Finite Group Databasebeta

← #34055533

Subgroups — #34055533

Order 19072.

418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750136C212yesmaximal, complemented
2#23749967C212yesmaximal, complemented
3#23749950C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic, complemented
5#23749878C211yesmaximal, characteristic, complemented
6#23749871C212yesmaximal, complemented
7#23749789C212yesmaximal, complemented
8#23749772C212yesmaximal, complemented
9#407×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2212yes—
11C2×Dic596C2211yescharacteristic, complemented
12C2×#14558725C2212yescomplemented
13C2×D1192C2211yescharacteristic, complemented
14#18011894—22no—
15#18011890C2212yes—
16#18011890C2212yes—
17#18011885C2212yes—
18#18011885C2212yes—
19#18011880—22no—
20C4×C22⋊D149—22no—
21C4×C22⋊D149—22no—
22#18011870C2212yes—
23#18011845C2212yescomplemented
24#18011843C2211yescharacteristic, complemented
25#18011843C2211yescharacteristic, complemented
26#18011836C2212yescomplemented
27#18011836C2212yescomplemented
28#18011833C2212yescomplemented
29#18011833C2212yescomplemented
30C23×C4×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C2×M16×C149C2211yescharacteristic
33C22⋊C8×C149C2212yes—
34C22⋊C8×C149C2212yes—
35#14558736—42no—
36#14558736—42no—
37C2×Dic298C2312yes—
38C2×D596C2312yes—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—22no—
42C2×C4×D149—22no—
43Dic596—41no—
44#14558725—42no—
45D1192—41no—
46C4⋊Dic149C2312yes—
47C4⋊Dic149C2312yes—
48#14558715—22no—
49#14558715—22no—
50C22⋊Dic149—22no—
51C22⋊Dic149—22no—
52C22⋊Dic149—22no—
53#14558713—22no—
54#14558713—22no—
55C4×Dic149—22no—
56C24×C149D411yescharacteristic
57C22×C4×C149—41no—
58C22×C4×C149—41no—
59C22×C4×C149D411yescharacteristic
60C22×C4×C149D412yes—
61C22×C4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63M16×C149—41no—
64M16×C149—41no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2312yes—
67C2×C8×C149C2311yescharacteristic
68C22×D149—22no—
69Dic298—22no—
70Dic298—22no—
71D596—22no—
72D596—22no—
73C22⋊D149—44no—
74C22⋊D149—44no—
75C22⋊D149—44no—
76C2×Dic149—22no—
77C2×Dic149—22no—
78C2×Dic149—22no—
79C4×D149—44no—
80C23×C149—41no—
81C23×C149—42no—
82C23×C149C2×D411yescharacteristic
83C23×C149C2×D412yes—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—21no—
87C2×C4×C149—21no—
88C2×C4×C149—42no—
89C2×C4×C149—41no—
90C2×C4×C149C2×D412yes—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—21no—
94C8×C149—22no—
95C8×C149—21no—
96C22×C149—21no—
97C22×C149—22no—
98C22×C149—22no—
99C22×C149—22no—
100C22×C149—22no—
101C22×C149—44no—
102C22×C149C22×D411yescharacteristic
103C2×D149—42no—
104C2×D149—42no—
105C2×D149—42no—
106C4×C149—21no—
107C4×C149—22no—
108C4×C149H(5,𝔽2)11yescharacteristic
109C4×C149H(5,𝔽2)11yescharacteristic
110Dic149—42no—
111Dic149—42no—
112Dic149—42no—
113C2×C149—41no—
114C2×C149—42no—
115C2×C149#53411yescharacteristic
116C2×C149#57512yes—
117D149—82no—
118C149#319711yescharacteristic, complemented, Sylow
119#3197—1491nomaximal, Sylow
120#525—1492no—
121#485—1492no—
122#482—1492no—
123#470—1491no—
124#469—1491no—
125#468—1492no—
126#452—1492no—
127#449—1492no—
128#407D14911yescharacteristic, complemented
129C2×#41—1492no—
130C23×C4C2×D14911yescharacteristic
131C2×Q16—1491no—
132C2×SD16—1492no—
133C2×D8—1491no—
134C2×M16C2×D14911yescharacteristic
135C2×M16C2×D14911yescharacteristic
136#123—2982no—
137C22⋊Q8—1492no—
138C22⋊Q8—1492no—
139#121—1492no—
140#121—1492no—
141#120—2982no—
142C4×D4—2982no—
143C4×D4—2982no—
144#117—1492no—
145#107—1492no—
146#106—1491no—
147#106—1491no—
148#103—1492no—
149#103—1492no—
150#102—1492no—
151#102—1492no—
152C22⋊C8C2×D14912yes—
153C22⋊C8C2×D14912yes—
154C24D59611yescharacteristic
155#41—5962no—
156#41—5962no—
157C2×Q8—1492no—
158C2×D4—2982no—
159C2×D4—2982no—
160C2×D4—2982no—
161C2×D4—1492no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—2982no—
165C22×C4D59611yescharacteristic
166C22×C4D59612yes—
167C22×C4C22×D14912yes—
168C22×C4C22×D14911yescharacteristic
169Q16—5961no—
170SD16—5962no—
171D8—5961no—
172M16—41no—
173M16—41no—
174C2×C8C22×D14911yescharacteristic
175C2×C8C22×D14912yes—
176C2×C8C22×D14911yescharacteristic
177C4⋊C4—2982no—
178C4⋊C4—2982no—
179C4⋊C4—1492no—
180C4⋊C4—1492no—
181C22⋊C4—2982no—
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C42—2982no—
187C23—41no—
188C23—42no—
189C23—2982no—
190C23C2×D59611yescharacteristic
191C23C2×D59612yes—
192Q8—2982no—
193Q8—2982no—
194D4—2982no—
195D4—2982no—
196D4—5964no—
197D4—5964no—
198D4—5964no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—2982no—
206C2×C4—2982no—
207C2×C4—2982no—
208C2×C4—5964no—
209C2×C4C2×D59612yes—
210C2×C4C2×D59611yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—5962no—
222C22—5962no—
223C22—5962no—
224C22C22×D59611yescharacteristic
225C4—22no—
226C4—21no—
227C4—5962no—
228C4—5962no—
229C4—5962no—
230C4#1801195611yescharacteristic
231C4#1801195611yescharacteristic
232C2—41no—
233C2—42no—
234C2—11922no—
235C2#2375018711yescharacteristic
236C2#2375042512yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#407×C149C2
socleC22×C149C22×D4
hypercenter#407D149
hypocenterC149#3197
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #23750136C2semidirect
2. #23749967C2semidirect
3. #23749950C2semidirect
4. #23749883C2semidirect
5. #23749878C2semidirect
6. #23749871C2semidirect
7. #23749789C2semidirect
8. #23749772C2semidirect
9. #407×C149C2semidirect
11. C2×Dic596C22semidirect
12. C2×#14558725C22semidirect
13. C2×D1192C22semidirect
23. #18011845C22semidirect
24. #18011843C22semidirect
25. #18011843C22semidirect
26. #18011836C22semidirect
27. #18011836C22semidirect
28. #18011833C22semidirect
29. #18011833C22semidirect
118. C149#3197semidirect
128. #407D149semidirect

Maximal subgroups

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

subgroupindex
#237501362
#237499672
#237499502
#237498832
#237498782
#237498712
#237497892
#237497722
#407×C1492
#3197149