Finite Group Databasebeta

← #34061560

Subgroups — #34061560

Order 19072.

412 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 146 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#23750660C212yesmaximal, complemented
2#23750657C212yesmaximal, complemented
3#23750656C212yesmaximal, complemented
4#23750652C212yesmaximal, complemented
5#23750650C212yesmaximal, complemented
6#23750598C212yesmaximal, complemented
7#23750597C211yesmaximal, characteristic, complemented
8D149⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
9#23750135C211yesmaximal, characteristic
10C2×#14558745C2211yescharacteristic
11C2×#14558745C2211yescharacteristic
12C2×#14558745C2212yescomplemented
13C2×D149⋊C8C2211yescharacteristic
14C2×D149⋊C8C2211yescharacteristic
15C22×#11924753C2212yescomplemented
16#18011978C2212yescomplemented
17C4⋊#11924753C2212yescomplemented
18#18011968C2212yes—
19#18011968C2212yes—
20#18011968C2212yes—
21C22⋊#11924753C2212yes—
22C22⋊#11924753C2212yescomplemented
23C22⋊#11924753C2212yescomplemented
24#18011966C2212yescomplemented
25C4×#11924753C2212yescomplemented
26C2×#14558735C2211yescharacteristic
27C22×C4×D149C2211yescharacteristic
28#18011893C412yes—
29#18011891C411yescharacteristic
30#18011890C411yescharacteristic
31#18011882C411yescharacteristic
32#18011879C412yes—
33D4×Dic149C2212yes—
34#18011871C2212yes—
35#18011869C2211yescharacteristic
36#121×C149C411yescharacteristic
37#14558745—41no—
38#14558745—41no—
39#14558745—42no—
40D149⋊C8—41no—
41D149⋊C8—41no—
42C2×#11924753—42no—
43C2×#11924753C2312yes—
44C2×#11924753C2312yes—
45C2×#11924753C2312yes—
46C2×#11924753C2312yes—
47C23×D149C2×C411yescharacteristic
48#14558735—41no—
49#14558735—41no—
50C2×Dic298C2×C411yescharacteristic
51C2×C22⋊D149C2×C412yes—
52C2×C22⋊D149C2×C412yes—
53C22×Dic149C2311yescharacteristic
54C22×Dic149C2312yes—
55C2×C4×D149—41no—
56C2×C4×D149—41no—
57C2×C4×D149C2×C411yescharacteristic
58C2×C4×D149C2×C411yescharacteristic
59C2×C4×D149C2311yescharacteristic
60C2×C4×D149C2311yescharacteristic
61C4⋊Dic149C2×C411yescharacteristic
62C4⋊Dic149C2×C412yes—
63#14558715C2×C412yes—
64C22⋊Dic149C2×C412yes—
65C22⋊Dic149C2×C412yes—
66#14558713C2×C412yes—
67#14558713C2×C412yes—
68C4×Dic149C2312yes—
69C2×D4×C149C2×C411yescharacteristic
70C2×D4×C149C2×C412yes—
71C22×C4×C149C2×C411yescharacteristic
72C4⋊C4×C149C2×C411yescharacteristic
73C22⋊C4×C149C2×C412yes—
74#11924753—22no—
75#11924753—22no—
76#11924753—22no—
77#11924753—22no—
78C22×D149—22no—
79C22×D149—41no—
80C22×D149—41no—
81C22×D149C22×C411yescharacteristic
82C22×D149C22×C411yescharacteristic
83Dic298—41no—
84C22⋊D149—24no—
85C22⋊D149—42no—
86C2×Dic149—21no—
87C2×Dic149—21no—
88C2×Dic149—22no—
89C2×Dic149—22no—
90C2×Dic149C22×C411yescharacteristic
91C2×Dic149C22×C412yes—
92C2×Dic149C22×C412yes—
93C2×Dic149C2411yescharacteristic
94C4×D149—21no—
95C4×D149—21no—
96C4×D149—21no—
97C4×D149—21no—
98C4×D149—41no—
99C4×D149—41no—
100C23×C149C22×C412yes—
101C23×C149C22×C411yescharacteristic
102D4×C149—41no—
103D4×C149—42no—
104C2×C4×C149—41no—
105C2×C4×C149C22×C411yescharacteristic
106C2×C4×C149C22×C411yescharacteristic
107C2×C4×C149C22×C412yes—
108C22×C149—21no—
109C22×C149—22no—
110C22×C149—22no—
111C22×C149—21no—
112C22×C149—21no—
113C22×C149—22no—
114C22×C149C23×C411yescharacteristic
115C2×D149—21no—
116C2×D149—21no—
117C2×D149—21no—
118C2×D149—21no—
119C2×D149—21no—
120C2×D149—44no—
121C2×D149#13112yes—
122C4×C149—21no—
123C4×C149—21no—
124C4×C149—22no—
125Dic149—21no—
126Dic149—22no—
127Dic149—22no—
128Dic149H(5,𝔽2)11yescharacteristic
129Dic149H(5,𝔽2)11yescharacteristic
