Finite Group Databasebeta

← #34060835

Subgroups — #34060835

Order 19072.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#23750628C211yesmaximal, characteristic, complemented
2C2×#18011972C212yesmaximal, complemented
3C2×#18011971C212yesmaximal
4C4×#14558745C211yesmaximal, characteristic, complemented
5C2×#18011897C211yesmaximal, characteristic
6C2×#14558745C2212yes—
7C2×#14558745C2212yes—
8#18011978—21no—
9C4⋊#11924753—21no—
10#18011972—24no—
11#18011971—24no—
12#18011966—21no—
13C4×#11924753—21no—
14C22×Dic298C2211yescharacteristic
15C22×C22⋊D149C2211yescharacteristic
16#18011897—21no—
17#18011897—21no—
18#18011897—21no—
19#18011897—21no—
20C2×C22⋊Dic149C411yescharacteristic
21C2×#14558713C411yescharacteristic
22C2×#14558713C411yescharacteristic
23C2×C4×Dic149C2211yescharacteristic
24C2×C22⋊C4×C149C411yescharacteristic
25#14558745—22no—
26#14558745—22no—
27#14558745—22no—
28#14558745D414yes—
29C2×#11924753—22no—
30C2×#11924753—22no—
31C23×D149C2×C411yescharacteristic
32C2×Dic298—22no—
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×Dic298—22no—
36C2×C22⋊D149—22no—
37C2×C22⋊D149—21no—
38C2×C22⋊D149—21no—
39C2×C22⋊D149—22no—
40C22×Dic149C2×C411yescharacteristic
41C22×Dic149C2×C411yescharacteristic
42C22×Dic149C2311yescharacteristic
43C22⋊Dic149—21no—
44C22⋊Dic149—21no—
45#14558713—21no—
46#14558713—21no—
47#14558713—21no—
48#14558713—21no—
49C4×Dic149D411yescharacteristic
50C4×Dic149D411yescharacteristic
51C4×Dic149D411yescharacteristic
52C4×Dic149D411yescharacteristic
53C24×C149C2×C411yescharacteristic
54C22×C4×C149C2×C411yescharacteristic
55C22×C4×C149C2×C411yescharacteristic
56C22⋊C4×C149—21no—
57C22⋊C4×C149—21no—
58#11924753—24no—
59#11924753—42no—
60C22×D149—21no—
61C22×D149—22no—
62C22×D149—41no—
63C22×D149—41no—
64Dic298—42no—
65Dic298—41no—
66Dic298—41no—
67C22⋊D149—42no—
68C22⋊D149—41no—
69C22⋊D149—41no—
70C2×Dic149—21no—
71C2×Dic149—22no—
72C2×Dic149—41no—
73C2×Dic149C22⋊C411yescharacteristic
74C2×Dic149C22⋊C411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D412yes—
77C2×Dic149C2×D411yescharacteristic
78C2×Dic149#4112yes—
79C23×C149—21no—
80C23×C149—22no—
81C23×C149—41no—
82C23×C149—41no—
83C23×C149C22×C411yescharacteristic
84C2×C4×C149—21no—
85C2×C4×C149—22no—
86C2×C4×C149—41no—
87C2×C4×C149C22⋊C411yescharacteristic
88C2×C4×C149C22⋊C411yescharacteristic
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149—41no—
94C22×C149—82no—
95C22×C149C2×C22⋊C411yescharacteristic
96C22×C149C4×D412yes—
97C2×D149—41no—
98C2×D149—41no—
99C2×D149—41no—
100C2×D149—82no—
101C4×C149—21no—
102C4×C149—21no—
103C4×C149—41no—
104Dic149—21no—
105Dic149—21no—
106Dic149—41no—
107Dic149#12112yes—
108Dic149#12411yescharacteristic
109Dic149#12711yescharacteristic
110C2×C149—22no—
111C2×C149—81no—
112C2×C149#39011yescharacteristic
113C2×C149#41311yescharacteristic
114C2×C149#41311yescharacteristic
115D149—81no—
116C149#196711yescharacteristic, complemented, Sylow
117#1967—1491nomaximal, Sylow
118C2×#124—1491no—
119#423—1491no—
120C2×#101—1492no—
121C2×#100—1492no—
122C4×M16—1491no—
123C22×Q8—1491no—
124C22×D4—1491no—
125C2×M16—1492no—
126C2×M16—1492no—
127#124—2981no—
128#124—2981no—
129#124—2981no—
130#124—2981no—
131C2×C22⋊C4—1491no—
132C2×C22⋊C4—1491no—
133C2×C22⋊C4—1491no—
134C2×C22⋊C4#1059701011yescharacteristic
135C2×C42—1491no—
136C4⋊C8—2981no—
137C4⋊C8—2981no—
138#101—2984no—
139#100—2984no—
140#97—2981no—
141C4×C8—2981no—
142C24—1491no—
143C24C2×#1059701011yescharacteristic
144C2×Q8—2982no—
145C2×Q8—2981no—
146C2×Q8—2981no—
147C2×Q8—2982no—
148C2×D4—2982no—
149C2×D4—2981no—
150C2×D4—2981no—
151C2×D4—2982no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4—1491no—
155C22×C4C2×#1059701011yescharacteristic
156C22×C4C2×#1059701011yescharacteristic
157M16—2982no—
158M16—2982no—
159M16—2982no—
160M16—1494no—
161C2×C8—2982no—
162C2×C8—2982no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C22⋊C4—2981no—
170C22⋊C4—2981no—
171C42—1491no—
172C42—1491no—
173C42—1491no—
174C42—1491no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—2981no—
180C23—2982no—
181C23—5961no—
182C23—5961no—
183C23C22×#1059701011yescharacteristic
184Q8—5962no—
185Q8—5961no—
186Q8—5961no—
187D4—5962no—
188D4—5961no—
189D4—5961no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—2981no—
194C2×C4—2982no—
195C2×C4—5961no—
196C2×C4—1491no—
197C2×C4—1491no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4—1492no—
201C2×C4—1492no—
202C2×C4C22⋊#1059701011yescharacteristic
203C2×C4C22⋊#1059701011yescharacteristic
204C8—2984no—
205C8—5962no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—5961no—
213C22—5961no—
214C22—5961no—
215C22—11922no—
216C22C2×C22⋊#1059701011yescharacteristic
217C22D4×#1059701012yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—2981no—
222C4—2981no—
223C4—5961no—
224C4—1492no—
225C4—1491no—
226C4—1491no—
227C2—22no—
228C2—81no—
229C2—11921no—
230C2#2375057711yescharacteristic
231C2#2375061111yescharacteristic
232C2#2375061211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C22
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1967
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
2. C2×#18011972C2semidirect
4. C4×#14558745C2semidirect
116. C149#1967semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×#180119722
C2×#180119712
C4×#145587452
C2×#180118972
#1967149