Finite Group Databasebeta

← #34055964

Subgroups — #34055964

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#23750255C211yesmaximal, characteristic
2#23750233C211yesmaximal, characteristic
3#23750032C211yesmaximal, characteristic, complemented
4#23750026C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749974C211yesmaximal, characteristic, complemented
7#23749968C211yesmaximal, characteristic
8#23749965C211yesmaximal, characteristic
9#23749959C211yesmaximal, characteristic
10#23749957C211yesmaximal, characteristic
11#23749929C211yesmaximal, characteristic, complemented
12#23749921C211yesmaximal, characteristic, complemented
13#23749910C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic
15#479×C149C211yesmaximal, characteristic, complemented
16#18011911C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011909C2211yescharacteristic
20#18011906—21no—
21#18011905—21no—
22#18011903—21no—
23#18011902C2211yescharacteristic
24#18011902C2211yescharacteristic
25#18011901—21no—
26#18011901—21no—
27#18011891—21no—
28#18011891C2211yescharacteristic
29#18011889—21no—
30#18011887C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32#18011869C2211yescharacteristic
33#18011868C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35#18011845C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011842C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298C2311yescharacteristic
62C2×C4×D149—21no—
63C2×C4×D149C2311yescharacteristic
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C4⋊Dic149—21no—
67C4⋊Dic149—21no—
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713D411yescharacteristic
87#14558713D411yescharacteristic
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C2×Q8×C149C2311yescharacteristic
92C2×C8×C149C2311yescharacteristic
93C2×C8×C149C2311yescharacteristic
94C4⋊C4×C149—21no—
95C4⋊C4×C149—21no—
96C4⋊C4×C149—21no—
97C4⋊C4×C149C2311yescharacteristic
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C42×C149—21no—
101C42×C149C2311yescharacteristic
102C22×D149C2×D411yescharacteristic
103Dic298—21no—
104Dic298—21no—
105Dic298—81no—
106Dic298—81no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149C2×D411yescharacteristic
112C2×Dic149C2×D411yescharacteristic
113C2×Dic149C2×D411yescharacteristic
114C4×D149—21no—
115C4×D149—21no—
116C4×D149—81no—
117#11924746—21no—
118#11924746—21no—
119Q8×C149—21no—
120Q8×C149—21no—
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#487—1491no—
161#485—1491no—
162#485—1491no—
163#484—1491no—
164#483—1491no—
165#479—1491no—
166#479D14911yescharacteristic, complemented
167#477—1491no—
168#475—1491no—
169#433—1491no—
170C4⋊Q8—2981no—
171C4⋊Q8—1491no—
172C4⋊Q8—1491no—
173C4⋊Q8—1491no—
174#126—2981no—
175#126—2981no—
176#125—2981no—
177#125—2981no—
178#125—2981no—
179#125—1491no—
180#125—1491no—
181#125C2×D14911yescharacteristic
182C22⋊Q8—2981no—
183C22⋊Q8—2981no—
184C22⋊Q8—1491no—
185C22⋊Q8—1491no—
186C4×Q8—1491no—
187C4×Q8C2×D14911yescharacteristic
188#117—1491no—
189#117—1491no—
190C2×C4⋊C4—1491no—
191#107—1491no—
192#107—1491no—
193#107—1491no—
194#107C2×D14911yescharacteristic
195#106—1491no—
196#106—1491no—
197#106—1491no—
198#106C2×D14911yescharacteristic
199C4⋊C8—1491no—
200C4⋊C8C2×D14911yescharacteristic
201#103—1491no—
202#103—1491no—
203#103—1491no—
204#103—1491no—
205#103—1491no—
206#103—1491no—
207#103C2×D14911yescharacteristic
208#103C2×D14911yescharacteristic
209C22⋊C8—1491no—
210C22⋊C8—1491no—
211#97—1491no—
212C4×C8—1491no—
213C2×Q8—2981no—
214C2×Q8—2981no—
215C2×Q8—1491no—
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⋊C4C22×D14911yescharacteristic
244C4⋊C4C22×D14911yescharacteristic
245C4⋊C4C22×D14911yescharacteristic
246C22⋊C4—2981no—
247C22⋊C4—2981no—
248C22⋊C4—2981no—
249C22⋊C4—1491no—
250C22⋊C4—1491no—
251C42—21no—
252C42—2981no—
253C42—2981no—
254C42—1491no—
255C42C22×D14911yescharacteristic
256C23—1491no—
257Q8—21no—
258Q8—21no—
259Q8—2981no—
260Q8—2981no—
261Q8—11921no—
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#1801195911yescharacteristic
303C2—5961no—
304C2#2375019811yescharacteristic
305C2#2375043411yescharacteristic
306C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#479×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#479D149
hypocenterC149#3242
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #23750032C2semidirect
4. #23750026C2semidirect
5. #23749992C2semidirect
6. #23749974C2semidirect
11. #23749929C2semidirect
12. #23749921C2semidirect
13. #23749910C2semidirect
15. #479×C149C2semidirect
153. C149#3242semidirect
166. #479D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237502332
#237500322
#237500262
#237499922
#237499742
#237499682
#237499652
#237499592
#237499572
#237499292
#237499212
#237499102
#237496852
#479×C1492
#3242149