Finite Group Databasebeta

← #49171429

Subgroups — #49171429

Order 37504.

350 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#34036848C211yesmaximal, characteristic, complemented
2#34036838C211yesmaximal, characteristic, complemented
3#34036483C211yesmaximal, characteristic, complemented
4#34036482C211yesmaximal, characteristic, complemented
5#34036478C211yesmaximal, characteristic, complemented
6#34036438C211yesmaximal, characteristic, complemented
7#34036437C211yesmaximal, characteristic, complemented
8#34036417C211yesmaximal, characteristic, complemented
9#34036342C211yesmaximal, characteristic
10#34036332C211yesmaximal, characteristic, complemented
11#34036253C211yesmaximal, characteristic, complemented
12SD16×Dic293C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14D8×Dic293C211yesmaximal, characteristic
15#463×C293C211yesmaximal, characteristic
16C2×#17989790C2211yescharacteristic
17#22627623C2211yescharacteristic
18#22627622C2211yescharacteristic
19#22627617—21no—
20#22627617—21no—
21#22627616C2211yescharacteristic
22#22627615C2211yescharacteristic
23#22627611C2211yescharacteristic
24#22627603—21no—
25#22627601—21no—
26#22627601—21no—
27#22627601—21no—
28Q8×Dic293C2211yescharacteristic
29C4×Dic586C2211yescharacteristic
30C4×Dic586C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32D4×Dic293C2211yescharacteristic
33D4×Dic293C2211yescharacteristic
34#22627580—21no—
35C2×#17989781—21no—
36#22627558C2211yescharacteristic
37#22627556C2211yescharacteristic
38#22627555C2211yescharacteristic
39#22627553C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627549C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C4×#14556873C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54#124×C293C2211yescharacteristic
55C4×D4×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C22×Dic293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65#17989790—22no—
66C2×#14556873C2311yescharacteristic
67C2×#14556873C2311yescharacteristic
68C4⋊Dic293—21no—
69C4⋊Dic293—21no—
70C4⋊Dic293D411yescharacteristic
71C4⋊Dic293C2311yescharacteristic
72C4⋊Dic293C2311yescharacteristic
73C4⋊Dic293C2311yescharacteristic
74#17989781—21no—
75#17989781—21no—
76#17989781—21no—
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81#17989781D411yescharacteristic
82#17989781D411yescharacteristic
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293C2311yescharacteristic
91C4×Dic293C2311yescharacteristic
92C2×Q8×C293C2311yescharacteristic
93C2×D4×C293C2311yescharacteristic
94C2×D4×C293C2311yescharacteristic
95C22×C4×C293—21no—
96SD16×C293—22no—
97D8×C293—22no—
98C2×C8×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C4⋊C4×C293C2311yescharacteristic
101C22⋊C4×C293—21no—
102C22⋊C4×C293—21no—
103C22⋊C4×C293—21no—
104C42×C293C2311yescharacteristic
105Dic586—22no—
106Dic586—21no—
107Dic586—21no—
108Dic586—81no—
109C2×Dic293—21no—
110C2×Dic293—21no—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—42no—
114C2×Dic293—42no—
115C2×Dic293—81no—
116C2×Dic293C2×D411yescharacteristic
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120#14556873—21no—
121#14556873—21no—
122C23×C293—21no—
123C23×C293—21no—
124Q8×C293—21no—
125Q8×C293—21no—
126D4×C293—21no—
127D4×C293—21no—
128D4×C293—21no—
129D4×C293#4112yes—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—81no—
133C2×C4×C293C2×D411yescharacteristic
134C2×C4×C293C2×D411yescharacteristic
135C2×C4×C293C2411yescharacteristic
136C8×C293—21no—
137C8×C293—21no—
138C22×C293—22no—
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—21no—
152Dic293—21no—
153Dic293—21no—
154Dic293—41no—
155Dic293—41no—
156Dic293—41no—
157Dic293—41no—
158Dic293#13512yes—
159C2×C293—42no—
160C2×C293—81no—
161C2×C293#54811yescharacteristic
162C2×C293C2×#13511yescharacteristic
163C2×C293#57711yescharacteristic