130C2×C149—41no—
131C2×C149—42no—
132C2×C149#51811yescharacteristic
133C2×C149C2×#13111yescharacteristic
134C2×C149#56811yescharacteristic
135D149—22no—
136D149—41no—
137C149#297611yescharacteristic, complemented, Sylow
138#2976—1491nomaximal, Sylow
139#525—1491no—
140#436—1492no—
141#435—1492no—
142#435—1492no—
143C8×D4—1492no—
144#433—1492no—
145#408—1492no—
146#407—1491no—
147C2×C22⋊C8—1491no—
148C2×#41—1491no—
149C23×C4—1491no—
150C2×M16—1491no—
151C2×M16—1491no—
152C2×M16—1492no—
153C22×C8—1492no—
154C22×C8—1491no—
155C22×C8—1491no—
156#123—1492no—
157C22⋊Q8—1491no—
158C22⋊Q8—1491no—
159#121—1491no—
160#121#1059701011yescharacteristic
161#120—1492no—
162C4×D4—1492no—
163C4×D4—1492no—
164#117—1491no—
165C4⋊C8—1492no—
166C4⋊C8—1492no—
167C22⋊C8—1492no—
168C22⋊C8—1492no—
169C22⋊C8—1492no—
170C22⋊C8—1492no—
171C22⋊C8—1492no—
172C22⋊C8—1492no—
173#97—1492no—
174C4×C8—1492no—
175C24—1491no—
176#41—5961no—
177#41—5961no—
178C2×Q8—1491no—
179C2×D4—1492no—
180C2×D4—1492no—
181C2×D4C2×#1059701012yes—
182C2×D4C2×#1059701011yescharacteristic
183C22×C4—5961no—
184C22×C4—5961no—
185C22×C4—1492no—
186C22×C4—1491no—
187C22×C4—1491no—
188C22×C4—1491no—
189C22×C4—1491no—
190C22×C4—1491no—
191C22×C4C2×#1059701011yescharacteristic
192M16—5961no—
193M16—5962no—
194M16—5961no—
195C2×C8—5962no—
196C2×C8—5961no—
197C2×C8—5961no—
198C2×C8—1492no—
199C2×C8—1492no—
200C2×C8—1492no—
201C2×C8—1492no—
202C4⋊C4—1491no—
203C4⋊C4—1492no—
204C4⋊C4—1492no—
205C4⋊C4C2×#1059701011yescharacteristic
206C22⋊C4—1492no—
207C22⋊C4—1492no—
208C22⋊C4—1492no—
209C22⋊C4—1492no—
210C22⋊C4C2×#1059701012yes—
211C42—1492no—
212C23—2982no—
213C23—5961no—
214C23—5961no—
215C23—1491no—
216C23—1491no—
217C23C22×#1059701011yescharacteristic
218C23C22×#1059701012yes—
219Q8—5961no—
220D4—42no—
221D4—41no—
222D4—2984no—
223D4—5962no—
224C2×C4—41no—
225C2×C4—2981no—
226C2×C4—2981no—
227C2×C4—2981no—
228C2×C4—2981no—
229C2×C4—2982no—
230C2×C4—2981no—
231C2×C4—2981no—
232C2×C4—2982no—
233C2×C4—5961no—
234C2×C4—5961no—
235C2×C4—1492no—
236C2×C4—1491no—
237C2×C4—1492no—
238C2×C4—1491no—
239C2×C4C22×#1059701012yes—
240C2×C4C22×#1059701011yescharacteristic
241C2×C4C22×#1059701011yescharacteristic
242C8—2982no—
243C8—2982no—
244C8—2982no—
245C8—2982no—
246C22—21no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—22no—
252C22—2981no—
253C22—2981no—
254C22—2981no—
255C22—2981no—
256C22—2981no—
257C22—5964no—
258C22—1492no—
259C22C23×#1059701011yescharacteristic
260C4—21no—
261C4—21no—
262C4—22no—
263C4—2981no—
264C4—2982no—
265C4—2982no—
266C4—1491no—
267C4—1491no—
268C2—41no—
269C2—42no—
270C2—2982no—
271C2—5961no—
272C2#2375069211yescharacteristic
273C2D149⋊#13111yescharacteristic
274C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#121×C149C4
prime radical#23750135C2
cosocleC2×Dic149C24
hypercenter#121#10597010
hypocenterC149#2976
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #23750660C2semidirect
2. #23750657C2semidirect
3. #23750656C2semidirect
4. #23750652C2semidirect
5. #23750650C2semidirect
6. #23750598C2semidirect
7. #23750597C2semidirect
8. D149⋊(C22⋊C8)C2semidirect
12. C2×#14558745C22semidirect
15. C22×#11924753C22semidirect
16. #18011978C22semidirect
17. C4⋊#11924753C22semidirect
22. C22⋊#11924753C22semidirect
23. C22⋊#11924753C22semidirect
24. #18011966C22semidirect
25. C4×#11924753C22semidirect
137. C149#2976semidirect

Maximal subgroups

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

subgroupindex
#237506602
#237506572
#237506562
#237506522
#237506502
#237505982
#237505972
D149⋊(C22⋊C8)2
#237501352
#2976149