Finite Group Databasebeta

← #49169348

Subgroups — #49169348

Order 37504.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036665C211yesmaximal, characteristic, complemented
2#34036660C211yesmaximal, characteristic, complemented
3#34036529C211yesmaximal, characteristic, complemented
4#34036510C211yesmaximal, characteristic, complemented
5#34036485C211yesmaximal, characteristic, complemented
6#34036482C211yesmaximal, characteristic, complemented
7#34036368C211yesmaximal, characteristic, complemented
8#34036363C211yesmaximal, characteristic
9#34036358C211yesmaximal, characteristic, complemented
10#34036221C211yesmaximal, characteristic, complemented
11SD16×Dic293C211yesmaximal, characteristic, complemented
12#34036216C211yesmaximal, characteristic, complemented
13#34036209C211yesmaximal, characteristic, complemented
14C2×C8×Dic293C211yesmaximal, characteristic, complemented
15#465×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989791C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19C22×#14556873C2211yescharacteristic
20#22627619—21no—
21#22627617—21no—
22#22627615C2211yescharacteristic
23#22627615C2211yescharacteristic
24#22627613C2211yescharacteristic
25#22627611C2211yescharacteristic
26#22627608—21no—
27#22627605—21no—
28#22627603C2211yescharacteristic
29#22627598C2211yescharacteristic
30Q8×Dic293C2211yescharacteristic
31#22627589C2211yescharacteristic
32D4×Dic293—21no—
33D4×Dic293C2211yescharacteristic
34#22627586C2211yescharacteristic
35#22627584—21no—
36#22627582—21no—
37#22627580—21no—
38C2×C4×Dic293C2211yescharacteristic
39#22627557C2211yescharacteristic
40#22627557C2211yescharacteristic
41#22627556C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627544C2211yescharacteristic
48C8×Dic293C2211yescharacteristic
49C8×Dic293C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C22⋊Q8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#106×C293C2211yescharacteristic
57#103×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59C2×Dic586C2311yescharacteristic
60C2×D1172C2311yescharacteristic
61C2×C22⋊D293—21no—
62C22×Dic293—21no—
63C22×Dic293D411yescharacteristic
64C22×Dic293D411yescharacteristic
65C2×C4×D293—21no—
66#17989792—22no—
67#17989791—22no—
68#17989787—22no—
69C2×#14556873—22no—
70C2×#14556873C2311yescharacteristic
71C2×#14556873C2311yescharacteristic
72C4⋊Dic293—21no—
73C4⋊Dic293—21no—
74C4⋊Dic293—21no—
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78#17989781—21no—
79#17989781—21no—
80#17989781—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293D411yescharacteristic
92C4×Dic293D411yescharacteristic
93C4×Dic293C2311yescharacteristic
94C4×Dic293C2311yescharacteristic
95C2×Q8×C293C2311yescharacteristic
96C2×D4×C293—21no—
97C2×D4×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99SD16×C293—22no—
100C2×C8×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293—21no—
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C22×D293—21no—
109Dic586—21no—
110Dic586—21no—
111D1172—21no—
112D1172—21no—
113C22⋊D293—42no—
114C2×Dic293—22no—
115C2×Dic293—22no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—42no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—42no—
125#14556873—21no—
126#14556873#4112yes—
127C23×C293—21no—
128C23×C293C2×D411yescharacteristic
129Q8×C293—21no—
130Q8×C293—21no—
131D4×C293—21no—
132D4×C293—21no—
133D4×C293—42no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293C2×D411yescharacteristic
140C2×C4×C293C2411yescharacteristic
141C8×C293—21no—
142C8×C293#4112yes—
143C22×C293—21no—
144C22×C293—21no—
145C22×C293—41no—
146C22×C293—41no—
147C22×C293—41no—
148C22×C293#13512yes—
149C22×C293C22×D411yescharacteristic
150C2×D293—41no—
151C2×D293—41no—
152C2×D293—41no—
153C4×C293—21no—
154C4×C293—41no—
155C4×C293—41no—
156C4×C293—41no—
157C4×C293C2×#4111yescharacteristic
158C4×C293C2×#4111yescharacteristic
159Dic293—21no—
160Dic293—21no—
161Dic293—21no—
162Dic293—41no—
163Dic293—41no—
164Dic293—41no—
165Dic293#13512yes—
166C2×C293—22no—
167C2×C293—81no—
168C2×C293#53211yescharacteristic
169C2×C293C2×#13511yescharacteristic
170C2×C293C2×#13511yescharacteristic
