Finite Group Databasebeta

← #34053961

Subgroups — #34053961

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×#18011957C211yesmaximal, characteristic, complemented
2C2×#18011939C211yesmaximal, characteristic, complemented
3C22×D1192C211yesmaximal, characteristic, complemented
4#23750189C211yesmaximal, characteristic, complemented
5#23749772C214yesmaximal, complemented
6#23749761C214yesmaximal, complemented
7#23749631C211yesmaximal, characteristic, complemented
8#23749622C211yesmaximal, characteristic, complemented
9#408×C149C211yesmaximal, characteristic, complemented
10#18011957—24no—
11#18011957—24no—
12C2×#14558737—21no—
13C2×#14558736C2211yescharacteristic
14C2×#14558736C2212yescomplemented
15C22×D596C2211yescharacteristic
16C22×D596C2211yescharacteristic, complemented
17C22×D596C2212yescomplemented
18C2×D4×D149—21no—
19C2×D4×D149—22no—
20#18011939—24no—
21C2×#14558725C2212yescomplemented
22C2×D1192—24no—
23C2×D1192C2212yescomplemented
24C2×D1192C2214yescomplemented
25#18011907—21no—
26#18011900—21no—
27#18011885C2214yescomplemented
28#18011879—22no—
29#18011870C2211yescharacteristic, complemented
30#18011836C2212yescomplemented
31#18011833C2212yescomplemented
32#18011833C2214yescomplemented
33C2×#41×C149C2211yescharacteristic
34C2×M16×C149C2211yescharacteristic, complemented
35C22×C8×C149C2211yescharacteristic, complemented
36C22⋊C8×C149C2214yescomplemented
37C23×D149—21no—
38C23×D149—22no—
39C23×D149—21no—
40#14558737—28no—
41#14558736—24no—
42#14558736—24no—
43#14558736—22no—
44#14558736D414yescomplemented
45C2×Dic298C2311yescharacteristic
46C2×D596—24no—
47C2×D596—24no—
48C2×D596—21no—
49C2×D596—22no—
50C2×D596—22no—
51C2×D596—22no—
52C2×D596—22no—
53C2×D596—21no—
54C2×D596D414yescomplemented
55C2×D596C2312yes—
56C2×D596C2312yes—
57C2×D596C2311yescharacteristic
58C2×C22⋊D149—21no—
59C2×C22⋊D149—22no—
60C2×C22⋊D149—24no—
61D4×D149—216no—
62D4×D149—28no—
63C2×C4×D149—21no—
64C2×C4×D149—22no—
65#14558725—24no—
66D1192—28no—
67D1192—24no—
68C4⋊Dic149C2312yes—
69C22⋊Dic149—21no—
70#14558713—24no—
71C4×Dic149—21no—
72#41×C149—22no—
73#41×C149—22no—
74C2×Q8×C149D411yescharacteristic
75C2×D4×C149D411yescharacteristic
76C2×D4×C149D412yes—
77C22×C4×C149C2312yes—
78C22×C4×C149C2311yescharacteristic
79M16×C149—22no—
80C2×C8×C149—22no—
81C2×C8×C149C2312yes—
82C2×C8×C149C2312yes—
83C22×D149—21no—
84C22×D149—22no—
85C22×D149—28no—
86C22×D149—24no—
87C22×D149—22no—
88C22×D149—42no—
89C22×D149—82no—
90C22×D149—84no—
91C22×D149—82no—
92Dic298—21no—
93Dic298C2×D412yes—
94D596—28no—
95D596—24no—
96D596—22no—
97D596—21no—
98D596—22no—
99D596—22no—
100D596—42no—
101D596C2×D412yes—
102D596C2×D414yes—
103C22⋊D149—28no—
104C22⋊D149—24no—
105C22⋊D149—84no—
106C2×Dic149—21no—
107C2×Dic149—22no—
108C4×D149—28no—
109C4×D149—24no—
110C23×C149C2×D412yes—
111C23×C149C2×D411yescharacteristic
112Q8×C149—22no—
113D4×C149—24no—
114D4×C149—22no—
115C2×C4×C149—22no—
116C2×C4×C149—22no—
117C2×C4×C149C2×D412yes—
118C2×C4×C149C2×D412yes—
119C2×C4×C149C2×D412yes—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2411yescharacteristic
122C8×C149—22no—
123C8×C149—22no—
124C22×C149—22no—
125C22×C149—22no—
126C22×C149—24no—
127C22×C149#12012yes—
128C22×C149C22×D411yescharacteristic
129C2×D149—24no—
130C2×D149—22no—
131C2×D149—44no—
132C2×D149—42no—
133C2×D149—42no—
134C2×D149—44no—
135C2×D149—84no—
136C2×D149—88no—
137C2×D149—84no—
138C4×C149—22no—
139C4×C149#12012yes—
140C4×C149C22×D411yescharacteristic
141C4×C149C22×D411yescharacteristic
142Dic149—22no—
143Dic149—42no—
144C2×C149—22no—
145C2×C149—42no—
146C2×C149C2×#12011yescharacteristic
147C2×C149#57612yes—
148D149—44no—
149D149—42no—
150D149—82no—
151C149#300811yescharacteristic, complemented, Sylow
152#3008—1491nomaximal, Sylow
153C2×H(5,𝔽2)—1491no—
154C2×AGL(1,ℤ/8)—1491no—
155C22×D8—1491no—
156#535—1491no—
