Finite Group Databasebeta

← #34061563

Subgroups — #34061563

Order 19072.

422 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 152 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#23750656C212yesmaximal, complemented
2#23750654C212yesmaximal, complemented
3#23750652C212yesmaximal, complemented
4D4×#11924753C212yesmaximal, complemented
5#23750649C212yesmaximal, complemented
6#23750599C211yesmaximal, characteristic, complemented
7#23750598C211yesmaximal, characteristic, complemented
8C2×C22⋊#11924753C212yesmaximal, complemented
9#23750131C211yesmaximal, characteristic
10C2×#14558746C2211yescharacteristic, complemented
11C2×#14558745C2211yescharacteristic, complemented
12C2×D149⋊C8C2211yescharacteristic, complemented
13C22×#11924753C2212yes—
14C22×#11924753C2212yes—
15C22×#11924753C2211yescharacteristic, complemented
16#18011978C2212yescomplemented
17C4⋊#11924753C2212yescomplemented
18#18011968C2212yescomplemented
19C22⋊#11924753C2212yes—
20C22⋊#11924753C2212yes—
21C22⋊#11924753C2212yes—
22C22⋊#11924753C2212yes—
23C22⋊#11924753C2212yescomplemented
24#18011966C2212yescomplemented
25C4×#11924753C2212yescomplemented
26C2×#14558735C2211yescharacteristic
27C23×Dic149C2211yescharacteristic
28#18011895C411yescharacteristic
29#18011892C411yescharacteristic
30#18011888C412yes—
31#18011883C412yes—
32#18011880C411yescharacteristic
33D4×Dic149C2212yes—
34#18011871C2212yes—
35#18011867C2211yescharacteristic
36#120×C149C411yescharacteristic
37#14558746—41no—
38#14558745—41no—
39D149⋊C8—41no—
40C2×#11924753—42no—
41C2×#11924753—42no—
42C2×#11924753—41no—
43C2×#11924753C2312yes—
44C2×#11924753C2312yes—
45C2×#11924753C2312yes—
46C2×#11924753C2312yes—
47#14558735—41no—
48#14558735—41no—
49C2×Dic298C2×C411yescharacteristic
50C2×C22⋊D149C2×C412yes—
51C2×C22⋊D149C2×C411yescharacteristic
52C2×C22⋊D149C2×C411yescharacteristic
53C22×Dic149—41no—
54C22×Dic149—41no—
55C22×Dic149C2×C412yes—
56C22×Dic149C2×C411yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2312yes—
59C22×Dic149C2311yescharacteristic
60C2×C4×D149C2311yescharacteristic
61C4⋊Dic149C2×C412yes—
62#14558715C2×C412yes—
63#14558715C2×C412yes—
64C22⋊Dic149C2×C411yescharacteristic
65C22⋊Dic149C2×C412yes—
66C22⋊Dic149C2×C412yes—
67#14558713C2×C412yes—
68C4×Dic149C2312yes—
69C24×C149C2×C411yescharacteristic
70C2×D4×C149C2×C412yes—
71C2×D4×C149C2×C411yescharacteristic
72C22⋊C4×C149C2×C411yescharacteristic
73C22⋊C4×C149C2×C412yes—
74#11924753—22no—
75#11924753—22no—
76#11924753—22no—
77#11924753—22no—
78C22×D149C22×C411yescharacteristic
79Dic298—41no—
80C22⋊D149—24no—
81C22⋊D149—41no—
82C22⋊D149—41no—
83C2×Dic149—21no—
84C2×Dic149—21no—
85C2×Dic149—22no—
86C2×Dic149—22no—
87C2×Dic149—21no—
88C2×Dic149—21no—
89C2×Dic149—41no—
90C2×Dic149—42no—
91C2×Dic149C22×C411yescharacteristic
92C2×Dic149C22×C412yes—
93C2×Dic149C22×C411yescharacteristic
94C2×Dic149C22×C412yes—
95C2×Dic149C2411yescharacteristic
96C4×D149—21no—
97C4×D149—21no—
98C23×C149—24no—
99C23×C149—41no—
100C23×C149C22×C411yescharacteristic
101C23×C149C22×C411yescharacteristic
102C23×C149C22×C412yes—
103D4×C149—24no—
104D4×C149—41no—
105C2×C4×C149C22×C411yescharacteristic
106C2×C4×C149C22×C412yes—
107C22×C149—22no—
108C22×C149—22no—
109C22×C149—21no—
110C22×C149—21no—
111C22×C149—22no—
112C22×C149—22no—
113C22×C149—44no—
114C22×C149#13114yes—
115C22×C149C23×C411yescharacteristic
116C2×D149—21no—
117C2×D149—22no—
118C4×C149—21no—
119C4×C149—22no—
120Dic149—22no—
121Dic149—21no—
122Dic149—21no—
123Dic149—22no—
124Dic149H(5,𝔽2)11yescharacteristic
