Finite Group Databasebeta

← #34060942

Subgroups — #34060942

Order 19072.

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

normal subgroups only

This group has 264 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
1#23750611C211yesmaximal, characteristic, complemented
2#23750604C211yesmaximal, characteristic, complemented
3#23750527C212yesmaximal, complemented
4#23750525C212yesmaximal, complemented
5#23750136C211yesmaximal, characteristic
6D149⋊M16—21no—
7#18011990—21no—
8#18011972—21no—
9#18011971C2212yes—
10#18011970—21no—
11#18011969C2212yes—
12C2×#14558736C2211yescharacteristic
13#18011894C411yescharacteristic, complemented
14#18011894C2211yescharacteristic
15#18011890—21no—
16#18011885—21no—
17#18011880C411yescharacteristic, complemented
18#18011880C2211yescharacteristic
19C4×C22⋊D149—21no—
20C4×C22⋊D149—21no—
21#18011870C411yescharacteristic, complemented
22C23×C4×C149C411yescharacteristic, complemented
23#14558746—41no—
24#14558745—22no—
25D149⋊C8—41no—
26C4⋊#10597010—41no—
27C22⋊#10597010—22no—
28C4×#10597010—41no—
29#14558736—41no—
30#14558736—41no—
31C2×Dic298D411yescharacteristic
32C2×D596D411yescharacteristic
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35C2×C22⋊D149C2×C411yescharacteristic
36C2×C22⋊D149C2311yescharacteristic
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C4⋊Dic149—21no—
40#14558715—21no—
41#14558715—21no—
42C22⋊Dic149—21no—
43C22⋊Dic149—21no—
44C22⋊Dic149C2×C411yescharacteristic
45C22⋊Dic149C2×C411yescharacteristic
46#14558713—21no—
47#14558713—21no—
48C4×Dic149—21no—
49C24×C149C2×C411yescharacteristic
50C22×C4×C149—21no—
51C22×C4×C149—21no—
52C22×C4×C149—41no—
53C22×C4×C149—41no—
54C22×C4×C149C2×C411yescharacteristic
55C22×C4×C149C2×C411yescharacteristic
56C2×#10597010—42no—
57#11924753—42no—
58C22×D149C22⋊C411yescharacteristic
59C22×D149C2×D411yescharacteristic
60Dic298—41no—
61D596—41no—
62C22⋊D149—41no—
63C22⋊D149—41no—
64C22⋊D149—42no—
65C22⋊D149—42no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149C22⋊C411yescharacteristic
69C2×Dic149C2×D411yescharacteristic
70C4×D149—21no—
71C4×D149—21no—
72C4×D149—21no—
73C4×D149—21no—
74C23×C149—21no—
75C23×C149—41no—
76C23×C149—42no—
77C23×C149C22×C411yescharacteristic
78C2×C4×C149—21no—
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149—42no—
82C2×C4×C149—41no—
83C2×C4×C149—41no—
84C2×C4×C149—41no—
85C2×C4×C149C22⋊C411yescharacteristic
86C2×C4×C149C22⋊C411yescharacteristic
87C22×C149—22no—
88C22×C149—21no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149—41no—
94C22×C149C2×C22⋊C411yescharacteristic
95C2×D149—21no—
96C2×D149—21no—
97C2×D149—41no—
98C2×D149—41no—
99#10597010—82no—
100C4×C149—21no—
101C4×C149—41no—
102C4×C149#9911yescharacteristic
103C4×C149#9911yescharacteristic
104Dic149—21no—
105Dic149—21no—
106Dic149—41no—
107Dic149—41no—
108C2×C149—21no—
109C2×C149—42no—
110C2×C149—41no—
111C2×C149C2×#9911yescharacteristic
112D149—41no—
113D149—41no—
114C149#212011yescharacteristic, complemented, Sylow
115#2120—1491nomaximal, Sylow
116#525—1491no—
117#413—1491no—
118#410—1491no—
119#352—1492no—
120AΣL(1,𝔽16)—1492no—
121C2×#41—1491no—
122C23×C4#1059701011yescharacteristic, complemented
123C2×M16—2981no—
124#123—1491no—
125#123—1491no—
126C22⋊Q8—2981no—
127#121—2981no—
128#120—1491no—
129#120—1491no—
130C4×D4—2981no—
131C4×D4—2981no—
132#117—2981no—
133#117—1491no—
134#101—2981no—
135#100—1492no—
136#99—2981no—
137#99—1492no—
138C24C2×#1059701011yescharacteristic
139#41—5961no—
140#41—5961no—
141C2×Q8—1491no—
142C2×D4—2981no—
143C2×D4—2981no—
144C2×D4—1491no—
145C2×D4—1491no—
146C2×D4—1491no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—1491no—
152C22×C4—1491no—
153C22×C4C2×#1059701011yescharacteristic
154C22×C4C2×#1059701011yescharacteristic
155M16—2982no—
156M16—5961no—
157C2×C8—5961no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—5961no—
162C22⋊C4—2981no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C22⋊C4—2981no—
166C22⋊C4—2982no—
167C22⋊C4—1491no—
168C22⋊C4—1491no—
169C42—2981no—
170C42—5961no—
171C23—21no—
172C23—41no—
173C23—42no—
174C23—1491no—
175C23—1491no—
176C23C22×#1059701011yescharacteristic
177Q8—5961no—
178D4—5961no—
179D4—5961no—
180D4—5961no—
181D4—5962no—
182D4—5962no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—2981no—
196C2×C4—5962no—
197C2×C4—1491no—
198C2×C4—1491no—
199C2×C4C22⋊#1059701011yescharacteristic
200C2×C4C22⋊#1059701011yescharacteristic
201C8—5962no—
202C22—22no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—42no—
207C22—42no—
208C22—41no—
209C22—2981no—
210C22—2981no—
211C22—5961no—
212C22—5961no—
213C22C2×C22⋊#1059701011yescharacteristic
214C4—21no—
215C4—41no—
216C4—2981no—
217C4—2981no—
218C4—5961no—
219C4—5961no—
220C4—11922no—
221C4#1801196911yescharacteristic
222C4#1801196911yescharacteristic
223C2—21no—
224C2—42no—
225C2—41no—
226C2—5961no—
227C2—5961no—
228C2C2×#1801196911yescharacteristic
subgroupG/H
centerC4#18011969
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC23×C4×C149C4
socleC2×C149C2×#99
prime radical#23750136C2
cosocleC2×C22⋊D149C23
hypercenterC23×C4#10597010
hypocenterC149#2120
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #23750611C2semidirect
2. #23750604C2semidirect
3. #23750527C2semidirect
4. #23750525C2semidirect
13. #18011894C4semidirect
17. #18011880C4semidirect
21. #18011870C4semidirect
22. C23×C4×C149C4semidirect
114. C149#2120semidirect
122. C23×C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237506042
#237505272
#237505252
#237501362
#2120149