Finite Group Databasebeta

← #34057043

Subgroups — #34057043

Order 19072.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750333C211yesmaximal, characteristic, complemented
2#23750275C211yesmaximal, characteristic
3#23750022C211yesmaximal, characteristic, complemented
4#23749954C211yesmaximal, characteristic, complemented
5#23749953C211yesmaximal, characteristic, complemented
6#23749942C211yesmaximal, characteristic, complemented
7#23749941C211yesmaximal, characteristic, complemented
8#23749913C211yesmaximal, characteristic, complemented
9#23749908C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11SD16×Dic149C211yesmaximal, characteristic, complemented
12C8×C22⋊D149C211yesmaximal, characteristic, complemented
13C2×#18011843C211yesmaximal, characteristic, complemented
14#106×D149C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C2×C8×D149C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011901—21no—
21#18011893—21no—
22#18011892—21no—
23#18011891—21no—
24#18011888—21no—
25#18011888—21no—
26#18011887C2211yescharacteristic
27#18011882C2211yescharacteristic
28Q8×Dic149C2211yescharacteristic
29D4×Dic149C2211yescharacteristic
30C4×C22⋊D149C2211yescharacteristic
31#18011871—21no—
32C2×C4⋊Dic149C2211yescharacteristic
33C2×C4⋊Dic149C2211yescharacteristic
34C4⋊C4×D149C2211yescharacteristic
35C4⋊C4×D149C2211yescharacteristic
36#18011843C2211yescharacteristic
37#18011843C2211yescharacteristic
38#18011843C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—44no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×C22⋊D149—21no—
63C2×C22⋊D149D411yescharacteristic
64C22×Dic149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C8×D149—22no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713D411yescharacteristic
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C2×Q8×C149C2311yescharacteristic
94C2×D4×C149—21no—
95C2×D4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97SD16×C149—22no—
98C2×C8×C149—22no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C22×D149C2×D411yescharacteristic
107Dic298—42no—
108Dic298—81no—
109C22⋊D149—42no—
110C22⋊D149SD1614yescomplemented
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—42no—
116C2×Dic149—42no—
117C2×Dic149—81no—
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C4×D149—21no—
122C4×D149—21no—
123C4×D149—42no—
124C4×D149—81no—
125#11924746—21no—
126#11924746—21no—
127C23×C149—21no—
128C23×C149C2×D411yescharacteristic
129Q8×C149—21no—
130Q8×C149—21no—
131D4×C149—21no—
132D4×C149—21no—
133D4×C149—42no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C8×C149—21no—
142C8×C149#4112yescomplemented
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—41no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149C2×SD1612yes—
149C22×C149C22×D411yescharacteristic
150C2×D149—21no—
151C2×D149—21no—
152C2×D149C2×SD1612yes—
153C4×C149—21no—
154C4×C149—41no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149C2×#4111yescharacteristic
158C4×C1492−1+411yescharacteristic
159Dic149—21no—
160Dic149—21no—
161Dic149—41no—
162Dic149—41no—
163Dic149—41no—
164Dic149—41no—
165Dic149C2×SD1612yes—
166C2×C149—22no—
167C2×C149—81no—
168C2×C149#54711yescharacteristic
169C2×C149C22×SD1611yescharacteristic
170C2×C149#57711yescharacteristic
171D149—22no—
172C149#333511yescharacteristic, complemented, Sylow
173#3335—1491nomaximal, Sylow
174#554—1491no—
175#547—1491no—
176#498—1491no—
177#483—1491no—
178#483—1491no—
179#481—1491no—
180#481—1491no—
181#476—1491no—
182#475—1491no—
