Finite Group Databasebeta

← #34054788

Subgroups — #34054788

Order 19072.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750179C211yesmaximal, characteristic, complemented
2C4×D4×D149C211yesmaximal, characteristic
3#23749962C211yesmaximal, characteristic, complemented
4#23749959C211yesmaximal, characteristic, complemented
5#23749904C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749828C211yesmaximal, characteristic, complemented
9#23749777C211yesmaximal, characteristic
10#23749774C211yesmaximal, characteristic
11#23749727C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14#23749680C211yesmaximal, characteristic, complemented
15#440×C149C211yesmaximal, characteristic, complemented
16C2×D4×D149C2211yescharacteristic
17C22×C4×D149—21no—
18C2×#14558725C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011910C2211yescharacteristic, complemented
22#18011909C2211yescharacteristic, complemented
23#18011901—21no—
24#18011891C2211yescharacteristic
25#18011889—21no—
26#18011887C2211yescharacteristic
27C4×Dic298—21no—
28C4×Dic298C2211yescharacteristic, complemented
29C4×D596C2211yescharacteristic
30D4×Dic149C2211yescharacteristic
31#18011873C2211yescharacteristic
32C4×C22⋊D149—21no—
33#18011871—21no—
34#18011868—21no—
35C4⋊C4×D149C2211yescharacteristic
36C22⋊C4×D149—21no—
37C42×D149C2211yescharacteristic
38#18011845C2211yescharacteristic, complemented
39#18011844C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011836C2211yescharacteristic, complemented
44#18011835C2211yescharacteristic, complemented
45#18011834C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011822C2211yescharacteristic, complemented
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic, complemented
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C2×Dic298—21no—
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×D149—21no—
70C2×C4×D149—44no—
71C2×C4×D149D411yescharacteristic
72C2×C4×D149D411yescharacteristic
73C2×C4×D149C2311yescharacteristic
74#14558725—22no—
75#14558724—22no—
76#14558723—22no—
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86#14558715—21no—
87#14558715—21no—
88C22⋊Dic149—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149D411yescharacteristic
95C4×Dic149D411yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×D4×C149C2311yescharacteristic
99C22×C4×C149—21no—
100SD16×C149—22no—
101C2×C8×C149C2311yescharacteristic
102C2×C8×C149C2311yescharacteristic
103C4⋊C4×C149—21no—
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C42×C149C2311yescharacteristic
109C22×D149—24no—
110C22×D149—21no—
111C22×D149—42no—
112C22×D149—42no—
113C22×D149C2×D411yescharacteristic
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117D596—21no—
118D596#4112yes—
119C22⋊D149—24no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C4×D149—22no—
128C4×D149—21no—
129C4×D149—21no—
130C4×D149—22no—
131C4×D149—42no—
132C4×D149—42no—
133C4×D149—42no—
134#11924746—21no—
135#11924746—21no—
136C23×C149—21no—
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149#4112yes—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—42no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2×D411yescharacteristic
147C2×C4×C149C2411yescharacteristic
148C8×C149—21no—
149C8×C149—21no—
150C22×C149—22no—
151C22×C149—41no—
152C22×C149—41no—
153C22×C149C22×D411yescharacteristic
154C2×D149—21no—
155C2×D149—21no—
156C2×D149—22no—
157C2×D149—48no—
158C2×D149—41no—
159C2×D149—41no—
160C2×D149#13712yes—
161C4×C149—21no—
162C4×C149—21no—
163C4×C149—41no—
164C4×C149—41no—
165C4×C149—41no—
166C4×C149C2×#4111yescharacteristic
167C4×C149C2×#4111yescharacteristic
168Dic149—21no—
169Dic149—21no—
170Dic149—41no—
171Dic149—41no—
172Dic149—41no—
173Dic149AGL(1,ℤ/8)12yes—
174C2×C149—42no—
175C2×C149#52511yescharacteristic
176C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C149C2×#13711yescharacteristic
178D149—22no—
179D149—42no—
180C149#311011yescharacteristic, complemented, Sylow
181#3110—1491nomaximal, Sylow
182#533—1491no—
183C2×C4×D4—1491no—
184#484—1491no—
185#484—1491no—
186#474—1491no—
187#474—1491no—
188#461—1491no—
189#461—1491no—
190#450—1491no—
191#450—1491no—
192#440—1491no—
193#440—1491no—
