Finite Group Databasebeta

← #34053955

Subgroups — #34053955

Order 19072.

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

normal subgroups only

This group has 784 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×#18011956C211yesmaximal, characteristic, complemented
2C2×#18011937C211yesmaximal, characteristic, complemented
3#23750192C211yesmaximal, characteristic, complemented
4#23749767C214yesmaximal, complemented
5#23749757C214yesmaximal, complemented
6#23749630C211yesmaximal, characteristic, complemented
7#23749622C211yesmaximal, characteristic, complemented
8#23749591C211yesmaximal, characteristic, complemented
9C22×D8×C149C211yesmaximal, characteristic, complemented
10#18011956—24no—
11#18011956—24no—
12C2×#14558736C2211yescharacteristic
13C2×#14558736C2211yescharacteristic
14C2×#14558735—21no—
15C2×#14558735C2212yescomplemented
16C22×C22⋊D149—22no—
17C2×D4×D149—21no—
18C2×D4×D149C2212yescomplemented
19#18011937—24no—
20C2×#14558724C2212yescomplemented
21C2×#14558721C2212yescomplemented
22C2×#14558720C2211yescharacteristic, complemented
23#18011907—21no—
24#18011898—21no—
25#18011882C2214yescomplemented
26#18011880—22no—
27#18011870C2211yescharacteristic, complemented
28#18011836C2212yescomplemented
29#18011833C2212yescomplemented
30#18011832C2214yescomplemented
31#18011823C2214yescomplemented
32C22×D4×C149C2211yescharacteristic
33C22×D4×C149C2211yescharacteristic, complemented
34C2×D8×C149—24no—
35C2×D8×C149C2214yescomplemented
36C22×C8×C149C2211yescharacteristic, complemented
37C23×D149—22no—
38#14558736—22no—
39#14558736—22no—
40#14558736—22no—
41#14558736D414yescomplemented
42#14558735—28no—
43#14558735—24no—
44#14558735—24no—
45C2×Dic298D411yescharacteristic
46C2×Dic298C2311yescharacteristic
47C2×D596D411yescharacteristic
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—216no—
50C2×C22⋊D149—22no—
51C2×C22⋊D149—24no—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—21no—
54C2×C22⋊D149D412yes—
55D4×D149—28no—
56D4×D149—24no—
57D4×D149—24no—
58C22×Dic149—22no—
59C2×C4×D149—21no—
60C2×C4×D149C2312yes—
61#14558724—24no—
62#14558721—24no—
63#14558720—22no—
64C2×#11924746C2312yes—
65C4⋊Dic149C2312yes—
66C22⋊Dic149—24no—
67C22⋊Dic149—21no—
68C4×Dic149—21no—
69C24×C149—21no—
70C24×C149—21no—
71C2×D4×C149—21no—
72C2×D4×C149—22no—
73C2×D4×C149—22no—
74C2×D4×C149—22no—
75C2×D4×C149—21no—
76C2×D4×C149D414yescomplemented
77C2×D4×C149C2312yes—
78C2×D4×C149C2312yes—
79C22×C4×C149C2311yescharacteristic
80D8×C149—28no—
81C2×C8×C149—22no—
82C2×C8×C149C2312yes—
83C22×D149—21no—
84C22×D149—28no—
85C22×D149—84no—
86C22×D149C2×D412yes—
87Dic298—22no—
88Dic298—21no—
89Dic298C2×D412yes—
90D596—22no—
91D596—21no—
92D596C2×D412yes—
93C22⋊D149—28no—
94C22⋊D149—28no—
95C22⋊D149—24no—
96C22⋊D149—24no—
97C22⋊D149—84no—
98C2×Dic149—28no—
99C2×Dic149—21no—
100C2×Dic149—22no—
101C2×Dic149C2×D412yes—
102C4×D149—24no—
103C4×D149—22no—
104C4×D149—22no—
105#11924746—22no—
106C23×C149—22no—
107C23×C149—24no—
108C23×C149—22no—
109C23×C149—42no—
110C23×C149—82no—
111C23×C149—82no—
112C23×C149C2×D411yescharacteristic
113D4×C149—24no—
114D4×C149—22no—
115D4×C149—22no—
116D4×C149—22no—
117D4×C149—42no—
118D4×C149C2×D414yes—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D412yes—
121C2×C4×C149C2×D412yes—
122C2×C4×C149C2411yescharacteristic
123C8×C149—22no—
124C22×C149—22no—
125C22×C149—24no—
126C22×C149—44no—
127C22×C149—42no—
128C22×C149—44no—
129C22×C149—84no—
130C22×C149—84no—
131C22×C149#12012yes—
132C22×C149C22×D411yescharacteristic
133C2×D149—22no—
134C2×D149—22no—
135C2×D149—24no—
136C2×D149—42no—
137C2×D149—88no—
138C4×C149#12012yes—
139C4×C149C22×D411yescharacteristic
140C4×C149C22×D411yescharacteristic
141Dic149—22no—
142Dic149—22no—
143Dic149—42no—
144C2×C149—22no—
145C2×C149—44no—
146C2×C149—82no—
147C2×C149C2×#12011yescharacteristic
148C2×C149#57612yes—
149D149—42no—
150D149—42no—
