Finite Group Databasebeta

← #34055424

Subgroups — #34055424

Order 19072.

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

normal subgroups only

This group has 446 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#23750170C212yesmaximal, complemented
2#23750022C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749970C212yesmaximal, complemented
5#23749878C211yesmaximal, characteristic, complemented
6#23749876C212yesmaximal, complemented
7#23749737C211yesmaximal, characteristic, complemented
8#23749736C211yesmaximal, characteristic, complemented
9#23749734C212yesmaximal, complemented
10M16×Dic149C211yesmaximal, characteristic, complemented
11#469×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—22no—
13C2×D1192C2211yescharacteristic
14C2×#14558721C2212yes—
15C2×#14558720C2211yescharacteristic
16#18011910C2212yes—
17#18011907C2212yes—
18#18011897—22no—
19#18011885C2212yes—
20#18011883—22no—
21D4×Dic149C2212yes—
22#18011873C2212yes—
23#18011871—22no—
24C2×C4×Dic149C2211yescharacteristic
25#18011843C2211yescharacteristic
26#18011842C2212yes—
27#18011833C2212yes—
28#18011832C2212yes—
29#18011831C2212yes—
30#18011821C2211yescharacteristic
31#18011821C2211yescharacteristic
32C8×Dic149C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×D8×C149C2211yescharacteristic
35C2×M16×C149C2211yescharacteristic
36#121×C149C2212yes—
37#106×C149C2211yescharacteristic
38#102×C149C2212yes—
39#14558735—48no—
40C2×Dic298—22no—
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45C22×Dic149—22no—
46C22×Dic149D412yes—
47C2×C4×D149—22no—
48D1192—22no—
49#14558721—24no—
50#14558720—22no—
51C2×#11924746C2311yescharacteristic
52C2×#11924746C2311yescharacteristic
53C4⋊Dic149C2312yes—
54#14558715—22no—
55C22⋊Dic149—22no—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149D412yes—
59C4×Dic149C2311yescharacteristic
60C4×Dic149C2311yescharacteristic
61C2×D4×C149—22no—
62C2×D4×C149C2312yes—
63C22×C4×C149C2311yescharacteristic
64D8×C149—22no—
65M16×C149—22no—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C4⋊C4×C149C2312yes—
69C22⋊C4×C149—22no—
70C22×D149—22no—
71Dic298—44no—
72D596—22no—
73D596—22no—
74C22⋊D149—44no—
75C22⋊D149—44no—
76C22⋊D149—44no—
77C2×Dic149—24no—
78C2×Dic149—22no—
79C2×Dic149—44no—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×D412yes—
82C4×D149—44no—
83#11924746—21no—
84#11924746#4112yescomplemented
85C23×C149—22no—
86C23×C149C2×D411yescharacteristic
87D4×C149—22no—
88D4×C149—22no—
89D4×C149—44no—
90C2×C4×C149—21no—
91C2×C4×C149—21no—
92C2×C4×C149—22no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2411yescharacteristic
95C8×C149—21no—
96C8×C149#4112yescomplemented
97C22×C149—21no—
98C22×C149—22no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149—42no—
102C22×C149C22×D411yescharacteristic
103C2×D149—42no—
104C2×D149—42no—
105C2×D149—42no—
106C4×C149—21no—
107C4×C149—42no—
108C4×C149C2×#4111yescharacteristic
109C4×C149C2×#4111yescharacteristic
110Dic149—22no—
111Dic149—42no—
112Dic149AGL(1,ℤ/8)14yes—
113C2×C149—41no—
114C2×C149—82no—
115C2×C149#53211yescharacteristic
116C2×C149C2×AGL(1,ℤ/8)12yes—
117D149—82no—
118C149#318411yescharacteristic, complemented, Sylow
119#3184—1491nomaximal, Sylow
120#532—1492no—
121#498—1491no—
122#493—1491no—
123#486—1492no—
124#469—1491no—
125#469—1492no—
126#469D14911yescharacteristic, complemented
127#442—1491no—
128#442—1491no—
129#442—1492no—
130C4×M16—1491no—
131C2×#41—2982no—
132C2×D8—1492no—
133C2×D8—1491no—
134C2×D8C2×D14911yescharacteristic
135C2×M16—1491no—
136C2×M16C2×D14911yescharacteristic
137C4⋊Q8—1492no—
138#127—1492no—
139#124—2982no—
140#121—2982no—
141#121—1492no—
142#121C2×D14912yes—
143C4×D4—2982no—
144C4×D4—1492no—
145C4×D4—1492no—
146C2×C42—1491no—
147#106—1491no—
148#106—1492no—
149#106C2×D14911yescharacteristic
150#102—1492no—
151#102—1492no—
152#102—1492no—
153#102C2×D14912yes—
154#97—1491no—
155#97—1491no—
156C4×C8—1491no—
157C4×C8—1491no—
158#41—5968no—
159C2×Q8—2982no—
160C2×D4—22no—
161C2×D4—2982no—
162C2×D4—2982no—
163C2×D4—2982no—
164C2×D4—1492no—
165C2×D4C22×D14912yes—
166C22×C4—2982no—
167C22×C4—2982no—
168C22×C4—1492no—
169C22×C4C22×D14911yescharacteristic
170D8—22no—
171D8—2984no—
172D8—2982no—
173M16—22no—
174M16—2982no—
175C2×C8—1491no—
176C2×C8—1491no—
177C2×C8C22×D14911yescharacteristic
178C2×C8C22×D14911yescharacteristic
179C4⋊C4—2982no—
180C4⋊C4—1492no—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C42—1492no—
187C42—1491no—
188C42—1491no—
189C23—22no—
190C23—2982no—
191C23D4×D14911yescharacteristic
192Q8—5964no—
193D4—22no—
194D4—22no—
195D4—44no—
196D4—2982no—
197D4—2982no—
198D4—5964no—
199D4—5964no—
200D4—5964no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—2984no—
205C2×C4—2982no—
206C2×C4—5964no—
207C2×C4—5964no—
208C2×C4—1492no—
209C2×C4—1492no—
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—2981no—
214C8—1492no—
215C8#1455873512yescomplemented
216C22—22no—
217C22—21no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—5962no—
222C22—5962no—
223C22—5962no—
224C22C2×D4×D14911yescharacteristic
225C4—21no—
226C4—42no—
227C4—2982no—
228C4—5962no—
229C4—1494no—
230C4#41×D14911yescharacteristic
231C4C2×#1455873511yescharacteristic
232C2—41no—
233C2—82no—
234C2—11922no—
235C2#2375017011yescharacteristic
236C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3184
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750170C2semidirect
2. #23750022C2semidirect
3. #23750000C2semidirect
4. #23749970C2semidirect
5. #23749878C2semidirect
6. #23749876C2semidirect
7. #23749737C2semidirect
8. #23749736C2semidirect
9. #23749734C2semidirect
10. M16×Dic149C2semidirect
11. #469×C149C2semidirect
84. #11924746#41semidirect
96. C8×C149#41semidirect
118. C149#3184semidirect
126. #469D149semidirect
215. C8#14558735semidirect

Maximal subgroups

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

subgroupindex
#237501702
#237500222
#237500002
#237499702
#237498782
#237498762
#237497372
#237497362
#237497342
M16×Dic1492
#469×C1492
#3184149