Finite Group Databasebeta

← #34056505

Subgroups — #34056505

Order 19072.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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
2D4×D596C211yesmaximal, characteristic, complemented
3#23749972C211yesmaximal, characteristic, complemented
4#23749939C212yesmaximal, complemented
5#23749906C211yesmaximal, characteristic, complemented
6#23749861C212yesmaximal, complemented
7#23749821C211yesmaximal, characteristic, complemented
8#23749761C212yesmaximal, complemented
9C4×D1192C211yesmaximal, characteristic, complemented
10C2×#18011833C212yesmaximal, complemented
11C8×D4×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—21no—
13C22×D596C2212yes—
14C2×D4×D149—21no—
15C2×D1192C2211yescharacteristic
16C2×D1192C2212yescomplemented
17#18011911C2211yescharacteristic, complemented
18#18011908C2211yescharacteristic
19#18011895—22no—
20#18011891—21no—
21#18011886—21no—
22#18011885C2212yes—
23#18011885C2212yescomplemented
24#18011881—22no—
25C4×D596C2211yescharacteristic
26C4×D596C2211yescharacteristic, complemented
27C2×C4⋊Dic149C2212yescomplemented
28#18011845C2212yescomplemented
29#18011845C2211yescharacteristic, complemented
30#18011833C2212yes—
31#18011833C2211yescharacteristic
32#18011833C2212yescomplemented
33#18011833C2212yescomplemented
34#18011833C2211yescharacteristic, complemented
35#18011833C2212yescomplemented
36C22×C8×C149C2212yescomplemented
37C4×D4×C149C2211yescharacteristic
38C4⋊C8×C149C2211yescharacteristic, complemented
39C22⋊C8×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42#14558735—44no—
43C2×Dic298—21no—
44C2×D596—24no—
45C2×D596—21no—
46C2×D596—22no—
47C2×D596—21no—
48C2×D596—42no—
49C2×D596C2312yes—
50C2×D596C2311yescharacteristic
51C2×D596C2311yescharacteristic
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54D4×D149—44no—
55C22×Dic149—22no—
56C2×C4×D149—21no—
57C2×C4×D149—21no—
58D1192—22no—
59D1192—42no—
60C4⋊Dic149—21no—
61C4⋊Dic149—22no—
62C4⋊Dic149C2312yes—
63C4⋊Dic149C2311yescharacteristic
64C4⋊Dic149C2311yescharacteristic
65#14558713—21no—
66#14558713—21no—
67#14558713—22no—
68#14558713—22no—
69C2×D4×C149D411yescharacteristic
70C22×C4×C149C2312yes—
71C2×C8×C149—42no—
72C2×C8×C149C2311yescharacteristic
73C2×C8×C149C2312yes—
74C2×C8×C149C2311yescharacteristic
75C4⋊C4×C149D411yescharacteristic
76C22⋊C4×C149D412yes—
77C42×C149C2311yescharacteristic
78C22×D149—21no—
79C22×D149—21no—
80C22×D149—22no—
81C22×D149—44no—
82C22×D149—44no—
83C22×D149—82no—
84Dic298—42no—
85D596—21no—
86D596—22no—
87D596—21no—
88D596—21no—
89D596—22no—
90D596—44no—
91D596—42no—
92D596—81no—
93D596#4112yescomplemented
94C22⋊D149—44no—
95C22⋊D149—44no—
96C2×Dic149—21no—
97C2×Dic149—21no—
98C2×Dic149—22no—
99C2×Dic149—44no—
100C4×D149—42no—
101C4×D149—42no—
102C23×C149C2×D412yes—
103D4×C149D814yescomplemented
104C2×C4×C149—22no—
105C2×C4×C149—22no—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C8×C149—21no—
111C8×C149—22no—
112C8×C149—21no—
113C22×C149—22no—
114C22×C149—22no—
115C22×C149C2×D814yes—
116C22×C149C22×D411yescharacteristic
117C2×D149—22no—
118C2×D149—41no—
119C2×D149—41no—
120C2×D149—42no—
121C2×D149—41no—
122C2×D149—41no—
123C2×D149—42no—
124C2×D149—42no—
125C2×D149—41no—
126C2×D149—88no—
127C4×C149—22no—
128C4×C149—21no—
129C4×C149C2×D812yes—
130C4×C149C2×#4111yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—41no—
133Dic149—41no—
134Dic149—42no—
135C2×C149—24no—
136C2×C149#54611yescharacteristic
137C2×C149C22×D811yescharacteristic
138C2×C149#57711yescharacteristic
139D149—42no—
140D149—81no—
141D149—82no—
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#459—1491no—
151#447—1492no—
152C4×D8—1491no—
