Finite Group Databasebeta

← #34055709

Subgroups — #34055709

Order 19072.

490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750159C211yesmaximal, characteristic, complemented
2#23750012C212yesmaximal, complemented
3#23749989C212yesmaximal, complemented
4#23749822C212yesmaximal, complemented
5#23749817C212yesmaximal, complemented
6#23749776C212yesmaximal, complemented
7#23749759C212yesmaximal, complemented
8#23749682C211yesmaximal, characteristic, complemented
9C2×#127×C149C211yesmaximal, characteristic, complemented
10C2×#14558724C2214yescomplemented
11C2×#14558721C2214yescomplemented
12#18011905—21no—
13#18011903C2211yescharacteristic, complemented
14#18011899C2211yescharacteristic, complemented
15#18011894—21no—
16#18011890C2211yescharacteristic
17#18011885C2211yescharacteristic
18C4×Dic298C2211yescharacteristic, complemented
19C4×D596C2211yescharacteristic, complemented
20C4×C22⋊D149—21no—
21#18011868—21no—
22C4⋊#11924746C2212yescomplemented
23#18011832C2214yescomplemented
24#18011832C2214yescomplemented
25C22⋊#11924746C2212yes—
26#18011822C2212yescomplemented
27C22×D4×C149—21no—
28C22×D4×C149—21no—
29C22×D4×C149C2212yes—
30#127×C149—21no—
31#127×C149—21no—
32#127×C149C2212yes—
33#127×C149C2212yes—
34C2×C42×C149C2211yescharacteristic
35C2×Dic298C2311yescharacteristic
36C2×D596C2311yescharacteristic
37C2×C22⋊D149—21no—
38C2×C4×D149—21no—
39#14558724—44no—
40#14558721—44no—
41C2×#11924746C2314yes—
42C4⋊Dic149C2311yescharacteristic
43C4⋊Dic149C2311yescharacteristic
44#14558715—21no—
45#14558715—21no—
46#14558715—21no—
47#14558715—21no—
48C22⋊Dic149—21no—
49#14558713—21no—
50#14558713—21no—
51#14558713—21no—
52#14558713—21no—
53C4×Dic149—21no—
54C24×C149—22no—
55C2×D4×C149—22no—
56C2×D4×C149—22no—
57C2×D4×C149—22no—
58C2×D4×C149—22no—
59C2×D4×C149—22no—
60C2×D4×C149—44no—
61C2×D4×C149—44no—
62C2×D4×C149—44no—
63C2×D4×C149C2314yes—
64C22×C4×C149D411yescharacteristic
65C22×C4×C149D411yescharacteristic
66C22×C4×C149C2311yescharacteristic
67C42×C149D411yescharacteristic
68C42×C149D411yescharacteristic
69C42×C149C2311yescharacteristic
70C42×C149C2311yescharacteristic
71C22×D149—21no—
72Dic298—22no—
73D596—22no—
74C22⋊D149—42no—
75C2×Dic149—21no—
76C2×Dic149—21no—
77C2×Dic149—21no—
78C4×D149—42no—
79#11924746—24no—
80C23×C149—24no—
81C23×C149—44no—
82C23×C149—44no—
83C23×C149—44no—
84C23×C149C2×D411yescharacteristic
85D4×C149—24no—
86D4×C149—24no—
87D4×C149—44no—
88D4×C149—44no—
89D4×C149—44no—
90D4×C149—44no—
91D4×C149—44no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2411yescharacteristic
101C22×C149—21no—
102C22×C149—21no—
103C22×C149—44no—
104C22×C149—44no—
105C22×C149—44no—
106C22×C149—88no—
107C22×C149AGL(1,ℤ/8)12yes—
108C22×C149C22×D411yescharacteristic
109C2×D149—41no—
110C2×D149—41no—
111C2×D149—41no—
112C4×C149—21no—
113C4×C149—21no—
114C4×C149—21no—
115C4×C149—21no—
116C4×C149AGL(1,ℤ/8)12yes—
117C4×C149H(5,𝔽2)12yes—
118Dic149—41no—
119Dic149—41no—
120Dic149—41no—
121C2×C149—22no—
122C2×C149—84no—
123C2×C149#53511yescharacteristic
124C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
125C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
126D149—81no—
127C149#321711yescharacteristic, complemented, Sylow
128#3217—1491nomaximal, Sylow
