Finite Group Databasebeta

← #34055939

Subgroups — #34055939

Order 19072.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750255C211yesmaximal, characteristic, complemented
2#23750229C211yesmaximal, characteristic
3#23750034C211yesmaximal, characteristic, complemented
4#23750024C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749948C211yesmaximal, characteristic, complemented
7#23749947C211yesmaximal, characteristic, complemented
8#23749942C211yesmaximal, characteristic, complemented
9#23749937C211yesmaximal, characteristic, complemented
10#23749927C211yesmaximal, characteristic, complemented
11#23749923C211yesmaximal, characteristic, complemented
12#23749913C211yesmaximal, characteristic, complemented
13#23749903C211yesmaximal, characteristic, complemented
14#23749687C211yesmaximal, characteristic, complemented
15#490×C149C211yesmaximal, characteristic, complemented
16#18011911C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011903C2211yescharacteristic
20#18011902C2211yescharacteristic
21#18011901—21no—
22#18011892—21no—
23#18011892—21no—
24#18011891—21no—
25#18011889—21no—
26#18011883—21no—
27#18011883—21no—
28#18011882C2211yescharacteristic
29#18011882C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31D4×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#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52#127×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#102×C149C2211yescharacteristic
55#102×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C4⋊Dic149—21no—
70C4⋊Dic149—21no—
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713D411yescharacteristic
88#14558713D411yescharacteristic
89C4×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C2×D4×C149—21no—
92C2×D4×C149—21no—
93C2×D4×C149C2311yescharacteristic
94C2×D4×C149C2311yescharacteristic
95C2×C8×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C4⋊C4×C149—21no—
98C4⋊C4×C149—21no—
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C42×C149C2311yescharacteristic
102C22×D149C2×D411yescharacteristic
103Dic298—81no—
104Dic298—81no—
105C22⋊D149—81no—
106C22⋊D149—81no—
107C2×Dic149—21no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—81no—
112C2×Dic149—81no—
113C2×Dic149C2×D411yescharacteristic
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C4×D149—21no—
117C4×D149—21no—
118C4×D149—81no—
119#11924746—21no—
120#11924746—21no—
121C23×C149—21no—
122C23×C149—21no—
123D4×C149—21no—
124D4×C149—21no—
125D4×C149—21no—
126D4×C149—21no—
127D4×C149—81no—
128D4×C149—81no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2411yescharacteristic
134C8×C149—21no—
135C8×C149—21no—
136C22×C149—41no—
137C22×C149—41no—
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149C22×D411yescharacteristic
143C2×D149—21no—
144C2×D149—21no—
145C2×D149—21no—
146C4×C149—21no—
147C4×C149—21no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C1492−1+411yescharacteristic
151C4×C1492−1+411yescharacteristic
152Dic149—21no—
153Dic149—21no—
154Dic149—21no—
155Dic149—41no—
156Dic149—41no—
157Dic149—41no—
158Dic149—41no—
159C2×C149—81no—
160C2×C149—81no—
161C2×C149#53611yescharacteristic
162C2×C149#57611yescharacteristic
163C2×C149#57711yescharacteristic
164D149—41no—
165C149#324111yescharacteristic, complemented, Sylow
166#3241—1491nomaximal, Sylow
167#544—1491no—
168#540—1491no—
169#501—1491no—
170#499—1491no—
171#490D14911yescharacteristic, complemented
172#486—1491no—
173#482—1491no—
174#482—1491no—
175#481—1491no—
176#480—1491no—
177#478—1491no—
178#478—1491no—
179#476—1491no—
180#474—1491no—
181#433—1491no—
182C4⋊Q8—2981no—
183C4⋊Q8—1491no—
184C4⋊Q8—1491no—
185#127C2×D14911yescharacteristic
186#125—2981no—
187#125—1491no—
188#125—1491no—
189#125C2×D14911yescharacteristic
190#123—2981no—
191#123—2981no—
192C22⋊Q8—2981no—
193C22⋊Q8—2981no—
194#121—2981no—
195#121—2981no—
196#121—1491no—
197#121—1491no—
198C4×D4—1491no—
199C4×D4—1491no—
200#117—1491no—
201#117—1491no—
202C2×C4⋊C4—1491no—
203#107—1491no—
204#107—1491no—
205#107—1491no—
206#107—1491no—
207#106—1491no—
208#106—1491no—
209#106—1491no—
210#106—1491no—
211C4⋊C8—1491no—
212C4⋊C8—1491no—
213#102—1491no—
214#102—1491no—
215#102—1491no—
216#102—1491no—
217#102C2×D14911yescharacteristic
218#102C2×D14911yescharacteristic
219#102C2×D14911yescharacteristic
220#102C2×D14911yescharacteristic
221C22⋊C8—1491no—
222C22⋊C8—1491no—
223#97C2×D14911yescharacteristic
224C4×C8—1491no—
225C2×Q8—2981no—
226C2×Q8—2981no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—2981no—
230C2×D4—2981no—
231C2×D4C22×D14911yescharacteristic
232C2×D4C22×D14911yescharacteristic
233C22×C4—2981no—
234C22×C4—2981no—
235C22×C4—2981no—
236C22×C4—1491no—
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8C22×D14911yescharacteristic
240C2×C8C22×D14911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4—1491no—
255C4⋊C4—1491no—
256C4⋊C4C22×D14911yescharacteristic
257C4⋊C4C22×D14911yescharacteristic
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—1491no—
264C22⋊C4—1491no—
265C42—2981no—
266C42—1491no—
267C42C22×D14911yescharacteristic
268C23—21no—
269C23—21no—
270C23—1491no—
271Q8—11921no—
272Q8—11921no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—11921no—
280D4—11921no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—2981no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—1491no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—11921no—
293C2×C4—11921no—
294C2×C4—11921no—
295C2×C4D4×D14911yescharacteristic
296C2×C4D4×D14911yescharacteristic
297C2×C4C23×D14911yescharacteristic
298C8—21no—
299C8—21no—
300C8—2981no—
301C8—2981no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—2981no—
309C22—2981no—
310C22—2981no—
311C22C2×D4×D14911yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—2981no—
317C4—2981no—
318C4—2981no—
319C4—5961no—
320C4—5961no—
321C4—5961no—
322C4—5961no—
323C4#1801195811yescharacteristic
324C4#1801195811yescharacteristic
325C2—81no—
326C2—81no—
327C2—5961no—
328C2#2375019511yescharacteristic
329C2#2375042911yescharacteristic
330C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
prime radical#23750229C2
hypercenter#490D149
hypocenterC149#3241
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23750255C2semidirect
3. #23750034C2semidirect
4. #23750024C2semidirect
5. #23749971C2semidirect
6. #23749948C2semidirect
7. #23749947C2semidirect
8. #23749942C2semidirect
9. #23749937C2semidirect
10. #23749927C2semidirect
11. #23749923C2semidirect
12. #23749913C2semidirect
13. #23749903C2semidirect
14. #23749687C2semidirect
15. #490×C149C2semidirect
165. C149#3241semidirect
171. #490D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237502292
#237500342
#237500242
#237499712
#237499482
#237499472
#237499422
#237499372
#237499272
#237499232
#237499132
#237499032
#237496872
#490×C1492
#3241149