Finite Group Databasebeta

← #34055952

Subgroups — #34055952

Order 19072.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750252C211yesmaximal, characteristic
2#23750236C211yesmaximal, characteristic
3#23750031C211yesmaximal, characteristic, complemented
4#23750027C211yesmaximal, characteristic, complemented
5#23749993C211yesmaximal, characteristic, complemented
6#23749965C211yesmaximal, characteristic
7#23749964C211yesmaximal, characteristic
8#23749959C211yesmaximal, characteristic
9#23749954C211yesmaximal, characteristic
10#23749934C211yesmaximal, characteristic, complemented
11#23749930C211yesmaximal, characteristic, complemented
12#23749918C211yesmaximal, characteristic, complemented
13#23749908C211yesmaximal, characteristic, complemented
14#23749684C211yesmaximal, characteristic
15#487×C149C211yesmaximal, characteristic, complemented
16#18011910C2211yescharacteristic
17#18011909—21no—
18#18011906—21no—
19#18011906—21no—
20#18011903C2211yescharacteristic
21#18011903C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011901—21no—
24#18011901—21no—
25#18011901—21no—
26#18011889—21no—
27#18011887—21no—
28#18011887C2211yescharacteristic
29#18011887C2211yescharacteristic
30Q8×Dic149C2211yescharacteristic
31Q8×Dic149C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011868C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011835C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53C4⋊Q8×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×C4×D149—21no—
61C2×C4×D149C2311yescharacteristic
62C2×#11924746C2311yescharacteristic
63C2×#11924746C2311yescharacteristic
64C4⋊Dic149—21no—
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149C2311yescharacteristic
68C4⋊Dic149C2311yescharacteristic
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71#14558715—21no—
72#14558715—21no—
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713D411yescharacteristic
86#14558713D411yescharacteristic
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C2×Q8×C149—21no—
92C2×Q8×C149C2311yescharacteristic
93C2×Q8×C149C2311yescharacteristic
94C2×C8×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102C22×D149C2×D411yescharacteristic
103Dic298—81no—
104C2×Dic149—21no—
105C2×Dic149—21no—
106C2×Dic149—21no—
107C2×Dic149—21no—
108C2×Dic149C2×D411yescharacteristic
109C2×Dic149C2×D411yescharacteristic
110C2×Dic149C2×D411yescharacteristic
111C4×D149—21no—
112C4×D149—21no—
113C4×D149—81no—
114#11924746—21no—
115#11924746—21no—
116Q8×C149—21no—
117Q8×C149—21no—
118Q8×C149—21no—
119Q8×C149—21no—
120Q8×C149—81no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149C2×D411yescharacteristic
126C2×C4×C149C2×D411yescharacteristic
127C2×C4×C149C2411yescharacteristic
128C8×C149—21no—
129C8×C149—21no—
130C22×C149C22×D411yescharacteristic
131C2×D149—21no—
132C2×D149—21no—
133C2×D149—21no—
134C4×C149—21no—
135C4×C149—21no—
136C4×C149—41no—
137C4×C149—41no—
138C4×C149—41no—
139C4×C149—41no—
140C4×C1492−1+411yescharacteristic
141C4×C1492−1+411yescharacteristic
142Dic149—21no—
143Dic149—21no—
144Dic149—21no—
145Dic149—41no—
146Dic149—41no—
147Dic149—41no—
148Dic149—41no—
149C2×C149#53611yescharacteristic
150C2×C149#57711yescharacteristic
151C2×C149#57811yescharacteristic
152D149—41no—
153C149#324211yescharacteristic, complemented, Sylow
154#3242—1491nomaximal, Sylow
155#544—1491no—
156#541—1491no—