194#440—1491no—
195#440D14911yescharacteristic, complemented
196#432—1491no—
197C22×D4—1491no—
198C23×C4—2981no—
199C2×SD16—1491no—
200C2×SD16—1491no—
201C2×SD16—1491no—
202C2×SD16C2×D14911yescharacteristic
203C4⋊Q8—1491no—
204C4⋊Q8—1491no—
205#125—2981no—
206C22⋊Q8—2981no—
207C22⋊Q8—1491no—
208C22⋊Q8—1491no—
209C4×Q8—2981no—
210C4×Q8—1491no—
211C4×Q8C2×D14911yescharacteristic, complemented
212C4×D4—2981no—
213C4×D4—2981no—
214C4×D4—1491no—
215C4×D4—1491no—
216C4×D4—1491no—
217C4×D4C2×D14911yescharacteristic
218#117—2981no—
219C2×C4⋊C4—1491no—
220C2×C22⋊C4—2981no—
221C2×C42—1491no—
222#107—1491no—
223#107—1491no—
224#107—1491no—
225#107C2×D14911yescharacteristic, complemented
226C4⋊C8—1491no—
227C4⋊C8—1491no—
228#103—1491no—
229#103—1491no—
230#103—1491no—
231#103C2×D14911yescharacteristic, complemented
232#102—1491no—
233#102—1491no—
234#102—1491no—
235#102C2×D14911yescharacteristic
236C22⋊C8—1491no—
237C22⋊C8—1491no—
238#97—1491no—
239#97C2×D14911yescharacteristic, complemented
240C24—2981no—
241C2×Q8—2981no—
242C2×Q8—1491no—
243C2×Q8C22×D14911yescharacteristic
244C2×D4—2982no—
245C2×D4—2982no—
246C2×D4—2981no—
247C2×D4—1491no—
248C2×D4C22×D14911yescharacteristic
249C22×C4—21no—
250C22×C4—2981no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—2981no—
254C22×C4—5964no—
255C22×C4—1491no—
256C22×C4—1491no—
257C22×C4—1491no—
258SD16—22no—
259SD16—2982no—
260SD16—2982no—
261SD16—2982no—
262C2×C8—1491no—
263C2×C8—1491no—
264C2×C8C22×D14911yescharacteristic
265C2×C8C22×D14911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—2981no—
273C4⋊C4—2981no—
274C4⋊C4—1491no—
275C4⋊C4—1491no—
276C4⋊C4C22×D14911yescharacteristic
277C4⋊C4C22×D14911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C42—21no—
285C42—2981no—
286C42—1491no—
287C42—1491no—
288C42—1491no—
289C42C22×D14911yescharacteristic
290C23—21no—
291C23—2984no—
292C23—2981no—
293C23—5962no—
294C23—5962no—
295C23—1491no—
296Q8—21no—
297Q8—21no—
298Q8—2981no—
299Q8—2981no—
300Q8—5962no—
301D4—21no—
302D4—2984no—
303D4—2981no—
304D4—1492no—
305D4#1455873612yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—2982no—
311C2×C4—2982no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—5962no—
318C2×C4—5962no—
319C2×C4—5962no—
320C2×C4—5962no—
321C2×C4—1491no—
322C2×C4—1491no—
323C2×C4—1491no—
324C2×C4D4×D14911yescharacteristic
325C2×C4D4×D14911yescharacteristic
326C2×C4C23×D14911yescharacteristic
327C8—21no—
328C8—21no—
329C8—2981no—
330C8—2981no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—2981no—
335C22—2981no—
336C22—2982no—
337C22—5968no—
338C22—5961no—
339C22—5961no—
340C22—1492no—
341C22C2×D4×D14911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2981no—
348C4—2981no—
349C4—5961no—
350C4—5961no—
351C4—5961no—
352C4—1492no—
353C4#41×D14911yescharacteristic
354C4C2×#1455873611yescharacteristic
355C2—42no—
356C2—2982no—
357C2—5962no—
358C2#2375013411yescharacteristic
359C2AGL(1,ℤ/8)×D14911yescharacteristic
360C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#440D149
hypocenterC149#3110
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23750179C2semidirect
3. #23749962C2semidirect
4. #23749959C2semidirect
5. #23749904C2semidirect
6. #23749903C2semidirect
7. #23749829C2semidirect
8. #23749828C2semidirect
11. #23749727C2semidirect
12. #23749725C2semidirect
13. #23749723C2semidirect
14. #23749680C2semidirect
15. #440×C149C2semidirect
21. #18011910C22semidirect
22. #18011909C22semidirect
28. C4×Dic298C22semidirect
38. #18011845C22semidirect
39. #18011844C22semidirect
40. #18011844C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011836C22semidirect
44. #18011835C22semidirect
45. #18011834C22semidirect
51. #18011822C22semidirect
53. C4×Q8×C149C22semidirect
55. #107×C149C22semidirect
56. #103×C149C22semidirect
58. #97×C149C22semidirect
180. C149#3110semidirect
195. #440D149semidirect
211. C4×Q8C2×D149semidirect
225. #107C2×D149semidirect
231. #103C2×D149semidirect
239. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501792
C4×D4×D1492
#237499622
#237499592
#237499042
#237499032
#237498292
#237498282
#237497772
#237497742
#237497272
#237497252
#237497232
#237496802
#440×C1492
#3110149