129C2×#127D14911yescharacteristic, complemented
130#529—1491no—
131#496—1492no—
132#490—1492no—
133#460—1492no—
134#459—1492no—
135#450—1492no—
136#447—1492no—
137#432—1491no—
138C22×D4—21no—
139C22×D4—21no—
140C22×D4C2×D14912yes—
141C2×SD16—1494no—
142C2×D8—1494no—
143#127—21no—
144#127—21no—
145#127C2×D14912yes—
146#127C2×D14912yes—
147#126—2981no—
148#125—1491no—
149#124—1491no—
150#123—2981no—
151C22⋊Q8—1491no—
152#121—1491no—
153C4×Q8—1491no—
154C4×D4—2981no—
155C4×D4—1491no—
156#117—2981no—
157C2×C42C2×D14911yescharacteristic
158C4⋊C8—1492no—
159#102—1494no—
160#102—1494no—
161C22⋊C8—1492no—
162#97—1492no—
163C24—22no—
164C2×Q8—1491no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—44no—
171C2×D4—44no—
172C2×D4—44no—
173C2×D4—2981no—
174C2×D4—1491no—
175C2×D4C22×D14914yes—
176C22×C4—2981no—
177C22×C4C22⋊D14911yescharacteristic
178C22×C4C22⋊D14911yescharacteristic
179C22×C4C22×D14911yescharacteristic
180SD16—5964no—
181D8—5964no—
182C2×C8—1494no—
183C4⋊C4—2981no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—1491no—
188C4⋊C4—1491no—
189C22⋊C4—2981no—
190C22⋊C4—2981no—
191C22⋊C4—2981no—
192C22⋊C4—2981no—
193C22⋊C4—2981no—
194C42—2981no—
195C42C22⋊D14911yescharacteristic
196C42C22⋊D14911yescharacteristic
197C42C22×D14911yescharacteristic
198C42C22×D14911yescharacteristic
199C23—24no—
200C23—44no—
201C23—44no—
202C23—44no—
203C23—2981no—
204C23C2×C22⋊D14911yescharacteristic
205Q8—2982no—
206D4—24no—
207D4—24no—
208D4—44no—
209D4—44no—
210D4—44no—
211D4—44no—
212D4—44no—
213D4—2982no—
214D4—5962no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—2981no—
219C2×C4—2981no—
220C2×C4—2981no—
221C2×C4—5962no—
222C2×C4C2×C22⋊D14911yescharacteristic
223C2×C4C2×C22⋊D14911yescharacteristic
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4C2×C22⋊D14911yescharacteristic
226C2×C4C2×C22⋊D14911yescharacteristic
227C2×C4C23×D14911yescharacteristic
228C8—2984no—
229C22—21no—
230C22—21no—
231C22—44no—
232C22—44no—
233C22—44no—
234C22—88no—
235C22—5961no—
236C22—5961no—
237C22—5961no—
238C22#1801193712yes—
239C22C22×C22⋊D14911yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—5961no—
245C4—5961no—
246C4—5961no—
247C4#1801193712yes—
248C4#1801195612yes—
249C2—22no—
250C2—84no—
251C2—11921no—
252C2#2375019211yescharacteristic
253C2C2×#1801193711yescharacteristic
254C2C2×#1801193711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#127×C149C2
socleC22×C149C22×D4
hypercenterC2×#127D149
hypocenterC149#3217
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #23750159C2semidirect
2. #23750012C2semidirect
3. #23749989C2semidirect
4. #23749822C2semidirect
5. #23749817C2semidirect
6. #23749776C2semidirect
7. #23749759C2semidirect
8. #23749682C2semidirect
9. C2×#127×C149C2semidirect
10. C2×#14558724C22semidirect
11. C2×#14558721C22semidirect
13. #18011903C22semidirect
14. #18011899C22semidirect
18. C4×Dic298C22semidirect
19. C4×D596C22semidirect
22. C4⋊#11924746C22semidirect
23. #18011832C22semidirect
24. #18011832C22semidirect
26. #18011822C22semidirect
127. C149#3217semidirect
129. C2×#127D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500122
#237499892
#237498222
#237498172
#237497762
#237497592
#237496822
C2×#127×C1492
#3217149