Finite Group Databasebeta

← #34060946

Subgroups — #34060946

Order 19072.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×#18011971C211yesmaximal, characteristic, complemented
2C2×#18011969C211yesmaximal, characteristic, complemented
3#23750527C212yesmaximal, complemented
4#23750525C212yesmaximal, complemented
5#23750184C211yesmaximal, characteristic
6C2×#14558745—21no—
7C2×C22⋊#10597010—21no—
8#18011971—21no—
9#18011971C2212yes—
10#18011969—21no—
11#18011969C2212yes—
12C22×C22⋊D149C2211yescharacteristic
13#18011894C411yescharacteristic, complemented
14#18011894C2211yescharacteristic
15#18011892—21no—
16#18011883—21no—
17#18011883—21no—
18#18011880C411yescharacteristic, complemented
19#18011880C2211yescharacteristic
20#18011879—21no—
21C2×C22⋊Dic149C411yescharacteristic, complemented
22C22×D4×C149C411yescharacteristic, complemented
23C22×#10597010—41no—
24#14558745—22no—
25#14558745—41no—
26C2×#11924753—41no—
27C22⋊#10597010—22no—
28C22⋊#10597010—41no—
29C23×D149D411yescharacteristic
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C2×C22⋊D149—41no—
33C2×C22⋊D149—41no—
34C2×C22⋊D149C2×C411yescharacteristic
35C2×C22⋊D149D411yescharacteristic
36C2×C22⋊D149D411yescharacteristic
37C2×C22⋊D149C2311yescharacteristic
38C22×Dic149—21no—
39C22×Dic149D411yescharacteristic
40#14558715—21no—
41#14558715—21no—
42C22⋊Dic149—21no—
43C22⋊Dic149—21no—
44C22⋊Dic149—21no—
45C22⋊Dic149C2×C411yescharacteristic, complemented
46C22⋊Dic149C2×C411yescharacteristic, complemented
47#14558713—21no—
48#14558713—21no—
49C24×C149C2×C411yescharacteristic
50C24×C149C2×C411yescharacteristic, complemented
51C2×D4×C149—21no—
52C2×D4×C149—21no—
53C2×D4×C149—41no—
54C2×D4×C149—41no—
55C22×C4×C149C2×C411yescharacteristic, complemented
56C2×#10597010—42no—
57C2×#10597010—82no—
58#11924753—42no—
59C22×D149—21no—
60C22×D149—21no—
61C22×D149—81no—
62C22×D149C22⋊C411yescharacteristic
63C22×D149C2×D411yescharacteristic
64C22⋊D149—41no—
65C22⋊D149—41no—
66C22⋊D149—41no—
67C22⋊D149—41no—
68C22⋊D149—81no—
69C22⋊D149—81no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—81no—
75C2×Dic149C22⋊C411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C23×C149—21no—
78C23×C149—21no—
79C23×C149—21no—
80C23×C149—41no—
81C23×C149—81no—
82C23×C149—81no—
83C23×C149C22⋊C411yescharacteristic
84C23×C149C22⋊C411yescharacteristic
85C23×C149C22×C411yescharacteristic
86D4×C149—42no—
87D4×C149—41no—
88D4×C149—41no—
89C2×C4×C149—21no—
90C2×C4×C149—41no—
91C22×C149—21no—
92C22×C149—21no—
93C22×C149—41no—
94C22×C149—41no—
95C22×C149—41no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149—41no—
99C22×C149—81no—
100C22×C149—81no—
101C22×C149—82no—
102C22×C149#9911yescharacteristic
103C22×C149#9911yescharacteristic
104C22×C149C2×C22⋊C411yescharacteristic
105C2×D149—21no—
106C2×D149—21no—
107C2×D149—42no—
108C2×D149—41no—
109C2×D149—41no—
110C2×D149—81no—
111#10597010—82no—
112C4×C149—41no—
113Dic149—21no—
114Dic149—21no—
115Dic149—41no—
116Dic149—41no—
117C2×C149—21no—
118C2×C149—21no—
119C2×C149—21no—
120C2×C149—41no—
121C2×C149—41no—
