Finite Group Databasebeta

← #34044920

Subgroups — #34044920

Order 19072.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#23750106C211yesmaximal, characteristic
2#23749667C211yesmaximal, characteristic, complemented
3C2×#18011837C211yesmaximal, characteristic
4#23749627C211yesmaximal, characteristic
5#23749494C211yesmaximal, characteristic, complemented
6#23749386C211yesmaximal, characteristic, complemented
7#343×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011876—21no—
10#18011873—21no—
11C4×C22⋊D149—22no—
12#18011870C2211yescharacteristic
13#18011869—21no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×#14558715—22no—
16C4⋊C4×D149—21no—
17C2×C4×Dic149C2211yescharacteristic
18#18011845—21no—
19#18011843—21no—
20#18011837C414yescomplemented
21#18011836—21no—
22#18011833—21no—
23C2×M16×C149C2211yescharacteristic
24C2×M16×C149C2211yescharacteristic
25C2×C4⋊C4×C149C2211yescharacteristic
26#14558736—21no—
27#14558736—21no—
28#14558736C2×C412yes—
29#14558736Q812yes—
30C2×Dic298D411yescharacteristic
31C2×D596D411yescharacteristic
32C2×C22⋊D149—21no—
33C22×Dic149—21no—
34C22×Dic149—21no—
35C2×C4×D149—22no—
36C2×C4×D149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149D411yescharacteristic
40C4⋊Dic149D411yescharacteristic
41#14558715—22no—
42#14558715—44no—
43C22⋊Dic149—21no—
44#14558713—22no—
45C4×Dic149—22no—
46C4×Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149C2×C412yescomplemented
49C22×C4×C149D412yes—
50C22×C4×C149C2311yescharacteristic
51M16×C149—21no—
52M16×C149—21no—
53M16×C149—21no—
54M16×C149C2×C412yescomplemented
55C2×C8×C149—21no—
56C2×C8×C149—21no—
57C4⋊C4×C149—21no—
58C4⋊C4×C149—21no—
59C22×D149—21no—
60Dic298—21no—
61Dic298C4⋊C412yescomplemented
62D596—21no—
63D596C4⋊C412yescomplemented
64C22⋊D149—22no—
65C22⋊D149—22no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—21no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—42no—
73C2×Dic149—41no—
74C4×D149—22no—
75C4×D149—22no—
76C4×D149—82no—
77C23×C149C2×D411yescharacteristic
78C2×C4×C149—22no—
79C2×C4×C149—42no—
80C2×C4×C149C22×C411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×Q811yescharacteristic
84C2×C4×C149#4111yescharacteristic
85C2×C4×C149#4111yescharacteristic
86C8×C149—22no—
87C8×C149—41no—
88C22×C149—21no—
89C22×C149—21no—
90C22×C149C4×D411yescharacteristic
91C22×C149#12011yescharacteristic
92C22×C149C22⋊Q811yescharacteristic
93C2×D149—22no—
94C2×D149—41no—
95C2×D149—41no—
96C4×C149—42no—
97C4×C149C2×C4⋊C411yescharacteristic
98C4×C149C4×D411yescharacteristic
99C4×C149C22⋊Q811yescharacteristic
100C4×C149#12311yescharacteristic
101Dic149—24no—
102Dic149—22no—
103Dic149—41no—
104Dic149—41no—
105Dic149—81no—
106C2×C149—21no—
107C2×C149—21no—
108C2×C149#38511yescharacteristic
109C2×C149#45311yescharacteristic
110C2×C149#45611yescharacteristic
111D149—42no—
112C149#185911yescharacteristic, complemented, Sylow
113#1859—1491nomaximal, Sylow
114#520—1491no—
115#428—1491no—
116C2×#104—1491no—
117#417—1491no—
118#384—1491no—
119#343D14911yescharacteristic, complemented
120#339—1491no—
121C2×#41—1491no—
122C2×M16C2×D14911yescharacteristic
123C2×M16C2×D14911yescharacteristic
124C4×Q8—2981no—
125C4×D4—2981no—
126C4×D4—2982no—
127#117—2981no—
128#117—1491no—
129C2×C4⋊C4—2981no—
130C2×C4⋊C4—2982no—
131C2×C4⋊C4—1491no—
132C2×C4⋊C4C2×D14911yescharacteristic
133C2×C42—1491no—
134#107—2981no—
135#106—2981no—
136#104—1494no—
137#103—2981no—
138#102—2981no—
139#41—2981no—
140#41—2981no—
141#41—1492no—
142#41—1492no—
143C2×Q8—1491no—
144C2×D4—2981no—
145C2×D4—1491no—
146C22×C4—2982no—
147C22×C4—2981no—
148C22×C4—2981no—
149C22×C4—2981no—
150C22×C4D59612yes—
151C22×C4C22×D14911yescharacteristic
152M16—21no—
153M16—21no—
154M16—21no—
155M16C4×D14912yescomplemented
156C2×C8—21no—
157C2×C8—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—2982no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C4⋊C4—5964no—
164C4⋊C4—1491no—
165C4⋊C4—1491no—
166C22⋊C4—2982no—
167C22⋊C4—2981no—
168C42—2982no—
169C42—2981no—
170C42—2981no—
171C42—1492no—
172C23—2981no—
173C23C2×D59611yescharacteristic
174Q8—2981no—
175Q8—1492no—
176D4—2982no—
177D4—2982no—
178D4—2981no—
179D4—1492no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4—2981no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—5962no—
191C2×C4—5961no—
192C2×C4—11922no—
193C2×C4C2×C4×D14911yescharacteristic
194C2×C4D4×D14911yescharacteristic
195C2×C4D4×D14911yescharacteristic
196C2×C4Q8×D14911yescharacteristic
197C2×C4#1455873511yescharacteristic
198C2×C4#1455873611yescharacteristic
199C8—22no—
200C8—41no—
201C22—21no—
202C22—21no—
203C22—2982no—
204C22—5961no—
205C22—5961no—
206C22C4×D59611yescharacteristic
207C22#1801188111yescharacteristic
208C22#1801189111yescharacteristic
209C4—42no—
210C4—2984no—
211C4—2982no—
212C4—5961no—
213C4—5961no—
214C4—11921no—
215C4C4⋊C4×D14911yescharacteristic
216C4#1801187111yescharacteristic
217C4#1801188911yescharacteristic
218C4#1801189311yescharacteristic
219C2—21no—
220C2—21no—
221C2—5962no—
222C2#2374949911yescharacteristic
223C2#2374979511yescharacteristic
224C2#2374981011yescharacteristic
subgroupG/H
centerC22#18011881
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#343×C149C2
socleC22×C149#120
prime radicalC2×#14558736C22
cosocleC22×C4×C149C23
hypercenter#343D149
hypocenterC149#1859
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. #23749667C2semidirect
5. #23749494C2semidirect
6. #23749386C2semidirect
7. #343×C149C2semidirect
20. #18011837C4semidirect
48. C4×Dic149C2×C4semidirect
54. M16×C149C2×C4semidirect
61. Dic298C4⋊C4semidirect
63. D596C4⋊C4semidirect
112. C149#1859semidirect
119. #343D149semidirect
155. M16C4×D149semidirect

Maximal subgroups

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

subgroupindex
#237501062
#237496672
C2×#180118372
#237496272
#237494942
#237493862
#343×C1492
#1859149