157#449—1494no—
158#447—1494no—
159#418—1491no—
160#416—1491no—
161#408D14911yescharacteristic, complemented
162H(5,𝔽2)—2984no—
163H(5,𝔽2)—2984no—
164C2×#41—2981no—
165C2×#41—1492no—
166C2×#41—1491no—
167C2×#41C2×D14911yescharacteristic
168C22×D4—2982no—
169C22×D4—2981no—
170C22×D4—1491no—
171C22×D4—1492no—
172C22×D4—1491no—
173AGL(1,ℤ/8)—2984no—
174C2×SD16—1492no—
175C2×D8—2984no—
176C2×D8—1494no—
177C2×D8—1492no—
178C2×M16C2×D14911yescharacteristic, complemented
179C22×C8C2×D14911yescharacteristic, complemented
180#127—2981no—
181#124—2981no—
182#121—1494no—
183#120—2982no—
184#117—1491no—
185#103—1492no—
186#102—1492no—
187#102—1494no—
188C22⋊C8C2×D14914yescomplemented
189C24—2982no—
190C24—2981no—
191C24—2981no—
192#41—22no—
193#41—22no—
194#41—2984no—
195#41—2984no—
196#41—2988no—
197#41—2982no—
198#41—1494no—
199C2×Q8—1491no—
200C2×Q8D59611yescharacteristic
201C2×D4—2984no—
202C2×D4—2984no—
203C2×D4—29816no—
204C2×D4—2988no—
205C2×D4—2982no—
206C2×D4—2981no—
207C2×D4—2984no—
208C2×D4—2982no—
209C2×D4—2982no—
210C2×D4—2982no—
211C2×D4—2982no—
212C2×D4—2981no—
213C2×D4—2981no—
214C2×D4—1494no—
215C2×D4—1492no—
216C2×D4—1491no—
217C2×D4—1492no—
218C2×D4D59612yes—
219C2×D4D59611yescharacteristic
220C22×C4—2982no—
221C22×C4—2981no—
222C22×C4C22×D14912yes—
223C22×C4C22×D14911yescharacteristic
224SD16—2984no—
225D8—2988no—
226D8—2984no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D14912yes—
230C2×C8C22×D14912yes—
231C4⋊C4—1492no—
232C22⋊C4—2981no—
233C22⋊C4—2984no—
234C42—2981no—
235C23—2988no—
236C23—2982no—
237C23—2981no—
238C23—2984no—
239C23—2982no—
240C23—5962no—
241C23—11922no—
242C23—11922no—
243C23—11924no—
244C23C2×D59612yes—
245C23C2×D59611yescharacteristic
246Q8—22no—
247Q8—2981no—
248Q8—1492no—
249D4—24no—
250D4—22no—
251D4—2988no—
252D4—2988no—
253D4—2984no—
254D4—2982no—
255D4—2981no—
256D4—2982no—
257D4—2982no—
258D4—2984no—
259D4—5962no—
260D4—1492no—
261D4—1494no—
262D4—11924no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—2988no—
266C2×C4—2981no—
267C2×C4—2984no—
268C2×C4—2982no—
269C2×C4D4×D14912yes—
270C2×C4D4×D14912yes—
271C2×C4C2×D59612yes—
272C2×C4C2×D59611yescharacteristic
273C2×C4C23×D14911yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—24no—
278C22—22no—
279C22—2984no—
280C22—2982no—
281C22—5964no—
282C22—5962no—
283C22—5964no—
284C22—5962no—
285C22—11924no—
286C22—11924no—
287C22—11928no—
288C22#1801188112yes—
289C22C22×D59611yescharacteristic
290C4—22no—
291C4—2982no—
292C4—5962no—
293C4#1801188112yes—
294C4C2×D4×D14911yescharacteristic
295C4C2×D4×D14911yescharacteristic
296C2—22no—
297C2—42no—
298C2—5964no—
299C2—5962no—
300C2—11922no—
301C2C2×#1801188111yescharacteristic
302C2#2375043012yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#408×C149C2
socleC22×C149C22×D4
hypercenter#408D149
hypocenterC149#3008
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#18011957C2semidirect
2. C2×#18011939C2semidirect
3. C22×D1192C2semidirect
4. #23750189C2semidirect
5. #23749772C2semidirect
6. #23749761C2semidirect
7. #23749631C2semidirect
8. #23749622C2semidirect
9. #408×C149C2semidirect
14. C2×#14558736C22semidirect
16. C22×D596C22semidirect
17. C22×D596C22semidirect
21. C2×#14558725C22semidirect
23. C2×D1192C22semidirect
24. C2×D1192C22semidirect
27. #18011885C22semidirect
29. #18011870C22semidirect
30. #18011836C22semidirect
31. #18011833C22semidirect
32. #18011833C22semidirect
34. C2×M16×C149C22semidirect
35. C22×C8×C149C22semidirect
36. C22⋊C8×C149C22semidirect
44. #14558736D4semidirect
54. C2×D596D4semidirect
151. C149#3008semidirect
161. #408D149semidirect
178. C2×M16C2×D149semidirect
179. C22×C8C2×D149semidirect
188. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119572
C2×#180119392
C22×D11922
#237501892
#237497722
#237497612
#237496312
#237496222
#408×C1492
#3008149