151C149#300811yescharacteristic, complemented, Sylow
152#3008—1491nomaximal, Sylow
153C2×H(5,𝔽2)—1491no—
154C2×AGL(1,ℤ/8)—1491no—
155C22×D8D14911yescharacteristic, complemented
156#535—1491no—
157#449—1494no—
158#447—1494no—
159#418—1491no—
160#416—1491no—
161#408—1491no—
162H(5,𝔽2)—2984no—
163H(5,𝔽2)—2984no—
164C2×#41—2981no—
165C2×#41—1492no—
166C2×#41—1491no—
167C2×#41—1491no—
168C22×D4—2981no—
169C22×D4—2982no—
170C22×D4—1492no—
171C22×D4C2×D14911yescharacteristic
172C22×D4C2×D14911yescharacteristic, complemented
173AGL(1,ℤ/8)—2984no—
174C2×SD16—1492no—
175C2×D8—24no—
176C2×D8—1492no—
177C2×D8C2×D14914yescomplemented
178C2×M16—1491no—
179C22×C8C2×D14911yescharacteristic, complemented
180#127—2981no—
181#124—2981no—
182#121—1494no—
183#120—2982no—
184#117—1491no—
185#103—1492no—
186#102—1494no—
187#102—1492no—
188C22⋊C8—1494no—
189C24—21no—
190C24—21no—
191C24—2982no—
192#41—2988no—
193#41—2984no—
194#41—2984no—
195#41—2982no—
196#41—2982no—
197#41—2982no—
198#41—1494no—
199C2×Q8—1491no—
200C2×Q8—1491no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—2988no—
207C2×D4—2984no—
208C2×D4—29816no—
209C2×D4—2982no—
210C2×D4—2981no—
211C2×D4—2984no—
212C2×D4—2984no—
213C2×D4—2982no—
214C2×D4—1492no—
215C2×D4—1491no—
216C2×D4—1491no—
217C2×D4C22⋊D14914yescomplemented
218C2×D4C22×D14912yes—
219C2×D4C22×D14912yes—
220C22×C4—2982no—
221C22×C4—2981no—
222C22×C4—1492no—
223C22×C4C22×D14911yescharacteristic
224SD16—2984no—
225D8—28no—
226D8—2984no—
227M16—2982no—
228C2×C8—22no—
229C2×C8—1492no—
230C2×C8C22×D14912yes—
231C4⋊C4—1492no—
232C22⋊C4—2981no—
233C22⋊C4—2984no—
234C42—2981no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—2988no—
242C23—2981no—
243C23—1492no—
244C23—11924no—
245C23D4×D14911yescharacteristic
246Q8—2981no—
247Q8—2982no—
248Q8—1492no—
249D4—22no—
250D4—22no—
251D4—22no—
252D4—24no—
253D4—42no—
254D4—2988no—
255D4—2988no—
256D4—2984no—
257D4—2984no—
258D4—2981no—
259D4—2982no—
260D4—1492no—
261D4—11924no—
262D4C2×C22⋊D14914yes—
263C2×C4—2988no—
264C2×C4—2981no—
265C2×C4—2982no—
266C2×C4—2982no—
267C2×C4—2984no—
268C2×C4—2982no—
269C2×C4—1492no—
270C2×C4D4×D14912yes—
271C2×C4D4×D14911yescharacteristic
272C2×C4C2×C22⋊D14912yes—
273C2×C4C23×D14911yescharacteristic
274C8—22no—
275C8—2982no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—44no—
280C22—42no—
281C22—84no—
282C22—84no—
283C22—2984no—
284C22—2982no—
285C22—2982no—
286C22—5962no—
287C22—11928no—
288C22#1801187912yes—
289C22C2×D4×D14911yescharacteristic
290C4—2982no—
291C4—2982no—
292C4—5962no—
293C4#1801187912yes—
294C4C2×D4×D14911yescharacteristic
295C4C22×C22⋊D14911yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—5962no—
300C2—5962no—
301C2C2×#1801187911yescharacteristic
302C2#2375042612yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×D8×C149C2
socleC22×C149C22×D4
hypercenterC22×D8D149
hypocenterC149#3008
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18011956C2semidirect
2. C2×#18011937C2semidirect
3. #23750192C2semidirect
4. #23749767C2semidirect
5. #23749757C2semidirect
6. #23749630C2semidirect
7. #23749622C2semidirect
8. #23749591C2semidirect
9. C22×D8×C149C2semidirect
15. C2×#14558735C22semidirect
18. C2×D4×D149C22semidirect
20. C2×#14558724C22semidirect
21. C2×#14558721C22semidirect
22. C2×#14558720C22semidirect
25. #18011882C22semidirect
27. #18011870C22semidirect
28. #18011836C22semidirect
29. #18011833C22semidirect
30. #18011832C22semidirect
31. #18011823C22semidirect
33. C22×D4×C149C22semidirect
35. C2×D8×C149C22semidirect
36. C22×C8×C149C22semidirect
41. #14558736D4semidirect
76. C2×D4×C149D4semidirect
151. C149#3008semidirect
155. C22×D8D149semidirect
172. C22×D4C2×D149semidirect
177. C2×D8C2×D149semidirect
179. C22×C8C2×D149semidirect
217. C2×D4C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119562
C2×#180119372
#237501922
#237497672
#237497572
#237496302
#237496222
#237495912
C22×D8×C1492
#3008149