Finite Group Databasebeta

← #49168604

Subgroups — #49168604

Order 37504.

384 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#125×D293C211yesmaximal, characteristic, complemented
2C4×#17989803C211yesmaximal, characteristic
3#34036438C211yesmaximal, characteristic, complemented
4#34036436C211yesmaximal, characteristic, complemented
5#34036434C211yesmaximal, characteristic, complemented
6#34036432C211yesmaximal, characteristic, complemented
7#34036430C211yesmaximal, characteristic, complemented
8#34036428C211yesmaximal, characteristic, complemented
9#34036426C211yesmaximal, characteristic, complemented
10#34036170C211yesmaximal, characteristic, complemented
11#34036168C211yesmaximal, characteristic, complemented
12#34036151C211yesmaximal, characteristic, complemented
13#34036129C211yesmaximal, characteristic
14#34036129C211yesmaximal, characteristic
15#479×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19#22627616C2211yescharacteristic
20#22627615C2211yescharacteristic
21#22627615C2211yescharacteristic
22#22627614—21no—
23#22627614—21no—
24Q8×Dic293C2211yescharacteristic
25C4×D1172—21no—
26C4×D1172C2211yescharacteristic
27#22627586—21no—
28#22627586C2211yescharacteristic
29#22627582—21no—
30#22627582C2211yescharacteristic
31C4⋊C4×D293—21no—
32C4⋊C4×D293—21no—
33C4⋊C4×D293C2211yescharacteristic
34C4⋊C4×D293C2211yescharacteristic
35C42×D293—21no—
36C42×D293C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627556C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627555C2211yescharacteristic
43C4⋊#14556873C2211yescharacteristic
44#22627553C2211yescharacteristic
45#22627553C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627548C2211yescharacteristic
48#22627546C2211yescharacteristic
49#22627546C2211yescharacteristic
50#22627544C2211yescharacteristic
51#22627544C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59#17989803—22no—
60#17989803Q814yes—
61C2×D1172—21no—
62C2×D1172C2311yescharacteristic
63C2×C4×D293—21no—
64C2×C4×D293—21no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293—21no—
68C2×C4×D293D411yescharacteristic
69C2×C4×D293D411yescharacteristic
70C2×C4×D293C2311yescharacteristic
71#17989785—22no—
72#17989785—22no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293D411yescharacteristic
93C4×Dic293D411yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293C2311yescharacteristic
96C2×C8×C293C2311yescharacteristic
97C2×C8×C293C2311yescharacteristic
98C4⋊C4×C293—21no—
99C4⋊C4×C293—21no—
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C42×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293—21no—
107C22×D293C2×D411yescharacteristic
108D1172—24no—
109D1172—21no—
110D1172C2×Q812yes—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293C2×D411yescharacteristic
115C2×Dic293C2×D411yescharacteristic
116C2×Dic293C2×D411yescharacteristic
117C4×D293—24no—
118C4×D293—41no—
119C4×D293—41no—
120C4×D293—42no—
121C4×D293—42no—
122C4×D293—42no—
123C4×D293—42no—
124C4×D293C2×Q812yes—
125C4×D293#4112yes—
126#14556873—21no—
127#14556873—21no—
128Q8×C293—21no—
129Q8×C293C2×Q812yes—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2×D411yescharacteristic
136C2×C4×C293C2411yescharacteristic
137C8×C293—21no—
138C8×C293—21no—
139C22×C293C22×D411yescharacteristic
140C2×D293—21no—
141C2×D293—21no—
142C2×D293—22no—
143C2×D293—41no—
144C2×D293—41no—
145C2×D293C22⋊Q812yes—
146C4×C293—22no—
147C4×C293—21no—
148C4×C293—21no—
149C4×C293—41no—
150C4×C293—41no—
151C4×C293—41no—
152C4×C293C22×Q811yescharacteristic
153C4×C293C2×#4111yescharacteristic
154Dic293—21no—
155Dic293—21no—
156Dic293—41no—
157Dic293—41no—
158Dic293—41no—
159Dic293C22⋊Q812yes—
160C2×C293C2×C22⋊Q811yescharacteristic
161C2×C293#57511yescharacteristic
162C2×C293#57511yescharacteristic
163D293—22no—
164D293—42no—
