Finite Group Databasebeta

← #49168602

Subgroups — #49168602

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×#17989801C211yesmaximal, characteristic
3#34036439C211yesmaximal, characteristic, complemented
4#34036437C211yesmaximal, characteristic, complemented
5#34036435C211yesmaximal, characteristic, complemented
6#34036433C211yesmaximal, characteristic, complemented
7#34036431C211yesmaximal, characteristic, complemented
8#34036429C211yesmaximal, characteristic, complemented
9#34036427C211yesmaximal, characteristic, complemented
10#34036170C211yesmaximal, characteristic, complemented
11#34036168C211yesmaximal, characteristic, complemented
12#34036151C211yesmaximal, characteristic, complemented
13#34036127C211yesmaximal, characteristic
14#34036127C211yesmaximal, characteristic
15#478×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989785C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19#22627616C2211yescharacteristic
20#22627615C2211yescharacteristic
21#22627615C2211yescharacteristic
22#22627614—21no—
23#22627614—21no—
24C4×Dic586C2211yescharacteristic
25#22627589C2211yescharacteristic
26D4×Dic293C2211yescharacteristic
27C4×C22⋊D293—21no—
28#22627584—21no—
29#22627582C2211yescharacteristic
30#22627580—21no—
31C4⋊C4×D293—21no—
32C4⋊C4×D293—21no—
33C4⋊C4×D293C2211yescharacteristic
34C4⋊C4×D293C2211yescharacteristic
35C2×C4×Dic293—21no—
36C42×D293C2211yescharacteristic
37#22627558C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627556C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627555C2211yescharacteristic
43C4⋊#14556873C2211yescharacteristic
44#22627553C2211yescharacteristic
45#22627553C2211yescharacteristic
46#22627549C2211yescharacteristic
47#22627549C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627547C2211yescharacteristic
50#22627545C2211yescharacteristic
51#22627545C2211yescharacteristic
52#125×C293C2211yescharacteristic
53C4×D4×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—22no—
60#17989801Q814yes—
61C2×Dic586C2311yescharacteristic
62C2×C22⋊D293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65C2×C4×D293—21no—
66C2×C4×D293—21no—
67C2×C4×D293D411yescharacteristic
68C2×C4×D293D411yescharacteristic
69C2×C4×D293C2311yescharacteristic
70#17989785—22no—
71#17989785—22no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C4⋊Dic293—21no—
75C4⋊Dic293—21no—
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87C22⋊Dic293—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293D411yescharacteristic
93C4×Dic293D411yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×D4×C293C2311yescharacteristic
96C22×C4×C293—21no—
97C2×C8×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C4⋊C4×C293—21no—
100C4⋊C4×C293—21no—
101C4⋊C4×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C22⋊C4×C293—21no—
105C42×C293C2311yescharacteristic
106C22×D293C2×D411yescharacteristic
107Dic586—21no—
108Dic586C2×Q812yes—
109C22⋊D293—24no—
110C2×Dic293—21no—
111C2×Dic293—24no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—42no—
116C2×Dic293C2×D411yescharacteristic
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C4×D293—41no—
120C4×D293—41no—
121C4×D293—42no—
122C4×D293—42no—
123C4×D293C2×Q812yes—
124C4×D293#4112yes—
125#14556873—21no—
126#14556873—21no—
127C23×C293—21no—
128D4×C293—21no—
129D4×C293C2×Q812yes—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—42no—
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2×D411yescharacteristic
136C2×C4×C293C2411yescharacteristic
137C8×C293—21no—
138C8×C293—21no—
139C22×C293—22no—
140C22×C293—41no—
141C22×C293—41no—
142C22×C293C22×D411yescharacteristic
143C2×D293—21no—
144C2×D293—21no—
145C2×D293C22⋊Q812yes—
146C4×C293—21no—
147C4×C293—21no—
148C4×C293—41no—
149C4×C293—41no—
150C4×C293—41no—
151C4×C293C22×Q811yescharacteristic
152C4×C293C2×#4111yescharacteristic
153Dic293—22no—
154Dic293—21no—
155Dic293—21no—
156Dic293—41no—
157Dic293—41no—
158Dic293—41no—
159Dic293C22⋊Q812yes—
160C2×C293—42no—
161C2×C293C2×C22⋊Q811yescharacteristic
162C2×C293#57511yescharacteristic
163C2×C293#57511yescharacteristic
164D293—22no—
165C293#308011yescharacteristic, complemented, Sylow
166#3080—2931nomaximal, Sylow
167C2×#125—2931no—
168C4×#41—2931no—
169#479—2931no—
170#479—2931no—
171#479—2931no—
172#479—2931no—
173#478—2931no—
174#478—2931no—
175#478—2931no—
176#478D29311yescharacteristic, complemented
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×Q8—2931no—
193C4×D4—2931no—
194C4×D4—5861no—
195C4×D4—5861no—
196C4×D4C2×D29311yescharacteristic
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#103—2931no—
220#103—2931no—
221#102—2931no—
222#102—2931no—
223#102C2×D29311yescharacteristic
224#102C2×D29311yescharacteristic
225#41—2934no—
226#41—5862no—
227C2×Q8—2931no—
228C2×D4—5861no—
229C2×D4C22×D29311yescharacteristic
230C22×C4—21no—
231C22×C4—2931no—
232C22×C4—2931no—
233C22×C4—2931no—
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—2931no—
247C4⋊C4—2931no—
248C4⋊C4—2931no—
249C4⋊C4—5861no—
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—21no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C42—2931no—
266C42—2931no—
267C42—2931no—
268C42—5861no—
269C42—5861no—
270C42—5861no—
271C42C22×D29311yescharacteristic
272C23—21no—
273C23—2931no—
274Q8—2932no—
275Q8—5861no—
276D4—21no—
277D4—5864no—
278D4Q8×D29312yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
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—5861no—
293C2×C4—11721no—
294C2×C4—11721no—
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—22no—
306C22—41no—
307C22—41no—
308C22—2932no—
309C22—5861no—
310C22—5861no—
311C22C2×D4×D29311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—2932no—
318C4—5862no—
319C4—5861no—
320C4—5861no—
321C4—11721no—
322C4—11721no—
323C4—11721no—
324C4C2×Q8×D29311yescharacteristic
325C4#41×D29311yescharacteristic
326C2—42no—
327C2—5862no—
328C2C22⋊Q8×D29311yescharacteristic
329C2#3403692511yescharacteristic
330C2#3403692611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#478×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989801C22
hypercenter#478D293
hypocenterC293#3080
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×D293C2semidirect
3. #34036439C2semidirect
4. #34036437C2semidirect
5. #34036435C2semidirect
6. #34036433C2semidirect
7. #34036431C2semidirect
8. #34036429C2semidirect
9. #34036427C2semidirect
10. #34036170C2semidirect
11. #34036168C2semidirect
12. #34036151C2semidirect
15. #478×C293C2semidirect
165. C293#3080semidirect
176. #478D293semidirect

Maximal subgroups

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

subgroupindex
#125×D2932
C4×#179898012
#340364392
#340364372
#340364352
#340364332
#340364312
#340364292
#340364272
#340361702
#340361682
#340361512
#340361272
#478×C2932
#3080293