Finite Group Databasebeta

← #34057384

Subgroups — #34057384

Order 19072.

348 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750357C211yesmaximal, characteristic
2#23750352C211yesmaximal, characteristic, complemented
3#23749981C211yesmaximal, characteristic, complemented
4#23749970C211yesmaximal, characteristic
5#23749927C211yesmaximal, characteristic, complemented
6#23749922C211yesmaximal, characteristic, complemented
7#23749908C211yesmaximal, characteristic, complemented
8#23749850C211yesmaximal, characteristic, complemented
9#23749844C211yesmaximal, characteristic, complemented
10#23749824C211yesmaximal, characteristic
11C8×Dic298C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13#23749716C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19#18011910—21no—
20#18011910C2211yescharacteristic
21#18011907C2211yescharacteristic
22#18011902C2211yescharacteristic
23#18011901—21no—
24#18011901—21no—
25#18011900C2211yescharacteristic
26#18011897—21no—
27#18011895—21no—
28#18011893—21no—
29Q8×Dic149C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32#18011876—21no—
33#18011876C2211yescharacteristic
34#18011876C2211yescharacteristic
35C4×D596C2211yescharacteristic
36D4×Dic149C2211yescharacteristic
37#18011871—21no—
38#18011844C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50C8×Dic149C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C22×Dic149—21no—
66C2×C4×D149—21no—
67#14558726—22no—
68#14558725—22no—
69#14558724—22no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149D411yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83#14558715D411yescharacteristic
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C2×D4×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C22⋊C4×C149—21no—
103C22⋊C4×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106Dic298—21no—
107Dic298—22no—
108Dic298—42no—
109Dic298#4112yes—
110D596—21no—
111D596—21no—
112C22⋊D149—42no—
113C22⋊D149—81no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—81no—
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C4×D149—81no—
123#11924746—21no—
124#11924746—21no—
125C23×C149—21no—
126Q8×C149—21no—
127Q8×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2411yescharacteristic
136C8×C149—21no—
137C8×C149—21no—
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149C22×D411yescharacteristic
142C2×D149—41no—
143C2×D149—41no—
144C2×D149—41no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149C2×#4111yescharacteristic
151C4×C1492−1+411yescharacteristic
152Dic149—22no—
153Dic149—21no—
154Dic149—21no—
155Dic149—21no—
156Dic149—41no—
157Dic149—41no—
158Dic149#13512yes—
159C2×C149—81no—
160C2×C149#54811yescharacteristic
161C2×C149C2×#13511yescharacteristic
162C2×C149#57711yescharacteristic
163D149—81no—
164C149#336511yescharacteristic, complemented, Sylow
165#3365—1491nomaximal, Sylow
166#559—1491no—
167#557—1491no—
168#488—1491no—
169#488D14911yescharacteristic, complemented
170#486—1491no—
171#478—1491no—
172#478—1491no—
173#475—1491no—
174#464—1491no—
175#464—1491no—
176#460—1491no—
177C8×Q8—1491no—
178C4×Q16—1491no—
179C4×SD16—1491no—
180C4×SD16—1491no—
181C2×Q16—1491no—
182C2×SD16—1491no—
183C2×SD16—1491no—
184C4⋊Q8—2981no—
185C4⋊Q8—1491no—
186#127—1491no—
187#125—2981no—
188#125—2981no—
189#125—1491no—
190#125C2×D14911yescharacteristic
191#124—2981no—
192#124—1491no—
193#124C2×D14911yescharacteristic
194#123—2981no—
195#123—2981no—
196C4×Q8—2981no—
197C4×Q8—1491no—
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—1491no—
204C4×D4—1491no—
205#107—1491no—
206#106—1491no—
207#106—1491no—
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211#103—1491no—
212#103—1491no—
213#103C2×D14911yescharacteristic
214#103C2×D14911yescharacteristic
215#102—1491no—
216#102—1491no—
217#102—1491no—
218#102—1491no—
219#102C2×D14911yescharacteristic
220#102C2×D14911yescharacteristic
221C4×C8—1491no—
222C4×C8—1491no—
223C4×C8C2×D14911yescharacteristic
224C2×Q8—2981no—
225C2×Q8—1491no—
226C2×Q8—1491no—
227C2×Q8C22×D14911yescharacteristic
228C2×D4—2981no—
229C2×D4—2981no—
230C2×D4—1491no—
231C2×D4C22×D14911yescharacteristic
232C22×C4—2981no—
233C22×C4—2981no—
234Q16—2982no—
235SD16—2982no—
236SD16—2982no—
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⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C42—2981no—
264C42—2981no—
265C42—2981no—
266C42—2981no—
267C42—1491no—
268C42—1491no—
269C42C22×D14911yescharacteristic
270C23—21no—
271C23—2981no—
272Q8—21no—
273Q8—21no—
274Q8—2982no—
275Q8—2981no—
276Q8—5962no—
277Q8—1492no—
278D4—21no—
279D4—21no—
280D4—2981no—
281D4—2981no—
282D4—5962no—
283D4—11921no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—1491no—
291C2×C4—1491no—
292C2×C4—1491no—
293C2×C4—1491no—
294C2×C4—11921no—
295C2×C4—11921no—
296C2×C4D4×D14911yescharacteristic
297C2×C4D4×D14911yescharacteristic
298C2×C4C23×D14911yescharacteristic
299C8—21no—
300C8—21no—
301C8—2981no—
302C8—2981no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—5961no—
307C22—5961no—
308C22—5961no—
309C22C2×D4×D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—2981no—
316C4—2981no—
317C4—2981no—
318C4—2982no—
319C4—5961no—
320C4—5961no—
321C4—1492no—
322C4#41×D14911yescharacteristic
323C4#1801195811yescharacteristic
324C2—81no—
325C2—11921no—
326C2#2375028311yescharacteristic
327C2#135×D14911yescharacteristic
328C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radical#18011907C22
hypercenter#488D149
hypocenterC149#3365
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #23750352C2semidirect
3. #23749981C2semidirect
5. #23749927C2semidirect
6. #23749922C2semidirect
7. #23749908C2semidirect
8. #23749850C2semidirect
9. #23749844C2semidirect
11. C8×Dic298C2semidirect
12. #23749717C2semidirect
13. #23749716C2semidirect
14. C4×#14558725C2semidirect
15. #488×C149C2semidirect
164. C149#3365semidirect
169. #488D149semidirect

Maximal subgroups

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

subgroupindex
#237503572
#237503522
#237499812
#237499702
#237499272
#237499222
#237499082
#237498502
#237498442
#237498242
C8×Dic2982
#237497172
#237497162
C4×#145587252
#488×C1492
#3365149