Finite Group Databasebeta

← #49171548

Subgroups — #49171548

Order 37504.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036865C211yesmaximal, characteristic
2#34036856C211yesmaximal, characteristic, complemented
3#34036487C211yesmaximal, characteristic, complemented
4#34036482C211yesmaximal, characteristic, complemented
5#34036433C211yesmaximal, characteristic, complemented
6#34036431C211yesmaximal, characteristic, complemented
7#34036417C211yesmaximal, characteristic, complemented
8#34036350C211yesmaximal, characteristic, complemented
9#34036350C211yesmaximal, characteristic, complemented
10#34036326C211yesmaximal, characteristic
11#34036257C211yesmaximal, characteristic, complemented
12#34036237C211yesmaximal, characteristic, complemented
13#34036226C211yesmaximal, characteristic, complemented
14#34036220C211yesmaximal, characteristic, complemented
15#490×C293C211yesmaximal, characteristic
16C2×Dic1172C2211yescharacteristic
17C2×#17989790C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19#22627623—21no—
20#22627623C2211yescharacteristic
21#22627615C2211yescharacteristic
22#22627614—21no—
23#22627614—21no—
24#22627611—21no—
25#22627611C2211yescharacteristic
26#22627611C2211yescharacteristic
27#22627605—21no—
28#22627605—21no—
29C4×Dic586C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31C4×Dic586C2211yescharacteristic
32#22627589—21no—
33#22627589C2211yescharacteristic
34#22627589C2211yescharacteristic
35D4×Dic293—21no—
36D4×Dic293C2211yescharacteristic
37D4×Dic293C2211yescharacteristic
38#22627557C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41C4⋊#14556873C2211yescharacteristic
42#22627553C2211yescharacteristic
43#22627553C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627547C2211yescharacteristic
47#22627547C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic
50#22627534C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52#127×C293C2211yescharacteristic
53#125×C293C2211yescharacteristic
54#102×C293C2211yescharacteristic
55#102×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#97×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×Dic586C2311yescharacteristic
63C22×Dic293—21no—
64C22×Dic293—21no—
65Dic1172—22no—
66#17989790—22no—
67#17989790—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293D411yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73C4⋊Dic293C2311yescharacteristic
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781D411yescharacteristic
81#17989781D411yescharacteristic
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293—21no—
92C4×Dic293C2311yescharacteristic
93C4×Dic293C2311yescharacteristic
94C2×D4×C293—21no—
95C2×D4×C293—21no—
96C2×D4×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293—21no—
101C4⋊C4×C293—21no—
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C42×C293C2311yescharacteristic
105Dic586—21no—
106Dic586—21no—
107Dic586—21no—
108Dic586—41no—
109Dic586—42no—
110Dic586#4112yes—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—81no—
116C2×Dic293—81no—
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121#14556873—21no—
122#14556873—21no—
123C23×C293—21no—
124C23×C293—21no—
125D4×C293—21no—
126D4×C293—21no—
127D4×C293—21no—
128D4×C293—21no—
129D4×C293—42no—
130D4×C293—81no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293C2×D411yescharacteristic
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2411yescharacteristic
136C8×C293—21no—
137C8×C293—21no—
138C22×C293—41no—
139C22×C293—41no—
140C22×C293—41no—
141C22×C293—41no—
142C22×C293—41no—
143C22×C293—41no—
144C22×C293C22×D411yescharacteristic
145C4×C293—21no—
146C4×C293—21no—
147C4×C293—41no—
148C4×C293—41no—
149C4×C293C2×#4111yescharacteristic
150C4×C2932−1+411yescharacteristic
151Dic293—22no—
152Dic293—21no—
153Dic293—21no—
154Dic293—21no—
155Dic293—21no—
156Dic293—41no—
157Dic293—41no—
158Dic293—41no—
