Finite Group Databasebeta

← #34053941

Subgroups — #34053941

Order 19072.

806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#14558736C211yesmaximal, characteristic, complemented
2C2×#18011937C212yesmaximal, complemented
3#23749768C214yesmaximal, complemented
4#23749763C212yesmaximal, complemented
5#23749758C212yesmaximal, complemented
6#23749624C212yesmaximal, complemented
7#23749589C211yesmaximal, characteristic, complemented
8C2×#121×C149C211yesmaximal, characteristic, complemented
9C2×#14558736—21no—
10C2×#14558736—21no—
11C2×#14558736—28no—
12C2×#14558736C2212yes—
13C2×#14558736C2212yescomplemented
14C22×Dic298C2211yescharacteristic, complemented
15C22×D596C2211yescharacteristic, complemented
16C22×C22⋊D149—21no—
17C22×C4×D149—21no—
18#18011937—28no—
19C2×#14558724C2214yescomplemented
20C2×#14558721C2214yescomplemented
21C2×#14558720C2212yescomplemented
22#18011834C2214yescomplemented
23#18011831C2214yescomplemented
24C22⋊#11924746C2212yescomplemented
25C22⋊#11924746C2212yescomplemented
26C22×D4×C149—21no—
27C22×D4×C149C2211yescharacteristic, complemented
28C23×C4×C149C2211yescharacteristic
29#121×C149—21no—
30#121×C149—21no—
31#121×C149C2212yes—
32#121×C149C2212yescomplemented
33C2×C4⋊C4×C149C2211yescharacteristic, complemented
34C2×C22⋊C4×C149—21no—
35C23×D149—21no—
36#14558736—28no—
37#14558736—28no—
38#14558736—24no—
39#14558736—24no—
40#14558736—24no—
41#14558736D418yescomplemented
42C2×Dic298—24no—
43C2×Dic298—21no—
44C2×Dic298C2312yes—
45C2×D596—24no—
46C2×D596—21no—
47C2×D596C2312yes—
48C2×C22⋊D149—28no—
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51C22×Dic149—21no—
52C2×C4×D149—28no—
53C2×C4×D149—22no—
54C2×C4×D149—22no—
55#14558724—28no—
56#14558721—28no—
57#14558720—24no—
58C2×#11924746C2314yes—
59C24×C149—21no—
60C24×C149D411yescharacteristic
61C2×D4×C149—22no—
62C2×D4×C149—22no—
63C2×D4×C149—24no—
64C2×D4×C149—21no—
65C2×D4×C149—44no—
66C2×D4×C149C2312yes—
67C22×C4×C149—24no—
68C22×C4×C149—21no—
69C22×C4×C149D411yescharacteristic
70C22×C4×C149D411yescharacteristic
71C22×C4×C149D411yescharacteristic
72C22×C4×C149C2311yescharacteristic
73C22×C4×C149C2311yescharacteristic
74C22×C4×C149C2311yescharacteristic
75C4⋊C4×C149—21no—
76C4⋊C4×C149C2312yes—
77C22⋊C4×C149—22no—
78C22⋊C4×C149—22no—
79C22×D149—24no—
80C22×D149—22no—
81C22×D149—42no—
82C22×D149—42no—
83Dic298—24no—
84Dic298—22no—
85Dic298C2×D414yescomplemented
86D596—24no—
87D596—22no—
88D596C2×D414yescomplemented
89C22⋊D149—28no—
90C22⋊D149—28no—
91C2×Dic149—24no—
92C2×Dic149—22no—
93C4×D149—28no—
94C4×D149—28no—
95#11924746—24no—
96C23×C149—22no—
97C23×C149—22no—
98C23×C149—22no—
99C23×C149—41no—
100C23×C149—42no—
101C23×C149—42no—
102C23×C149—42no—
103C23×C149C2×D411yescharacteristic
104C23×C149C2×D411yescharacteristic
105C23×C149C2×D411yescharacteristic
106D4×C149—24no—
107D4×C149—44no—
108D4×C149—44no—
109D4×C149—42no—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149—22no—
114C2×C4×C149—22no—
115C2×C4×C149—22no—
116C2×C4×C149—42no—
117C2×C4×C149C2×D414yes—
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2411yescharacteristic
122C22×C149—21no—
123C22×C149—21no—
124C22×C149—21no—
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—21no—
128C22×C149—21no—
129C22×C149—44no—
130C22×C149—42no—
131C22×C149—42no—
132C22×C149—42no—
133C22×C149—84no—
134C22×C149#12012yes—
135C22×C149AGL(1,ℤ/8)12yescomplemented
136C22×C149C22×D411yescharacteristic
137C2×D149—24no—
138C2×D149—48no—
139C2×D149—42no—
140C2×D149—42no—
141C4×C149—21no—
142C4×C149—21no—
143C4×C149—42no—
144C4×C149#12012yes—
145C4×C149C22×D412yes—
146Dic149—24no—
147C2×C149—22no—
148C2×C149—22no—
149C2×C149—41no—
150C2×C149—82no—
151C2×C149C2×#12011yescharacteristic
152C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C149#57511yescharacteristic
154D149—44no—
155C149#300611yescharacteristic, complemented, Sylow
156#3006—1491nomaximal, Sylow
157C22×#41—1491no—
158C2×AGL(1,ℤ/8)—1492no—
