Finite Group Databasebeta

← #34055158

Subgroups — #34055158

Order 19072.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011942C211yesmaximal, characteristic, complemented
2C2×#18011939C211yesmaximal, characteristic, complemented
3C2×#18011936C211yesmaximal, characteristic, complemented
4#23750171C211yesmaximal, characteristic, complemented
5C2×#18011900C211yesmaximal, characteristic, complemented
6#23750018C212yesmaximal, complemented
7#23750011C212yesmaximal, complemented
8#23750010C212yesmaximal, complemented
9#23750006C212yesmaximal, complemented
10M16×Dic149C211yesmaximal, characteristic, complemented
11C2×#137×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C22×D596C2211yescharacteristic
14#18011942—24no—
15#18011939—24no—
16#18011936—24no—
17C2×#14558726C2212yescomplemented
18C2×#14558725C2212yes—
19C2×#14558723C2212yes—
20C2×#14558723C2212yescomplemented
21C2×D1192C2212yes—
22C2×#14558721C2212yes—
23C2×#14558720C2211yescharacteristic
24#18011909C2211yescharacteristic, complemented
25#18011907C2211yescharacteristic, complemented
26#18011900—22no—
27#18011900C2212yes—
28#18011900C2212yes—
29#18011900C2211yescharacteristic, complemented
30#18011898C2211yescharacteristic, complemented
31#18011883—22no—
32C4×C22⋊D149—22no—
33C2×#14558713—22no—
34C2×C4×Dic149C2211yescharacteristic
35#18011821C2212yescomplemented
36C8×Dic149C2212yescomplemented
37C2×#41×C149C2211yescharacteristic
38C22×Q8×C149C2211yescharacteristic
39#137×C149—24no—
40C2×Q16×C149C2212yescomplemented
41C2×SD16×C149C2212yescomplemented
42C2×M16×C149C2211yescharacteristic
43C23×D149—21no—
44#14558736—22no—
45#14558736—22no—
46C2×Dic298C2311yescharacteristic
47C2×D596—22no—
48C2×D596—22no—
49C2×D596—21no—
50C2×D596C2311yescharacteristic
51C2×D596C2312yes—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—21no—
54C22×Dic149D412yes—
55C2×C4×D149—21no—
56#14558726—24no—
57#14558725—24no—
58#14558723—24no—
59#14558723—24no—
60D1192—24no—
61#14558721—24no—
62#14558720D414yescomplemented
63C2×#11924746C2312yes—
64#14558715—22no—
65C22⋊Dic149—22no—
66#14558713—24no—
67#14558713—24no—
68#14558713—22no—
69C4×Dic149D412yes—
70C4×Dic149C2311yescharacteristic
71C4×Dic149C2311yescharacteristic
72#41×C149—22no—
73#41×C149—22no—
74C2×Q8×C149—21no—
75C2×Q8×C149—22no—
76C2×Q8×C149—22no—
77C2×Q8×C149C2311yescharacteristic
78C2×Q8×C149C2312yes—
79C2×D4×C149—21no—
80C2×D4×C149C2311yescharacteristic
81C22×C4×C149—21no—
82C22×C4×C149—21no—
83C22×C4×C149C2311yescharacteristic
84Q16×C149—24no—
85SD16×C149—24no—
86M16×C149D414yescomplemented
87C2×C8×C149C2312yes—
88C22×D149—21no—
89C22×D149—22no—
90C22×D149—44no—
91C22×D149—42no—
92Dic298—21no—
93Dic298—21no—
94D596—22no—
95D596—21no—
96D596—22no—
97D596—21no—
98D596—42no—
99C22⋊D149—44no—
100C22⋊D149—42no—
101C2×Dic149—21no—
102C2×Dic149—42no—
103C2×Dic149C2×D412yes—
104C2×Dic149C2×D412yes—
105C4×D149—42no—
106#11924746C2×D414yes—
107C23×C149—21no—
108C23×C149C2×D411yescharacteristic
109Q8×C149—21no—
110Q8×C149—22no—
111Q8×C149—22no—
112Q8×C149—21no—
113Q8×C149—42no—
114D4×C149—21no—
115D4×C149—21no—
116D4×C149—42no—
117C2×C4×C149—21no—
118C2×C4×C149—22no—
119C2×C4×C149—42no—
120C2×C4×C149—42no—
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D412yes—
123C2×C4×C149C2×D412yes—
124C2×C4×C149C2411yescharacteristic
125C8×C149C2×D414yes—
126C22×C149—22no—
127C22×C149—41no—
128C22×C149—42no—
129C22×C149#12712yes—
130C22×C149C22×D411yescharacteristic
131C2×D149—41no—
132C2×D149—42no—
133C2×D149—42no—
134C2×D149—44no—
135C2×D149—84no—
136C4×C149—41no—
137C4×C149—42no—
138C4×C149#12712yes—
139C4×C149C22×D411yescharacteristic
140C4×C149C22×D411yescharacteristic
141Dic149—22no—
142Dic149—22no—
143Dic149—41no—
144C2×C149—22no—
145C2×C149—81no—
146C2×C149C2×#12711yescharacteristic
147C2×C149#57512yes—
148D149—81no—
149D149—82no—
