Finite Group Databasebeta

← #34055167

Subgroups — #34055167

Order 19072.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18011944C211yesmaximal, characteristic, complemented
2C2×#18011939C211yesmaximal, characteristic, complemented
3C2×#18011933C211yesmaximal, characteristic, complemented
4C22×#14558725C211yesmaximal, characteristic, complemented
5#23750201C211yesmaximal, characteristic, complemented
6#23750194C211yesmaximal, characteristic, complemented
7#23750019C212yesmaximal, complemented
8#23750014C212yesmaximal, complemented
9#23750009C212yesmaximal, complemented
10#23749998C212yesmaximal, complemented
11#405×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C2×#14558736C2211yescharacteristic
14C22×Dic298C2211yescharacteristic
15C22×D596C2211yescharacteristic
16#18011944—24no—
17#18011939—24no—
18#18011933—24no—
19C2×Dic596C2211yescharacteristic, complemented
20C2×Dic596C2212yescomplemented
21C2×#14558725—24no—
22C2×#14558725C2212yes—
23C2×#14558725C2212yes—
24C2×#14558725C2212yes—
25C2×#14558725C2211yescharacteristic, complemented
26C2×#14558725C2211yescharacteristic, complemented
27C2×#14558725C2212yescomplemented
28C2×D1192C2212yes—
29C2×D1192C2211yescharacteristic, complemented
30#18011911C2212yescomplemented
31#18011908C2212yes—
32#18011899C2212yes—
33#18011899C2212yescomplemented
34#18011895—22no—
35#18011891—22no—
36#18011886—22no—
37#18011881—22no—
38C2×M16×C149C2211yescharacteristic
39C22×C8×C149C2211yescharacteristic
40#117×C149C2211yescharacteristic
41#97×C149C2212yescomplemented
42C4×C8×C149C2212yescomplemented
43C23×D149—21no—
44#14558736—22no—
45#14558736—22no—
46#14558736—22no—
47#14558736—22no—
48C2×Dic298—21no—
49C2×Dic298—22no—
50C2×Dic298—22no—
51C2×Dic298C2311yescharacteristic
52C2×Dic298C2312yes—
53C2×Dic298C2311yescharacteristic
54C2×D596—22no—
55C2×D596—22no—
56C2×D596—21no—
57C2×D596—24no—
58C2×D596C2311yescharacteristic
59C2×D596C2312yes—
60C2×D596C2311yescharacteristic
61C2×C22⋊D149—21no—
62C2×C22⋊D149—21no—
63C22×Dic149—21no—
64C2×C4×D149—21no—
65C2×C4×D149—21no—
66Dic596—22no—
67Dic596—24no—
68#14558725—24no—
69#14558725—24no—
70#14558725—24no—
71#14558725—22no—
72#14558725—22no—
73#14558725—24no—
74D1192—24no—
75D1192—22no—
76C4⋊Dic149—24no—
77#14558713—24no—
78#14558713—24no—
79C22×C4×C149C2311yescharacteristic
80M16×C149D414yescomplemented
81C2×C8×C149D414yescomplemented
82C2×C8×C149C2312yes—
83C2×C8×C149C2311yescharacteristic
84C2×C8×C149C2311yescharacteristic
85C4⋊C4×C149D412yes—
86C22⋊C4×C149D412yes—
87C42×C149C2312yes—
88C22×D149—21no—
89C22×D149—21no—
90C22×D149—22no—
91C22×D149—42no—
92C22×D149—82no—
93Dic298—22no—
94Dic298—21no—
95Dic298—22no—
96Dic298—21no—
97Dic298—21no—
98Dic298—21no—
99Dic298—42no—
100D596—21no—
101D596—22no—
102D596—21no—
103D596—21no—
104D596—22no—
105D596—21no—
106D596—42no—
107D596—84no—
108C22⋊D149—42no—
109C22⋊D149—42no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—22no—
113C2×Dic149—42no—
114C4×D149—42no—
115C4×D149—42no—
116C23×C149C2×D411yescharacteristic
117C2×C4×C149C2×D414yes—
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2×D412yes—
120C2×C4×C149C2×D412yes—
121C2×C4×C149C2411yescharacteristic
122C8×C149C2×D412yes—
123C8×C149C2×D414yes—
124C8×C149C2×D412yes—
125C22×C149—22no—
126C22×C149#12712yes—
127C22×C149C22×D411yescharacteristic
128C2×D149—41no—
129C2×D149—41no—
130C2×D149—42no—
131C2×D149—42no—
132C2×D149—44no—
133C2×D149—42no—
134C2×D149—84no—
135C4×C149—24no—
136C4×C149#12712yes—
137C4×C149C22×D411yescharacteristic
138C4×C149C22×D411yescharacteristic
139Dic149—41no—
140Dic149—41no—
141Dic149—42no—
142C2×C149—22no—
143C2×C149C2×#12711yescharacteristic
144C2×C149#57712yes—
145D149—81no—
146D149—81no—
147D149—82no—
148C149#315411yescharacteristic, complemented, Sylow
149#3154—1491nomaximal, Sylow
150C2×#137—1491no—
151C2×AGL(1,ℤ/8)—1491no—
