Finite Group Databasebeta

← #34045142

Subgroups — #34045142

Order 19072.

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

normal subgroups only

This group has 598 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
1C2×#18011880C211yesmaximal, characteristic
2C22×C22⋊Dic149C211yesmaximal, characteristic, complemented
3C2×#18011825C212yesmaximal, complemented
4#23749391C212yesmaximal, complemented
5#379×C149C211yesmaximal, characteristic, complemented
6C22×C22⋊D149C412yescomplemented
7C22×C22⋊D149C2211yescharacteristic
8C23×Dic149—21no—
9#18011880—22no—
10#18011880—21no—
11#18011880—21no—
12C2×C22⋊Dic149—24no—
13C2×C22⋊Dic149—21no—
14C2×C22⋊Dic149C412yescomplemented
15C2×C22⋊Dic149C2212yes—
16C2×C22⋊Dic149C2211yescharacteristic
17#18011825—24no—
18C25×C149C2211yescharacteristic
19C2×C22⋊C4×C149—22no—
20C2×C22⋊C4×C149C2212yes—
21C23×D149C2×C411yescharacteristic, complemented
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149—22no—
25C2×C22⋊D149—21no—
26C2×C22⋊D149—21no—
27C2×C22⋊D149—22no—
28C2×C22⋊D149—44no—
29C22×Dic149—24no—
30C22×Dic149—22no—
31C22×Dic149—44no—
32C22×Dic149C2×C411yescharacteristic, complemented
33C22×Dic149C2×C412yescomplemented
34C22⋊Dic149—24no—
35C22⋊Dic149—22no—
36C22⋊Dic149—22no—
37C22⋊Dic149—22no—
38C22⋊Dic149—21no—
39C22⋊Dic149—21no—
40C22⋊Dic149D414yescomplemented
41C24×C149—22no—
42C24×C149—22no—
43C24×C149—44no—
44C24×C149C2×C412yes—
45C24×C149D411yescharacteristic
46C24×C149D412yes—
47C24×C149D411yescharacteristic
48C24×C149C2311yescharacteristic
49C22×C4×C149—22no—
50C22⋊C4×C149—22no—
51C22⋊C4×C149—22no—
52C22⋊C4×C149—44no—
53C22×D149—21no—
54C22×D149—22no—
55C22×D149—42no—
56C22⋊D149—44no—
57C22⋊D149—44no—
58C22⋊D149—41no—
59C22⋊D149—42no—
60C22⋊D149—41no—
61C2×Dic149—21no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—24no—
65C2×Dic149—48no—
66C2×Dic149—44no—
67C2×Dic149—42no—
68C23×C149—24no—
69C23×C149—21no—
70C23×C149—21no—
71C23×C149—24no—
72C23×C149—24no—
73C23×C149—24no—
74C23×C149—21no—
75C23×C149—24no—
76C23×C149—21no—
77C23×C149—42no—
78C23×C149—42no—
79C23×C149—42no—
80C23×C149—42no—
81C23×C149—48no—
82C23×C149—48no—
83C23×C149C22⋊C412yes—
84C23×C149C22⋊C412yes—
85C23×C149C22×C411yescharacteristic
86C23×C149C2×D412yes—
87C23×C149C2×D411yescharacteristic
88C23×C149C2×D411yescharacteristic
89C23×C149#4112yes—
90C2×C4×C149—44no—
91C2×C4×C149—42no—
92C22×C149—24no—
93C22×C149—24no—
94C22×C149—22no—
95C22×C149—22no—
96C22×C149—22no—
97C22×C149—22no—
98C22×C149—22no—
99C22×C149—22no—
100C22×C149—22no—
101C22×C149—22no—
102C22×C149—42no—
103C22×C149—42no—
104C22×C149—48no—
105C22×C149—48no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149#9914yescomplemented
109C22×C149C2×C22⋊C411yescharacteristic
110C22×C149C4×D412yes—
111C22×C149#12011yescharacteristic
112C22×C149#12112yes—
113C22×C149#12311yescharacteristic
114C2×D149—41no—
115C2×D149—42no—
116C2×D149—82no—
117C4×C149—82no—
118Dic149—44no—
119Dic149—41no—
120Dic149—42no—
121C2×C149—21no—
122C2×C149—22no—
123C2×C149—22no—
124C2×C149—24no—
125C2×C149—21no—
