Finite Group Databasebeta

← #34059564

Subgroups — #34059564

Order 19072.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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×#18011968C211yesmaximal, characteristic
2C2×(C2×#10597010)⋊C4C211yesmaximal, characteristic
3#23749482C211yesmaximal, characteristic
4C23×#10597010—21no—
5C22×#11924753—21no—
6#18011968—21no—
7#18011968C412yescomplemented
8(C2×#10597010)⋊C4—21no—
9(C2×#10597010)⋊C4C412yescomplemented
10C22×C4×D149C2211yescharacteristic
11C2×C4⋊Dic149C411yescharacteristic, complemented
12C2×#14558713—21no—
13#18011818—21no—
14C2×C4⋊C4×C149C411yescharacteristic, complemented
15C22×#10597010—22no—
16C22×#10597010—22no—
17C22×#10597010—22no—
18C22×#10597010—41no—
19C22×#10597010—41no—
20C22×#10597010—41no—
21C22×#10597010—41no—
22C2×#11924753—22no—
23C2×#11924753—41no—
24C2×#11924753—41no—
25C23×D149D411yescharacteristic
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C2×C4×D149—41no—
29C2×C4×D149—41no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149Q811yescharacteristic
34C4⋊Dic149—41no—
35#14558713—41no—
36#14558713—41no—
37C22×C4×C149—21no—
38C22×C4×C149C2×C411yescharacteristic
39C4⋊C4×C149—41no—
40C2×#10597010—24no—
41C2×#10597010—42no—
42C2×#10597010—42no—
43C2×#10597010—42no—
44C2×#10597010—42no—
45C2×#10597010—42no—
46C2×#10597010—42no—
47#11924753—42no—
48C22×D149—21no—
49C22×D149—21no—
50C22×D149—21no—
51C22×D149—21no—
52C22×D149C22⋊C411yescharacteristic
53C22×D149C4⋊C411yescharacteristic
54C22×D149D811yescharacteristic
55C22×D149SD1611yescharacteristic
56C22×D149SD1611yescharacteristic
57C22×D149Q1611yescharacteristic
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—41no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C4⋊C411yescharacteristic
65C4×D149—41no—
66C4×D149—41no—
67C4×D149—41no—
68C4×D149—41no—
69C23×C149C22⋊C411yescharacteristic
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149—41no—
73C2×C4×C149—41no—
74C2×C4×C149—41no—
75C2×C4×C149C4211yescharacteristic
76C2×C4×C149C4⋊C411yescharacteristic
77C22×C149#9511yescharacteristic
78C22×C149#9911yescharacteristic
79C22×C149#9911yescharacteristic
80C22×C149#10211yescharacteristic
81C22×C149#10311yescharacteristic
82C22×C149#10411yescharacteristic
83C22×C149#10411yescharacteristic
84C2×D149—21no—
85C2×D149—21no—
86C2×D149—21no—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—21no—
91C2×D149—21no—
92C2×D149—21no—
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C2×D149#10211yescharacteristic
97C2×D149#10311yescharacteristic
98C2×D149#10611yescharacteristic
99C2×D149#10711yescharacteristic
100#10597010—44no—
101C4×C149—21no—
102C4×C149—21no—
103C4×C149—81no—
104Dic149—21no—
105Dic149—21no—
106Dic149—81no—
107C2×C149#32711yescharacteristic
108C2×C149#32711yescharacteristic
109C2×C149#32811yescharacteristic
110C2×C149#32811yescharacteristic
111C2×C149#33911yescharacteristic
112C2×C149#34011yescharacteristic
113C2×C149#34211yescharacteristic
114D149—21no—
115D149—21no—
116D149—21no—
117D149—21no—
118C149#129411yescharacteristic, complemented, Sylow
119#1294—1491nomaximal, Sylow
120C2×C22⋊C8—1491no—
121#380—1491no—
122C2×#95—1491no—
123C23×C4—2981no—
124C23×C4—1491no—
125C22×C8—2981no—
126C2×C4⋊C4—1491no—
127C2×C4⋊C4#1059701011yescharacteristic, complemented
128C2×C22⋊C4—2981no—
129C22⋊C8—2981no—
130C22⋊C8—1492no—
131#95—2981no—
132#95—2981no—
133#95—1492no—
134C24—1491no—
135C22×C4—21no—
136C22×C4—2982no—
137C22×C4—2982no—
138C22×C4—2982no—
139C22×C4—2981no—
140C22×C4—5961no—
141C22×C4—5961no—
142C22×C4—5961no—
143C22×C4—5961no—
144C22×C4—5961no—
145C22×C4—5961no—
146C22×C4—1491no—
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4C2×#1059701011yescharacteristic
152C2×C8—2982no—
153C2×C8—5961no—
154C2×C8—5961no—
155C4⋊C4—41no—
156C4⋊C4—5961no—
157C22⋊C4—5961no—
158C22⋊C4—5961no—
159C23—2981no—
160C23—2981no—
161C23—2981no—
162C23—2981no—
163C23—1491no—
164C23—1491no—
165C23—1491no—
166C23—1491no—
167C23—1491no—
168C23—1491no—
169C23C22⋊#1059701011yescharacteristic
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—2981no—
176C2×C4—2981no—
177C2×C4—2984no—
178C2×C4—5961no—
179C2×C4—5961no—
180C2×C4—5961no—
181C2×C4—5961no—
182C2×C4—5962no—
183C2×C4—5962no—
184C2×C4—5962no—
185C2×C4—5962no—
186C2×C4—5962no—
187C2×C4—5962no—
188C2×C4—5961no—
189C2×C4—5961no—
190C2×C4—5961no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4C4×#1059701011yescharacteristic
194C2×C4C4⋊#1059701011yescharacteristic
195C8—5962no—
196C22—2981no—
197C22—2981no—
198C22—2981no—
199C22—2981no—
200C22—2981no—
201C22—2981no—
202C22—2981no—
203C22—2981no—
204C22—2981no—
205C22—2981no—
206C22—2981no—
207C22—2981no—
208C22—1491no—
209C22—1491no—
210C22—1491no—
211C22—1491no—
212C22(C2×#10597010)⋊C411yescharacteristic
213C22#1801196911yescharacteristic
214C22#1801197011yescharacteristic
215C22#1801197311yescharacteristic
216C22#1801197411yescharacteristic
217C22#1801197511yescharacteristic
218C22#1801197611yescharacteristic
219C4—21no—
220C4—21no—
221C4—81no—
222C4—2981no—
223C4—2981no—
224C4—5964no—
225C4—11921no—
226C2—2981no—
227C2—2981no—
228C2—2981no—
229C2—2981no—
230C2#2375047611yescharacteristic
231C2#2375047711yescharacteristic
232C2#2375047811yescharacteristic
233C2#2375047911yescharacteristic
234C2#2375049511yescharacteristic
235C2#2375049811yescharacteristic
236C2#2375050311yescharacteristic
subgroupG/H
centerC23C22⋊#10597010
commutatorC2×C4×C149C42
FrattiniC22×C4C2×#10597010
FittingC2×C4⋊C4×C149C4
socleC23×C149C22⋊C4
prime radicalC23×D149D4
cosocleC22×C4×D149C22
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1294
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. #18011968C4semidirect
9. (C2×#10597010)⋊C4C4semidirect
11. C2×C4⋊Dic149C4semidirect
14. C2×C4⋊C4×C149C4semidirect
118. C149#1294semidirect
127. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119682
C2×(C2×#10597010)⋊C42
#237494822
#1294149