164C293#336011yescharacteristic, complemented, Sylow
165#3360—2931nomaximal, Sylow
166#556—2931no—
167#554—2931no—
168#488—2931no—
169#488—2931no—
170#487—2931no—
171#479—2931no—
172#479—2931no—
173#476—2931no—
174#463—2931no—
175#463D29311yescharacteristic
176#461—2931no—
177C8×Q8—2931no—
178C4×SD16—2931no—
179C4×SD16—2931no—
180C4×D8—2931no—
181C2×SD16—2931no—
182C2×SD16C2×D29311yescharacteristic
183C2×D8C2×D29311yescharacteristic
184C4⋊Q8—2931no—
185C4⋊Q8—2931no—
186#126—5861no—
187#126—5861no—
188#125—2931no—
189#125—2931no—
190#124—2931no—
191#124C2×D29311yescharacteristic
192C22⋊Q8—5861no—
193C22⋊Q8—5861no—
194C22⋊Q8—5861no—
195C22⋊Q8—5861no—
196C4×Q8—2931no—
197C4×Q8—2931no—
198C4×Q8—2931no—
199C4×D4—2931no—
200C4×D4—2931no—
201C4×D4—2931no—
202C4×D4C2×D29311yescharacteristic
203#117—5861no—
204C2×C4⋊C4—5861no—
205#107—2931no—
206#106—2931no—
207#106—2931no—
208C4⋊C8—2931no—
209C4⋊C8—2931no—
210C4⋊C8C2×D29311yescharacteristic
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103—2931no—
215#103—2931no—
216#103C2×D29311yescharacteristic
217#102—2931no—
218#102—2931no—
219#102—2931no—
220#102C2×D29311yescharacteristic
221C4×C8—2931no—
222C4×C8—2931no—
223C4×C8—2931no—
224C2×Q8—2931no—
225C2×Q8—2931no—
226C2×Q8—5861no—
227C2×Q8C22×D29311yescharacteristic
228C2×D4C22×D29311yescharacteristic
229C2×D4C22×D29311yescharacteristic
230C22×C4—21no—
231C22×C4—5861no—
232C22×C4—5861no—
233C22×C4—5861no—
234SD16—22no—
235SD16—5862no—
236D8—22no—
237C2×C8—2931no—
238C2×C8—2931no—
239C2×C8C22×D29311yescharacteristic
240C2×C8C22×D29311yescharacteristic
241C4⋊C4—2931no—
242C4⋊C4—2931no—
243C4⋊C4—2931no—
244C4⋊C4—2931no—
245C4⋊C4—2931no—
246C4⋊C4—2931no—
247C4⋊C4—5861no—
248C4⋊C4—5861no—
249C4⋊C4—5861no—
250C4⋊C4—5861no—
251C4⋊C4—5861no—
252C4⋊C4—5861no—
253C4⋊C4—5861no—
254C4⋊C4—5861no—
255C4⋊C4—5861no—
256C4⋊C4C22×D29311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—5861no—
261C22⋊C4—5861no—
262C22⋊C4—5861no—
263C22⋊C4—5861no—
264C22⋊C4—5861no—
265C42—2931no—
266C42—2931no—
267C42—5861no—
268C42—5861no—
269C42C22×D29311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—23441no—
275Q8—5862no—
276Q8—5861no—
277Q8—5861no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#1798980112yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—2931no—
286C2×C4—2931no—
287C2×C4—2931no—
288C2×C4—2931no—
289C2×C4—23441no—
290C2×C4—5861no—
291C2×C4—5861no—
292C2×C4—5861no—
293C2×C4—5861no—
294C2×C4—11722no—
295C2×C4—11722no—
296C2×C4D4×D29311yescharacteristic
297C2×C4D4×D29311yescharacteristic
298C2×C4C23×D29311yescharacteristic
299C8—21no—
300C8—21no—
301C8—5861no—
302C8—5861no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D29311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—2932no—
315C4—5861no—
316C4—5861no—
317C4—5861no—
318C4—11721no—
319C4—11721no—
320C4—11721no—
321C4—11721no—
322C4C2×#1798980111yescharacteristic
323C4#2262767111yescharacteristic
324C2—42no—
325C2—81no—
326C2#3403678511yescharacteristic
327C2#135×D29311yescharacteristic
328C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#463×C293C2
socleC22×C293C22×D4
prime radicalC2×D8×C293C22
hypercenter#463D293
hypocenterC293#3360
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #34036848C2semidirect
2. #34036838C2semidirect
3. #34036483C2semidirect
4. #34036482C2semidirect
5. #34036478C2semidirect
6. #34036438C2semidirect
7. #34036437C2semidirect
8. #34036417C2semidirect
10. #34036332C2semidirect
11. #34036253C2semidirect
12. SD16×Dic293C2semidirect
13. C4×#17989790C2semidirect
164. C293#3360semidirect

Maximal subgroups

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

subgroupindex
#340368482
#340368382
#340364832
#340364822
#340364782
#340364382
#340364372
#340364172
#340363422
#340363322
#340362532
SD16×Dic2932
C4×#179897902
D8×Dic2932
#463×C2932
#3360293