126C2×C149—42no—
127C2×C149#38611yescharacteristic
128C2×C149C2×#9912yes—
129D149—81no—
130C149#189811yescharacteristic, complemented, Sylow
131#1898—1491nomaximal, Sylow
132C2×#120—1491no—
133C22×C22⋊C4—1491no—
134C2×#99—1492no—
135#379D14911yescharacteristic, complemented
136#342—1492no—
137C25C2×D14911yescharacteristic
138C22×D4—1491no—
139C22×D4—1492no—
140C23×C4—2981no—
141#120—2982no—
142#120—2981no—
143#120—2981no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—2981no—
146C2×C22⋊C4—2984no—
147C2×C22⋊C4—1492no—
148C2×C22⋊C4—1491no—
149C2×C22⋊C4—1492no—
150C2×C22⋊C4C2×D14912yes—
151#99—2984no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—1491no—
156C24C4×D14912yes—
157C24C22⋊D14912yes—
158C24D59611yescharacteristic
159C24D59611yescharacteristic
160C24C22×D14911yescharacteristic
161C2×D4—2982no—
162C2×D4—2981no—
163C2×D4—2981no—
164C2×D4—2982no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—5964no—
168C22×C4—22no—
169C22×C4—2984no—
170C22×C4—2982no—
171C22×C4—5964no—
172C22×C4—1491no—
173C22×C4—1492no—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—44no—
177C22⋊C4—2984no—
178C22⋊C4—2982no—
179C22⋊C4—2981no—
180C22⋊C4—2981no—
181C22⋊C4—2982no—
182C22⋊C4—2982no—
183C22⋊C4—1494no—
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—2981no—
200C23—2982no—
201C23—5962no—
202C23#1455871312yes—
203C23#1455871312yes—
204C23C2×C4×D14911yescharacteristic
205C23D4×D14912yes—
206C23C2×C22⋊D14911yescharacteristic
207C23C2×D59611yescharacteristic
208C23#1455873512yes—
209D4—5964no—
210D4—5964no—
211D4—5961no—
212D4—5962no—
213D4—5961no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—2981no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—2984no—
220C2×C4—5968no—
221C2×C4—5964no—
222C2×C4—5962no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—5961no—
240C22—5962no—
241C22—11922no—
242C22#1801182514yescomplemented
243C22C2×#1455871311yescharacteristic
244C22#1801187112yes—
245C22#1801188111yescharacteristic
246C22#1801188312yes—
247C22#1801189511yescharacteristic
248C4—82no—
249C4—5964no—
250C4—5961no—
251C4—5962no—
252C2—22no—
253C2—21no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—11921no—
259C2#2374950211yescharacteristic
260C2C2×#1801182512yes—
subgroupG/H
centerC22C2×#14558713
commutatorC23×C149C22×C4
FrattiniC24C22×D149
Fitting#379×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011880C2
cosocleC24×C149C23
hypercenter#379D149
hypocenterC149#1898
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic149C2semidirect
3. C2×#18011825C2semidirect
4. #23749391C2semidirect
5. #379×C149C2semidirect
6. C22×C22⋊D149C4semidirect
14. C2×C22⋊Dic149C4semidirect
21. C23×D149C2×C4semidirect
32. C22×Dic149C2×C4semidirect
33. C22×Dic149C2×C4semidirect
40. C22⋊Dic149D4semidirect
108. C22×C149#99semidirect
130. C149#1898semidirect
135. #379D149semidirect
242. C22#18011825semidirect

Maximal subgroups

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

subgroupindex
C2×#180118802
C22×C22⋊Dic1492
C2×#180118252
#237493912
#379×C1492
#1898149