Finite Group Databasebeta

← #34056503

Subgroups — #34056503

Order 19072.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750278C211yesmaximal, characteristic, complemented
2#23750260C211yesmaximal, characteristic, complemented
3#23749937C212yesmaximal, complemented
4#23749902C211yesmaximal, characteristic, complemented
5#23749860C212yesmaximal, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749760C212yesmaximal, complemented
8C4×D1192C211yesmaximal, characteristic, complemented
9C8×D596C211yesmaximal, characteristic, complemented
10#102×D149C212yesmaximal, complemented
11#486×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15C2×D1192C2211yescharacteristic
16C2×#14558721C2212yescomplemented
17C2×C8×D149C2212yescomplemented
18#18011896—22no—
19#18011887—21no—
20#18011886C2212yescomplemented
21#18011882—21no—
22#18011882C2212yes—
23#18011879—22no—
24C4×D596C2211yescharacteristic
25C4×D596C2211yescharacteristic
26C4×D596C2211yescharacteristic, complemented
27C4⋊C4×D149C2212yescomplemented
28#18011845C2211yescharacteristic, complemented
29#18011844C2212yescomplemented
30C4⋊#11924746C2211yescharacteristic, complemented
31#18011833C2211yescharacteristic
32#18011833C2211yescharacteristic, complemented
33#18011832C2212yescomplemented
34#18011831C2212yes—
35#18011823C2212yescomplemented
36C4⋊Q8×C149C2211yescharacteristic, complemented
37#127×C149C2211yescharacteristic
38#102×C149C2212yescomplemented
39#102×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42#14558737—44no—
43C2×D596—22no—
44C2×D596D411yescharacteristic
45C2×D596C2311yescharacteristic
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—22no—
48C2×C22⋊D149—22no—
49D4×D149—24no—
50D4×D149—42no—
51D4×D149—44no—
52C2×C4×D149—22no—
53C2×C4×D149—21no—
54C2×C4×D149—21no—
55C2×C4×D149C2312yes—
56D1192—22no—
57#14558721—42no—
58C2×#11924746C2312yes—
59C8×D149—42no—
60C4⋊Dic149D411yescharacteristic
61C4⋊Dic149C2311yescharacteristic
62C4⋊Dic149C2311yescharacteristic
63#14558715—22no—
64C22⋊Dic149—22no—
65#14558713—22no—
66#14558713—21no—
67#14558713—21no—
68#14558713D412yes—
69C2×Q8×C149—21no—
70C2×D4×C149—21no—
71C2×D4×C149—21no—
72C2×D4×C149C2312yes—
73C2×C8×C149C2311yescharacteristic
74C2×C8×C149C2311yescharacteristic
75C4⋊C4×C149—21no—
76C4⋊C4×C149C2312yes—
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79C22×D149—21no—
80C22×D149—44no—
81C22×D149—44no—
82C22×D149—82no—
83C22×D149C2×D412yes—
84D596—21no—
85D596—21no—
86D596—21no—
87D596—44no—
88D596D814yescomplemented
89D596#4112yescomplemented
90C22⋊D149—44no—
91C22⋊D149—44no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149C2×D412yes—
95C4×D149—22no—
96C4×D149—22no—
97C4×D149—44no—
98C4×D149—42no—
99C4×D149—42no—
100#11924746—22no—
101C23×C149—22no—
102Q8×C149—42no—
103D4×C149—22no—
104D4×C149—22no—
105D4×C149—42no—
106D4×C149—81no—
107C2×C4×C149—22no—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2411yescharacteristic
111C8×C149—21no—
112C8×C149—21no—
113C22×C149—42no—
114C22×C149—42no—
115C22×C149—42no—
116C22×C149C22×D411yescharacteristic
117C2×D149—22no—
118C2×D149—22no—
119C2×D149—22no—
120C2×D149—41no—
121C2×D149—41no—
122C2×D149—41no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—88no—
126C2×D149C2×D814yes—
127C4×C149—21no—
128C4×C149—42no—
129C4×C149C2×D812yes—
130C4×C149C2×#4111yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—22no—
133Dic149—41no—
134Dic149—41no—
135C2×C149—82no—
136C2×C149#54611yescharacteristic
137C2×C149C22×D811yescharacteristic
138C2×C149#57711yescharacteristic
139D149—24no—
140D149—42no—
141D149—81no—
142C149#329411yescharacteristic, complemented, Sylow
143#3294—1491nomaximal, Sylow
144#547—1491no—
145D42—1491no—
146#486D14911yescharacteristic, complemented
