Finite Group Databasebeta

← #34060097

Subgroups — #34060097

Order 19072.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750596C211yesmaximal, characteristic, complemented
2#23750568C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#121×D149C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×C22⋊#10597010—21no—
8#18011968C2212yescomplemented
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yescomplemented
12C2×D4×D149—21no—
13C2×D4×D149C411yescharacteristic, complemented
14C22×C4×D149C2211yescharacteristic
15#18011886C2211yescharacteristic
16#18011885C411yescharacteristic, complemented
17#18011884—21no—
18#18011883—21no—
19#18011882C2211yescharacteristic
20C4⋊C4×D149C411yescharacteristic, complemented
21C22⋊C4×D149—21no—
22#121×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24#14558746—42no—
25C2×#11924753—22no—
26C22⋊#10597010—42no—
27C23×D149—21no—
28C23×D149D411yescharacteristic
29C2×D596—21no—
30C2×D596C2×C411yescharacteristic
31C2×C22⋊D149—21no—
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34D4×D149—42no—
35D4×D149—44no—
36C22×Dic149D411yescharacteristic
37C2×C4×D149—21no—
38C2×C4×D149—42no—
39C2×C4×D149C2×C411yescharacteristic
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149C2311yescharacteristic
43C4⋊Dic149C2×C411yescharacteristic
44#14558715—21no—
45C22⋊Dic149—21no—
46#14558713—21no—
47#14558713—21no—
48C2×D4×C149—21no—
49C2×D4×C149C2×C411yescharacteristic
50C22×C4×C149C2×C411yescharacteristic
51C4⋊C4×C149C2×C411yescharacteristic
52C22⋊C4×C149—21no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55C2×#10597010—42no—
56#11924753—42no—
57C22×D149—22no—
58C22×D149—22no—
59C22×D149—21no—
60C22×D149—41no—
61C22×D149—42no—
62C22×D149—42no—
63C22×D149—42no—
64C22×D149C22⋊C411yescharacteristic
65C22×D149C2×D411yescharacteristic
66D596—41no—
67D596—42no—
68C22⋊D149—42no—
69C22⋊D149—42no—
70C22⋊D149—42no—
71C2×Dic149—21no—
72C2×Dic149—41no—
73C2×Dic149C22⋊C411yescharacteristic
74C2×Dic149C2×D411yescharacteristic
75C4×D149—22no—
76C4×D149—22no—
77C4×D149—41no—
78C4×D149—41no—
79C4×D149—42no—
80C23×C149—21no—
81C23×C149C22⋊C411yescharacteristic
82D4×C149—41no—
83D4×C149—42no—
84C2×C4×C149—21no—
85C2×C4×C149—41no—
86C2×C4×C149C22⋊C411yescharacteristic
87C2×C4×C149C22×C411yescharacteristic
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149—41no—
94C22×C149C2×C22⋊C411yescharacteristic
95C2×D149—21no—
96C2×D149—21no—
97C2×D149—21no—
98C2×D149—21no—
99C2×D149—44no—
100C2×D149—41no—
101C2×D149—41no—
102C2×D149—41no—
103C2×D149—84no—
104C2×D149#9912yes—
105C2×D149AGL(1,ℤ/8)12yes—
106#10597010—82no—
107C4×C149—21no—
108C4×C149—21no—
109C4×C149—41no—
110Dic149—21no—
111Dic149—21no—
112Dic149—41no—
113C2×C149—41no—
114C2×C149—81no—
115C2×C149C2×#9911yescharacteristic
116C2×C149#41811yescharacteristic
117C2×C149#42111yescharacteristic
118D149—22no—
119D149—22no—
120D149—81no—
121C149#151011yescharacteristic, complemented, Sylow
122#1510—1491nomaximal, Sylow
123C2×#121—1491no—
124#407—1491no—
125#381—1491no—
126#327—1492no—
127#327—1492no—
128C22×D4—2981no—
129C22×D4—1491no—
130C23×C4—1491no—
131C2×M16—2981no—
132#121—2981no—
133#121—2981no—
134#121—1491no—
135#121—1491no—
136#121—1491no—
137#121#1059701011yescharacteristic, complemented
138C2×C4⋊C4—1491no—
139C2×C22⋊C4—2981no—
140C2×C22⋊C4—2981no—
141C22⋊C8—2981no—
142C22⋊C8—1492no—
143#95—2981no—
144#95—1492no—
145C24—2981no—
146C24—1491no—
147C2×D4—21no—
148C2×D4—2981no—
149C2×D4—2981no—
150C2×D4—2981no—
151C2×D4—2981no—
152C2×D4—5962no—
153C2×D4—5964no—
154C2×D4—1491no—
155C2×D4C2×#1059701011yescharacteristic
156C22×C4—2981no—
157C22×C4—2982no—
158C22×C4—5962no—
159C22×C4—1491no—
160C22×C4—1491no—
161C22×C4—1491no—
162C22×C4—1491no—
163C22×C4—1491no—
164C22×C4C2×#1059701011yescharacteristic
165M16—5962no—
166C2×C8—2982no—
167C4⋊C4—2981no—
168C4⋊C4—1491no—
169C4⋊C4C2×#1059701011yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—2981no—
172C22⋊C4—2981no—
173C22⋊C4—2981no—
174C22⋊C4—5962no—
175C23—21no—
176C23—2982no—
177C23—2982no—
178C23—2981no—
179C23—5961no—
180C23—5962no—
181C23—5962no—
182C23—5962no—
183C23—1491no—
184C23—1491no—
185C23C22⋊#1059701011yescharacteristic
186D4—41no—
187D4—42no—
188D4—5961no—
189D4—5962no—
190D4—5962no—
191D4—5962no—
192D4—5962no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2981no—
198C2×C4—5961no—
199C2×C4—5961no—
200C2×C4—5962no—
201C2×C4—5961no—
202C2×C4—5962no—
203C2×C4—5962no—
204C2×C4—5962no—
205C2×C4—1491no—
206C2×C4—1491no—
207C2×C4C22⋊#1059701011yescharacteristic
208C2×C4C22×#1059701011yescharacteristic
209C8—5962no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2981no—
217C22—2981no—
218C22—2981no—
219C22—2981no—
220C22—5964no—
221C22—5961no—
222C22—5961no—
223C22—5961no—
224C22—1492no—
225C22—1492no—
226C22—11924no—
227C22C2×C22⋊#1059701011yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—2981no—
232C4—2981no—
233C4—5961no—
234C4—11922no—
235C2—41no—
236C2—81no—
237C2—2982no—
238C2—2982no—
239C2—11921no—
240C2D149⋊#9911yescharacteristic
241C2#2375061711yescharacteristic
242C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#121×C149C4
socleC22×C149C2×C22⋊C4
prime radical#121×D149C2
cosocleC2×C4×D149C23
hypercenter#121#10597010
hypocenterC149#1510
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750596C2semidirect
2. #23750568C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
8. #18011968C22semidirect
11. (C2×#10597010)⋊C4C22semidirect
13. C2×D4×D149C4semidirect
16. #18011885C4semidirect
20. C4⋊C4×D149C4semidirect
22. #121×C149C4semidirect
121. C149#1510semidirect
137. #121#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
#237505682
#237504772
#237504762
#121×D1492
#1510149