Finite Group Databasebeta

← #34056504

Subgroups — #34056504

Order 19072.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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#23750279C211yesmaximal, characteristic, complemented
2#23749971C211yesmaximal, characteristic, complemented
3#23749936C212yesmaximal, complemented
4#23749905C211yesmaximal, characteristic, complemented
5#23749859C212yesmaximal, complemented
6#23749817C211yesmaximal, characteristic, complemented
7#23749759C212yesmaximal, complemented
8C4×#14558721C211yesmaximal, characteristic, complemented
9D4×#11924746C211yesmaximal, characteristic, complemented
10C2×#18011832C212yesmaximal, complemented
11D42×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—21no—
13C2×#14558721C2211yescharacteristic
14C2×#14558721C2212yescomplemented
15C22×#11924746C2212yescomplemented
16#18011911C2211yescharacteristic, complemented
17#18011895—22no—
18#18011891—21no—
19#18011885C2212yescomplemented
20C4×D596C2211yescharacteristic, complemented
21C2×C4⋊Dic149C2212yescomplemented
22#18011844C2212yescomplemented
23#18011844C2211yescharacteristic, complemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011832C2212yes—
26#18011832C2211yescharacteristic
27#18011832C2212yescomplemented
28#18011832C2212yescomplemented
29#18011832C2212yescomplemented
30#18011831C2211yescharacteristic, complemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C22×D4×C149—21no—
34C22×D4×C149C2212yes—
35#127×C149C2211yescharacteristic
36#121×C149—21no—
37#121×C149C2212yes—
38#120×C149—22no—
39C4×D4×C149C2211yescharacteristic
40C4×D4×C149C2211yescharacteristic
41#14558735—44no—
42C2×Dic298—21no—
43C2×D596C2311yescharacteristic
44C2×C22⋊D149—22no—
45C22×Dic149—22no—
46C2×C4×D149—21no—
47#14558721—22no—
48#14558721—42no—
49C2×#11924746—42no—
50C2×#11924746C2311yescharacteristic
51C2×#11924746C2312yes—
52C2×#11924746C2311yescharacteristic
53C4⋊Dic149—21no—
54C4⋊Dic149—22no—
55C4⋊Dic149C2312yes—
56C4⋊Dic149C2311yescharacteristic
57#14558713—21no—
58#14558713—22no—
59C24×C149—22no—
60C2×D4×C149—24no—
61C2×D4×C149—22no—
62C2×D4×C149—22no—
63C2×D4×C149—21no—
64C2×D4×C149—21no—
65C2×D4×C149—42no—
66C2×D4×C149—44no—
67C2×D4×C149D411yescharacteristic
68C2×D4×C149C2312yes—
69C2×D4×C149C2311yescharacteristic
70C22×C4×C149—21no—
71C22×C4×C149C2312yes—
72C4⋊C4×C149D411yescharacteristic
73C4⋊C4×C149C2311yescharacteristic
74C22⋊C4×C149—21no—
75C22⋊C4×C149—22no—
76C22⋊C4×C149D412yes—
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79Dic298—42no—
80D596—21no—
81D596—21no—
82C22⋊D149—44no—
83C2×Dic149—21no—
84C2×Dic149—22no—
85C2×Dic149—44no—
86C4×D149—42no—
87#11924746—21no—
88#11924746—22no—
89#11924746—21no—
90C23×C149—21no—
91C23×C149—22no—
92C23×C149—44no—
93C23×C149—44no—
94C23×C149—82no—
95C23×C149C2×D412yes—
96D4×C149—22no—
97D4×C149—21no—
98D4×C149—22no—
99D4×C149—44no—
100D4×C149—44no—
101D4×C149—42no—
102D4×C149—81no—
103D4×C149D814yescomplemented
104D4×C149#4112yescomplemented
105C2×C4×C149—22no—
106C2×C4×C149—22no—
107C2×C4×C149—21no—
108C2×C4×C149—42no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D412yes—
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2411yescharacteristic
113C22×C149—22no—
114C22×C149—22no—
115C22×C149—22no—
116C22×C149—41no—
117C22×C149—41no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149—42no—
121C22×C149—88no—
122C22×C149C2×D814yes—
123C22×C149C22×D411yescharacteristic
124C2×D149—41no—
125C2×D149—41no—
126C2×D149—41no—
127C4×C149—22no—
128C4×C149—21no—
129C4×C149—41no—
130C4×C149C2×D812yes—
131C4×C149C2×#4111yescharacteristic
132C4×C149H(5,𝔽2)11yescharacteristic
133Dic149—41no—
134Dic149—42no—
135C2×C149—24no—
136C2×C149—42no—
137C2×C149—82no—
138C2×C149#54611yescharacteristic
