Finite Group Databasebeta

← #34056507

Subgroups — #34056507

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#23750280C211yesmaximal, characteristic, complemented
2#23750260C211yesmaximal, characteristic, complemented
3#23749971C211yesmaximal, characteristic, complemented
4#23749937C212yesmaximal, complemented
5#23749906C211yesmaximal, characteristic, complemented
6#23749858C212yesmaximal, complemented
7#23749757C212yesmaximal, complemented
8C4×#14558721C211yesmaximal, characteristic, complemented
9#23749690C211yesmaximal, characteristic, complemented
10#102×D149C212yesmaximal, complemented
11#459×C149C211yesmaximal, characteristic, complemented
12C2×#14558736—21no—
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15C2×#14558721C2211yescharacteristic
16C2×C8×D149C2212yescomplemented
17#18011911C2211yescharacteristic, complemented
18#18011893—22no—
19#18011890—21no—
20#18011882—21no—
21#18011882C2212yes—
22#18011882C2212yescomplemented
23#18011879—22no—
24C4×D596C2211yescharacteristic
25C4×D596C2211yescharacteristic
26C4⋊C4×D149C2212yescomplemented
27#18011845C2212yescomplemented
28#18011844C2211yescharacteristic, complemented
29#18011833C2212yes—
30#18011832C2212yescomplemented
31#18011832C2211yescharacteristic, complemented
32#18011832C2212yescomplemented
33#18011831C2211yescharacteristic
34#18011823C2212yescomplemented
35C4×#11924746C2211yescharacteristic, complemented
36C2×D8×C149C2212yescomplemented
37#127×C149C2211yescharacteristic
38C4×D4×C149C2211yescharacteristic, complemented
39C4⋊C8×C149C2211yescharacteristic, complemented
40#102×C149C2212yescomplemented
41C23×D149—22no—
42#14558736—44no—
43C2×Dic298—21no—
44C2×D596D411yescharacteristic
45C2×D596C2311yescharacteristic
46C2×C22⋊D149—22no—
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×D149C2312yes—
55#14558721—22no—
56C2×#11924746C2311yescharacteristic
57C2×#11924746C2311yescharacteristic
58C8×D149—42no—
59C4⋊Dic149—21no—
60C4⋊Dic149D411yescharacteristic
61C4⋊Dic149C2312yes—
62C4⋊Dic149C2311yescharacteristic
63#14558715—22no—
64C22⋊Dic149—22no—
65C22⋊Dic149—22no—
66#14558713—21no—
67#14558713D412yes—
68C2×D4×C149—21no—
69C2×D4×C149—21no—
70C2×D4×C149C2311yescharacteristic
71C2×D4×C149C2312yes—
72C22×C4×C149—21no—
73D8×C149—42no—
74C2×C8×C149C2312yes—
75C4⋊C4×C149C2311yescharacteristic
76C22⋊C4×C149—21no—
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82C22×D149C2×D412yes—
83Dic298—42no—
84D596—21no—
85D596D814yescomplemented
86D596#4112yescomplemented
87C22⋊D149—44no—
88C22⋊D149—44no—
89C22⋊D149—44no—
90C2×Dic149—21no—
91C2×Dic149—22no—
92C2×Dic149C2×D412yes—
93C4×D149—22no—
94C4×D149—22no—
95C4×D149—44no—
96C4×D149—42no—
97#11924746—21no—
98#11924746—21no—
99C23×C149—22no—
100C23×C149—21no—
101D4×C149—21no—
102D4×C149—22no—
103D4×C149—22no—
104D4×C149—21no—
105D4×C149—42no—
106D4×C149—81no—
107C2×C4×C149—21no—
108C2×C4×C149—42no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2411yescharacteristic
112C8×C149—22no—
113C22×C149—41no—
114C22×C149—42no—
115C22×C149—41no—
116C22×C149—42no—
117C22×C149—42no—
118C22×C149—41no—
119C22×C149C22×D411yescharacteristic
120C2×D149—22no—
121C2×D149—22no—
122C2×D149—22no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—88no—
126C2×D149C2×D814yes—
127C4×C149—21no—
128C4×C149—41no—
129C4×C149C2×D812yes—
130C4×C149C2×#4111yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—22no—
133Dic149—41no—
134Dic149—42no—
135C2×C149—82no—
136C2×C149—81no—
137C2×C149#54611yescharacteristic
138C2×C149C22×D811yescharacteristic
139C2×C149#57711yescharacteristic
140D149—24no—
141D149—42no—
142C149#329411yescharacteristic, complemented, Sylow
143#3294—1491nomaximal, Sylow