122C2×C149—81no—
123C2×C149C2×#9911yescharacteristic
124D149—41no—
125D149—41no—
126C149#212111yescharacteristic, complemented, Sylow
127#2121—1491nomaximal, Sylow
128#534—1491no—
129C2×#100—1491no—
130C2×#99—1491no—
131#352—1492no—
132AΣL(1,𝔽16)—1492no—
133C22×D4—1491no—
134C22×D4#1059701011yescharacteristic, complemented
135C2×M16—2981no—
136#123—2981no—
137#123—1491no—
138#123—1491no—
139#121—2981no—
140#121—2981no—
141#120—2981no—
142#120—1491no—
143#120—1491no—
144C2×C22⋊C4—2981no—
145C2×C22⋊C4—1491no—
146#100—2981no—
147#100—1492no—
148#99—2981no—
149#99—1492no—
150C24—1491no—
151C24C2×#1059701011yescharacteristic
152C24C2×#1059701011yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—2981no—
158C2×D4—2981no—
159C2×D4—5961no—
160C2×D4—5961no—
161C2×D4—1491no—
162C2×D4—1491no—
163C2×D4—1491no—
164C2×D4—1491no—
165C22×C4—2981no—
166C22×C4—5961no—
167C22×C4—1491no—
168C22×C4C2×#1059701011yescharacteristic, complemented
169M16—2982no—
170M16—5961no—
171C2×C8—5961no—
172C4⋊C4—2981no—
173C4⋊C4—2981no—
174C22⋊C4—2981no—
175C22⋊C4—2981no—
176C22⋊C4—2981no—
177C22⋊C4—2981no—
178C22⋊C4—2981no—
179C22⋊C4—2982no—
180C22⋊C4—5961no—
181C22⋊C4—1491no—
182C22⋊C4—1491no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—81no—
188C23—81no—
189C23—2981no—
190C23—2981no—
191C23—1491no—
192C23—1491no—
193C23—11921no—
194C23C22⋊#1059701011yescharacteristic
195C23C22⋊#1059701011yescharacteristic
196C23C22×#1059701011yescharacteristic
197D4—42no—
198D4—41no—
199D4—41no—
200D4—5961no—
201D4—5961no—
202D4—5961no—
203D4—5961no—
204D4—11921no—
205D4—11921no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2981no—
211C2×C4—2981no—
212C2×C4—5962no—
213C2×C4—1491no—
214C2×C4—1491no—
215C2×C4—11921no—
216C2×C4—11922no—
217C8—5962no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—81no—
227C22—81no—
228C22—82no—
229C22—2981no—
230C22—2981no—
231C22—5961no—
232C22—5961no—
233C22—5962no—
234C22—11921no—
235C22#1801196911yescharacteristic
236C22#1801196911yescharacteristic
237C22C2×C22⋊#1059701011yescharacteristic
238C4—41no—
239C4—2981no—
240C4—2981no—
241C4—5961no—
242C4—5961no—
243C4—11922no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—81no—
250C2—5961no—
251C2—5961no—
252C2C2×#1801196911yescharacteristic
subgroupG/H
centerC2C2×#18011969
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC22×D4×C149C4
socleC2×C149C2×#99
prime radical#23750184C2
cosocleC2×C22⋊D149C23
hypercenterC22×D4#10597010
hypocenterC149#2121
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#18011971C2semidirect
2. C2×#18011969C2semidirect
3. #23750527C2semidirect
4. #23750525C2semidirect
13. #18011894C4semidirect
18. #18011880C4semidirect
21. C2×C22⋊Dic149C4semidirect
22. C22×D4×C149C4semidirect
45. C22⋊Dic149C2×C4semidirect
46. C22⋊Dic149C2×C4semidirect
50. C24×C149C2×C4semidirect
55. C22×C4×C149C2×C4semidirect
126. C149#2121semidirect
134. C22×D4#10597010semidirect
152. C24C2×#10597010semidirect
168. C22×C4C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119712
C2×#180119692
#237505272
#237505252
#237501842
#2121149