159C2×C293—81no—
160C2×C293—81no—
161C2×C293#54811yescharacteristic
162C2×C293#57511yescharacteristic
163C2×C293#57711yescharacteristic
164C293#337111yescharacteristic, complemented, Sylow
165#3371—2931nomaximal, Sylow
166#559—2931no—
167#557—2931no—
168#490D29311yescharacteristic
169#489—2931no—
170#488—2931no—
171#479—2931no—
172#478—2931no—
173#476—2931no—
174#464—2931no—
175#464—2931no—
176#460—2931no—
177#446—2931no—
178#441—2931no—
179#440—2931no—
180C4×SD16—2931no—
181C2×Q16—2931no—
182C2×SD16—2931no—
183C2×SD16—2931no—
184C4⋊Q8—2931no—
185C4⋊Q8—5861no—
186#127C2×D29311yescharacteristic
187#125—2931no—
188#125—5861no—
189#125—5861no—
190#125C2×D29311yescharacteristic
191#124—2931no—
192#124—2931no—
193#124—5861no—
194#123—5861no—
195#123—5861no—
196C4×Q8—2931no—
197C4×Q8—2931no—
198C4×Q8—2931no—
199C4×Q8—2931no—
200C4×Q8—2931no—
201C4×Q8—5861no—
202C4×D4—2931no—
203C4×D4—2931no—
204C4×D4—5861no—
205#107—2931no—
206#106—2931no—
207#106—2931no—
208C4⋊C8—2931no—
209C4⋊C8—2931no—
210C4⋊C8—2931no—
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103—2931no—
215#102—2931no—
216#102—2931no—
217#102C2×D29311yescharacteristic
218#102C2×D29311yescharacteristic
219#102C2×D29311yescharacteristic
220#102C2×D29311yescharacteristic
221#97—2931no—
222#97C2×D29311yescharacteristic
223C4×C8—2931no—
224C2×Q8—2931no—
225C2×Q8—2931no—
226C2×Q8—2931no—
227C2×Q8—5861no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D29311yescharacteristic
231C2×D4C22×D29311yescharacteristic
232C22×C4—5861no—
233C22×C4—5861no—
234Q16—5862no—
235SD16—5862no—
236SD16—5862no—
237C2×C8—2931no—
238C2×C8—2931no—
239C2×C8C22×D29311yescharacteristic
240C2×C8C22×D29311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—2931no—
244C4⋊C4—2931no—
245C4⋊C4—2931no—
246C4⋊C4—2931no—
247C4⋊C4—2931no—
248C4⋊C4—5861no—
249C4⋊C4—5861no—
250C4⋊C4—5861no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4C22×D29311yescharacteristic
256C4⋊C4C22×D29311yescharacteristic
257C22⋊C4—5861no—
258C22⋊C4—5861no—
259C22⋊C4—5861no—
260C22⋊C4—5861no—
261C22⋊C4—5861no—
262C22⋊C4—5861no—
263C42—2931no—
264C42—2931no—
265C42—5861no—
266C42—5861no—
267C42—5861no—
268C42—5861no—
269C42C22×D29311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—2932no—
273Q8—5861no—
274Q8—5861no—
275Q8—5861no—
276Q8—11721no—
277Q8—11722no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—2931no—
287C2×C4—2931no—
288C2×C4—2931no—
289C2×C4—2931no—
290C2×C4—23441no—
291C2×C4—23441no—
292C2×C4—5861no—
293C2×C4—5861no—
294C2×C4—5861no—
295C2×C4—5861no—
296C2×C4D4×D29311yescharacteristic
297C2×C4D4×D29311yescharacteristic
298C2×C4C23×D29311yescharacteristic
299C8—21no—
300C8—21no—
301C8—5861no—
302C8—5861no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D29311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—5862no—
315C4—5861no—
316C4—5861no—
317C4—5861no—
318C4—5861no—
319C4—11721no—
320C4—11721no—
321C4—11721no—
322C4#41×D29311yescharacteristic
323C4#2262767111yescharacteristic
324C2—81no—
325C2—81no—
326C2#3403678711yescharacteristic
327C2#3403692511yescharacteristic
328C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#490×C293C2
socleC22×C293C22×D4
prime radical#127×C293C22
hypercenter#490D293
hypocenterC293#3371
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #34036856C2semidirect
3. #34036487C2semidirect
4. #34036482C2semidirect
5. #34036433C2semidirect
6. #34036431C2semidirect
7. #34036417C2semidirect
8. #34036350C2semidirect
9. #34036350C2semidirect
11. #34036257C2semidirect
12. #34036237C2semidirect
13. #34036226C2semidirect
14. #34036220C2semidirect
164. C293#3371semidirect

Maximal subgroups

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

subgroupindex
#340368652
#340368562
#340364872
#340364822
#340364332
#340364312
#340364172
#340363502
#340363262
#340362572
#340362372
#340362262
#340362202
#490×C2932
#3371293