Finite Group Databasebeta

← #34056923

Subgroups — #34056923

Order 19072.

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

normal subgroups only

This group has 448 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#23750345C211yesmaximal, characteristic, complemented
2D4×D596C211yesmaximal, characteristic
3#23749972C211yesmaximal, characteristic, complemented
4#23749950C212yesmaximal, complemented
5#23749906C211yesmaximal, characteristic, complemented
6#23749871C212yesmaximal, complemented
7#23749826C211yesmaximal, characteristic, complemented
8#23749778C212yesmaximal, complemented
9C4×#14558725C211yesmaximal, characteristic, complemented
10#23749631C212yesmaximal, complemented
11#436×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yes—
13C2×D4×D149—21no—
14C2×#14558725C2211yescharacteristic
15C2×#14558725C2212yescomplemented
16#18011911C2211yescharacteristic, complemented
17#18011908C2211yescharacteristic
18#18011904—22no—
19#18011898—21no—
20#18011890C2212yescomplemented
21#18011886—21no—
22#18011885C2212yes—
23#18011881—22no—
24C4×Dic298C2211yescharacteristic, complemented
25#18011876—21no—
26C4×D596C2211yescharacteristic
27#18011870C2212yescomplemented
28#18011845C2212yescomplemented
29#18011843C2211yescharacteristic, complemented
30#18011836C2211yescharacteristic, complemented
31#18011833C2212yes—
32#18011833C2211yescharacteristic
33#18011833C2212yescomplemented
34#18011833C2212yescomplemented
35#18011833C2212yescomplemented
36C2×M16×C149C2212yescomplemented
37C4×D4×C149C2211yescharacteristic
38C4⋊C8×C149C2211yescharacteristic, complemented
39C22⋊C8×C149C2212yescomplemented
40C4×C8×C149C2211yescharacteristic, complemented
41C23×D149—22no—
42C2×Dic298—21no—
43C2×Dic298C2311yescharacteristic
44C2×D596—24no—
45C2×D596—21no—
46C2×D596—22no—
47C2×D596—21no—
48C2×D596—42no—
49C2×D596C2312yes—
50C2×D596C2311yescharacteristic
51C2×C22⋊D149—22no—
52D4×D149—44no—
53C2×C4×D149—21no—
54#14558725—22no—
55#14558725—42no—
56C4⋊Dic149—21no—
57C4⋊Dic149C2312yes—
58C4⋊Dic149C2311yescharacteristic
59C4⋊Dic149C2311yescharacteristic
60#14558715—21no—
61#14558715—22no—
62C22⋊Dic149—22no—
63C22⋊Dic149—22no—
64#14558713—21no—
65#14558713—22no—
66C4×Dic149—22no—
67C4×Dic149—21no—
68C2×D4×C149D411yescharacteristic
69C22×C4×C149C2312yes—
70M16×C149—42no—
71C2×C8×C149C2311yescharacteristic
72C2×C8×C149C2312yes—
73C2×C8×C149C2311yescharacteristic
74C4⋊C4×C149D411yescharacteristic
75C22⋊C4×C149D412yes—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—22no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82Dic298—21no—
83Dic298—21no—
84Dic298—42no—
85D596—22no—
86D596—21no—
87D596—22no—
88D596—44no—
89D596—42no—
90D596—81no—
91D596#4112yes—
92C22⋊D149—44no—
93C2×Dic149—21no—
94C2×Dic149—22no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C4×D149—42no—
98C23×C149C2×D412yes—
99D4×C149—22no—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D412yes—
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2411yescharacteristic
106C8×C149—21no—
107C8×C149—22no—
108C8×C149—21no—
109C22×C149—22no—
110C22×C149—22no—
111C22×C149—22no—
112C22×C149C22×D411yescharacteristic
113C2×D149—22no—
114C2×D149—41no—
115C2×D149—41no—
116C2×D149—42no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—88no—
120C4×C149—22no—
121C4×C149—21no—
122C4×C149AGL(1,ℤ/8)12yes—
123C4×C149C2×#4111yescharacteristic
124C4×C149H(5,𝔽2)11yescharacteristic
125Dic149—41no—
126Dic149—41no—
127Dic149—42no—
128Dic149—41no—
129C2×C149—42no—
130C2×C149#54611yescharacteristic
131C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C149#57711yescharacteristic
133D149—42no—
134D149—82no—
135C149#332411yescharacteristic, complemented, Sylow
136#3324—1491nomaximal, Sylow
137#556—1491no—
