Finite Group Databasebeta

← #49170678

Subgroups — #49170678

Order 37504.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036821C211yesmaximal, characteristic, complemented
2#34036785C211yesmaximal, characteristic
3#34036482C211yesmaximal, characteristic, complemented
4#34036473C211yesmaximal, characteristic, complemented
5#34036440C211yesmaximal, characteristic, complemented
6#34036439C211yesmaximal, characteristic, complemented
7#34036369C211yesmaximal, characteristic, complemented
8#34036349C211yesmaximal, characteristic, complemented
9#34036288C211yesmaximal, characteristic, complemented
10#34036284C211yesmaximal, characteristic, complemented
11#34036221C211yesmaximal, characteristic, complemented
12C8×C22⋊D293C211yesmaximal, characteristic, complemented
13#34036122C211yesmaximal, characteristic, complemented
14C2×#22627549C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C22×Dic586C2211yescharacteristic
18C2×#17989792C2211yescharacteristic
19C2×#17989792C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627619—21no—
22#22627615—21no—
23#22627615C2211yescharacteristic
24#22627611C2211yescharacteristic
25#22627610—21no—
26#22627608—21no—
27#22627604C2211yescharacteristic
28#22627601—21no—
29#22627600C2211yescharacteristic
30#22627596—21no—
31Q8×Dic293C2211yescharacteristic
32#22627589C2211yescharacteristic
33D4×Dic293—21no—
34C4×C22⋊D293C2211yescharacteristic
35#22627582C2211yescharacteristic
36#22627580—21no—
37C2×C4⋊Dic293C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#106×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586—22no—
62C2×Dic586—21no—
63C2×Dic586—41no—
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66C2×C22⋊D293—21no—
67C2×C22⋊D293D411yescharacteristic
68C22×Dic293—21no—
69C22×Dic293—21no—
70C22×Dic293—21no—
71C2×C4×D293C2311yescharacteristic
72#17989792—22no—
73#17989792—41no—
74C2×#14556873C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C8×D293—41no—
77C4⋊Dic293—21no—
78C4⋊Dic293—21no—
79C4⋊Dic293—21no—
80C4⋊Dic293—21no—
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293D411yescharacteristic
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C4×Dic293C2311yescharacteristic
98C2×Q8×C293C2311yescharacteristic
99C2×D4×C293—21no—
100C2×D4×C293C2311yescharacteristic
101C22×C4×C293C2311yescharacteristic
102SD16×C293—41no—
103C2×C8×C293—41no—
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C4⋊C4×C293—21no—
107C4⋊C4×C293C2311yescharacteristic
108C4⋊C4×C293C2311yescharacteristic
109C22⋊C4×C293—21no—
110C22⋊C4×C293—21no—
111C22×D293C2×D411yescharacteristic
112Dic586—21no—
113Dic586—21no—
114Dic586—21no—
115Dic586—42no—
116Dic586#4112yes—
117C22⋊D293—22no—
118C22⋊D293—42no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—42no—
124C2×Dic293—42no—
125C2×Dic293—42no—
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C2×Dic293C2×D411yescharacteristic
129C4×D293—21no—
130C4×D293—21no—
131#14556873—21no—
132#14556873—21no—
133C23×C293—21no—
134C23×C293C2×D411yescharacteristic
135Q8×C293—21no—
136Q8×C293—21no—
137D4×C293—21no—
138D4×C293—21no—
139D4×C293—42no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2411yescharacteristic
147C8×C293—21no—
148C8×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293#13512yes—
155C22×C293C22×D411yescharacteristic
156C2×D293—21no—
157C2×D293—21no—
158C2×D293—21no—
159C4×C293—21no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293—41no—
163C4×C293C2×#4111yescharacteristic
164C4×C293H(5,𝔽2)11yescharacteristic
165Dic293—21no—
166Dic293—22no—
167Dic293—21no—
168Dic293—21no—
169Dic293—41no—
170Dic293—41no—
171Dic293—41no—
172C2×C293—22no—
173C2×C293—81no—
174C2×C293#54611yescharacteristic
175C2×C293C2×#13511yescharacteristic
176C2×C293#57811yescharacteristic
177D293—41no—
178C293#330011yescharacteristic, complemented, Sylow