153C8×D4D14911yescharacteristic, complemented
154C2×#102—1492no—
155C2×#41—2981no—
156C22×D4—2981no—
157C22×D4—1492no—
158C2×D8—1491no—
159C2×D8—1492no—
160C22×C8C2×D14912yescomplemented
161C4⋊Q8—1491no—
162#127—1491no—
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
172C2×C4⋊C4—1492no—
173#107—1491no—
174#107—1492no—
175C4⋊C8C2×D14911yescharacteristic, complemented
176#102—1491no—
177#102—1492no—
178#102—1492no—
179#102—1492no—
180#102—1491no—
181#102—1492no—
182C22⋊C8C2×D14912yescomplemented
183C4×C8C2×D14911yescharacteristic, complemented
184C24—2982no—
185#41—5964no—
186C2×Q8—2981no—
187C2×D4—2984no—
188C2×D4—2982no—
189C2×D4—2982no—
190C2×D4—2982no—
191C2×D4—2981no—
192C2×D4—2981no—
193C2×D4—5962no—
194C2×D4—5964no—
195C2×D4—1492no—
196C2×D4—1491no—
197C2×D4—1491no—
198C2×D4D59611yescharacteristic
199C22×C4—2982no—
200C22×C4—2981no—
201C22×C4—2981no—
202C22×C4C22×D14912yes—
203D8—2982no—
204D8—5962no—
205C2×C8—42no—
206C2×C8C22×D14911yescharacteristic
207C2×C8C22×D14911yescharacteristic
208C2×C8C22×D14912yes—
209C4⋊C4—2982no—
210C4⋊C4—2981no—
211C4⋊C4—1491no—
212C4⋊C4—1492no—
213C4⋊C4—1491no—
214C4⋊C4D59611yescharacteristic
215C22⋊C4—2981no—
216C22⋊C4—2981no—
217C22⋊C4—2982no—
218C22⋊C4—2982no—
219C22⋊C4D59612yes—
220C42C22×D14911yescharacteristic
221C23—2981no—
222C23—2981no—
223C23—2982no—
224C23—5964no—
225C23—5964no—
226C23—11922no—
227C23C2×D59612yes—
228Q8—5962no—
229D4—2981no—
230D4—2982no—
231D4—2981no—
232D4—2981no—
233D4—2982no—
234D4—5964no—
235D4—5964no—
236D4—5964no—
237D4—5962no—
238D4—1492no—
239D4—11921no—
240D4D119214yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—2981no—
244C2×C4—2981no—
245C2×C4—2982no—
246C2×C4—5964no—
247C2×C4—5962no—
248C2×C4—5962no—
249C2×C4C2×D59611yescharacteristic
250C2×C4C2×D59612yes—
251C2×C4C2×D59611yescharacteristic
252C2×C4C23×D14911yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—2982no—
259C22—5961no—
260C22—5961no—
261C22—5962no—
262C22—5961no—
263C22—5962no—
264C22—5961no—
265C22—5961no—
266C22—5962no—
267C22—11928no—
268C22C2×D119214yes—
269C22C22×D59611yescharacteristic
270C4—21no—
271C4—22no—
272C4—5961no—
273C4—5961no—
274C4—5962no—
275C4C2×D119212yes—
276C4#41×D14911yescharacteristic
277C4#1801195611yescharacteristic
278C2—24no—
279C2—5962no—
280C2—11922no—
281C2—11921no—
282C2#2375027011yescharacteristic
283C2C22×D119211yescharacteristic
284C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC8×D4×C149C2
socleC22×C149C22×D4
hypercenterC8×D4D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23750279C2semidirect
2. D4×D596C2semidirect
3. #23749972C2semidirect
4. #23749939C2semidirect
5. #23749906C2semidirect
6. #23749861C2semidirect
7. #23749821C2semidirect
8. #23749761C2semidirect
9. C4×D1192C2semidirect
10. C2×#18011833C2semidirect
11. C8×D4×C149C2semidirect
16. C2×D1192C22semidirect
17. #18011911C22semidirect
23. #18011885C22semidirect
26. C4×D596C22semidirect
27. C2×C4⋊Dic149C22semidirect
28. #18011845C22semidirect
29. #18011845C22semidirect
32. #18011833C22semidirect
33. #18011833C22semidirect
34. #18011833C22semidirect
35. #18011833C22semidirect
36. C22×C8×C149C22semidirect
38. C4⋊C8×C149C22semidirect
39. C22⋊C8×C149C22semidirect
40. C4×C8×C149C22semidirect
93. D596#41semidirect
103. D4×C149D8semidirect
142. C149#3294semidirect
153. C8×D4D149semidirect
160. C22×C8C2×D149semidirect
175. C4⋊C8C2×D149semidirect
182. C22⋊C8C2×D149semidirect
183. C4×C8C2×D149semidirect
240. D4D1192semidirect

Maximal subgroups

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

subgroupindex
#237502792
D4×D5962
#237499722
#237499392
#237499062
#237498612
#237498212
#237497612
C4×D11922
C2×#180118332
C8×D4×C1492
#3294149