Finite Group Databasebeta

← #34060664

Subgroups — #34060664

Order 19072.

432 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C23×#11924753C211yesmaximal, characteristic, complemented
2C2×C22⋊#11924753C212yesmaximal, complemented
3C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
4#23750491C212yesmaximal, complemented
5C2×D4×Dic149C211yesmaximal, characteristic
6C22×#11924753—24no—
7C22×#11924753—22no—
8C22×#11924753C2212yes—
9C22×#11924753C2212yes—
10C22⋊#11924753—24no—
11C22⋊#11924753—22no—
12C23×Dic149C2211yescharacteristic
13C23×Dic149C2211yescharacteristic
14D4×Dic149—22no—
15D4×Dic149—22no—
16C2×C4⋊Dic149C411yescharacteristic
17C2×C22⋊Dic149C411yescharacteristic
18C2×C22⋊Dic149C411yescharacteristic
19C2×C4×Dic149C2211yescharacteristic
20C22×D4×C149C411yescharacteristic
21C2×#11924753—28no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×#11924753D414yescomplemented
28C22×Dic149—22no—
29C22×Dic149—22no—
30C22×Dic149—22no—
31C22×Dic149—21no—
32C22×Dic149—21no—
33C22×Dic149—22no—
34C22×Dic149C2×C411yescharacteristic
35C22×Dic149C2×C411yescharacteristic
36C22×Dic149C2×C411yescharacteristic
37C22×Dic149D412yes—
38C22×Dic149D412yes—
39C22×Dic149C2311yescharacteristic
40C4⋊Dic149—22no—
41C22⋊Dic149—22no—
42C22⋊Dic149—22no—
43C4×Dic149—21no—
44C4×Dic149—21no—
45C24×C149C2×C411yescharacteristic
46C24×C149C2×C411yescharacteristic
47C2×D4×C149—22no—
48C2×D4×C149—22no—
49C2×D4×C149C814yescomplemented
50C22×C4×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—24no—
56C2×Dic149—22no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—41no—
62C2×Dic149—42no—
63C2×Dic149—41no—
64C2×Dic149C22⋊C412yes—
65C2×Dic149C2×D412yes—
66C2×Dic149C2×D411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C2×Dic149#4112yes—
69C23×C149—22no—
70C23×C149—22no—
71C23×C149—21no—
72C23×C149—22no—
73C23×C149—21no—
74C23×C149—22no—
75C23×C149C22⋊C412yes—
76C23×C149C2×C812yes—
77C23×C149C2×C812yescomplemented
78C23×C149M1612yes—
79C23×C149C22×C411yescharacteristic
80D4×C149—28no—
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149C2×C812yescomplemented
84C22×C149—22no—
85C22×C149—22no—
86C22×C149—24no—
87C22×C149—24no—
88C22×C149—22no—
89C22×C149—24no—
90C22×C149—41no—
91C22×C149—41no—
92C22×C149—42no—
93C22×C149C22⋊C814yescomplemented
94C22×C149C2×C22⋊C411yescharacteristic
95C22×C149C4×D412yes—
96C22×C149C22×C811yescharacteristic
97C22×C149C2×M1611yescharacteristic
98C22×C149#13112yes—
99C4×C149—22no—
100Dic149—22no—
101Dic149—41no—
102Dic149—41no—
103Dic149#12011yescharacteristic
104Dic149#12112yes—
105Dic149#12311yescharacteristic
106C2×C149—24no—
107C2×C149—42no—
108C2×C149#38611yescharacteristic
109C2×C149C2×C22⋊C811yescharacteristic
110C2×C149#40811yescharacteristic
111C2×C149C8×D412yes—
112C2×C149#43512yes—
113C149#186911yescharacteristic, complemented, Sylow
114#1869—1491nomaximal, Sylow
115C23×C8—1491no—
116C2×C4×D4—1491no—
117C2×C22⋊C8—1491no—
118C2×C22⋊C8—1492no—
119#336—1492no—
120C22×D4#1059701011yescharacteristic
121C23×C4—1491no—
122C23×C4—1491no—
123C22×C8—2982no—
124C22×C8—2984no—
125C22×C8—1492no—
126C22×C8—1492no—
127C4×D4—2982no—
128C4×D4—2982no—
129C2×C4⋊C4—1491no—
130C2×C22⋊C4—1491no—
131C2×C22⋊C4—1491no—
132C2×C42—1491no—
133C22⋊C8—2982no—
134C22⋊C8—2984no—
135C24C2×#1059701011yescharacteristic
136C24C2×#1059701011yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4#1192475314yescomplemented
140C22×C4—2982no—
141C22×C4—2982no—
142C22×C4—2982no—
143C22×C4—2981no—
144C22×C4—2981no—
145C22×C4—2982no—
146C22×C4—1491no—
147C22×C4—1491no—
148C22×C4—1492no—
149C22×C4—1492no—
150C22×C4—1491no—
151C22×C4—1491no—
152C22×C4C2×#1059701011yescharacteristic
153C2×C8—2988no—
154C2×C8—2982no—
155C2×C8—2982no—
156C2×C8—2982no—
157C2×C8—2982no—
158C2×C8—2982no—
159C2×C8—1494no—
160C4⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2982no—
163C42—2981no—
164C42—2981no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23—22no—
171C23C22⋊#1059701012yes—
172C23C2×#1192475312yes—
173C23C2×#1192475312yescomplemented
174C23#1455874512yes—
175C23C22×#1059701011yescharacteristic
176D4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2984no—
182C2×C4—2982no—
183C2×C4—2981no—
184C2×C4—2981no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—5961no—
188C2×C4—5962no—
189C2×C4—5961no—
190C2×C4—1492no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4—1492no—
194C2×C4—1492no—
195C2×C4C2×#1192475312yescomplemented
196C8—2984no—
197C8—5962no—
198C22—24no—
199C22—22no—
200C22—22no—
201C22—24no—
202C22—22no—
203C22—24no—
204C22—42no—
205C22—41no—
206C22—41no—
207C22C22⋊#1192475314yescomplemented
208C22C2×C22⋊#1059701011yescharacteristic
209C22D4×#1059701012yes—
210C22C22×#1192475311yescharacteristic
211C22C2×#1455874511yescharacteristic
212C22#1801199812yes—
213C4—22no—
214C4—2982no—
215C4—5961no—
216C4—5961no—
217C4—1491no—
218C4—1492no—
219C4—1491no—
220C2—24no—
221C2—42no—
222C2#2375057311yescharacteristic
223C2C2×C22⋊#1192475311yescharacteristic
224C2#2375059811yescharacteristic
225C2D4×#1192475312yes—
226C2#2375065612yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutatorC22×C149C22×C8
Fitting, prime radicalC22×D4×C149C4
socleC23×C149C22×C4
cosocleC22×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149#1869
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11924753C2semidirect
2. C2×C22⋊#11924753C2semidirect
3. C2×C22⋊#11924753C2semidirect
4. #23750491C2semidirect
27. C2×#11924753D4semidirect
49. C2×D4×C149C8semidirect
77. C23×C149C2×C8semidirect
83. C2×C4×C149C2×C8semidirect
93. C22×C149C22⋊C8semidirect
113. C149#1869semidirect
139. C2×D4#11924753semidirect
173. C23C2×#11924753semidirect
195. C2×C4C2×#11924753semidirect
207. C22C22⋊#11924753semidirect

Maximal subgroups

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

subgroupindex
C23×#119247532
C2×C22⋊#119247532
#237504912
C2×D4×Dic1492
#1869149