Finite Group Databasebeta

← #34044644

Subgroups — #34044644

Order 19072.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#18011956C211yesmaximal, characteristic
2C2×#18011839C212yesmaximal, complemented
3#23749624C212yesmaximal, complemented
4C2×#18011828C211yesmaximal, characteristic, complemented
5#390×C149C211yesmaximal, characteristic, complemented
6#18011956—22no—
7#18011956—24no—
8#18011956C414yescomplemented
9C2×#14558736C2212yes—
10C2×#14558735—22no—
11C22×C22⋊D149—22no—
12C2×D4×D149—22no—
13C2×#14558720C2212yescomplemented
14#18011839—24no—
15#18011834—22no—
16#18011831—22no—
17#18011828—22no—
18C22×D4×C149C2211yescharacteristic
19C2×C4⋊C4×C149C2211yescharacteristic, complemented
20C2×C22⋊C4×C149—22no—
21C2×C42×C149C2211yescharacteristic, complemented
22C23×D149—22no—
23#14558736—22no—
24#14558736—22no—
25#14558736C2×C414yes—
26#14558736D414yes—
27#14558735—28no—
28#14558735—28no—
29C2×Dic298D412yes—
30C2×D596D412yes—
31C2×C22⋊D149—24no—
32C2×C22⋊D149—28no—
33C2×C22⋊D149—28no—
34C2×C22⋊D149—22no—
35D4×D149—28no—
36D4×D149—28no—
37C22×Dic149—22no—
38C2×C4×D149—22no—
39#14558720—22no—
40#14558720—22no—
41C2×#11924746—22no—
42C24×C149D412yes—
43C2×D4×C149—22no—
44C2×D4×C149—22no—
45C2×D4×C149C2×C412yes—
46C2×D4×C149D412yes—
47C22×C4×C149—21no—
48C22×C4×C149—21no—
49C22×C4×C149C2311yescharacteristic
50C4⋊C4×C149—22no—
51C22⋊C4×C149—44no—
52C42×C149—22no—
53C22×D149—22no—
54C22×D149—28no—
55C22×D149—82no—
56C22×D149—82no—
57Dic298—22no—
58Dic298C22⋊C414yescomplemented
59D596—22no—
60D596C22⋊C414yescomplemented
61C22⋊D149—216no—
62C22⋊D149—24no—
63C22⋊D149—24no—
64C2×Dic149—28no—
65C2×Dic149—22no—
66C4×D149—24no—
67C4×D149—24no—
68#11924746—42no—
69C23×C149—22no—
70C23×C149—22no—
71C23×C149—42no—
72C23×C149—42no—
73C23×C149C22⋊C414yes—
74C23×C149C2×D411yescharacteristic
75D4×C149—24no—
76D4×C149—24no—
77C2×C4×C149—22no—
78C2×C4×C149—41no—
79C2×C4×C149—41no—
80C2×C4×C149—42no—
81C2×C4×C149—41no—
82C2×C4×C149C22×C411yescharacteristic
83C2×C4×C149C2×D412yes—
84C2×C4×C149C2×D412yes—
85C2×C4×C149C2×D411yescharacteristic
86C22×C149—21no—
87C22×C149—21no—
88C22×C149—24no—
89C22×C149—44no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149—82no—
93C22×C149C2×C22⋊C411yescharacteristic
94C22×C149#12011yescharacteristic
95C22×C149#12011yescharacteristic
96C2×D149—24no—
97C2×D149—42no—
98C2×D149—42no—
99C2×D149—88no—
100C4×C149—42no—
101C4×C149—81no—
102C4×C149C2×C22⋊C412yes—
103C4×C149#12012yes—
104Dic149—24no—
105C2×C149—21no—
106C2×C149—21no—
107C2×C149—44no—
108C2×C149#37911yescharacteristic
109C2×C149#45311yescharacteristic
110C2×C149#45511yescharacteristic
111D149—44no—
112C149#179211yescharacteristic, complemented, Sylow
113#1792—1491nomaximal, Sylow
114C2×H(5,𝔽2)—1491no—
115C2×#104—1492no—
116#417—1492no—
117C2×#100—1491no—
118#390D14911yescharacteristic, complemented
119H(5,𝔽2)—2984no—
120H(5,𝔽2)—2982no—
121H(5,𝔽2)—1494no—
122C2×#41—2982no—
123C2×#41—1492no—
124C22×D4—2982no—
125C22×D4—2982no—
126C22×D4C2×D14911yescharacteristic
127C2×M16—1492no—
128C2×C4⋊C4C2×D14911yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D14911yescharacteristic, complemented
131#104—2984no—
132#103—2982no—
133#102—2982no—
134#100—2982no—
135C24—2982no—
136C24C22⋊D14912yes—
137#41—2988no—
138#41—2988no—
139#41—2982no—
140#41—2982no—
141#41—1494no—
142#41—1494no—
143C2×Q8—1492no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—2988no—
147C2×D4—2988no—
148C2×D4—2984no—
149C2×D4—2988no—
150C2×D4—2982no—
151C2×D4—2988no—
152C2×D4—1492no—
153C2×D4C4×D14912yes—
154C2×D4D59612yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—2982no—
158C22×C4—2982no—
159C22×C4C22×D14911yescharacteristic
160M16—2982no—
161M16—2982no—
162C2×C8—2982no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—2988no—
171C23—2982no—
172C23—11922no—
173C23—11922no—
174C23#1455871314yes—
175C23C2×C22⋊D14911yescharacteristic
176Q8—2982no—
177Q8—1494no—
178D4—24no—
179D4—24no—
180D4—29816no—
181D4—2984no—
182D4—2984no—
183D4—2982no—
184D4—1494no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—2988no—
191C2×C4—2982no—
192C2×C4—2984no—
193C2×C4—2984no—
194C2×C4C2×C4×D14911yescharacteristic
195C2×C4D4×D14912yes—
196C2×C4D4×D14912yes—
197C2×C4C2×D59611yescharacteristic
198C8—5962no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—2984no—
207C22—5962no—
208C22—5962no—
209C22—11928no—
210C22C2×#1455871311yescharacteristic
211C22#1801187911yescharacteristic
212C22#1801187911yescharacteristic
213C4—42no—
214C4—81no—
215C4—2984no—
216C4C22⋊C4×D14912yes—
217C4#1801188112yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—5964no—
222C2#2374948011yescharacteristic
223C2#2374979211yescharacteristic
224C2#2374980211yescharacteristic
subgroupG/H
centerC22#18011879
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#390×C149C2
socleC22×C149#120
prime radicalC2×#18011956C2
cosocleC22×C4×C149C23
hypercenter#390D149
hypocenterC149#1792
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#18011839C2semidirect
3. #23749624C2semidirect
4. C2×#18011828C2semidirect
5. #390×C149C2semidirect
8. #18011956C4semidirect
13. C2×#14558720C22semidirect
19. C2×C4⋊C4×C149C22semidirect
21. C2×C42×C149C22semidirect
58. Dic298C22⋊C4semidirect
60. D596C22⋊C4semidirect
112. C149#1792semidirect
118. #390D149semidirect
128. C2×C4⋊C4C2×D149semidirect
130. C2×C42C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119562
C2×#180118392
#237496242
C2×#180118282
#390×C1492
#1792149