147#480—1492no—
148#474—1491no—
149#466—1492no—
150#459—1491no—
151#447—1492no—
152C4×D8—1491no—
153C8×D4—1491no—
154C2×#102—1492no—
155C2×#41—2981no—
156C22×D4—2981no—
157C22×D4—1492no—
158C2×D8—1492no—
159C2×D8—1491no—
160C22×C8—1492no—
161C4⋊Q8C2×D14911yescharacteristic, complemented
162#127C2×D14911yescharacteristic
163#123—2982no—
164C22⋊Q8—2981no—
165#121—2981no—
166#121—1492no—
167#121—1492no—
168#120—2982no—
169C4×D4—1491no—
170C4×D4—1491no—
171C4×D4—1491no—
172C2×C4⋊C4—1492no—
173#107—1491no—
174#107—1492no—
175C4⋊C8—1491no—
176#102—1492no—
177#102—1491no—
178#102—1491no—
179#102—1492no—
180#102C2×D14912yescomplemented
181#102C2×D14912yescomplemented
182C22⋊C8—1492no—
183C4×C8C2×D14911yescharacteristic, complemented
184C24—2982no—
185#41—5964no—
186C2×Q8—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—2982no—
190C2×D4—2984no—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—5962no—
194C2×D4—5964no—
195C2×D4—1491no—
196C2×D4—1491no—
197C2×D4—1491no—
198C2×D4C22×D14912yes—
199C22×C4—2982no—
200C22×C4—2981no—
201C22×C4—2981no—
202C22×C4—1492no—
203D8—2982no—
204D8—5962no—
205C2×C8—5962no—
206C2×C8—1492no—
207C2×C8C22×D14911yescharacteristic
208C2×C8C22×D14911yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—2982no—
211C4⋊C4—1491no—
212C4⋊C4—1491no—
213C4⋊C4—1491no—
214C4⋊C4C22×D14912yes—
215C22⋊C4—2982no—
216C22⋊C4—2982no—
217C22⋊C4—2981no—
218C22⋊C4—2981no—
219C22⋊C4—1492no—
220C42C22×D14911yescharacteristic
221C23—22no—
222C23—2981no—
223C23—2981no—
224C23—5964no—
225C23—5964no—
226C23—1492no—
227C23—11922no—
228Q8—42no—
229D4—22no—
230D4—22no—
231D4—42no—
232D4—81no—
233D4—2981no—
234D4—2981no—
235D4—2981no—
236D4—5964no—
237D4—5964no—
238D4—5964no—
239D4—1494no—
240D4—1492no—
241C2×C4—22no—
242C2×C4—2982no—
243C2×C4—2982no—
244C2×C4—2981no—
245C2×C4—2981no—
246C2×C4—5964no—
247C2×C4—5962no—
248C2×C4—5962no—
249C2×C4—1492no—
250C2×C4D4×D14911yescharacteristic
251C2×C4D4×D14911yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—21no—
254C8—21no—
255C8—2982no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—2982no—
260C22—2982no—
261C22—2982no—
262C22—5961no—
263C22—5961no—
264C22—5961no—
265C22—5961no—
266C22—5961no—
267C22—1494no—
268C22—11928no—
269C22C2×D4×D14911yescharacteristic
270C4—21no—
271C4—42no—
272C4—2982no—
273C4—5961no—
274C4—5961no—
275C4D8×D14912yes—
276C4#41×D14911yescharacteristic
277C4#1801195711yescharacteristic
278C2—82no—
279C2—2984no—
280C2—5962no—
281C2—11921no—
282C2#2375026811yescharacteristic
283C2C2×D8×D14911yescharacteristic
284C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
hypercenter#486D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23750278C2semidirect
2. #23750260C2semidirect
3. #23749937C2semidirect
4. #23749902C2semidirect
5. #23749860C2semidirect
6. #23749817C2semidirect
7. #23749760C2semidirect
8. C4×D1192C2semidirect
9. C8×D596C2semidirect
10. #102×D149C2semidirect
11. #486×C149C2semidirect
16. C2×#14558721C22semidirect
17. C2×C8×D149C22semidirect
20. #18011886C22semidirect
26. C4×D596C22semidirect
27. C4⋊C4×D149C22semidirect
28. #18011845C22semidirect
29. #18011844C22semidirect
30. C4⋊#11924746C22semidirect
32. #18011833C22semidirect
33. #18011832C22semidirect
35. #18011823C22semidirect
36. C4⋊Q8×C149C22semidirect
38. #102×C149C22semidirect
39. #102×C149C22semidirect
40. C4×C8×C149C22semidirect
88. D596D8semidirect
89. D596#41semidirect
142. C149#3294semidirect
146. #486D149semidirect
161. C4⋊Q8C2×D149semidirect
180. #102C2×D149semidirect
181. #102C2×D149semidirect
183. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502782
#237502602
#237499372
#237499022
#237498602
#237498172
#237497602
C4×D11922
C8×D5962
#102×D1492
#486×C1492
#3294149