Finite Group Databasebeta

← #49171482

Subgroups — #49171482

Order 37504.

348 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#34036862C211yesmaximal, characteristic
2#34036855C211yesmaximal, characteristic, complemented
3#34036484C211yesmaximal, characteristic, complemented
4#34036482C211yesmaximal, characteristic, complemented
5#34036474C211yesmaximal, characteristic
6#34036429C211yesmaximal, characteristic, complemented
7#34036428C211yesmaximal, characteristic, complemented
8#34036413C211yesmaximal, characteristic, complemented
9#34036351C211yesmaximal, characteristic, complemented
10#34036349C211yesmaximal, characteristic, complemented
11#34036327C211yesmaximal, characteristic
12C8×Dic586C211yesmaximal, characteristic, complemented
13#34036221C211yesmaximal, characteristic, complemented
14#34036214C211yesmaximal, characteristic, complemented
15C4×SD16×C293C211yesmaximal, characteristic, complemented
16C2×#17989792C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18#22627623—21no—
19#22627623C2211yescharacteristic
20#22627620C2211yescharacteristic
21#22627616—21no—
22#22627616C2211yescharacteristic
23#22627615—21no—
24#22627615C2211yescharacteristic
25#22627612C2211yescharacteristic
26#22627611C2211yescharacteristic
27#22627610—21no—
28#22627607—21no—
29#22627606—21no—
30Q8×Dic293C2211yescharacteristic
31Q8×Dic293C2211yescharacteristic
32C4×Dic586—21no—
33C4×Dic586C2211yescharacteristic
34#22627589C2211yescharacteristic
35#22627586C2211yescharacteristic
36C4×C22⋊D293—21no—
37#22627557C2211yescharacteristic
38#22627555C2211yescharacteristic
39C4⋊#14556873C2211yescharacteristic
40#22627553C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627549C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627544C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×Dic586D411yescharacteristic
61C2×Dic586C2311yescharacteristic
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C4×D293—21no—
66#17989792—22no—
67#17989789—22no—
68C2×#14556873C2311yescharacteristic
69C2×#14556873C2311yescharacteristic
70C4⋊Dic293—21no—
71C4⋊Dic293—21no—
72C4⋊Dic293—21no—
73C4⋊Dic293D411yescharacteristic
74C4⋊Dic293C2311yescharacteristic
75C4⋊Dic293C2311yescharacteristic
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—
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88C4×Dic293—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C2×Q8×C293C2311yescharacteristic
94C2×D4×C293C2311yescharacteristic
95C22×C4×C293—21no—
96SD16×C293—22no—
97C2×C8×C293C2311yescharacteristic
98C2×C8×C293C2311yescharacteristic
99C4⋊C4×C293—21no—
100C4⋊C4×C293C2311yescharacteristic
101C4⋊C4×C293C2311yescharacteristic
102C22⋊C4×C293—21no—
103C42×C293—21no—
104C42×C293C2311yescharacteristic
105C22×D293—21no—
106Dic586—22no—
107Dic586—21no—
108Dic586—21no—
109Dic586—42no—
110D1172—21no—
111D1172—21no—
112C22⋊D293—42no—
113C22⋊D293—81no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293C2×D411yescharacteristic
118C2×Dic293C2×D411yescharacteristic
119C2×Dic293C2×D411yescharacteristic
120C2×Dic293C2×D411yescharacteristic
121C4×D293—81no—
122#14556873—21no—
123#14556873—21no—
124C23×C293—21no—
125Q8×C293—21no—
126Q8×C293#4112yes—
127D4×C293—21no—
128D4×C293—21no—
129C2×C4×C293—21no—
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—41no—
139C22×C293—41no—
140C22×C293—41no—
141C22×C293C22×D411yescharacteristic
142C2×D293—41no—
143C2×D293—41no—
144C2×D293—41no—
145C4×C293—22no—
146C4×C293—21no—
147C4×C293—21no—
148C4×C293—41no—
149C4×C293—41no—
150C4×C293C2×#4111yescharacteristic
151C4×C2932−1+411yescharacteristic
152Dic293—21no—
153Dic293—21no—
154Dic293—21no—