125Dic149H(5,𝔽2)11yescharacteristic
126C2×C149—24no—
127C2×C149—41no—
128C2×C149—41no—
129C2×C149#51811yescharacteristic
130C2×C149C2×#13112yes—
131D149—41no—
132C149#297711yescharacteristic, complemented, Sylow
133#2977—1491nomaximal, Sylow
134#525—1491no—
135#435—1492no—
136#435—1492no—
137C8×D4—1492no—
138C8×D4—1492no—
139#433—1492no—
140#408—1491no—
141#408—1491no—
142C2×C22⋊C8—1492no—
143C2×#41—1491no—
144C23×C4—1491no—
145C2×M16—1491no—
146C2×M16—1491no—
147C22×C8—1492no—
148C22×C8—1492no—
149C22×C8—1491no—
150C22×C8—1491no—
151#123—1491no—
152#123—1491no—
153C22⋊Q8—1492no—
154#121—1492no—
155#120—1491no—
156#120#1059701011yescharacteristic
157C4×D4—1492no—
158C4×D4—1492no—
159#117—1491no—
160C4⋊C8—1492no—
161C4⋊C8—1492no—
162C22⋊C8—1492no—
163C22⋊C8—1492no—
164C22⋊C8—1492no—
165C22⋊C8—1492no—
166C22⋊C8—1492no—
167C22⋊C8—1492no—
168#97—1492no—
169C4×C8—1492no—
170C24C2×#1059701011yescharacteristic
171#41—5961no—
172#41—5961no—
173C2×Q8—1491no—
174C2×D4—1492no—
175C2×D4—1491no—
176C2×D4—1491no—
177C2×D4C2×#1059701012yes—
178C2×D4C2×#1059701011yescharacteristic
179C22×C4—5961no—
180C22×C4—5961no—
181C22×C4—1491no—
182C22×C4—1492no—
183C22×C4—1491no—
184C22×C4—1491no—
185C22×C4—1492no—
186C22×C4—1491no—
187M16—5961no—
188M16—5961no—
189C2×C8—5961no—
190C2×C8—5962no—
191C2×C8—5962no—
192C2×C8—5961no—
193C2×C8—1492no—
194C2×C8—1492no—
195C2×C8—1492no—
196C2×C8—1492no—
197C4⋊C4—1492no—
198C4⋊C4—1492no—
199C4⋊C4—1492no—
200C22⋊C4—1491no—
201C22⋊C4—1492no—
202C22⋊C4—1492no—
203C22⋊C4—1492no—
204C22⋊C4C2×#1059701011yescharacteristic
205C22⋊C4C2×#1059701012yes—
206C42—1492no—
207C23—24no—
208C23—41no—
209C23—1491no—
210C23C22×#1059701011yescharacteristic
211C23C22×#1059701011yescharacteristic
212C23C22×#1059701012yes—
213Q8—5961no—
214D4—24no—
215D4—41no—
216D4—2984no—
217D4—5961no—
218D4—5961no—
219C2×C4—2981no—
220C2×C4—2981no—
221C2×C4—2982no—
222C2×C4—2982no—
223C2×C4—2981no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—2981no—
227C2×C4—5962no—
228C2×C4—5961no—
229C2×C4—1492no—
230C2×C4—1492no—
231C2×C4—1491no—
232C2×C4—1491no—
233C2×C4—1491no—
234C2×C4C22×#1059701012yes—
235C2×C4C22×#1059701011yescharacteristic
236C8—2982no—
237C8—2982no—
238C8—2982no—
239C8—2982no—
240C22—22no—
241C22—22no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—44no—
247C22—2981no—
248C22—2982no—
249C22#1801199814yes—
250C22C23×#1059701011yescharacteristic
251C4—21no—
252C4—22no—
253C4—2981no—
254C4—2982no—
255C4—2981no—
256C4—2982no—
257C4—1491no—
258C4—1491no—
259C2—24no—
260C2—41no—
261C2—41no—
262C2—5961no—
263C2#2375069211yescharacteristic
264C2C2×#1801199812yes—
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#120×C149C4
prime radical#23750131C2
cosocleC2×Dic149C24
hypercenter#120#10597010
hypocenterC149#2977
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #23750656C2semidirect
2. #23750654C2semidirect
3. #23750652C2semidirect
4. D4×#11924753C2semidirect
5. #23750649C2semidirect
6. #23750599C2semidirect
7. #23750598C2semidirect
8. C2×C22⋊#11924753C2semidirect
10. C2×#14558746C22semidirect
11. C2×#14558745C22semidirect
12. C2×D149⋊C8C22semidirect
15. C22×#11924753C22semidirect
16. #18011978C22semidirect
17. C4⋊#11924753C22semidirect
18. #18011968C22semidirect
23. C22⋊#11924753C22semidirect
24. #18011966C22semidirect
25. C4×#11924753C22semidirect
132. C149#2977semidirect

Maximal subgroups

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

subgroupindex
#237506562
#237506542
#237506522
D4×#119247532
#237506492
#237505992
#237505982
C2×C22⋊#119247532
#237501312
#2977149