no—
186C4⋊Q8—1461no—
187C4⋊Q8C2×D7311yescharacteristic
188#125—731no—
189#125—731no—
190#125—1461no—
191C22⋊Q8—1461no—
192C22⋊Q8—1461no—
193C4×Q8—731no—
194C4×Q8C2×D7311yescharacteristic
195C4×D4—731no—
196C4×D4—731no—
197C4×D4—1461no—
198C4×D4—1461no—
199#117—731no—
200#117—731no—
201#117—1461no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—1461no—
205#107—731no—
206#107—731no—
207#106—731no—
208#106—731no—
209#106—731no—
210#106—731no—
211#106C2×D7311yescharacteristic
212#106C2×D7311yescharacteristic
213C4⋊C8—731no—
214C4⋊C8—731no—
215C4⋊C8—731no—
216C4⋊C8C2×D7311yescharacteristic
217#103—731no—
218#103—731no—
219#103C2×D7311yescharacteristic
220#103C2×D7311yescharacteristic
221#102—731no—
222#102—731no—
223#102—731no—
224#102—731no—
225#41—734no—
226#41—1462no—
227C2×Q8—21no—
228C2×Q8—1461no—
229C2×Q8C22×D7311yescharacteristic
230C2×D4—731no—
231C2×D4—1461no—
232C22×C4—731no—
233C22×C4—1461no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4—1461no—
238M16—1462no—
239C2×C8—731no—
240C2×C8—731no—
241C2×C8—1462no—
242C2×C8C22×D7311yescharacteristic
243C2×C8C22×D7311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—731no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4C22×D7311yescharacteristic
260C4⋊C4C22×D7311yescharacteristic
261C4⋊C4C22×D7311yescharacteristic
262C22⋊C4—731no—
263C22⋊C4—731no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C42—21no—
268C42—731no—
269C42—1461no—
270C42—1461no—
271C42C22×D7311yescharacteristic
272C23—731no—
273C23—1461no—
274Q8—21no—
275Q8—81no—
276Q8—5841no—
277Q8Q8×D7312yes—
278D4—732no—
279D4—1464no—
280D4—1461no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4—5841no—
288C2×C4—5841no—
289C2×C4—731no—
290C2×C4—732no—
291C2×C4—732no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—1464no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4D4×D7311yescharacteristic
299C2×C4D4×D7311yescharacteristic
300C2×C4C23×D7311yescharacteristic
301C8—21no—
302C8—21no—
303C8—1461no—
304C8—1461no—
305C22—2921no—
306C22—2921no—
307C22—732no—
308C22—1462no—
309C22—1461no—
310C22—1461no—
311C22C2×D4×D7311yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2921no—
319C4—2921no—
320C4—2921no—
321C4—732no—
322C4—1461no—
323C4—1461no—
324C4C2×Q8×D7311yescharacteristic
325C4#41×D7311yescharacteristic
326C2—2922no—
327C2—1462no—
328C2C22⋊Q8×D7311yescharacteristic
329C2#1798939311yescharacteristic
330C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#475×C73C2
socleC22×C73C22×D4
hypercenter#475D73
hypocenterC73#3084
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #17989214C2semidirect
3. #17988896C2semidirect
4. #17988894C2semidirect
5. #17988888C2semidirect
6. #17988886C2semidirect
7. #17988876C2semidirect
8. #17988874C2semidirect
9. #17988870C2semidirect
10. #17988626C2semidirect
11. #106×D73C2semidirect
12. #17988612C2semidirect
15. #475×C73C2semidirect
60. #11924029Q8semidirect
166. C73#3084semidirect
176. #475D73semidirect