183#465—1491no—
184#465D14911yescharacteristic, complemented
185C4×SD16—1491no—
186C8×D4—1491no—
187C2×#106—1491no—
188C2×#106—1491no—
189C2×#41—2981no—
190C2×SD16C2×D14911yescharacteristic
191C22×C8—1491no—
192C22×C8C2×D14911yescharacteristic
193C4⋊Q8—1491no—
194C4⋊Q8—1491no—
195#125—2981no—
196#123—2981no—
197#123—2981no—
198C22⋊Q8—2981no—
199C22⋊Q8—2981no—
200C22⋊Q8—2981no—
201C22⋊Q8—1491no—
202C22⋊Q8C2×D14911yescharacteristic
203#121—1491no—
204#121C2×D14911yescharacteristic
205C4×Q8—1491no—
206C4×D4—2981no—
207C4×D4—1491no—
208C4×D4—1491no—
209C2×C4⋊C4—1491no—
210C2×C4⋊C4—1491no—
211C2×C4⋊C4—1491no—
212C2×C4⋊C4—1491no—
213#106—1491no—
214#106—1491no—
215#106—1491no—
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220#106—1491no—
221#106C2×D14911yescharacteristic
222C4⋊C8—1491no—
223#103—1491no—
224#103—1491no—
225#103C2×D14911yescharacteristic
226#102—1491no—
227#102—1491no—
228#102C2×D14911yescharacteristic
229C22⋊C8—1491no—
230C22⋊C8—1491no—
231C4×C8—1491no—
232#41—5964no—
233C2×Q8—2981no—
234C2×Q8—2981no—
235C2×Q8C22×D14911yescharacteristic
236C2×D4—21no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—2981no—
241C22×C4—2981no—
242C22×C4—2981no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—1491no—
246C22×C4C22×D14911yescharacteristic
247SD16—22no—
248C2×C8—22no—
249C2×C8—2982no—
250C2×C8—1491no—
251C2×C8—1491no—
252C2×C8C22×D14911yescharacteristic
253C2×C8C22×D14911yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4—1491no—
268C4⋊C4C22×D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—1491no—
276C22⋊C4—1491no—
277C42—2981no—
278C42—1491no—
279C23—21no—
280C23—1491no—
281C23D4×D14911yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—5962no—
285Q8—11921no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—5962no—
290D4—1494no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—5962no—
303C2×C4—5962no—
304C2×C4—5962no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—11921no—
309C2×C4—11921no—
310C2×C4D4×D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—21no—
313C8—2981no—
314C8—2981no—
315C8#1455873512yescomplemented
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2981no—
322C22—2981no—
323C22—1492no—
324C22SD16×D14912yes—
325C22C2×D4×D14911yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2981no—
331C4—2981no—
332C4—5961no—
333C4—5961no—
334C4—5961no—
335C4—5961no—
336C4—1492no—
337C4C2×#1455873511yescharacteristic
338C4#1801195811yescharacteristic
339C2—22no—
340C2—81no—
341C2—2982no—
342C2#2375027511yescharacteristic
343C2C2×SD16×D14911yescharacteristic
344C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
prime radical#23750275C2
hypercenter#465D149
hypocenterC149#3335
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23750333C2semidirect
3. #23750022C2semidirect
4. #23749954C2semidirect
5. #23749953C2semidirect
6. #23749942C2semidirect
7. #23749941C2semidirect
8. #23749913C2semidirect
9. #23749908C2semidirect
10. #23749851C2semidirect
11. SD16×Dic149C2semidirect
12. C8×C22⋊D149C2semidirect
13. C2×#18011843C2semidirect
14. #106×D149C2semidirect
15. #465×C149C2semidirect
110. C22⋊D149SD16semidirect
142. C8×C149#41semidirect
172. C149#3335semidirect
184. #465D149semidirect
315. C8#14558735semidirect

Maximal subgroups

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

subgroupindex
#237503332
#237502752
#237500222
#237499542
#237499532
#237499422
#237499412
#237499132
#237499082
#237498512
SD16×Dic1492
C8×C22⋊D1492
C2×#180118432
#106×D1492
#465×C1492
#3335149