139C2×C149C22×D811yescharacteristic
140C2×C149#57711yescharacteristic
141D149—81no—
142C149#329411yescharacteristic, complemented, Sylow
143#3294—1491nomaximal, Sylow
144#547—1491no—
145D42D14911yescharacteristic, complemented
146#486—1491no—
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—21no—
157C22×D4C2×D14912yes—
158C2×D8—1491no—
159C2×D8—1492no—
160C22×C8—1492no—
161C4⋊Q8—1491no—
162#127C2×D14911yescharacteristic
163#123—2982no—
164C22⋊Q8—2981no—
165#121—21no—
166#121—1492no—
167#121C2×D14912yes—
168#120—22no—
169C4×D4—1491no—
170C4×D4C2×D14911yescharacteristic
171C4×D4C2×D14911yescharacteristic
172C2×C4⋊C4—1492no—
173#107—1491no—
174#107—1492no—
175C4⋊C8—1491no—
176#102—1491no—
177#102—1492no—
178#102—1492no—
179#102—1492no—
180#102—1492no—
181#102—1491no—
182C22⋊C8—1492no—
183C4×C8—1491no—
184C24—22no—
185#41—5964no—
186C2×Q8—2981no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—42no—
193C2×D4—44no—
194C2×D4—2982no—
195C2×D4—1491no—
196C2×D4C22⋊D14911yescharacteristic
197C2×D4C22×D14912yes—
198C2×D4C22×D14911yescharacteristic
199C22×C4—21no—
200C22×C4—2982no—
201C22×C4—2981no—
202C22×C4C22×D14912yes—
203D8—2982no—
204D8—5962no—
205C2×C8—5962no—
206C2×C8—1491no—
207C2×C8—1491no—
208C2×C8—1492no—
209C4⋊C4—2982no—
210C4⋊C4—2981no—
211C4⋊C4—1491no—
212C4⋊C4—1492no—
213C4⋊C4C22⋊D14911yescharacteristic
214C4⋊C4C22×D14911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—2981no—
218C22⋊C4—2982no—
219C22⋊C4C22⋊D14912yes—
220C42C22×D14911yescharacteristic
221C23—21no—
222C23—22no—
223C23—44no—
224C23—44no—
225C23—82no—
226C23—2981no—
227C23C2×C22⋊D14912yes—
228Q8—5962no—
229D4—22no—
230D4—21no—
231D4—22no—
232D4—44no—
233D4—44no—
234D4—42no—
235D4—81no—
236D4—2981no—
237D4—2981no—
238D4—5964no—
239D4#1455872114yescomplemented
240D4#1455873512yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—2981no—
246C2×C4—2982no—
247C2×C4—5964no—
248C2×C4—5962no—
249C2×C4C2×C22⋊D14911yescharacteristic
250C2×C4C2×C22⋊D14912yes—
251C2×C4C2×C22⋊D14911yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—2981no—
254C8—2981no—
255C8—2982no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—88no—
265C22—5961no—
266C22—5961no—
267C22—5961no—
268C22C2×#1455872114yes—
269C22C22×C22⋊D14911yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—5961no—
274C4—5962no—
275C4C2×#1455872112yes—
276C4C2×#1455873511yescharacteristic
277C4#1801195611yescharacteristic
278C2—24no—
279C2—42no—
280C2—82no—
281C2—11921no—
282C2#2375026911yescharacteristic
283C2C22×#1455872111yescharacteristic
284C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingD42×C149C2
socleC22×C149C22×D4
hypercenterD42D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #23750279C2semidirect
2. #23749971C2semidirect
3. #23749936C2semidirect
4. #23749905C2semidirect
5. #23749859C2semidirect
6. #23749817C2semidirect
7. #23749759C2semidirect
8. C4×#14558721C2semidirect
9. D4×#11924746C2semidirect
10. C2×#18011832C2semidirect
11. D42×C149C2semidirect
14. C2×#14558721C22semidirect
15. C22×#11924746C22semidirect
16. #18011911C22semidirect
19. #18011885C22semidirect
20. C4×D596C22semidirect
21. C2×C4⋊Dic149C22semidirect
22. #18011844C22semidirect
23. #18011844C22semidirect
24. C4⋊#11924746C22semidirect
27. #18011832C22semidirect
28. #18011832C22semidirect
29. #18011832C22semidirect
30. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
103. D4×C149D8semidirect
104. D4×C149#41semidirect
142. C149#3294semidirect
145. D42D149semidirect
239. D4#14558721semidirect
240. D4#14558735semidirect

Maximal subgroups

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

subgroupindex
#237502792
#237499712
#237499362
#237499052
#237498592
#237498172
#237497592
C4×#145587212
D4×#119247462
C2×#180118322
D42×C1492
#3294149