Finite Group Databasebeta

← #34055283

Subgroups — #34055283

Order 19072.

408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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#23750173C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic, complemented
3#23750034C211yesmaximal, characteristic, complemented
4#23749989C211yesmaximal, characteristic, complemented
5#23749984C211yesmaximal, characteristic, complemented
6#23749875C212yesmaximal, complemented
7#23749868C212yesmaximal, complemented
8SD16×Dic149C212yesmaximal, complemented
9D8×Dic149C212yesmaximal, complemented
10#23749577C211yesmaximal, characteristic, complemented
11#496×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—21no—
13C2×#14558719C2212yes—
14#18011911C2211yescharacteristic
15#18011904—21no—
16#18011903C2211yescharacteristic
17#18011898—21no—
18#18011893—21no—
19#18011887C2211yescharacteristic
20#18011882—21no—
21#18011882C2211yescharacteristic
22#18011882C2212yes—
23Q8×Dic149C2211yescharacteristic
24D4×Dic149—21no—
25D4×Dic149C2211yescharacteristic
26D4×Dic149C2212yes—
27#18011871—21no—
28#18011867—21no—
29C42×D149C2211yescharacteristic
30#18011845C2212yes—
31#18011843C2212yes—
32#18011835C2212yes—
33#18011832C2212yes—
34#18011832C2212yes—
35#18011832C2212yes—
36#18011822C2211yescharacteristic
37C8×Dic149C2212yes—
38C2×SD16×C149C2212yes—
39C2×D8×C149C2212yes—
40#127×C149C2211yescharacteristic
41#124×C149C2211yescharacteristic
42#97×C149C2211yescharacteristic
43#14558735—44no—
44C2×Dic298—21no—
45C2×C22⋊D149—22no—
46C2×C22⋊D149—21no—
47C22×Dic149—22no—
48C22×Dic149—21no—
49C2×C4×D149D411yescharacteristic
50C2×C4×D149D411yescharacteristic
51C2×C4×D149C2311yescharacteristic
52#14558719—24no—
53C2×#11924746C2312yes—
54C4⋊Dic149—21no—
55C4⋊Dic149—21no—
56C4⋊Dic149C2312yes—
57C4⋊Dic149C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558715—21no—
60#14558715—21no—
61#14558715—21no—
62C22⋊Dic149—21no—
63C22⋊Dic149—21no—
64C22⋊Dic149—22no—
65C22⋊Dic149—22no—
66#14558713—21no—
67C4×Dic149—21no—
68C4×Dic149D411yescharacteristic
69C4×Dic149D411yescharacteristic
70C4×Dic149C2311yescharacteristic
71C2×Q8×C149C2311yescharacteristic
72C2×D4×C149—21no—
73C2×D4×C149—21no—
74C2×D4×C149C2311yescharacteristic
75C2×D4×C149C2312yes—
76SD16×C149—24no—
77D8×C149—24no—
78C2×C8×C149C2312yes—
79C22⋊C4×C149—21no—
80C22⋊C4×C149—21no—
81C42×C149C2311yescharacteristic
82C22×D149C2×D411yescharacteristic
83Dic298—42no—
84C22⋊D149—42no—
85C22⋊D149—44no—
86C2×Dic149—22no—
87C2×Dic149—21no—
88C2×Dic149—21no—
89C2×Dic149—42no—
90C2×Dic149—44no—
91C2×Dic149C2×D411yescharacteristic
92C2×Dic149C2×D411yescharacteristic
93C2×Dic149C2×D411yescharacteristic
94C4×D149—22no—
95C4×D149—22no—
96C4×D149—41no—
97#11924746—22no—
98C23×C149—21no—
99C23×C149—22no—
100Q8×C149—22no—
101D4×C149—22no—
102D4×C149—22no—
103D4×C149—22no—
104D4×C149—42no—
105D4×C149—42no—
106C2×C4×C149—21no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C8×C149#4114yescomplemented
111C22×C149—41no—
112C22×C149—42no—
113C22×C149—42no—
114C22×C149—41no—
115C22×C149—42no—
116C22×C149—41no—
117C22×C149C22×D411yescharacteristic
118C2×D149—21no—
119C2×D149—21no—
120C2×D149—21no—
121C4×C149—21no—
122C4×C149—21no—
123C4×C149—41no—
124C4×C149C2×#4112yes—
125Dic149—21no—
126Dic149—21no—
127Dic149—41no—
128Dic149—42no—
129Dic149—41no—
130Dic149AGL(1,ℤ/8)12yes—
131C2×C149—82no—
132C2×C149—81no—
133C2×C149#53211yescharacteristic
