Finite Group Databasebeta

← #34057563

Subgroups — #34057563

Order 19072.

338 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750352C211yesmaximal, characteristic, complemented
2#23750331C211yesmaximal, characteristic
3#23750025C211yesmaximal, characteristic, complemented
4#23750022C211yesmaximal, characteristic, complemented
5#23749931C211yesmaximal, characteristic, complemented
6#23749929C211yesmaximal, characteristic, complemented
7#23749928C211yesmaximal, characteristic
8#23749922C211yesmaximal, characteristic
9#23749919C211yesmaximal, characteristic, complemented
10#23749904C211yesmaximal, characteristic
11C8×Dic298C211yesmaximal, characteristic, complemented
12C4×#14558725C211yesmaximal, characteristic
13#23749712C211yesmaximal, characteristic
14#23749712C211yesmaximal, characteristic
15#499×C149C211yesmaximal, characteristic, complemented
16C2×#14558725C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011902C2211yescharacteristic
22#18011901—21no—
23#18011901—21no—
24#18011891—21no—
25#18011889—21no—
26#18011889—21no—
27C4×Dic298C2211yescharacteristic
28C4×Dic298C2211yescharacteristic
29#18011876—21no—
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32C4×D596C2211yescharacteristic
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35C4⋊C4×D149—21no—
36#18011844C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298D411yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67#14558725Q814yescomplemented
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149D411yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×C8×C149C2311yescharacteristic
93C2×C8×C149C2311yescharacteristic
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C42×C149C2311yescharacteristic
103C22×D149—21no—
104Dic298—21no—
105Dic298—22no—
106Dic298—42no—
107Dic298—81no—
108Dic298C2×Q812yes—
109D596—21no—
110D596C2×Q812yes—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C4×D149—42no—
119C4×D149—81no—
120C4×D149—81no—
121#11924746—21no—
122#11924746—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149C2×D411yescharacteristic
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2411yescharacteristic
130C8×C149—21no—
131C8×C149C2×Q812yes—
132C22×C149C22×D411yescharacteristic
133C2×D149—22no—
134C2×D149—41no—
135C2×D149—41no—
136C4×C149—21no—
137C4×C149—21no—
138C4×C149—41no—
139C4×C149—41no—
140C4×C149—41no—
141C4×C149—41no—
142C4×C149C22×Q811yescharacteristic
143C4×C1492−1+411yescharacteristic
144Dic149—22no—
145Dic149—21no—
146Dic149—21no—
147Dic149—21no—
148Dic149—41no—
149Dic149—41no—
150Dic149#13512yes—
151C2×C149D4×Q811yescharacteristic
152C2×C149C2×#13511yescharacteristic
153C2×C149#57711yescharacteristic
154D149—42no—
155C149#338111yescharacteristic, complemented, Sylow
156#3381—1491nomaximal, Sylow
157#557—1491no—
158#554—1491no—
159#499—1491no—
160#499D14911yescharacteristic, complemented
161#498—1491no—
162#479—1491no—
163#479—1491no—
164#478—1491no—
165#478—1491no—
166#477—1491no—
167#474—1491no—
168C8×Q8—1491no—
169C4×SD16—1491no—
170C4×SD16—1491no—
171C4×SD16—1491no—
172C2×SD16—1491no—
173C4⋊Q8—2981no—
174C4⋊Q8—1491no—
175C4⋊Q8—1491no—
176#125—2981no—
177#125—2981no—
178#125—1491no—
179#125—1491no—
180#125C2×D14911yescharacteristic
181#125C2×D14911yescharacteristic
182C22⋊Q8—2981no—
183C22⋊Q8—2981no—
184C22⋊Q8—2981no—
185C4×Q8—2981no—
186C4×Q8—1491no—
187C4×Q8—1491no—
188C4×Q8—1491no—
189C4×Q8—1491no—
190C4×D4—1491no—
191C4×D4—1491no—
192C4×D4—1491no—
193C2×C4⋊C4—2981no—
194#107—1491no—
195#107—1491no—
196#107C2×D14911yescharacteristic
197#107C2×D14911yescharacteristic
198#106—1491no—
199#106—1491no—
200#106—1491no—
201#106C2×D14911yescharacteristic
202#106C2×D14911yescharacteristic
203C4⋊C8—1491no—
204C4⋊C8—1491no—
205C4⋊C8—1491no—
206#103—1491no—
207#103—1491no—
208#103—1491no—
209#102—1491no—
210#102—1491no—
211#102—1491no—
212C4×C8—1491no—
213C4×C8—1491no—
214C4×C8C2×D14911yescharacteristic
215C2×Q8—2981no—
216C2×Q8—2981no—
217C2×Q8—1491no—
218C2×Q8—1491no—
219C2×D4—1491no—
220C22×C4—2981no—
221C22×C4—2981no—
222C22×C4—2981no—
223SD16—1494no—
224C2×C8—1491no—
225C2×C8—1491no—
226C2×C8C22×D14911yescharacteristic
227C2×C8C22×D14911yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—2981no—
233C4⋊C4—2981no—
234C4⋊C4—2981no—
235C4⋊C4—2981no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—1491no—
242C4⋊C4—1491no—
243C4⋊C4—1491no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4C22×D14911yescharacteristic
247C4⋊C4C22×D14911yescharacteristic
248C4⋊C4C22×D14911yescharacteristic
249C4⋊C4C22×D14911yescharacteristic
250C22⋊C4—2981no—
251C22⋊C4—2981no—
252C22⋊C4—2981no—
253C42—2981no—
254C42—2981no—
255C42—2981no—
256C42—1491no—
257C42—1491no—
258C42C22×D14911yescharacteristic
259C23—2981no—
260Q8—2982no—
261Q8—2981no—
262Q8—5962no—
263Q8—1492no—
264Q8—11921no—
265D4—2981no—
266D4—1492no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—2981no—
274C2×C4—5962no—
275C2×C4—1491no—
276C2×C4—1491no—
277C2×C4—1491no—
278C2×C4—1491no—
279C2×C4—11921no—
280C2×C4—11921no—
281C2×C4D4×D14911yescharacteristic
282C2×C4D4×D14911yescharacteristic
283C2×C4C23×D14911yescharacteristic
284C8—21no—
285C8—2981no—
286C8—2981no—
287C8Q8×D14912yes—
288C22—2982no—
289C22—5961no—
290C22—5961no—
291C22C2×D4×D14911yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—2981no—
299C4—2981no—
300C4—2981no—
301C4—2982no—
302C4—5961no—
303C4—5961no—
304C4—1492no—
305C4C2×Q8×D14911yescharacteristic
306C4#1801195911yescharacteristic
307C2—5962no—
308C2#2375029011yescharacteristic
309C2#135×D14911yescharacteristic
310C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#499×C149C2
socleC22×C149C22×D4
prime radicalC2×D596C23
hypercenter#499D149
hypocenterC149#3381
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #23750352C2semidirect
3. #23750025C2semidirect
4. #23750022C2semidirect
5. #23749931C2semidirect
6. #23749929C2semidirect
9. #23749919C2semidirect
11. C8×Dic298C2semidirect
15. #499×C149C2semidirect
67. #14558725Q8semidirect
155. C149#3381semidirect
160. #499D149semidirect

Maximal subgroups

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

subgroupindex
#237503522
#237503312
#237500252
#237500222
#237499312
#237499292
#237499282
#237499222
#237499192
#237499042
C8×Dic2982
C4×#145587252
#237497122
#499×C1492
#3381149