Finite Group Databasebeta

← #34044919

Subgroups — #34044919

Order 19072.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#23750108C211yesmaximal, characteristic
2#23749667C211yesmaximal, characteristic, complemented
3#23749626C211yesmaximal, characteristic
4#23749495C211yesmaximal, characteristic, complemented
5#23749393C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×#104×C149C211yesmaximal, characteristic
8C2×#14558720C2211yescharacteristic
9Q8×Dic149—21no—
10D4×Dic149—21no—
11D4×Dic149—22no—
12#18011870—21no—
13#18011870C2211yescharacteristic
14C2×C4⋊Dic149—21no—
15C2×C4⋊Dic149—22no—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×C4⋊Dic149C2211yescharacteristic
18#18011845—21no—
19#18011843—21no—
20#18011835—21no—
21#18011832—21no—
22C2×#41×C149C2211yescharacteristic
23C2×M16×C149C2211yescharacteristic
24C2×C42×C149C2211yescharacteristic
25#104×C149C414yescomplemented
26C22×Dic149—22no—
27C22×Dic149—21no—
28C22×Dic149D412yes—
29#14558720—21no—
30#14558720—21no—
31C2×#11924746—21no—
32C4⋊Dic149—22no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149—44no—
38C4⋊Dic149D411yescharacteristic
39C4⋊Dic149D411yescharacteristic
40C22⋊Dic149—22no—
41C22⋊Dic149—21no—
42C4×Dic149—22no—
43C4×Dic149—21no—
44#41×C149—21no—
45#41×C149—21no—
46#41×C149C2×C412yes—
47#41×C149Q812yes—
48C2×Q8×C149D411yescharacteristic
49C2×D4×C149—21no—
50C2×D4×C149D411yescharacteristic
51C22×C4×C149—21no—
52C22×C4×C149—21no—
53C22×C4×C149C2311yescharacteristic
54M16×C149—21no—
55M16×C149C2×C412yescomplemented
56C2×C8×C149—21no—
57C42×C149—21no—
58C42×C149C2×C412yescomplemented
59C2×Dic149—21no—
60C2×Dic149—22no—
61C2×Dic149—21no—
62C2×Dic149—42no—
63C2×Dic149—42no—
64C2×Dic149—41no—
65C2×Dic149—82no—
66#11924746—41no—
67C23×C149—21no—
68C23×C149C2×D411yescharacteristic
69Q8×C149—21no—
70Q8×C149C4⋊C412yescomplemented
71D4×C149—22no—
72D4×C149—22no—
73D4×C149—21no—
74D4×C149C4⋊C412yescomplemented
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149C22×C411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×Q811yescharacteristic
85C2×C4×C149#4111yescharacteristic
86C2×C4×C149#4111yescharacteristic
87C8×C149—22no—
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—22no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149C4×D411yescharacteristic
94C22×C149#12011yescharacteristic
95C22×C149C22⋊Q811yescharacteristic
96C4×C149—24no—
97C4×C149—22no—
98C4×C149C2×C4⋊C411yescharacteristic
99C4×C149C4×D411yescharacteristic
100C4×C149C22⋊Q811yescharacteristic
101C4×C149#12311yescharacteristic
102Dic149—42no—
103Dic149—41no—
104Dic149—41no—
105Dic149—81no—
106C2×C149—21no—
107C2×C149—21no—
108C2×C149—42no—
109C2×C149#38511yescharacteristic
110C2×C149#45311yescharacteristic
111C2×C149#45611yescharacteristic
112C149#185911yescharacteristic, complemented, Sylow
113#1859—1491nomaximal, Sylow
114#520—1491no—
115#428—1491no—
116C2×#104D14911yescharacteristic
117#417—1491no—
118#384—1491no—
119#343—1491no—
120#339—1491no—
121C2×#41C2×D14911yescharacteristic
122C2×M16—1491no—
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⋊C4—1491no—
133C2×C42C2×D14911yescharacteristic
134#107—2981no—
135#106—2981no—
136#104Dic14914yescomplemented
137#103—2981no—
138#102—2981no—
139#41—21no—
140#41—21no—
141#41C2×Dic14912yes—
142#41Dic29812yes—
143C2×Q8D59611yescharacteristic
144C2×D4—21no—
145C2×D4D59611yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2982no—
149C22×C4—2981no—
150C22×C4—1492no—
151C22×C4C22×D14911yescharacteristic
152M16—21no—
153M16—2981no—
154M16—2981no—
155M16C2×Dic14912yescomplemented
156C2×C8—21no—
157C2×C8—2981no—
158C4⋊C4—2982no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C4⋊C4—5964no—
164C4⋊C4—1491no—
165C4⋊C4—1491no—
166C22⋊C4—2982no—
167C22⋊C4—2981no—
168C42—21no—
169C42—2982no—
170C42—2981no—
171C42C2×Dic14912yescomplemented
172C23—21no—
173C23D4×D14911yescharacteristic
174Q8—21no—
175Q8C4⋊Dic14912yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic14912yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2981no—
187C2×C4—2982no—
188C2×C4—2981no—
189C2×C4—5962no—
190C2×C4—5962no—
191C2×C4—5961no—
192C2×C4—11922no—
193C2×C4C22×Dic14911yescharacteristic
194C2×C4D4×D14911yescharacteristic
195C2×C4C2×D59611yescharacteristic
196C2×C4C2×Dic29811yescharacteristic
197C2×C4#1455873511yescharacteristic
198C2×C4#1455873511yescharacteristic
199C8—22no—
200C8—5961no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22D4×Dic14911yescharacteristic
207C22#1801188111yescharacteristic
208C22#1801188811yescharacteristic
209C4—24no—
210C4—22no—
211C4—5962no—
212C4—5961no—
213C4—5961no—
214C4—11921no—
215C4C2×C4⋊Dic14911yescharacteristic
216C4D4×Dic14911yescharacteristic
217C4#1801188811yescharacteristic
218C4#1801189511yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#2374950011yescharacteristic
223C2#2374979411yescharacteristic
224C2#2374980911yescharacteristic
subgroupG/H
centerC22#18011881
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#104×C149C2
socleC22×C149#120
prime radicalC2×#41×C149C22
cosocleC22×C4×C149C23
hypercenterC2×#104D149
hypocenterC149#1859
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #23749667C2semidirect
4. #23749495C2semidirect
5. #23749393C2semidirect
6. #23749385C2semidirect
25. #104×C149C4semidirect
55. M16×C149C2×C4semidirect
58. C42×C149C2×C4semidirect
70. Q8×C149C4⋊C4semidirect
74. D4×C149C4⋊C4semidirect
112. C149#1859semidirect
136. #104Dic149semidirect
155. M16C2×Dic149semidirect
171. C42C2×Dic149semidirect
175. Q8C4⋊Dic149semidirect
179. D4C4⋊Dic149semidirect

Maximal subgroups

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

subgroupindex
#237501082
#237496672
#237496262
#237494952
#237493932
#237493852
C2×#104×C1492
#1859149