Finite Group Databasebeta

← C151×#18999 #50323924

Subgroups — C151×#18999 #50323924

Order 38656.

850 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 222 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×#563×C151C211yesmaximal, characteristic
2#3236×C151C212yesmaximal, complemented
3#3140×C151C211yesmaximal, characteristic
4#1664×C151C218yesmaximal, complemented
5#1533×C151C211yesmaximal, characteristic
6#1528×C151C212yesmaximal, complemented
7#563×C151—24no—
8#563×C151—22no—
9#563×C151C2214yes—
10#533×C151C2211yescharacteristic
11C2×C4⋊Q8×C151—21no—
12C2×#126×C151—22no—
13C2×#125×C151C2212yes—
14C2×#124×C151C2211yescharacteristic
15C2×#123×C151—21no—
16C2×C22⋊Q8×C151—22no—
17#501×C151C2214yescomplemented
18#491×C151C2214yescomplemented
19#489×C151C2214yes—
20#488×C151—22no—
21#484×C151—22no—
22#483×C151—22no—
23#479×C151—24no—
24#432×C151C2212yes—
25#419×C151—21no—
26#418×C151—21no—
27C4×M16×C151C2211yescharacteristic
28#330×C151C2218yescomplemented
29#329×C151C2214yes—
30C22×Q8×C151—21no—
31C22×Q8×C151D411yescharacteristic
32C22×D4×C151D411yescharacteristic
33C23×C4×C151—21no—
34C2×M16×C151—21no—
35C4⋊Q8×C151—24no—
36C4⋊Q8×C151—24no—
37C4⋊Q8×C151C2312yes—
38#126×C151—28no—
39#126×C151—28no—
40#125×C151—22no—
41#125×C151—22no—
42#125×C151—21no—
43#125×C151D414yes—
44#125×C151C2314yes—
45#124×C151—22no—
46#124×C151D412yes—
47#124×C151C2312yes—
48#123×C151—24no—
49#123×C151—24no—
50C22⋊Q8×C151—28no—
51C22⋊Q8×C151—28no—
52C22⋊Q8×C151—22no—
53C4×Q8×C151—22no—
54#117×C151—21no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151D412yes—
59C2×C4⋊C4×C151D412yes—
60C2×C22⋊C4×C151—22no—
61C2×C22⋊C4×C151—21no—
62C2×C22⋊C4×C151—22no—
63C2×C42×C151—21no—
64C2×C42×C151C2311yescharacteristic
65#107×C151—24no—
66#106×C151—24no—
67C4⋊C8×C151—22no—
68#103×C151—24no—
69#103×C151—24no—
70#103×C151—24no—
71#102×C151—24no—
72C22⋊C8×C151—22no—
73#97×C151C2312yes—
74#97×C151C2314yes—
75C4×C8×C151—21no—
76C24×C151—21no—
77C2×Q8×C151—24no—
78C2×Q8×C151—21no—
79C2×Q8×C151—22no—
80C2×Q8×C151—42no—
81C2×Q8×C151—82no—
82C2×Q8×C151C2×D412yes—
83C2×D4×C151—21no—
84C2×D4×C151—42no—
85C2×D4×C151C2×D412yes—
86C22×C4×C151—22no—
87C22×C4×C151—21no—
88C22×C4×C151—22no—
89C22×C4×C151—24no—
90C22×C4×C151—82no—
91C22×C4×C151C2×D411yescharacteristic
92C22×C4×C151C2×D412yes—
93M16×C151—42no—
94C2×C8×C151—22no—
95C2×C8×C151—24no—
96C4⋊C4×C151—28no—
97C4⋊C4×C151—24no—
98C4⋊C4×C151—24no—
99C4⋊C4×C151—22no—
100C4⋊C4×C151—22no—
101C4⋊C4×C151—24no—
102C4⋊C4×C151—24no—
103C4⋊C4×C151—22no—
104C4⋊C4×C151—22no—
105C4⋊C4×C151—42no—
106C4⋊C4×C151C2×D414yes—
107C4⋊C4×C151C2×D414yes—
108C22⋊C4×C151—28no—
109C22⋊C4×C151—24no—
110C22⋊C4×C151—24no—
111C22⋊C4×C151—24no—
112C22⋊C4×C151—41no—
113C42×C151—24no—
114C42×C151—41no—
115C42×C151C2×D411yescharacteristic
116C42×C151C2×D412yes—
117C42×C151C2411yescharacteristic
118C23×C151—22no—
119C23×C151—44no—
120C23×C151—42no—
121C23×C151#12011yescharacteristic
122Q8×C151—42no—
123Q8×C151—44no—
124Q8×C151—81no—
125Q8×C151—84no—
126D4×C151—42no—
127D4×C151—81no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—24no—
131C2×C4×C151—24no—
132C2×C4×C151—42no—
133C2×C4×C151—44no—
134C2×C4×C151—42no—
135C2×C4×C151—44no—
136C2×C4×C151—42no—
137C2×C4×C151—84no—
138C2×C4×C151#12011yescharacteristic
139C2×C4×C151#12012yes—
140C2×C4×C151C22×D412yes—
141C2×C4×C151C22×D411yescharacteristic
142C8×C151—44no—
143C8×C151—42no—
144C22×C151—22no—
145C22×C151—42no—
146C22×C151—44no—
147C22×C151—84no—
148C22×C151#45512yes—
149C22×C151C2×#12011yescharacteristic
150C4×C151—21no—
151C4×C151—21no—
152C4×C151—22no—
153C4×C151—22no—
154C4×C151—44no—
155C4×C151—42no—
156C4×C151—44no—
157C4×C151—82no—