144#547—1491no—
145D42—1491no—
146#486—1491no—
147#480—1492no—
148#474—1491no—
149#466—1492no—
150#459D14911yescharacteristic, complemented
151#447—1492no—
152C4×D8—1491no—
153C8×D4—1491no—
154C2×#102—1492no—
155C2×#41—2981no—
156C22×D4—2981no—
157C22×D4—1492no—
158C2×D8—1491no—
159C2×D8C2×D14912yescomplemented
160C22×C8—1492no—
161C4⋊Q8—1491no—
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×D4C2×D14911yescharacteristic, complemented
172C2×C4⋊C4—1492no—
173#107—1492no—
174#107—1491no—
175C4⋊C8C2×D14911yescharacteristic, complemented
176#102—1492no—
177#102—1491no—
178#102—1492no—
179#102—1492no—
180#102—1491no—
181#102C2×D14912yescomplemented
182C22⋊C8—1492no—
183C4×C8—1491no—
184C24—2982no—
185#41—5964no—
186C2×Q8—2981no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—2984no—
190C2×D4—2982no—
191C2×D4—2982no—
192C2×D4—2982no—
193C2×D4—5962no—
194C2×D4—5964no—
195C2×D4—1491no—
196C2×D4—1491no—
197C2×D4C22×D14912yes—
198C2×D4C22×D14911yescharacteristic
199C22×C4—21no—
200C22×C4—2982no—
201C22×C4—2981no—
202C22×C4—1492no—
203D8—42no—
204D8—2982no—
205C2×C8—5962no—
206C2×C8—1491no—
207C2×C8—1491no—
208C2×C8C22×D14912yes—
209C4⋊C4—2982no—
210C4⋊C4—2981no—
211C4⋊C4—1492no—
212C4⋊C4—1491no—
213C4⋊C4—1491no—
214C4⋊C4C22×D14911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2982no—
217C22⋊C4—2982no—
218C22⋊C4—2981no—
219C22⋊C4—1492no—
220C42C22×D14911yescharacteristic
221C23—21no—
222C23—22no—
223C23—2981no—
224C23—5964no—
225C23—5964no—
226C23—1492no—
227C23—11922no—
228Q8—5962no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—2981no—
236D4—5964no—
237D4—5964no—
238D4—5964no—
239D4—1494no—
240D4—1492no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—2982no—
244C2×C4—2982no—
245C2×C4—2981no—
246C2×C4—2982no—
247C2×C4—5964no—
248C2×C4—5962no—
249C2×C4—1492no—
250C2×C4D4×D14911yescharacteristic
251C2×C4D4×D14911yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—22no—
254C8—2981no—
255C8—2981no—
256C22—42no—
257C22—41no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—2982no—
263C22—2982no—
264C22—2982no—
265C22—5961no—
266C22—5961no—
267C22—1494no—
268C22—11928no—
269C22C2×D4×D14911yescharacteristic
270C4—21no—
271C4—41no—
272C4—2982no—
273C4—5961no—
274C4—5962no—
275C4D8×D14912yes—
276C4#41×D14911yescharacteristic
277C4#1801195611yescharacteristic
278C2—82no—
279C2—81no—
280C2—2984no—
281C2—5962no—
282C2#2375027211yescharacteristic
283C2C2×D8×D14911yescharacteristic
284C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#459×C149C2
socleC22×C149C22×D4
hypercenter#459D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23750280C2semidirect
2. #23750260C2semidirect
3. #23749971C2semidirect
4. #23749937C2semidirect
5. #23749906C2semidirect
6. #23749858C2semidirect
7. #23749757C2semidirect
8. C4×#14558721C2semidirect
9. #23749690C2semidirect
10. #102×D149C2semidirect
11. #459×C149C2semidirect
16. C2×C8×D149C22semidirect
17. #18011911C22semidirect
22. #18011882C22semidirect
26. C4⋊C4×D149C22semidirect
27. #18011845C22semidirect
28. #18011844C22semidirect
30. #18011832C22semidirect
31. #18011832C22semidirect
32. #18011832C22semidirect
34. #18011823C22semidirect
35. C4×#11924746C22semidirect
36. C2×D8×C149C22semidirect
38. C4×D4×C149C22semidirect
39. C4⋊C8×C149C22semidirect
40. #102×C149C22semidirect
85. D596D8semidirect
86. D596#41semidirect
142. C149#3294semidirect
150. #459D149semidirect
159. C2×D8C2×D149semidirect
171. C4×D4C2×D149semidirect
175. C4⋊C8C2×D149semidirect
181. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502802
#237502602
#237499712
#237499372
#237499062
#237498582
#237497572
C4×#145587212
#237496902
#102×D1492
#459×C1492
#3294149