157#501—1491no—
158#499—1491no—
159#491—1491no—
160#487D14911yescharacteristic, complemented
161#485—1491no—
162#485—1491no—
163#484—1491no—
164#483—1491no—
165#479—1491no—
166#479—1491no—
167#477—1491no—
168#475—1491no—
169#433—1491no—
170C4⋊Q8—2981no—
171C4⋊Q8—1491no—
172C4⋊Q8C2×D14911yescharacteristic
173C4⋊Q8C2×D14911yescharacteristic
174#126—2981no—
175#126—2981no—
176#125—2981no—
177#125—2981no—
178#125—2981no—
179#125—1491no—
180#125—1491no—
181#125—1491no—
182C22⋊Q8—2981no—
183C22⋊Q8—2981no—
184C22⋊Q8—1491no—
185C22⋊Q8—1491no—
186C4×Q8—1491no—
187C4×Q8—1491no—
188#117—1491no—
189#117—1491no—
190C2×C4⋊C4—1491no—
191#107—1491no—
192#107—1491no—
193#107—1491no—
194#107—1491no—
195#106—1491no—
196#106—1491no—
197#106—1491no—
198#106—1491no—
199C4⋊C8—1491no—
200C4⋊C8—1491no—
201#103—1491no—
202#103—1491no—
203#103—1491no—
204#103—1491no—
205#103C2×D14911yescharacteristic
206#103C2×D14911yescharacteristic
207#103C2×D14911yescharacteristic
208#103C2×D14911yescharacteristic
209C22⋊C8—1491no—
210C22⋊C8—1491no—
211#97—1491no—
212C4×C8C2×D14911yescharacteristic
213C2×Q8—21no—
214C2×Q8—2981no—
215C2×Q8C22×D14911yescharacteristic
216C2×Q8C22×D14911yescharacteristic
217C22×C4—2981no—
218C22×C4—1491no—
219C2×C8—1491no—
220C2×C8—1491no—
221C2×C8C22×D14911yescharacteristic
222C2×C8C22×D14911yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—2981no—
227C4⋊C4—2981no—
228C4⋊C4—2981no—
229C4⋊C4—2981no—
230C4⋊C4—2981no—
231C4⋊C4—2981no—
232C4⋊C4—2981no—
233C4⋊C4—2981no—
234C4⋊C4—2981no—
235C4⋊C4—2981no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—1491no—
239C4⋊C4—1491no—
240C4⋊C4—1491no—
241C4⋊C4—1491no—
242C4⋊C4—1491no—
243C4⋊C4—1491no—
244C4⋊C4C22×D14911yescharacteristic
245C4⋊C4C22×D14911yescharacteristic
246C22⋊C4—2981no—
247C22⋊C4—2981no—
248C22⋊C4—2981no—
249C22⋊C4—1491no—
250C22⋊C4—1491no—
251C42—2981no—
252C42—2981no—
253C42—2981no—
254C42—1491no—
255C42C22×D14911yescharacteristic
256C23—1491no—
257Q8—21no—
258Q8—21no—
259Q8—21no—
260Q8—21no—
261Q8—81no—
262Q8—11921no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—2981no—
268C2×C4—2981no—
269C2×C4—2981no—
270C2×C4—2981no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—1491no—
274C2×C4—1491no—
275C2×C4—1491no—
276C2×C4—11921no—
277C2×C4D4×D14911yescharacteristic
278C2×C4D4×D14911yescharacteristic
279C2×C4C23×D14911yescharacteristic
280C8—21no—
281C8—21no—
282C8—2981no—
283C8—2981no—
284C22—2981no—
285C22—2981no—
286C22—2981no—
287C22C2×D4×D14911yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—2981no—
295C4—2981no—
296C4—2981no—
297C4—5961no—
298C4—5961no—
299C4—5961no—
300C4—5961no—
301C4#1801195811yescharacteristic
302C4#1801195811yescharacteristic
303C2—5961no—
304C2#2375019511yescharacteristic
305C2#2375043111yescharacteristic
306C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#487D149
hypocenterC149#3242
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #23750031C2semidirect
4. #23750027C2semidirect
5. #23749993C2semidirect
10. #23749934C2semidirect
11. #23749930C2semidirect
12. #23749918C2semidirect
13. #23749908C2semidirect
15. #487×C149C2semidirect
153. C149#3242semidirect
160. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237502522
#237502362
#237500312
#237500272
#237499932
#237499652
#237499642
#237499592
#237499542
#237499342
#237499302
#237499182
#237499082
#237496842
#487×C1492
#3242149