134C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C149#57511yescharacteristic
136D149—41no—
137C149#317111yescharacteristic, complemented, Sylow
138#3171—1491nomaximal, Sylow
139#532—1491no—
140#529—1491no—
141#501—1491no—
142#496D14911yescharacteristic, complemented
143#490—1491no—
144#489—1491no—
145#469—1492no—
146#468—1492no—
147C4×SD16—1492no—
148C4×D8—1492no—
149C4×M16—1491no—
150C2×#41—2981no—
151C2×SD16C2×D14912yes—
152C2×D8C2×D14912yes—
153C2×M16—1492no—
154C4⋊Q8—1491no—
155#127C2×D14911yescharacteristic
156#126—2981no—
157#125—1491no—
158#124—2981no—
159#124C2×D14911yescharacteristic
160#123—2981no—
161C22⋊Q8—1491no—
162#121—2981no—
163#121—1491no—
164#121—1492no—
165C4×Q8—1491no—
166C4×D4—2981no—
167C4×D4—2981no—
168C4×D4—1491no—
169C4×D4—1492no—
170#117—2981no—
171C2×C42—1491no—
172#107—1492no—
173#106—1492no—
174#103—1492no—
175#102—1492no—
176#102—1492no—
177#102—1492no—
178#97—1491no—
179#97C2×D14911yescharacteristic
180C4×C8—1492no—
181#41—5964no—
182C2×Q8—2981no—
183C2×Q8C22×D14911yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—2981no—
187C2×D4—2982no—
188C2×D4C22×D14911yescharacteristic
189C2×D4C22×D14912yes—
190C22×C4—2981no—
191C22×C4—2982no—
192C22×C4—1491no—
193C22×C4—1491no—
194C22×C4—1491no—
195SD16—24no—
196D8—24no—
197M16—2984no—
198C2×C8—1492no—
199C2×C8C22×D14912yes—
200C4⋊C4—2981no—
201C4⋊C4—2981no—
202C4⋊C4—2981no—
203C4⋊C4—2981no—
204C4⋊C4—2981no—
205C4⋊C4—1491no—
206C4⋊C4—1491no—
207C4⋊C4—1492no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—2981no—
211C22⋊C4—2981no—
212C22⋊C4—2982no—
213C22⋊C4—2982no—
214C22⋊C4—2981no—
215C42—2981no—
216C42—1491no—
217C42—1491no—
218C42—1491no—
219C42C22×D14911yescharacteristic
220C23—21no—
221C23—22no—
222C23—1491no—
223Q8—22no—
224Q8—5962no—
225D4—22no—
226D4—22no—
227D4—22no—
228D4—42no—
229D4—42no—
230D4—5962no—
231D4—5964no—
232C2×C4—21no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4—2981no—
236C2×C4—2981no—
237C2×C4—2982no—
238C2×C4—5961no—
239C2×C4—5962no—
240C2×C4—5964no—
241C2×C4—1491no—
242C2×C4—1491no—
243C2×C4—1491no—
244C2×C4D4×D14911yescharacteristic
245C2×C4D4×D14911yescharacteristic
246C2×C4C23×D14911yescharacteristic
247C8—2982no—
248C8#1455873514yescomplemented
249C22—42no—
250C22—41no—
251C22—42no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—2981no—
256C22—2981no—
257C22—2981no—
258C22C2×D4×D14911yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—2981no—
263C4—2981no—
264C4—5962no—
265C4—5961no—
266C4—5961no—
267C4—1492no—
268C4C2×#1455873512yes—
269C2—82no—
270C2—81no—
271C2—5961no—
272C2#2375017311yescharacteristic
273C2AGL(1,ℤ/8)×D14911yescharacteristic
274C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#496×C149C2
socleC22×C149C22×D4
hypercenter#496D149
hypocenterC149#3171
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23750173C2semidirect
2. #23750154C2semidirect
3. #23750034C2semidirect
4. #23749989C2semidirect
5. #23749984C2semidirect
6. #23749875C2semidirect
7. #23749868C2semidirect
8. SD16×Dic149C2semidirect
9. D8×Dic149C2semidirect
10. #23749577C2semidirect
11. #496×C149C2semidirect
110. C8×C149#41semidirect
137. C149#3171semidirect
142. #496D149semidirect
248. C8#14558735semidirect

Maximal subgroups

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

subgroupindex
#237501732
#237501542
#237500342
#237499892
#237499842
#237498752
#237498682
SD16×Dic1492
D8×Dic1492
#237495772
#496×C1492
#3171149