159C2×#121D14911yescharacteristic, complemented
160#449—1494no—
161#448—1492no—
162#447—1492no—
163#417—1492no—
164#407—1491no—
165C2×#41—2988no—
166C2×#41—2981no—
167C2×#41—2981no—
168C2×#41—1492no—
169C2×#41—1492no—
170C22×Q8—1491no—
171C22×D4—21no—
172C22×D4—2981no—
173C22×D4—1491no—
174C22×D4C2×D14911yescharacteristic, complemented
175C23×C4—2981no—
176C23×C4C2×D14911yescharacteristic
177AGL(1,ℤ/8)—2988no—
178C2×SD16—1494no—
179C2×D8—1494no—
180C2×M16—1492no—
181#121—21no—
182#121—21no—
183#121C2×D14912yes—
184#121C2×D14912yescomplemented
185C2×C4⋊C4C2×D14911yescharacteristic, complemented
186C2×C22⋊C4—21no—
187#103—1494no—
188#102—1494no—
189C22⋊C8—1492no—
190C22⋊C8—1492no—
191C24—21no—
192C24—2981no—
193C24C22⋊D14911yescharacteristic
194#41—2988no—
195#41—2988no—
196#41—2984no—
197#41—2984no—
198#41—2984no—
199#41—1498no—
200C2×Q8—2984no—
201C2×Q8—2981no—
202C2×Q8—1492no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—24no—
206C2×D4—21no—
207C2×D4—44no—
208C2×D4—2984no—
209C2×D4—2988no—
210C2×D4—2982no—
211C2×D4—2982no—
212C2×D4—2981no—
213C2×D4—1492no—
214C2×D4C22×D14912yes—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—2988no—
218C22×C4—2981no—
219C22×C4—2982no—
220C22×C4—2982no—
221C22×C4C22⋊D14911yescharacteristic
222C22×C4C22⋊D14911yescharacteristic
223C22×C4C22⋊D14911yescharacteristic
224C22×C4C22×D14911yescharacteristic
225C22×C4C22×D14911yescharacteristic
226C22×C4C22×D14911yescharacteristic
227SD16—2988no—
228D8—2988no—
229M16—2984no—
230C2×C8—1494no—
231C4⋊C4—21no—
232C4⋊C4C22×D14912yes—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—41no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—2984no—
243C23—2982no—
244C23—5962no—
245C23—5962no—
246C23C2×C22⋊D14911yescharacteristic
247C23C2×C22⋊D14911yescharacteristic
248C23C2×C22⋊D14911yescharacteristic
249Q8—2984no—
250Q8—2982no—
251Q8—1494no—
252D4—24no—
253D4—44no—
254D4—44no—
255D4—42no—
256D4—2984no—
257D4—2988no—
258D4—2988no—
259D4—2982no—
260D4—1494no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—2988no—
269C2×C4—2984no—
270C2×C4—2982no—
271C2×C4—2988no—
272C2×C4D4×D14914yes—
273C2×C4C2×C22⋊D14911yescharacteristic
274C2×C4C2×C22⋊D14911yescharacteristic
275C2×C4C2×C22⋊D14911yescharacteristic
276C2×C4C23×D14911yescharacteristic
277C8—2984no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—84no—
290C22—2984no—
291C22—5968no—
292C22—5962no—
293C22—5962no—
294C22#1801187912yes—
295C22#1801193712yescomplemented
296C22C22×C22⋊D14911yescharacteristic
297C4—21no—
298C4—21no—
299C4—42no—
300C4—2984no—
301C4#1801187912yes—
302C4C2×D4×D14912yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—82no—
307C2—5964no—
308C2C2×#1801187911yescharacteristic
309C2C2×#1801193711yescharacteristic
310C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#121×C149C2
socleC22×C149C22×D4
hypercenterC2×#121D149
hypocenterC149#3006
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14558736C2semidirect
2. C2×#18011937C2semidirect
3. #23749768C2semidirect
4. #23749763C2semidirect
5. #23749758C2semidirect
6. #23749624C2semidirect
7. #23749589C2semidirect
8. C2×#121×C149C2semidirect
13. C2×#14558736C22semidirect
14. C22×Dic298C22semidirect
15. C22×D596C22semidirect
19. C2×#14558724C22semidirect
20. C2×#14558721C22semidirect
21. C2×#14558720C22semidirect
22. #18011834C22semidirect
23. #18011831C22semidirect
24. C22⋊#11924746C22semidirect
25. C22⋊#11924746C22semidirect
27. C22×D4×C149C22semidirect
32. #121×C149C22semidirect
33. C2×C4⋊C4×C149C22semidirect
41. #14558736D4semidirect
85. Dic298C2×D4semidirect
88. D596C2×D4semidirect
135. C22×C149AGL(1,ℤ/8)semidirect
155. C149#3006semidirect
159. C2×#121D149semidirect
174. C22×D4C2×D149semidirect
184. #121C2×D149semidirect
185. C2×C4⋊C4C2×D149semidirect
295. C22#18011937semidirect

Maximal subgroups

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

subgroupindex
C22×#145587362
C2×#180119372
#237497682
#237497632
#237497582
#237496242
#237495892
C2×#121×C1492
#3006149