Finite Group Databasebeta

← #34055044

Subgroups — #34055044

Order 19072.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750255C211yesmaximal, characteristic, complemented
2#23750193C211yesmaximal, characteristic
3#23749991C211yesmaximal, characteristic, complemented
4#23749988C211yesmaximal, characteristic, complemented
5#23749986C211yesmaximal, characteristic, complemented
6#23749984C211yesmaximal, characteristic, complemented
7#23749981C211yesmaximal, characteristic, complemented
8#23749972C211yesmaximal, characteristic, complemented
9#23749970C211yesmaximal, characteristic, complemented
10#23749628C211yesmaximal, characteristic, complemented
11#23749625C211yesmaximal, characteristic, complemented
12#23749620C211yesmaximal, characteristic, complemented
13#102×D149C211yesmaximal, characteristic, complemented
14#23749579C211yesmaximal, characteristic, complemented
15#488×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×D4×D149C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011911C2211yescharacteristic, complemented
21#18011910—21no—
22#18011910C2211yescharacteristic, complemented
23#18011908C2211yescharacteristic
24#18011907C2211yescharacteristic
25#18011902C2211yescharacteristic, complemented
26#18011901—21no—
27#18011900C2211yescharacteristic
28#18011891—21no—
29#18011889—21no—
30#18011884—21no—
31#18011884—21no—
32#18011881—21no—
33#18011881—21no—
34#18011869C2211yescharacteristic
35#18011868C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37#18011835C2211yescharacteristic, complemented
38#18011835C2211yescharacteristic, complemented
39#18011833C2211yescharacteristic
40#18011833C2211yescharacteristic
41#18011833C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic, complemented
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49#18011822C2211yescharacteristic, complemented
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53#124×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic, complemented
55#103×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558737—22no—
61#14558737—22no—
62C2×Dic298—21no—
63C2×Dic298—21no—
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596C2311yescharacteristic
68C2×D596C2311yescharacteristic
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72D4×D149—22no—
73D4×D149—22no—
74C2×C4×D149—21no—
75C2×C4×D149—21no—
76C2×C4×D149C2311yescharacteristic
77#14558719—22no—
78C2×#11924746C2311yescharacteristic
79C2×#11924746C2311yescharacteristic
80C8×D149—22no—
81C4⋊Dic149—21no—
82C4⋊Dic149—21no—
83C4⋊Dic149C2311yescharacteristic
84C4⋊Dic149C2311yescharacteristic
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88#14558715D411yescharacteristic
89#14558715D411yescharacteristic
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—42no—
111C22×D149—81no—
112C22×D149—81no—
113C22×D149C2×D411yescharacteristic
114Dic298—81no—
115Dic298—81no—
116D596—21no—
117D596—21no—
118D596—21no—
119D596—21no—
120D596—42no—
121D596—81no—
122D596—81no—
123C22⋊D149—42no—
124C22⋊D149—81no—
125C22⋊D149—81no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C2×Dic149C2×D411yescharacteristic
131C4×D149—42no—
132C4×D149—81no—
133C4×D149#4112yes—
134C4×D149#4112yes—
135#11924746—21no—
136#11924746—21no—
137C23×C149—21no—
138Q8×C149—21no—
139Q8×C149—21no—
140D4×C149—21no—
141D4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C8×C149—21no—
149C8×C149—21no—
150C22×C149—41no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149C22×D411yescharacteristic
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—41no—
157C2×D149—41no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149—41no—
161C2×D149—41no—
162C2×D149—84no—
163C2×D149#12412yes—
164C4×C149—21no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149C2×#4111yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149#12412yes—
176C2×C149—81no—
177C2×C149C2×#12411yescharacteristic
178C2×C149#57611yescharacteristic
179C2×C149#57711yescharacteristic
180D149—22no—
181D149—81no—
182D149—81no—
183C149#313611yescharacteristic, complemented, Sylow
184#3136—1491nomaximal, Sylow
185#544—1491no—
186#535—1491no—
187#490—1491no—
188#490—1491no—
189#489—1491no—
190#489—1491no—
191#488—1491no—
192#488D14911yescharacteristic, complemented
193#486—1491no—
194#486—1491no—