138D42—1491no—
139#486—1491no—
140#482—1492no—
141#474—1491no—
142#468—1492no—
143#460—1491no—
144#450—1492no—
145C4×SD16—1491no—
146#436D14911yescharacteristic, complemented
147#418—1492no—
148C22×D4—2981no—
149C22×D4—1492no—
150C2×SD16—1491no—
151C2×SD16—1492no—
152C2×M16C2×D14912yescomplemented
153C4⋊Q8—1491no—
154#127—1491no—
155#126—2982no—
156#124—2981no—
157C22⋊Q8—1492no—
158#121—2981no—
159#121—1492no—
160#120—2982no—
161C4×Q8—2981no—
162C4×Q8—1491no—
163C4×D4—1491no—
164C4×D4C2×D14911yescharacteristic
165#117—1492no—
166#107—1492no—
167#106—1491no—
168C4⋊C8C2×D14911yescharacteristic, complemented
169#103—1491no—
170#102—1491no—
171#102—1492no—
172#102—1492no—
173#102—1492no—
174#102—1492no—
175C22⋊C8C2×D14912yescomplemented
176C4×C8C2×D14911yescharacteristic, complemented
177C24—2982no—
178C2×Q8—2981no—
179C2×Q8—1491no—
180C2×D4—2984no—
181C2×D4—2982no—
182C2×D4—2982no—
183C2×D4—2981no—
184C2×D4—2981no—
185C2×D4—5962no—
186C2×D4—5964no—
187C2×D4—1492no—
188C2×D4—1491no—
189C2×D4D59611yescharacteristic
190C22×C4—2981no—
191C22×C4C22×D14912yes—
192SD16—2982no—
193SD16—5962no—
194M16—42no—
195C2×C8C22×D14911yescharacteristic
196C2×C8C22×D14911yescharacteristic
197C2×C8C22×D14912yes—
198C4⋊C4—2982no—
199C4⋊C4—2981no—
200C4⋊C4—2981no—
201C4⋊C4—1491no—
202C4⋊C4—1492no—
203C4⋊C4—1491no—
204C4⋊C4D59611yescharacteristic
205C22⋊C4—2982no—
206C22⋊C4—2982no—
207C22⋊C4—2981no—
208C22⋊C4—2982no—
209C22⋊C4D59612yes—
210C42—2982no—
211C42—2981no—
212C42C22×D14911yescharacteristic
213C23—2981no—
214C23—2982no—
215C23—5964no—
216C23—5964no—
217C23—11922no—
218C23C2×D59612yes—
219Q8—2981no—
220Q8—2981no—
221Q8—5962no—
222D4—22no—
223D4—2982no—
224D4—2981no—
225D4—2982no—
226D4—5964no—
227D4—5964no—
228D4—5962no—
229D4—1492no—
230D4—11921no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—2981no—
234C2×C4—2981no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—5962no—
238C2×C4C2×D59612yes—
239C2×C4C2×D59611yescharacteristic
240C2×C4C2×D59611yescharacteristic
241C2×C4C23×D14911yescharacteristic
242C8—21no—
243C8—21no—
244C8—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—2982no—
249C22—5961no—
250C22—5961no—
251C22—5962no—
252C22—5962no—
253C22—5962no—
254C22—11928no—
255C22C22×D59611yescharacteristic
256C4—21no—
257C4—22no—
258C4—5961no—
259C4—5962no—
260C4—5961no—
261C4—5961no—
262C4#1801193912yes—
263C4#41×D14911yescharacteristic
264C4#1801195611yescharacteristic
265C2—42no—
266C2—5962no—
267C2—11922no—
268C2#2375027011yescharacteristic
269C2C2×#1801193911yescharacteristic
270C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#436×C149C2
socleC22×C149C22×D4
prime radicalD4×D596C2
hypercenter#436D149
hypocenterC149#3324
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #23750345C2semidirect
3. #23749972C2semidirect
4. #23749950C2semidirect
5. #23749906C2semidirect
6. #23749871C2semidirect
7. #23749826C2semidirect
8. #23749778C2semidirect
9. C4×#14558725C2semidirect
10. #23749631C2semidirect
11. #436×C149C2semidirect
15. C2×#14558725C22semidirect
16. #18011911C22semidirect
20. #18011890C22semidirect
24. C4×Dic298C22semidirect
27. #18011870C22semidirect
28. #18011845C22semidirect
29. #18011843C22semidirect
30. #18011836C22semidirect
33. #18011833C22semidirect
34. #18011833C22semidirect
35. #18011833C22semidirect
36. C2×M16×C149C22semidirect
38. C4⋊C8×C149C22semidirect
39. C22⋊C8×C149C22semidirect
40. C4×C8×C149C22semidirect
135. C149#3324semidirect
146. #436D149semidirect
152. C2×M16C2×D149semidirect
168. C4⋊C8C2×D149semidirect
175. C22⋊C8C2×D149semidirect
176. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237503452
D4×D5962
#237499722
#237499502
#237499062
#237498712
#237498262
#237497782
C4×#145587252
#237496312
#436×C1492
#3324149