158C2×C151—22no—
159C2×C151—82no—
160C2×C151C2×#45511yescharacteristic
161C2×C151#302012yes—
162#18999C15111yesmaximal, characteristic, direct product factor, Sylow
163C151#1899911yescharacteristic, direct product factor, Sylow
164C2×#563C2×C15111yescharacteristic
165#3236C2×C15112yescomplemented
166#3140C2×C15111yescharacteristic
167#1664C2×C15118yescomplemented
168#1533C2×C15111yescharacteristic
169#1528C2×C15112yescomplemented
170#563—24no—
171#563—22no—
172#563C22×C15114yes—
173#533C22×C15111yescharacteristic
174C2×C4⋊Q8—21no—
175C2×#126—22no—
176C2×#125C22×C15112yes—
177C2×#124C22×C15111yescharacteristic
178C2×#123—21no—
179C2×C22⋊Q8—22no—
180#501C22×C15114yescomplemented
181#491C22×C15114yescomplemented
182#489C22×C15114yes—
183#488—22no—
184#484—22no—
185#483—22no—
186#479—24no—
187#432C22×C15112yes—
188#419—21no—
189#418—21no—
190C4×M16C22×C15111yescharacteristic
191#330C22×C15118yescomplemented
192#329C22×C15114yes—
193C22×Q8—21no—
194C22×Q8D4×C15111yescharacteristic
195C22×D4D4×C15111yescharacteristic
196C23×C4—21no—
197C2×M16—21no—
198C4⋊Q8—24no—
199C4⋊Q8—24no—
200C4⋊Q8C23×C15112yes—
201#126—28no—
202#126—28no—
203#125—22no—
204#125—22no—
205#125—21no—
206#125D4×C15114yes—
207#125C23×C15114yes—
208#124—22no—
209#124D4×C15112yes—
210#124C23×C15112yes—
211#123—24no—
212#123—24no—
213C22⋊Q8—28no—
214C22⋊Q8—28no—
215C22⋊Q8—22no—
216C4×Q8—22no—
217#117—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4D4×C15112yes—
222C2×C4⋊C4D4×C15112yes—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—22no—
226C2×C42—21no—
227C2×C42C23×C15111yescharacteristic
228#107—24no—
229#106—24no—
230C4⋊C8—22no—
231#103—24no—
232#103—24no—
233#103—24no—
234#102—24no—
235C22⋊C8—22no—
236#97C23×C15114yes—
237#97C23×C15112yes—
238C4×C8—21no—
239C24—21no—
240C2×Q8—24no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—42no—
244C2×Q8—82no—
245C2×Q8C2×D4×C15112yes—
246C2×D4—21no—
247C2×D4—42no—
248C2×D4C2×D4×C15112yes—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—24no—
253C22×C4—82no—
254C22×C4C2×D4×C15111yescharacteristic
255C22×C4C2×D4×C15112yes—
256M16—42no—
257C2×C8—22no—
258C2×C8—24no—
259C4⋊C4—28no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4C2×D4×C15114yes—
270C4⋊C4C2×D4×C15114yes—
271C22⋊C4—28no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—24no—
275C22⋊C4—41no—
276C42—24no—
277C42—41no—
278C42C2×D4×C15111yescharacteristic
279C42C2×D4×C15112yes—
280C42C24×C15111yescharacteristic
281C23—22no—
282C23—44no—
283C23—42no—
284C23#120×C15111yescharacteristic
285Q8—42no—
286Q8—44no—
287Q8—81no—
288Q8—84no—
289D4—42no—
290D4—81no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—84no—
301C2×C4#120×C15111yescharacteristic
302C2×C4#120×C15112yes—
303C2×C4C22×D4×C15112yes—
304C2×C4C22×D4×C15111yescharacteristic
305C8—42no—
306C8—44no—
307C22—22no—
308C22—42no—
309C22—44no—
310C22—84no—
311C22#455×C15112yes—
312C22C2×#120×C15111yescharacteristic
313C4—21no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—44no—
318C4—42no—
319C4—44no—
320C4—82no—
321C2—22no—
322C2—82no—
323C2C2×#455×C15111yescharacteristic
324C2#3020×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3236×C151C2semidirect
4. #1664×C151C2semidirect
6. #1528×C151C2semidirect
17. #501×C151C22semidirect
18. #491×C151C22semidirect
28. #330×C151C22semidirect
162. #18999C151direct (N × H)
163. C151#18999direct (N × H)
165. #3236C2×C151semidirect
167. #1664C2×C151semidirect
169. #1528C2×C151semidirect
180. #501C22×C151semidirect
181. #491C22×C151semidirect
191. #330C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#563×C1512
#3236×C1512
#3140×C1512
#1664×C1512
#1533×C1512
#1528×C1512
#18999151