152C2×#135—1491no—
153C22×SD16—1491no—
154#536—1491no—
155#535—1491no—
156#497—1492no—
157#496—1492no—
158#495—1492no—
159#492—1492no—
160#405D14911yescharacteristic, complemented
161C2×#41—1491no—
162C2×#41—1491no—
163C22×Q8—1491no—
164C22×D4—1491no—
165#137—2984no—
166AGL(1,ℤ/8)—2984no—
167#135—2984no—
168C2×Q16—1491no—
169C2×Q16—1492no—
170C2×SD16—2984no—
171C2×SD16—1492no—
172C2×SD16—1492no—
173C2×SD16—1492no—
174C2×SD16—1491no—
175C2×SD16—1491no—
176C2×SD16—1492no—
177C2×D8—1492no—
178C2×D8—1491no—
179C2×M16C2×D14911yescharacteristic
180C22×C8C2×D14911yescharacteristic
181C4⋊Q8—1492no—
182#127—1492no—
183#124—1492no—
184#124—1492no—
185#123—2982no—
186C22⋊Q8—2982no—
187#121—2982no—
188#120—2982no—
189#117C2×D14911yescharacteristic
190#97C2×D14912yescomplemented
191C4×C8C2×D14912yescomplemented
192C24—2981no—
193#41—2982no—
194#41—2982no—
195#41—2982no—
196#41—2982no—
197C2×Q8—2981no—
198C2×Q8—2982no—
199C2×Q8—2982no—
200C2×Q8—1491no—
201C2×Q8—1492no—
202C2×Q8—1491no—
203C2×D4—2981no—
204C2×D4—2981no—
205C2×D4—2982no—
206C2×D4—2982no—
207C2×D4—2981no—
208C2×D4—2984no—
209C2×D4—1491no—
210C2×D4—1492no—
211C2×D4—1491no—
212C22×C4—2981no—
213C22×C4—2981no—
214C22×C4—2981no—
215C22×C4C22×D14911yescharacteristic
216Q16—2982no—
217Q16—2984no—
218SD16—2984no—
219SD16—2984no—
220SD16—2982no—
221SD16—2982no—
222SD16—2984no—
223SD16—2984no—
224D8—2982no—
225D8—2984no—
226M16D59614yescomplemented
227C2×C8D59614yescomplemented
228C2×C8C22×D14911yescharacteristic
229C2×C8C22×D14912yes—
230C2×C8C22×D14911yescharacteristic
231C4⋊C4—2984no—
232C4⋊C4D59612yes—
233C22⋊C4—2984no—
234C22⋊C4—2984no—
235C22⋊C4D59612yes—
236C42C22×D14912yes—
237C23—2981no—
238C23—2982no—
239C23—2981no—
240C23—5962no—
241C23—11922no—
242C23C2×D59611yescharacteristic
243Q8—2982no—
244Q8—2981no—
245Q8—2982no—
246Q8—2981no—
247Q8—2981no—
248Q8—2981no—
249Q8—5962no—
250D4—2981no—
251D4—2982no—
252D4—2981no—
253D4—2981no—
254D4—2982no—
255D4—2981no—
256D4—5962no—
257D4—5962no—
258D4—5962no—
259D4—11924no—
260C2×C4—2981no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—5962no—
264C2×C4—5962no—
265C2×C4—5962no—
266C2×C4C2×D59614yes—
267C2×C4C2×D59611yescharacteristic
268C2×C4C2×D59612yes—
269C2×C4C2×D59612yes—
270C2×C4C23×D14911yescharacteristic
271C8C2×D59612yes—
272C8C2×D59612yes—
273C8C2×D59614yes—
274C22—22no—
275C22—5961no—
276C22—5961no—
277C22—5962no—
278C22—5962no—
279C22—5964no—
280C22—5962no—
281C22—11924no—
282C22#1801190812yes—
283C22C22×D59611yescharacteristic
284C4—24no—
285C4—5961no—
286C4—5961no—
287C4—5962no—
288C4#1801190812yes—
289C4C22×D59611yescharacteristic
290C4C22×D59611yescharacteristic
291C2—22no—
292C2—11922no—
293C2—11921no—
294C2—11921no—
295C2C2×#1801190811yescharacteristic
296C2#2375043712yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#405×C149C2
socleC22×C149C22×D4
hypercenter#405D149
hypocenterC149#3154
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C2×#18011939C2semidirect
3. C2×#18011933C2semidirect
4. C22×#14558725C2semidirect
5. #23750201C2semidirect
6. #23750194C2semidirect
7. #23750019C2semidirect
8. #23750014C2semidirect
9. #23750009C2semidirect
10. #23749998C2semidirect
11. #405×C149C2semidirect
19. C2×Dic596C22semidirect
20. C2×Dic596C22semidirect
25. C2×#14558725C22semidirect
26. C2×#14558725C22semidirect
27. C2×#14558725C22semidirect
29. C2×D1192C22semidirect
30. #18011911C22semidirect
33. #18011899C22semidirect
41. #97×C149C22semidirect
42. C4×C8×C149C22semidirect
80. M16×C149D4semidirect
81. C2×C8×C149D4semidirect
148. C149#3154semidirect
160. #405D149semidirect
190. #97C2×D149semidirect
191. C4×C8C2×D149semidirect
226. M16D596semidirect
227. C2×C8D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C2×#180119392
C2×#180119332
C22×#145587252
#237502012
#237501942
#237500192
#237500142
#237500092
#237499982
#405×C1492
#3154149