Finite Group Databasebeta

← #34045775

Subgroups — #34045775

Order 19072.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#14558725C211yesmaximal, characteristic
2C22×#14558723C211yesmaximal, characteristic
3C2×#18011909C211yesmaximal, characteristic, complemented
4C2×#18011834C211yesmaximal, characteristic, complemented
5#23749526C211yesmaximal, characteristic
6#23749379C211yesmaximal, characteristic, complemented
7C2×#103×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C22×D596C2211yescharacteristic
10C2×#14558725—22no—
11C2×#14558725—22no—
12C2×#14558725—22no—
13C2×#14558723—22no—
14C2×#14558723—22no—
15C2×#14558723—22no—
16C22×#11924746C2211yescharacteristic
17#18011909—22no—
18#18011909—22no—
19C2×#14558715—22no—
20C2×#14558713—22no—
21C2×C4×Dic149C2211yescharacteristic
22#18011834—22no—
23C22×Q8×C149C2211yescharacteristic
24C22×C8×C149C2211yescharacteristic
25C2×C4⋊C4×C149C2211yescharacteristic
26#103×C149—22no—
27C23×D149—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×Dic298—21no—
32C2×Dic298—21no—
33C2×Dic298D412yes—
34C2×D596—21no—
35C2×D596—21no—
36C2×D596—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596D412yes—
40C22×Dic149—21no—
41C22×Dic149D412yes—
42#14558725—28no—
43#14558723—28no—
44C2×#11924746—21no—
45C2×#11924746—21no—
46C2×#11924746D412yes—
47#14558715—28no—
48#14558713—44no—
49C4×Dic149—21no—
50C4×Dic149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149—21no—
56C2×Q8×C149D412yes—
57C22×C4×C149—21no—
58C22×C4×C149—21no—
59C22×C4×C149C2311yescharacteristic
60C2×C8×C149—21no—
61C2×C8×C149—21no—
62C2×C8×C149D412yes—
63C4⋊C4×C149—21no—
64C4⋊C4×C149—21no—
65C22×D149—22no—
66C22×D149—41no—
67C22×D149—41no—
68C22×D149—42no—
69C22×D149—42no—
70Dic298—22no—
71Dic298—22no—
72Dic298—41no—
73Dic298—41no—
74D596—22no—
75D596—22no—
76D596—41no—
77D596—41no—
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149—22no—
81C2×Dic149—41no—
82C2×Dic149—41no—
83C2×Dic149SD1614yescomplemented
84#11924746—22no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87Q8×C149—22no—
88Q8×C149—41no—
89Q8×C149—41no—
90C2×C4×C149—22no—
91C2×C4×C149—41no—
92C2×C4×C149—41no—
93C2×C4×C149—41no—
94C2×C4×C149—42no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149#4111yescharacteristic
101C8×C149—22no—
102C22×C149#12011yescharacteristic
103C22×C149#12111yescharacteristic
104C22×C149#12711yescharacteristic
105C22×C149C2×SD1612yes—
106C22×C149#13712yes—
107C2×D149—42no—
108C2×D149—44no—
109C2×D149—82no—
110C2×D149—81no—
111C2×D149—81no—
112C4×C149—42no—
113C4×C149—81no—
114C4×C149#12011yescharacteristic
115C4×C149#12011yescharacteristic
116C4×C149#12111yescharacteristic
117C4×C149#12111yescharacteristic
118Dic149—24no—
119Dic149—42no—
120C2×C149#39211yescharacteristic
121C2×C149#44812yes—
122C2×C149#46112yes—
123C2×C149#49211yescharacteristic
124C2×C149#49711yescharacteristic
125D149—82no—
126C149#201311yescharacteristic, complemented, Sylow
127#2013—1491nomaximal, Sylow
128C22×SD16—1491no—
129C22×SD16—1491no—
130C2×C4⋊Q8—1491no—
131C2×#103—1491no—
132C2×#103D14911yescharacteristic, complemented
133#390—1491no—
134#336—1491no—
135C22×Q8—1491no—
136C22×Q8C2×D14911yescharacteristic
137C22×D4—1491no—
138C2×SD16—2982no—
139C2×SD16—2982no—
140C2×SD16—2982no—
141C2×SD16—2982no—
142C2×SD16—2982no—
143C2×SD16—2982no—
144C22×C8—1491no—
145C22×C8C2×D14911yescharacteristic
146C4⋊Q8—2982no—
147C4⋊Q8—2982no—
148C2×C4⋊C4—2982no—
149C2×C4⋊C4C2×D14911yescharacteristic
150C2×C22⋊C4—2982no—
151C2×C42—1491no—
152#103—22no—
153#103—2982no—
154C24—2981no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—2981no—
161C2×Q8—2981no—
162C2×Q8—2981no—
163C2×Q8—2981no—
164C2×Q8—2981no—
165C2×Q8—1492no—
166C2×Q8D59612yes—
167C2×D4—2981no—
168C2×D4—2981no—
169C2×D4—2981no—
170C2×D4—2981no—
171C2×D4—2981no—
172C2×D4—1492no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—2981no—
176C22×C4—1492no—
177C22×C4C22×D14911yescharacteristic
178SD16—2988no—
179SD16—2988no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—2981no—
183C2×C8—2981no—
184C2×C8—1492no—
185C2×C8C22⋊D14912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2988no—
189C22⋊C4—5964no—
190C42—2981no—
191C42—2981no—
192C23—2982no—
193C23—5961no—
194C23—5962no—
195C23—5962no—
196C23—5961no—
197C23D4×D14911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—2982no—
203Q8—2982no—
204Q8—5961no—
205Q8—5961no—
206D4—2982no—
207D4—2982no—
208D4—5961no—
209D4—5961no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—2982no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—5961no—
219C2×C4—5961no—
220C2×C4—1494no—
221C2×C4D4×D14911yescharacteristic
222C2×C4D4×D14911yescharacteristic
223C2×C4D4×D14911yescharacteristic
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4C2×D59611yescharacteristic
226C2×C4#1455873611yescharacteristic
227C8—22no—
228C8—2982no—
229C22—5962no—
230C22—5964no—
231C22—11921no—
232C22—11921no—
233C22—11922no—
234C22#1801188111yescharacteristic
235C22#1801188411yescharacteristic
236C22#1801190711yescharacteristic
237C22SD16×D14912yes—
238C22#1801194312yes—
239C4—42no—
240C4—81no—
241C4—2984no—
242C4—5962no—
243C4#1801187911yescharacteristic
244C4#1801188111yescharacteristic
245C4#1801188411yescharacteristic
246C4#1801188511yescharacteristic
247C2—11922no—
248C2#2374953411yescharacteristic
249C2#2374976512yes—
250C2#2374982912yes—
251C2#2374999611yescharacteristic
252C2#2375001811yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
prime radicalC22×D596C22
hypercenterC2×#103D149
hypocenterC149#2013
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#18011909C2semidirect
4. C2×#18011834C2semidirect
6. #23749379C2semidirect
7. C2×#103×C149C2semidirect
83. C2×Dic149SD16semidirect
126. C149#2013semidirect
132. C2×#103D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587252
C22×#145587232
C2×#180119092
C2×#180118342
#237495262
#237493792
C2×#103×C1492
#2013149