150C149#315311yescharacteristic, complemented, Sylow
151#3153—1491nomaximal, Sylow
152C2×#137—1491no—
153C2×#137D14911yescharacteristic, complemented
154C2×AGL(1,ℤ/8)—1491no—
155C2×AGL(1,ℤ/8)—1491no—
156#532—1491no—
157C2×#124—1491no—
158#497—1492no—
159#496—1492no—
160#495—1492no—
161#495—1492no—
162C4×M16—1491no—
163C2×#41—1491no—
164C2×#41C2×D14911yescharacteristic
165C22×Q8C2×D14911yescharacteristic
166C22×D4—1491no—
167#137—24no—
168#137—2984no—
169AGL(1,ℤ/8)—2984no—
170AGL(1,ℤ/8)—2984no—
171C2×Q16—1492no—
172C2×Q16C2×D14912yescomplemented
173C2×SD16—1492no—
174C2×SD16—1492no—
175C2×SD16—1492no—
176C2×SD16C2×D14912yescomplemented
177C2×D8—1492no—
178C2×D8—1492no—
179C2×M16—1491no—
180C2×M16C2×D14911yescharacteristic
181C4⋊Q8—1491no—
182#127—1491no—
183#124—2982no—
184#124—1492no—
185#124—1492no—
186#124—1491no—
187#124—1491no—
188#121—2982no—
189C4×D4—2982no—
190C2×C22⋊C4—2982no—
191C2×C42—1491no—
192#97—1492no—
193C4×C8—1492no—
194C24—2981no—
195#41—22no—
196#41—22no—
197#41—2982no—
198#41—2982no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—1491no—
203C2×Q8C22×D14912yes—
204C2×Q8C22×D14911yescharacteristic
205C2×D4—21no—
206C2×D4—2981no—
207C2×D4—2982no—
208C2×D4—2982no—
209C2×D4—2981no—
210C2×D4—2982no—
211C2×D4—1492no—
212C2×D4—1491no—
213C2×D4C22×D14911yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—2981no—
217C22×C4—1492no—
218C22×C4C22×D14911yescharacteristic
219Q16—24no—
220Q16—2984no—
221SD16—24no—
222SD16—2984no—
223SD16—2984no—
224SD16—2984no—
225D8—2984no—
226D8—2984no—
227M16—1494no—
228M16C22⋊D14914yescomplemented
229C2×C8—1492no—
230C2×C8C22×D14912yes—
231C4⋊C4—2982no—
232C22⋊C4—2984no—
233C22⋊C4—2984no—
234C22⋊C4—2982no—
235C22⋊C4—2982no—
236C42—1492no—
237C42—1491no—
238C42—1491no—
239C23—21no—
240C23—2982no—
241C23—2981no—
242C23—5964no—
243C23—5962no—
244C23D4×D14911yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—2981no—
251Q8—2981no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—2982no—
256D4—2981no—
257D4—2981no—
258D4—2982no—
259D4—5964no—
260D4—5962no—
261D4—5962no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—2981no—
267C2×C4—5962no—
268C2×C4—5962no—
269C2×C4—1492no—
270C2×C4—1492no—
271C2×C4D4×D14911yescharacteristic
272C2×C4D4×D14912yes—
273C2×C4C2×C22⋊D14912yes—
274C2×C4C23×D14911yescharacteristic
275C8—1494no—
276C8C2×C22⋊D14914yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—5961no—
281C22—5962no—
282C22—5962no—
283C22—5964no—
284C22—11924no—
285C22#1801190712yes—
286C22C2×D4×D14911yescharacteristic
287C4—41no—
288C4—42no—
289C4—2982no—
290C4—2982no—
291C4—5961no—
292C4#1801190712yes—
293C4C2×D4×D14911yescharacteristic
294C4C22×C22⋊D14911yescharacteristic
295C2—22no—
296C2—81no—
297C2—11922no—
298C2—11921no—
299C2C2×#1801190711yescharacteristic
300C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#137×C149C2
socleC22×C149C22×D4
hypercenterC2×#137D149
hypocenterC149#3153
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
2. C2×#18011939C2semidirect
3. C2×#18011936C2semidirect
4. #23750171C2semidirect
5. C2×#18011900C2semidirect
6. #23750018C2semidirect
7. #23750011C2semidirect
8. #23750010C2semidirect
9. #23750006C2semidirect
10. M16×Dic149C2semidirect
11. C2×#137×C149C2semidirect
17. C2×#14558726C22semidirect
20. C2×#14558723C22semidirect
24. #18011909C22semidirect
25. #18011907C22semidirect
29. #18011900C22semidirect
30. #18011898C22semidirect
35. #18011821C22semidirect
36. C8×Dic149C22semidirect
40. C2×Q16×C149C22semidirect
41. C2×SD16×C149C22semidirect
62. #14558720D4semidirect
86. M16×C149D4semidirect
150. C149#3153semidirect
153. C2×#137D149semidirect
172. C2×Q16C2×D149semidirect
176. C2×SD16C2×D149semidirect
228. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C2×#180119392
C2×#180119362
#237501712
C2×#180119002
#237500182
#237500112
#237500102
#237500062
M16×Dic1492
C2×#137×C1492
#3153149