Finite Group Databasebeta

← #34054945

Subgroups — #34054945

Order 19072.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750238C211yesmaximal, characteristic, complemented
2#23750097C211yesmaximal, characteristic
3#23749969C211yesmaximal, characteristic, complemented
4#23749968C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749831C211yesmaximal, characteristic, complemented
7#23749830C211yesmaximal, characteristic, complemented
8#23749777C211yesmaximal, characteristic
9#23749777C211yesmaximal, characteristic
10#23749724C211yesmaximal, characteristic, complemented
11#23749722C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13#23749712C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21#18011911C2211yescharacteristic, complemented
22#18011906—21no—
23#18011906—21no—
24#18011902—21no—
25#18011902—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28#18011876C2211yescharacteristic, complemented
29#18011876C2211yescharacteristic, complemented
30C4×D596C2211yescharacteristic
31D4×Dic149C2211yescharacteristic
32#18011873C2211yescharacteristic
33C4×C22⋊D149—21no—
34#18011871—21no—
35#18011869C2211yescharacteristic
36#18011868C2211yescharacteristic
37C2×#14558713—21no—
38C22⋊C4×D149—21no—
39#18011844C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41C4⋊#11924746C2211yescharacteristic, complemented
42#18011836C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011834C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52#125×C149C2211yescharacteristic, complemented
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56C4⋊C8×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64D4×D149—22no—
65D4×D149—22no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70#14558725—22no—
71#14558725—22no—
72#14558724—22no—
73#14558724—22no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713D411yescharacteristic
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—24no—
110C22×D149—81no—
111C22×D149—81no—
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—21no—
117D596—21no—
118D596#4112yes—
119C22⋊D149—24no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—81no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—21no—
128C4×D149—21no—
129C4×D149—81no—
130C4×D149—81no—
131#11924746—21no—
132#11924746—21no—
133C23×C149—21no—
134D4×C149—21no—
135D4×C149#4112yes—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—81no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C8×C149—21no—
144C8×C149—21no—
145C22×C149—22no—
146C22×C149—41no—
147C22×C149—41no—
148C22×C149C22×D411yescharacteristic
149C2×D149—21no—
150C2×D149—22no—
151C2×D149—21no—
152C2×D149—21no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—84no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C149C2×#4111yescharacteristic
163Dic149—21no—
164Dic149—21no—
165Dic149—21no—
166Dic149—41no—
167Dic149—41no—
168Dic149—41no—
169C2×C149—42no—
170C2×C149#52511yescharacteristic
171C2×C149#57711yescharacteristic
172C2×C149#57711yescharacteristic
173D149—41no—
174D149—42no—
175C149#312311yescharacteristic, complemented, Sylow
176#3123—1491nomaximal, Sylow
177#541—1491no—
178#518—1491no—
179#485—1491no—
180#485—1491no—
181#478—1491no—
182#478D14911yescharacteristic, complemented
183#461—1491no—
184#461—1491no—
185#450—1491no—
186#450—1491no—
187#440—1491no—
188#440—1491no—
189C4×SD16—1491no—
190C4×SD16—1491no—
191#433—1491no—
192C22×D4—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C4⋊Q8—1491no—
198#126—2981no—
199#126—2981no—
200#125—2981no—
201#125—2981no—
202#125C2×D14911yescharacteristic, complemented
203C22⋊Q8—1491no—
204C22⋊Q8—1491no—
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212C4×D4C2×D14911yescharacteristic
213#117—1491no—
214#117—1491no—
215C2×C22⋊C4—2981no—
216C2×C22⋊C4—2981no—
217#107—1491no—
218#107C2×D14911yescharacteristic, complemented
219#106—1491no—
220#106C2×D14911yescharacteristic, complemented
221C4⋊C8—1491no—
222C4⋊C8C2×D14911yescharacteristic, complemented
223#103—1491no—
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#102—1491no—
228#102—1491no—
229#102C2×D14911yescharacteristic
230#102C2×D14911yescharacteristic
231C22⋊C8—1491no—
232C22⋊C8—1491no—
233#97—1491no—
234C4×C8—1491no—
235C24—2981no—
236C2×Q8—1491no—
237C2×Q8—1491no—
238C2×D4—2982no—
239C2×D4—2982no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4C22×D14911yescharacteristic
243C22×C4—21no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—1491no—
248SD16—2982no—
249SD16—2982no—
250SD16—2982no—
251SD16—2982no—
252C2×C8—1491no—
253C2×C8—1491no—
254C2×C8C22×D14911yescharacteristic
255C2×C8C22×D14911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—1491no—
278C22⋊C4—1491no—
279C42—2981no—
280C42—2981no—
281C42—2981no—
282C42—1491no—
283C42C22×D14911yescharacteristic
284C23—21no—
285C23—2984no—
286C23—2981no—
287C23—1491no—
288C23—11921no—
289C23—11921no—
290Q8—2981no—
291Q8—2981no—
292Q8—2981no—
293Q8—2981no—
294D4—21no—
295D4—2984no—
296D4—2981no—
297D4—1492no—
298D4#1455873712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—2981no—
308C2×C4—1491no—
309C2×C4—1491no—
310C2×C4—1491no—
311C2×C4—11921no—
312C2×C4—11921no—
313C2×C4—11921no—
314C2×C4D4×D14911yescharacteristic
315C2×C4D4×D14911yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—21no—
318C8—21no—
319C8—2981no—
320C8—2981no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2981no—
325C22—2981no—
326C22—2981no—
327C22—2982no—
328C22—5961no—
329C22—5961no—
330C22—11924no—
331C22C2×D4×D14911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2981no—
338C4—2981no—
339C4—2981no—
340C4—5961no—
341C4—5961no—
342C4—5961no—
343C4#41×D14911yescharacteristic
344C4C2×#1455873711yescharacteristic
345C2—42no—
346C2—5961no—
347C2—5962no—
348C2#2375013811yescharacteristic
349C2#2375043211yescharacteristic
350C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#478D149
hypocenterC149#3123
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750238C2semidirect
3. #23749969C2semidirect
4. #23749968C2semidirect
5. #23749922C2semidirect
6. #23749831C2semidirect
7. #23749830C2semidirect
10. #23749724C2semidirect
11. #23749722C2semidirect
12. #23749716C2semidirect
13. #23749712C2semidirect
14. #23749685C2semidirect
15. #478×C149C2semidirect
21. #18011911C22semidirect
28. #18011876C22semidirect
29. #18011876C22semidirect
39. #18011844C22semidirect
40. #18011842C22semidirect
41. C4⋊#11924746C22semidirect
42. #18011836C22semidirect
43. #18011836C22semidirect
44. #18011834C22semidirect
45. #18011834C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
52. #125×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. C4⋊C8×C149C22semidirect
175. C149#3123semidirect
182. #478D149semidirect
202. #125C2×D149semidirect
218. #107C2×D149semidirect
220. #106C2×D149semidirect
222. C4⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237500972
#237499692
#237499682
#237499222
#237498312
#237498302
#237497772
#237497242
#237497222
#237497162
#237497122
#237496852
#478×C1492
#3123149