179#3300—2931nomaximal, Sylow
180#552—2931no—
181#548—2931no—
182#488—2931no—
183#485—2931no—
184#480—2931no—
185#479—2931no—
186#467—2931no—
187#465D29311yescharacteristic, complemented
188#464—2931no—
189#452—2931no—
190#451—2931no—
191C4×Q16—2931no—
192C8×D4—2931no—
193#416—2931no—
194C2×#103—2931no—
195C2×#41—2931no—
196C22×Q8—2931no—
197C2×Q16—2931no—
198C2×Q16—2931no—
199C2×SD16C2×D29311yescharacteristic
200C22×C8—2931no—
201C22×C8C2×D29311yescharacteristic
202#126—5861no—
203#125—2931no—
204#125—5861no—
205#124—2931no—
206#124—5861no—
207#123—5861no—
208C22⋊Q8—2931no—
209C22⋊Q8—2931no—
210C22⋊Q8—5861no—
211C22⋊Q8C2×D29311yescharacteristic
212#121—5861no—
213#121C2×D29311yescharacteristic
214C4×Q8—2931no—
215C4×Q8—2931no—
216C4×D4—2931no—
217C4×D4—5861no—
218#117—2931no—
219#117—5861no—
220C2×C4⋊C4—2931no—
221#107—2931no—
222#107—2931no—
223#106C2×D29311yescharacteristic
224C4⋊C8—2931no—
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103C2×D29311yescharacteristic
232#102—2931no—
233#102—2931no—
234#102C2×D29311yescharacteristic
235C22⋊C8—2931no—
236C22⋊C8—2931no—
237C4×C8—2931no—
238#41—5862no—
239#41—11721no—
240C2×Q8—2931no—
241C2×Q8—2931no—
242C2×Q8—5862no—
243C2×Q8—5861no—
244C2×Q8—11721no—
245C2×Q8C22×D29311yescharacteristic
246C2×D4—21no—
247C2×D4—2931no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C22×C4—2931no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4C22×D29311yescharacteristic
255Q16—5862no—
256Q16—11721no—
257SD16—41no—
258C2×C8—41no—
259C2×C8—2931no—
260C2×C8—2931no—
261C2×C8—11721no—
262C2×C8C22×D29311yescharacteristic
263C2×C8C22×D29311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2931no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4—5861no—
275C4⋊C4C22×D29311yescharacteristic
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2931no—
280C22⋊C4—2931no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—2931no—
287C42—5861no—
288C42—5861no—
289C42—5861no—
290C23—21no—
291C23—2931no—
292C23D4×D29311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—2932no—
296Q8—5861no—
297Q8—5861no—
298Q8—5861no—
299Q8—11722no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—5862no—
304D4—11722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2931no—
311C2×C4—2931no—
312C2×C4—2931no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—11722no—
320C2×C4—11722no—
321C2×C4—11722no—
322C2×C4D4×D29311yescharacteristic
323C2×C4C23×D29311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5861no—
327C8—5861no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—5861no—
334C22—5861no—
335C22—5861no—
336C22#2262764512yes—
337C22C2×D4×D29311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—5861no—
343C4—5862no—
344C4—5861no—
345C4—5861no—
346C4—11721no—
347C4—11721no—
348C4—11721no—
349C4#41×D29311yescharacteristic
350C4#2262766911yescharacteristic
351C2—22no—
352C2—81no—
353C2—11721no—
354C2#3403676811yescharacteristic
355C2C2×#2262764511yescharacteristic
356C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036785C2
hypercenter#465D293
hypocenterC293#3300
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #34036821C2semidirect
3. #34036482C2semidirect
4. #34036473C2semidirect
5. #34036440C2semidirect
6. #34036439C2semidirect
7. #34036369C2semidirect
8. #34036349C2semidirect
9. #34036288C2semidirect
10. #34036284C2semidirect
11. #34036221C2semidirect
12. C8×C22⋊D293C2semidirect
13. #34036122C2semidirect
14. C2×#22627549C2semidirect
15. #465×C293C2semidirect
178. C293#3300semidirect
187. #465D293semidirect

Maximal subgroups

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

subgroupindex
#340368212
#340367852
#340364822
#340364732
#340364402
#340364392
#340363692
#340363492
#340362882
#340362842
#340362212
C8×C22⋊D2932
#340361222
C2×#226275492
#465×C2932
#3300293