Finite Group Databasebeta

← #34060882

Subgroups — #34060882

Order 19072.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750567C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750503C212yesmaximal
4#23750503C212yesmaximal
5C2×#18011889C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C2×C22⋊#10597010C2212yes—
8C2×C22⋊#10597010C2212yes—
9C2×C4×#10597010—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4—21no—
12C22×Dic298C411yescharacteristic, complemented
13C22×C4×D149C2211yescharacteristic
14#18011889—21no—
15#18011889—21no—
16#18011889—21no—
17#18011889—21no—
18C2×#14558715C411yescharacteristic, complemented
19C2×#14558715C411yescharacteristic, complemented
20C2×#14558713C2211yescharacteristic
21C2×#14558713C2211yescharacteristic
22C2×C4⋊C4×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C22×#10597010—22no—
25C4⋊#10597010—42no—
26C22⋊#10597010—22no—
27C22⋊#10597010—24no—
28C22⋊#10597010Q814yescomplemented
29C4×#10597010—42no—
30C23×D149C2311yescharacteristic
31C2×Dic298—21no—
32C2×Dic298—21no—
33C2×Dic298—42no—
34C22×Dic149C2×C411yescharacteristic
35C22×Dic149C2×C411yescharacteristic
36C22×Dic149C2×C411yescharacteristic
37C2×C4×D149—42no—
38C2×C4×D149D411yescharacteristic
39C2×C4×D149D411yescharacteristic
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42#14558715—21no—
43#14558715—21no—
44#14558715—21no—
45#14558715—21no—
46#14558713—21no—
47#14558713—21no—
48#14558713—21no—
49#14558713—21no—
50C22×C4×C149C2×C411yescharacteristic
51C22×C4×C149C2×C411yescharacteristic
52C22×C4×C149C2×C411yescharacteristic
53C4⋊C4×C149—21no—
54C4⋊C4×C149—21no—
55C2×#10597010—24no—
56C2×#10597010—42no—
57C2×#10597010—42no—
58C2×#10597010—42no—
59C2×#10597010—42no—
60C2×#10597010—42no—
61C22×D149—41no—
62C22×D149—41no—
63C22×D149C2×D411yescharacteristic
64C22×D149C2×D411yescharacteristic
65C22×D149C2×Q812yes—
66C22×D149#4112yes—
67Dic298—42no—
68Dic298—42no—
69C2×Dic149—22no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—41no—
73C2×Dic149—41no—
74C2×Dic149C22⋊C411yescharacteristic
75C2×Dic149C22⋊C411yescharacteristic
76C4×D149—22no—
77C4×D149—22no—
78C4×D149—41no—
79C4×D149—41no—
80C23×C149C22×C411yescharacteristic
81C2×C4×C149—21no—
82C2×C4×C149—21no—
83C2×C4×C149—41no—
84C2×C4×C149—41no—
85C2×C4×C149—41no—
86C2×C4×C149C22⋊C411yescharacteristic
87C2×C4×C149C22⋊C411yescharacteristic
88C22×C149—21no—
89C22×C149—21no—
90C22×C149C2×C22⋊C411yescharacteristic
91C22×C149C4×Q812yes—
92C2×D149—21no—
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149—42no—
97C2×D149—42no—
98C2×D149C22⋊Q812yes—
99C2×D149#12411yescharacteristic
100C2×D149C4⋊Q811yescharacteristic
101#10597010—44no—
102#10597010—82no—
103C4×C149—21no—
104C4×C149—21no—
105C4×C149—41no—
106C4×C149—41no—
107Dic149—21no—
108Dic149—41no—
109Dic149—41no—
110Dic149#9912yes—
111C2×C149—22no—
112C2×C149#39111yescharacteristic
113C2×C149C2×#9911yescharacteristic
114C2×C149#41011yescharacteristic
115D149—22no—
116D149—21no—
117D149—21no—
118C149#199611yescharacteristic, complemented, Sylow
119#1996—1491nomaximal, Sylow
120C2×C22⋊Q8—1491no—
121#380—1491no—
122C4×C22⋊C4—1491no—
123#342—1492no—
124#342—1492no—
125C22×Q8—1491no—
126C23×C4—1491no—
127C22⋊Q8—2981no—
128C22⋊Q8—2981no—
129C22⋊Q8—2981no—
130C22⋊Q8—2981no—
131C2×C4⋊C4—2981no—
132C2×C4⋊C4—1491no—
133C2×C4⋊C4—1491no—
134C2×C4⋊C4#1059701011yescharacteristic, complemented
135C2×C22⋊C4—1492no—
136C2×C22⋊C4—1491no—
137C2×C22⋊C4—1491no—
138C2×C22⋊C4—1492no—
139C2×C42—2981no—
140#95—2981no—
141#95—2981no—
142C24—1491no—
143C2×Q8—2981no—
144C2×Q8—2981no—
145C2×Q8—5962no—
146C22×C4—2982no—
147C22×C4—2982no—
148C22×C4—5962no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4—1491no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4—1491no—
155C22×C4—1491no—
156C22×C4C2×#1059701011yescharacteristic
157C22×C4C2×#1059701011yescharacteristic
158C22×C4C2×#1059701011yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2981no—
162C4⋊C4—2981no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—5962no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C22⋊C4—2981no—
170C22⋊C4—2982no—
171C22⋊C4—2984no—
172C22⋊C4—1494no—
173C42—5962no—
174C23—5961no—
175C23—5961no—
176C23—1491no—
177C23—1491no—
178C23—1492no—
179C23—1492no—
180C23C22×#1059701011yescharacteristic
181Q8—5962no—
182Q8—5962no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—2984no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—5961no—
195C2×C4—5961no—
196C2×C4—5962no—
197C2×C4—5962no—
198C2×C4—5961no—
199C2×C4—5961no—
200C2×C4—5962no—
201C2×C4—5962no—
202C2×C4—5962no—
203C2×C4—1491no—
204C2×C4—1491no—
205C2×C4C22⋊#1059701011yescharacteristic
206C2×C4C22⋊#1059701011yescharacteristic
207C22—21no—
208C22—21no—
209C22—2981no—
210C22—2981no—
211C22—2981no—
212C22—2981no—
213C22—5962no—
214C22—5962no—
215C22—1492no—
216C22—1491no—
217C22—1491no—
218C22C2×C22⋊#1059701011yescharacteristic
219C22Q8×#1059701012yes—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—2981no—
225C4—5964no—
226C4—5961no—
227C4—5961no—
228C4—1492no—
229C4—11922no—
230C2—22no—
231C2—2982no—
232C2—2981no—
233C2—2981no—
234C2(C2×#10597010)⋊Q811yescharacteristic
235C2D149⋊#9911yescharacteristic
236C2#2375060411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radical, cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1996
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C22×Dic298C4semidirect
18. C2×#14558715C4semidirect
19. C2×#14558715C4semidirect
22. C2×C4⋊C4×C149C4semidirect
28. C22⋊#10597010Q8semidirect
118. C149#1996semidirect
134. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505672
C4×C22⋊#105970102
#237505032
C2×#180118892
#1996149