195#418—1491no—
196#417—1491no—
197#416—1491no—
198C2×#102—1491no—
199#405—1491no—
200C2×#41—1491no—
201C22×D4—1491no—
202C2×M16—1491no—
203C22×C8—1491no—
204C4⋊Q8—2981no—
205C4⋊Q8—1491no—
206C4⋊Q8—1491no—
207#127—1491no—
208#127—1491no—
209#125—2981no—
210#125—1491no—
211#125C2×D14911yescharacteristic, complemented
212#124—1491no—
213#124C2×D14911yescharacteristic
214C22⋊Q8—2981no—
215C22⋊Q8—2981no—
216#121—2981no—
217#121—2981no—
218#120—2981no—
219#120—2981no—
220#117—1491no—
221#117—1491no—
222C2×C4⋊C4—1491no—
223#103—1491no—
224#103—1491no—
225#103C2×D14911yescharacteristic, complemented
226#103C2×D14911yescharacteristic, complemented
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102—1491no—
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102—1491no—
236#102—1491no—
237#102C2×D14911yescharacteristic
238#102C2×D14911yescharacteristic
239#97—1491no—
240#97—1491no—
241C4×C8—1491no—
242C4×C8C2×D14911yescharacteristic, complemented
243C24—2981no—
244#41—2982no—
245#41—2982no—
246C2×Q8—2981no—
247C2×Q8—2981no—
248C2×Q8C22×D14911yescharacteristic
249C2×D4—2981no—
250C2×D4—2982no—
251C2×D4—2982no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—2981no—
256C2×D4—2981no—
257C2×D4—1491no—
258C2×D4—1491no—
259C2×D4C22×D14911yescharacteristic
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263M16—2982no—
264C2×C8—2982no—
265C2×C8—1491no—
266C2×C8—1491no—
267C2×C8C22×D14911yescharacteristic
268C2×C8C22×D14911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—1491no—
277C4⋊C4—1491no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4C22×D14911yescharacteristic
281C4⋊C4C22×D14911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—1491no—
288C22⋊C4—1491no—
289C42—2981no—
290C42—1491no—
291C42C22×D14911yescharacteristic
292C23—21no—
293C23—2981no—
294C23—2981no—
295C23—5962no—
296C23—1491no—
297C23—11921no—
298C23—11921no—
299Q8—21no—
300Q8—21no—
301Q8—11921no—
302Q8—11921no—
303D4—21no—
304D4—21no—
305D4—2981no—
306D4—2981no—
307D4—2981no—
308D4—2981no—
309D4—5962no—
310D4—5962no—
311D4—11921no—
312D4—11921no—
313D4—11921no—
314D4—11921no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2981no—
319C2×C4—2981no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4—1492no—
325C2×C4—1492no—
326C2×C4—11921no—
327C2×C4D4×D14911yescharacteristic
328C2×C4D4×D14911yescharacteristic
329C2×C4C23×D14911yescharacteristic
330C8—21no—
331C8—21no—
332C8—2981no—
333C8—2981no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2981no—
338C22—2981no—
339C22—5961no—
340C22—5961no—
341C22—5961no—
342C22—5961no—
343C22—5961no—
344C22—5961no—
345C22—1492no—
346C22—11924no—
347C22C2×D4×D14911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2981no—
354C4—2981no—
355C4—5961no—
356C4—5961no—
357C4—1492no—
358C4#41×D14911yescharacteristic
359C4#41×D14911yescharacteristic
360C2—81no—
361C2—2982no—
362C2—11921no—
363C2—11921no—
364C2#124×D14911yescharacteristic
365C2#2375042711yescharacteristic
366C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radical#23750193C2
hypercenter#488D149
hypocenterC149#3136
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
1. #23750255C2semidirect
3. #23749991C2semidirect
4. #23749988C2semidirect
5. #23749986C2semidirect
6. #23749984C2semidirect
7. #23749981C2semidirect
8. #23749972C2semidirect
9. #23749970C2semidirect
10. #23749628C2semidirect
11. #23749625C2semidirect
12. #23749620C2semidirect
13. #102×D149C2semidirect
14. #23749579C2semidirect
15. #488×C149C2semidirect
20. #18011911C22semidirect
22. #18011910C22semidirect
25. #18011902C22semidirect
37. #18011835C22semidirect
38. #18011835C22semidirect
41. #18011833C22semidirect
42. #18011833C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. #18011822C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
52. #125×C149C22semidirect
54. #103×C149C22semidirect
55. #103×C149C22semidirect
58. C4×C8×C149C22semidirect
183. C149#3136semidirect
192. #488D149semidirect
211. #125C2×D149semidirect
225. #103C2×D149semidirect
226. #103C2×D149semidirect
242. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502552
#237501932
#237499912
#237499882
#237499862
#237499842
#237499812
#237499722
#237499702
#237496282
#237496252
#237496202
#102×D1492
#237495792
#488×C1492
#3136149