165C293#308011yescharacteristic, complemented, Sylow
166#3080—2931nomaximal, Sylow
167C2×#125—2931no—
168C4×#41—2931no—
169#479—2931no—
170#479—2931no—
171#479—2931no—
172#479D29311yescharacteristic, complemented
173#478—2931no—
174#478—2931no—
175#478—2931no—
176#478—2931no—
177#428—2931no—
178#428—2931no—
179#423—2931no—
180#417—2931no—
181#417—2931no—
182C2×#41—2931no—
183C2×M16—2931no—
184C2×M16—2931no—
185#125—2931no—
186#125—2931no—
187#125—2931no—
188#125—5861no—
189#125—5861no—
190#125C2×D29311yescharacteristic
191C4×Q8—2931no—
192C4×Q8C2×D29311yescharacteristic
193C4×D4—2931no—
194C4×D4—2931no—
195C4×D4—5861no—
196C4×D4—5861no—
197#117—2931no—
198#117—5861no—
199C2×C4⋊C4—2931no—
200C2×C4⋊C4—2931no—
201C2×C4⋊C4—5861no—
202C2×C4⋊C4—5861no—
203C2×C42—2931no—
204C2×C42—5861no—
205#107—2931no—
206#107—2931no—
207#107—2931no—
208#107C2×D29311yescharacteristic
209#106—2931no—
210#106—2931no—
211#106—2931no—
212#106C2×D29311yescharacteristic
213C4⋊C8—2931no—
214C4⋊C8—2931no—
215C4⋊C8—2931no—
216C4⋊C8C2×D29311yescharacteristic
217#103—2931no—
218#103—2931no—
219#103C2×D29311yescharacteristic
220#103C2×D29311yescharacteristic
221#102—2931no—
222#102—2931no—
223#102—2931no—
224#102—2931no—
225#41—2934no—
226#41—5862no—
227C2×Q8C22×D29311yescharacteristic
228C2×D4—2931no—
229C2×D4—5861no—
230C22×C4—2931no—
231C22×C4—2931no—
232C22×C4—2931no—
233C22×C4—5861no—
234C22×C4—5861no—
235C22×C4—5861no—
236C22×C4—5861no—
237C22×C4—5861no—
238M16—5862no—
239M16—5862no—
240C2×C8—2931no—
241C2×C8—2931no—
242C2×C8C22×D29311yescharacteristic
243C2×C8C22×D29311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—2931no—
248C4⋊C4—2931no—
249C4⋊C4—2931no—
250C4⋊C4—5861no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4C22×D29311yescharacteristic
260C4⋊C4C22×D29311yescharacteristic
261C4⋊C4C22×D29311yescharacteristic
262C22⋊C4—5861no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C42—21no—
266C42—2931no—
267C42—2931no—
268C42—2931no—
269C42—5861no—
270C42—5861no—
271C42C22×D29311yescharacteristic
272C23—2931no—
273C23—5861no—
274Q8—21no—
275Q8Q8×D29312yes—
276D4—2932no—
277D4—5864no—
278D4—5861no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—2931no—
284C2×C4—2932no—
285C2×C4—2932no—
286C2×C4—2931no—
287C2×C4—2931no—
288C2×C4—5864no—
289C2×C4—5861no—
290C2×C4—5861no—
291C2×C4—5861no—
292C2×C4—11721no—
293C2×C4—11721no—
294C2×C4—11722no—
295C2×C4—11722no—
296C2×C4—11722no—
297C2×C4—11722no—
298C2×C4D4×D29311yescharacteristic
299C2×C4D4×D29311yescharacteristic
300C2×C4C23×D29311yescharacteristic
301C8—21no—
302C8—21no—
303C8—5861no—
304C8—5861no—
305C22—2932no—
306C22—5861no—
307C22—5861no—
308C22—5862no—
309C22—11721no—
310C22—11721no—
311C22C2×D4×D29311yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2932no—
319C4—5861no—
320C4—5861no—
321C4—11721no—
322C4—11721no—
323C4—11721no—
324C4C2×Q8×D29311yescharacteristic
325C4#41×D29311yescharacteristic
326C2—5862no—
327C2—11722no—
328C2C22⋊Q8×D29311yescharacteristic
329C2#3403692611yescharacteristic
330C2#3403692811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#479×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989803C22
hypercenter#479D293
hypocenterC293#3080
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #125×D293C2semidirect
3. #34036438C2semidirect
4. #34036436C2semidirect
5. #34036434C2semidirect
6. #34036432C2semidirect
7. #34036430C2semidirect
8. #34036428C2semidirect
9. #34036426C2semidirect
10. #34036170C2semidirect
11. #34036168C2semidirect
12. #34036151C2semidirect
15. #479×C293C2semidirect
165. C293#3080semidirect
172. #479D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#125×D2932
C4×#179898032
#340364382
#340364362
#340364342
#340364322
#340364302
#340364282
#340364262
#340361702
#340361682
#340361512
#340361292
#479×C2932
#3080293