155Dic293—41no—
156Dic293—41no—
157Dic293—41no—
158Dic293#13512yes—
159C2×C293—81no—
160C2×C293#54811yescharacteristic
161C2×C293C2×#13511yescharacteristic
162C2×C293#57711yescharacteristic
163D293—81no—
164C293#336511yescharacteristic, complemented, Sylow
165#3365—2931nomaximal, Sylow
166#559—2931no—
167#557—2931no—
168#488—2931no—
169#488—2931no—
170#486—2931no—
171#478—2931no—
172#478—2931no—
173#475—2931no—
174#464—2931no—
175#464—2931no—
176#460—2931no—
177C8×Q8—2931no—
178C4×Q16—2931no—
179C4×SD16—2931no—
180C4×SD16D29311yescharacteristic, complemented
181C2×Q16—2931no—
182C2×SD16—2931no—
183C2×SD16C2×D29311yescharacteristic
184C4⋊Q8—2931no—
185C4⋊Q8—5861no—
186#127—2931no—
187#125—2931no—
188#125—2931no—
189#125—5861no—
190#125—5861no—
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—5861no—
201C4×Q8C2×D29311yescharacteristic
202C4×D4—2931no—
203C4×D4—5861no—
204C4×D4C2×D29311yescharacteristic
205#107—2931no—
206#106—2931no—
207#106C2×D29311yescharacteristic
208C4⋊C8—2931no—
209C4⋊C8—2931no—
210C4⋊C8—2931no—
211#103—2931no—
212#103—2931no—
213#103—2931no—
214#103C2×D29311yescharacteristic
215#102—2931no—
216#102—2931no—
217#102—2931no—
218#102—2931no—
219#102—2931no—
220#102C2×D29311yescharacteristic
221C4×C8—2931no—
222C4×C8—2931no—
223C4×C8C2×D29311yescharacteristic
224C2×Q8—2931no—
225C2×Q8—2931no—
226C2×Q8—5861no—
227C2×Q8C22×D29311yescharacteristic
228C2×D4—2931no—
229C2×D4—5861no—
230C2×D4—5861no—
231C2×D4C22×D29311yescharacteristic
232C22×C4—21no—
233C22×C4—5861no—
234Q16—5862no—
235SD16—22no—
236SD16—5862no—
237C2×C8—2931no—
238C2×C8—2931no—
239C2×C8C22×D29311yescharacteristic
240C2×C8C22×D29311yescharacteristic
241C4⋊C4—21no—
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⋊C4C22×D29311yescharacteristic
256C4⋊C4C22×D29311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—5861no—
259C22⋊C4—5861no—
260C22⋊C4—5861no—
261C22⋊C4—5861no—
262C22⋊C4—5861no—
263C42—21no—
264C42—2931no—
265C42—2931no—
266C42—5861no—
267C42—5861no—
268C42—5861no—
269C42C22×D29311yescharacteristic
270C23—21no—
271C23—5861no—
272Q8—21no—
273Q8—5862no—
274Q8—5861no—
275Q8—5861no—
276Q8—11722no—
277Q8#1798980212yes—
278D4—21no—
279D4—21no—
280D4—23441no—
281D4—5861no—
282D4—5861no—
283D4—11722no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—2931no—
289C2×C4—2931no—
290C2×C4—2931no—
291C2×C4—2931no—
292C2×C4—23441no—
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—11721no—
307C22—11721no—
308C22—11721no—
309C22C2×D4×D29311yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—2932no—
316C4—5861no—
317C4—5861no—
318C4—5861no—
319C4—11721no—
320C4—11721no—
321C4—11721no—
322C4C2×#1798980211yescharacteristic
323C4#2262767111yescharacteristic
324C2—81no—
325C2—23441no—
326C2#3403678811yescharacteristic
327C2#135×D29311yescharacteristic
328C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
prime radical#22627620C22
hypercenterC4×SD16D293
hypocenterC293#3365
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #34036855C2semidirect
3. #34036484C2semidirect
4. #34036482C2semidirect
6. #34036429C2semidirect
7. #34036428C2semidirect
8. #34036413C2semidirect
9. #34036351C2semidirect
10. #34036349C2semidirect
12. C8×Dic586C2semidirect
13. #34036221C2semidirect
14. #34036214C2semidirect
15. C4×SD16×C293C2semidirect
164. C293#3365semidirect
180. C4×SD16D293semidirect

Maximal subgroups

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

subgroupindex
#340368622
#340368552
#340364842
#340364822
#340364742
#340364292
#340364282
#340364132
#340363512
#340363492
#340363272
C8×Dic5862
#340362212
#340362142
C4×SD16×C2932
#3365293