171D293—81no—
172C293#316811yescharacteristic, complemented, Sylow
173#3168—2931nomaximal, Sylow
174#529—2931no—
175#529—2931no—
176#499—2931no—
177#495—2931no—
178#488—2931no—
179#488—2931no—
180#467—2931no—
181#466—2931no—
182#465—2931no—
183#465D29311yescharacteristic, complemented
184C4×Q16—2931no—
185C4×SD16—2931no—
186C4×SD16—2931no—
187C4×D8—2931no—
188C2×C4×C8—2931no—
189C2×Q16—2931no—
190C2×SD16—2931no—
191C2×SD16C2×D29311yescharacteristic
192C2×D8—2931no—
193C22×C8—2931no—
194C22×C8C2×D29311yescharacteristic
195#126—5861no—
196#126—5861no—
197#125—2931no—
198#125—2931no—
199#124—2931no—
200#124—2931no—
201#123—5861no—
202#123—5861no—
203C22⋊Q8—2931no—
204C22⋊Q8C2×D29311yescharacteristic
205#121—2931no—
206#121C2×D29311yescharacteristic
207C4×Q8—2931no—
208C4×Q8—2931no—
209C4×D4—2931no—
210C4×D4—2931no—
211C4×D4—5861no—
212C4×D4—5861no—
213#117—5861no—
214#117—5861no—
215C2×C42—2931no—
216#107—2931no—
217#107—2931no—
218#106—2931no—
219#106C2×D29311yescharacteristic
220#103—2931no—
221#103—2931no—
222#103—2931no—
223#103C2×D29311yescharacteristic
224#102—2931no—
225#102—2931no—
226#102—2931no—
227#102C2×D29311yescharacteristic
228C4×C8—2931no—
229C4×C8—2931no—
230C4×C8—2931no—
231C4×C8—2931no—
232C2×Q8—2931no—
233C2×Q8C22×D29311yescharacteristic
234C2×D4—21no—
235C2×D4—2931no—
236C2×D4—5861no—
237C2×D4C22×D29311yescharacteristic
238C22×C4—2931no—
239C22×C4—2931no—
240C22×C4—5861no—
241C22×C4—5861no—
242C22×C4C22×D29311yescharacteristic
243Q16—5862no—
244SD16—22no—
245SD16—5862no—
246D8—5862no—
247C2×C8—22no—
248C2×C8—2931no—
249C2×C8—2931no—
250C2×C8—5862no—
251C2×C8C22×D29311yescharacteristic
252C2×C8C22×D29311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2931no—
255C4⋊C4—2931no—
256C4⋊C4—5861no—
257C4⋊C4—5861no—
258C4⋊C4—5861no—
259C4⋊C4—5861no—
260C4⋊C4—5861no—
261C4⋊C4—5861no—
262C4⋊C4—5861no—
263C4⋊C4C22×D29311yescharacteristic
264C4⋊C4C22×D29311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5861no—
268C22⋊C4—5861no—
269C22⋊C4—5861no—
270C22⋊C4—5861no—
271C22⋊C4—5861no—
272C22⋊C4—5861no—
273C22⋊C4—5861no—
274C22⋊C4—5861no—
275C42—2931no—
276C42—2931no—
277C42—2931no—
278C42—2931no—
279C42—5861no—
280C42—5861no—
281C23—21no—
282C23—5861no—
283C23D4×D29311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5861no—
287Q8—5861no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—5861no—
292D4—5861no—
293D4—11722no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2931no—
300C2×C4—2931no—
301C2×C4—2931no—
302C2×C4—2931no—
303C2×C4—5862no—
304C2×C4—5862no—
305C2×C4—5861no—
306C2×C4—5861no—
307C2×C4—5861no—
308C2×C4—11722no—
309C2×C4—11722no—
310C2×C4D4×D29311yescharacteristic
311C2×C4C23×D29311yescharacteristic
312C8—21no—
313C8—2932no—
314C8—5861no—
315C8#1798980112yes—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—11721no—
322C22—11721no—
323C22—11721no—
324C22#2262764512yes—
325C22C2×D4×D29311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2932no—
331C4—5861no—
332C4—5861no—
333C4—5861no—
334C4—11721no—
335C4—11721no—
336C4—11721no—
337C4#41×D29311yescharacteristic
338C4C2×#1798980111yescharacteristic
339C2—22no—
340C2—81no—
341C2—23441no—
342C2#3403667411yescharacteristic
343C2#135×D29311yescharacteristic
344C2C2×#2262764511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#465×C293C2
socleC22×C293C22×D4
prime radical#34036363C2
hypercenter#465D293
hypocenterC293#3168
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. #34036665C2semidirect
2. #34036660C2semidirect
3. #34036529C2semidirect
4. #34036510C2semidirect
5. #34036485C2semidirect
6. #34036482C2semidirect
7. #34036368C2semidirect
9. #34036358C2semidirect
10. #34036221C2semidirect
11. SD16×Dic293C2semidirect
12. #34036216C2semidirect
13. #34036209C2semidirect
14. C2×C8×Dic293C2semidirect
15. #465×C293C2semidirect
172. C293#3168semidirect
183. #465D293semidirect

Maximal subgroups

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

subgroupindex
#340366652
#340366602
#340365292
#340365102
#340364852
#340364822
#340363682
#340363632
#340363582
#340362212
SD16×Dic2932
#340362162
#340362092
C2×C8×Dic2932
#465×C2932
#3168293