Finite Group Databasebeta

← #34045713

Subgroups — #34045713

Order 19072.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#18011937C211yesmaximal, characteristic
2#23750199C211yesmaximal, characteristic, complemented
3C2×#18011839C211yesmaximal, characteristic, complemented
4#23749630C211yesmaximal, characteristic, complemented
5C2×#18011830C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×#124×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011937—22no—
10#18011937—22no—
11C2×#14558724—21no—
12C2×#14558721—21no—
13C2×#14558720C2211yescharacteristic
14C2×#14558720C2211yescharacteristic
15#18011909—21no—
16#18011900—21no—
17#18011894—22no—
18#18011887—22no—
19#18011870C2211yescharacteristic
20#18011839—22no—
21#18011832—22no—
22#18011830—22no—
23C22×Q8×C149C2211yescharacteristic
24C22×D4×C149C2211yescharacteristic
25#124×C149—22no—
26#124×C149—22no—
27C2×C22⋊C4×C149—22no—
28C2×C42×C149C2211yescharacteristic
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33C2×Dic298D411yescharacteristic
34C2×D596D411yescharacteristic
35C2×C22⋊D149—21no—
36C2×C4×D149—21no—
37#14558724—24no—
38#14558721—24no—
39#14558720—21no—
40#14558720—21no—
41#14558720—21no—
42#14558720D412yes—
43C2×#11924746—21no—
44C2×#11924746—21no—
45C4⋊Dic149D412yes—
46#14558715—24no—
47C22⋊Dic149—21no—
48#14558713—24no—
49C4×Dic149—21no—
50C24×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149—21no—
56C2×Q8×C149—21no—
57C2×D4×C149—21no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149D412yes—
63C22×C4×C149—21no—
64C22×C4×C149D412yes—
65C22×C4×C149C2311yescharacteristic
66C22⋊C4×C149—28no—
67C42×C149—21no—
68C42×C149D412yes—
69C22×D149—21no—
70Dic298—21no—
71Dic298—21no—
72D596—21no—
73D596—21no—
74C22⋊D149—41no—
75C22⋊D149—41no—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C4×D149—41no—
79C4×D149—41no—
80#11924746—22no—
81#11924746—41no—
82C23×C149—22no—
83C23×C149—44no—
84C23×C149—41no—
85C23×C149—41no—
86C23×C149C2×D411yescharacteristic
87Q8×C149—41no—
88Q8×C149—41no—
89Q8×C149—41no—
90Q8×C149—41no—
91D4×C149—22no—
92D4×C149—22no—
93D4×C149—41no—
94D4×C149—41no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—22no—
99C2×C4×C149—42no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149#4111yescharacteristic
106C22×C149—22no—
107C22×C149—44no—
108C22×C149—42no—
109C22×C149—82no—
110C22×C149—82no—
111C22×C149#12011yescharacteristic
112C22×C149#12011yescharacteristic
113C22×C149#12111yescharacteristic
114C2×D149—41no—
115C2×D149—42no—
116C4×C149—42no—
117C4×C149—42no—
118C4×C149#12011yescharacteristic
119C4×C149#12111yescharacteristic
120C4×C149#12111yescharacteristic
121C4×C149#12711yescharacteristic
122Dic149—41no—
123Dic149—42no—
124C2×C149—21no—
125C2×C149—21no—
126C2×C149—82no—
127C2×C149#39211yescharacteristic
128C2×C149#45412yes—
129D149—81no—
130C149#200311yescharacteristic, complemented, Sylow
131#2003—1491nomaximal, Sylow
132C2×AGL(1,ℤ/8)—1491no—
133#536—1491no—
134C2×#124D14911yescharacteristic, complemented
135C2×#104—1491no—
136#418—1491no—
137C2×#101—1491no—
138#339—1491no—
139C2×#41—1491no—
140C22×Q8C2×D14911yescharacteristic
141C22×D4C2×D14911yescharacteristic
142AGL(1,ℤ/8)—2982no—
143AGL(1,ℤ/8)—2982no—
144C2×SD16—2981no—
145C2×D8—2981no—
146C2×M16—1491no—
147C2×M16—1491no—
148C4⋊Q8—2981no—
149#124—22no—
150#124—22no—
151#124—2981no—
152#123—2982no—
153C22⋊Q8—2982no—
154#117—1491no—
155C2×C22⋊C4—22no—
156C2×C42C2×D14911yescharacteristic
157#104—2982no—
158#102—2982no—
159#101—2982no—
160C24—21no—
161#41—2981no—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1491no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—2981no—
178C2×D4—1491no—
179C2×D4C22⋊D14912yes—
180C22×C4—21no—
181C22×C4—2981no—
182C22×C4C22⋊D14912yes—
183C22×C4C22×D14911yescharacteristic
184SD16—2984no—
185D8—2984no—
186M16—2981no—
187M16—2981no—
188M16—2981no—
189M16—1492no—
190C2×C8—2981no—
191C2×C8—2981no—
192C4⋊C4—2984no—
193C4⋊C4—1492no—
194C22⋊C4—28no—
195C22⋊C4—2984no—
196C22⋊C4—2981no—
197C42—21no—
198C42—2981no—
199C42C22⋊D14912yes—
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—2981no—
205C23C2×C22⋊D14911yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—2981no—
211Q8—2981no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—2981no—
217D4—2981no—
218D4—5961no—
219D4—5961no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—2982no—
226C2×C4—2981no—
227C2×C4—5961no—
228C2×C4—5961no—
229C2×C4D4×D14911yescharacteristic
230C2×C4D4×D14911yescharacteristic
231C2×C4D4×D14911yescharacteristic
232C2×C4C2×C22⋊D14911yescharacteristic
233C2×C4C2×C22⋊D14911yescharacteristic
234C2×C4#1455873511yescharacteristic
235C8—2982no—
236C8—5961no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—5961no—
243C22—5962no—
244C22#1801187911yescharacteristic
245C22#1801188011yescharacteristic
246C22#1801188311yescharacteristic
247C4—42no—
248C4—42no—
249C4—5961no—
250C4—5962no—
251C4#1801187911yescharacteristic
252C4#1801188211yescharacteristic
253C4#1801188311yescharacteristic
254C4#1801190711yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—11921no—
259C2#2374953311yescharacteristic
260C2#2374979712yes—
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#124×C149C2
socleC22×C149#120
prime radicalC2×#18011937C2
hypercenterC2×#124D149
hypocenterC149#2003
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #23750199C2semidirect
3. C2×#18011839C2semidirect
4. #23749630C2semidirect
5. C2×#18011830C2semidirect
6. #23749385C2semidirect
7. C2×#124×C149C2semidirect
130. C149#2003semidirect
134. C2×#124D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
#237501992
C2×#180118392
#237496302
C2×#180118302
#237493852
C2×#124×C1492
#2003149