Finite Group Databasebeta

← #34044986

Subgroups — #34044986

Order 19072.

408 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14558720C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D149C211yesmaximal, characteristic
3C2×#18011823C212yesmaximal, complemented
4#23749379C212yesmaximal, complemented
5C2×C22⋊C8×C149C211yesmaximal, characteristic, complemented
6C22×C22⋊D149C411yescharacteristic
7C22×C4×D149C2211yescharacteristic
8C2×#14558720—24no—
9C2×#14558720—22no—
10C22×#11924746C2212yes—
11C4×C22⋊D149—22no—
12C4×C22⋊D149—22no—
13C2×#14558715C411yescharacteristic
14C2×C22⋊Dic149C411yescharacteristic
15C2×#14558713C411yescharacteristic
16C2×C4×Dic149C2211yescharacteristic
17#18011823—24no—
18C23×C4×C149C2211yescharacteristic
19C22×C8×C149C2212yes—
20C22⋊C8×C149—22no—
21C23×D149C2×C411yescharacteristic
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149—22no—
25C22×Dic149C2×C411yescharacteristic
26C22×Dic149C2×C411yescharacteristic
27C22×Dic149C2×C411yescharacteristic
28C2×C4×D149—22no—
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149—22no—
32#14558720—28no—
33C2×#11924746—22no—
34C2×#11924746—22no—
35C2×#11924746D414yescomplemented
36#14558715—22no—
37C22⋊Dic149—22no—
38#14558713—22no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C24×C149C2×C411yescharacteristic
42C22×C4×C149—22no—
43C22×C4×C149—22no—
44C22×C4×C149C2×C411yescharacteristic
45C22×C4×C149D412yes—
46C22×C4×C149D412yes—
47C22×C4×C149C2311yescharacteristic
48C2×C8×C149—22no—
49C2×C8×C149—22no—
50C2×C8×C149—22no—
51C22×D149—21no—
52C22×D149—22no—
53C22×D149—21no—
54C22×D149—22no—
55C22×D149M1612yescomplemented
56C22⋊D149—28no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149M1612yescomplemented
64C4×D149—41no—
65C4×D149—42no—
66C4×D149—41no—
67#11924746—24no—
68C23×C149—22no—
69C23×C149—21no—
70C23×C149—21no—
71C23×C149—22no—
72C23×C149C22⋊C412yes—
73C23×C149C22×C411yescharacteristic
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—24no—
77C2×C4×C149—22no—
78C2×C4×C149C22⋊C412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149#4112yes—
83C8×C149—42no—
84C22×C149—22no—
85C22×C149—22no—
86C22×C149—22no—
87C22×C149—42no—
88C22×C149—42no—
89C22×C149C2×C22⋊C411yescharacteristic
90C22×C149C4×D412yes—
91C22×C149C2×M1611yescharacteristic
92C22×C149C2×M1611yescharacteristic
93C22×C149#13112yes—
94C2×D149—22no—
95C2×D149—24no—
96C2×D149—41no—
97C2×D149—41no—
98C2×D149—42no—
99C4×C149—22no—
100C4×C149#12011yescharacteristic
101C4×C149#12112yes—
102C4×C149#12311yescharacteristic
103Dic149—22no—
104Dic149—41no—
105Dic149—41no—
106C2×C149—42no—
107C2×C149#38611yescharacteristic
108C2×C149#40711yescharacteristic
109C2×C149#40811yescharacteristic
110C2×C149#43512yes—
111C2×C149#43612yes—
112D149—42no—
113C149#187011yescharacteristic, complemented, Sylow
114#1870—1491nomaximal, Sylow
115C22×M16—1491no—
116C2×C4×D4—1491no—
117C2×C22⋊C8—1492no—
118C2×C22⋊C8D14911yescharacteristic, complemented
119#336—1492no—
120C22×D4—1491no—
121C23×C4—1491no—
122C23×C4C2×D14911yescharacteristic
123C2×M16—2982no—
124C2×M16—2984no—
125C22×C8—1492no—
126C22×C8C2×D14912yes—
127C4×D4—2982no—
128C4×D4—2982no—
129C2×C4⋊C4—1491no—
130C2×C22⋊C4—1491no—
131C2×C22⋊C4—1491no—
132C2×C42—1491no—
133C22⋊C8—22no—
134C22⋊C8—2984no—
135C24—1491no—
136C24C4×D14911yescharacteristic
137C2×D4—2982no—
138C2×D4—2982no—
139C2×D4—2982no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—2982no—
143C22×C4—2981no—
144C22×C4—2981no—
145C22×C4—2982no—
146C22×C4—1491no—
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4C4×D14911yescharacteristic
150C22×C4C22⋊D14912yes—
151C22×C4D59612yes—
152C22×C4C22×D14911yescharacteristic
153M16—2988no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—2982no—
158C2×C8—2982no—
159C2×C8—1494no—
160C4⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C42—2981no—
164C42—2981no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—2981no—
170C23—2982no—
171C23—2981no—
172C23—2982no—
173C23—1492no—
174C23#1455871312yes—
175C23C2×C4×D14911yescharacteristic
176D4—2988no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—2981no—
182C2×C4—2981no—
183C2×C4—2982no—
184C2×C4—2981no—
185C2×C4—2981no—
186C2×C4—2982no—
187C2×C4—5961no—
188C2×C4—5962no—
189C2×C4—5961no—
190C2×C4—1492no—
191C2×C4#1455871312yes—
192C2×C4D4×D14912yes—
193C2×C4C2×C22⋊D14911yescharacteristic
194C2×C4C2×D59611yescharacteristic
195C2×C4#1455873512yes—
196C8—42no—
197C8—2984no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—2984no—
204C22—2982no—
205C22—5962no—
206C22—5961no—
207C22—5961no—
208C22C2×#1455871311yescharacteristic
209C22#1801187112yes—
210C22M16×D14911yescharacteristic
211C22M16×D14911yescharacteristic
212C22#1801191712yes—
213C4—22no—
214C4—2982no—
215C4—5961no—
216C4—5961no—
217C4#1801188111yescharacteristic
218C4#1801188312yes—
219C4#1801189511yescharacteristic
220C2—42no—
221C2—5962no—
222C2#2374950211yescharacteristic
223C2#2374958811yescharacteristic
224C2#2374959111yescharacteristic
225C2#2374969912yes—
226C2#2374970012yes—
subgroupG/H
center, FrattiniC22×C4C22×D149
commutator, socleC23×C149C22×C4
FittingC2×C22⋊C8×C149C2
prime radicalC22×C22⋊D149C4
cosocleC22×C4×C149C23
hypercenterC2×C22⋊C8D149
hypocenterC149#1870
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#14558720C2semidirect
3. C2×#18011823C2semidirect
4. #23749379C2semidirect
5. C2×C22⋊C8×C149C2semidirect
35. C2×#11924746D4semidirect
55. C22×D149M16semidirect
63. C2×Dic149M16semidirect
113. C149#1870semidirect
118. C2×C22⋊C8D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587202
C2×C4×C22⋊D1492
C2×#180118232
#237493792
C2×C22⋊C8×C1492
#1870149