Finite Group Databasebeta

← C151×#10012 #50314937

Subgroups — C151×#10012 #50314937

Order 38656.

734 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 122 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
1#3100×C151C212yesmaximal, complemented
2#2397×C151C211yesmaximal, characteristic, complemented
3#1963×C151C211yesmaximal, characteristic, complemented
4#1486×C151C212yesmaximal, complemented
5#1274×C151C211yesmaximal, characteristic, complemented
6#532×C151C2211yescharacteristic
7C2×C4×D4×C151—22no—
8C2×C4×D4×C151C2212yes—
9#480×C151—22no—
10#474×C151—22no—
11#459×C151—22no—
12#447×C151—22no—
13C4×D8×C151—24no—
14#431×C151C2212yes—
15#423×C151C2211yescharacteristic
16C2×#104×C151—22no—
17#399×C151—22no—
18#392×C151—22no—
19#376×C151C2211yescharacteristic
20D4⋊C8×C151—24no—
21C2×#41×C151—21no—
22C22×D4×C151—22no—
23C22×D4×C151D412yes—
24C23×C4×C151—22no—
25C2×D8×C151—24no—
26C2×M16×C151—21no—
27C4⋊Q8×C151D411yescharacteristic, complemented
28#127×C151D411yescharacteristic, complemented
29#124×C151—21no—
30#121×C151—22no—
31C4×D4×C151—22no—
32C4×D4×C151—22no—
33C4×D4×C151—22no—
34C4×D4×C151—22no—
35C4×D4×C151—22no—
36C4×D4×C151—44no—
37C4×D4×C151—44no—
38C2×C4⋊C4×C151—22no—
39C2×C4⋊C4×C151D412yes—
40C2×C22⋊C4×C151—24no—
41C2×C22⋊C4×C151—22no—
42C2×C42×C151D412yes—
43C2×C42×C151C2311yescharacteristic
44#107×C151—24no—
45C4⋊C8×C151—22no—
46C4⋊C8×C151—22no—
47#104×C151—44no—
48#102×C151—24no—
49#102×C151—24no—
50C22⋊C8×C151—22no—
51C4×C8×C151D414yescomplemented
52#95×C151—22no—
53C24×C151—22no—
54#41×C151—42no—
55#41×C151—42no—
56C2×Q8×C151—21no—
57C2×D4×C151—22no—
58C2×D4×C151—22no—
59C2×D4×C151—22no—
60C2×D4×C151—21no—
61C2×D4×C151—44no—
62C2×D4×C151—44no—
63C2×D4×C151—48no—
64C2×D4×C151—41no—
65C22×C4×C151—22no—
66C22×C4×C151—22no—
67C22×C4×C151—42no—
68C22×C4×C151—42no—
69C22×C4×C151—41no—
70C22×C4×C151—44no—
71C22×C4×C151—44no—
72C22×C4×C151C2×D412yes—
73C22×C4×C151C2×D411yescharacteristic
74D8×C151—48no—
75M16×C151—42no—
76C2×C8×C151—24no—
77C2×C8×C151—41no—
78C4⋊C4×C151—22no—
79C4⋊C4×C151—22no—
80C4⋊C4×C151—22no—
81C4⋊C4×C151—44no—
82C22⋊C4×C151—48no—
83C22⋊C4×C151—42no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C42×C151—22no—
87C42×C151D814yescomplemented
88C42×C151C2×D411yescharacteristic
89C42×C151C2×D412yes—
90C42×C151#4111yescharacteristic
91C23×C151—24no—
92C23×C151—44no—
93C23×C151—42no—
94C23×C151—42no—
95C23×C151—44no—
96C23×C151—41no—
97C23×C151#12011yescharacteristic
98Q8×C151—42no—
99D4×C151—24no—
100D4×C151—24no—
101D4×C151—42no—
102D4×C151—42no—
103D4×C151—44no—
104D4×C151—416no—
105D4×C151—42no—
106D4×C151—82no—
107C2×C4×C151—24no—
108C2×C4×C151—42no—
109C2×C4×C151—44no—
110C2×C4×C151—41no—
111C2×C4×C151—42no—
112C2×C4×C151—44no—
113C2×C4×C151—84no—
114C2×C4×C151—81no—
115C2×C4×C151—82no—
116C2×C4×C151—81no—
117C2×C4×C151—82no—
118C2×C4×C151#12012yes—
119C2×C4×C151#12112yes—
120C2×C4×C151#12111yescharacteristic
121C2×C4×C151#12711yescharacteristic
122C2×C4×C151C2×D812yes—
123C2×C4×C151AGL(1,ℤ/8)12yes—
124C8×C151—44no—
125C8×C151—81no—
126C22×C151—22no—
127C22×C151—48no—
128C22×C151—44no—
129C22×C151—84no—
130C22×C151—82no—
131C22×C151—82no—
132C22×C151—82no—
133C22×C151—81no—
134C22×C151#39211yescharacteristic
135C22×C151#44712yes—
136C4×C151—22no—
137C4×C151—22no—
138C4×C151—44no—
139C4×C151—82no—
140C4×C151—81no—
141C4×C151#45912yes—
142C4×C151#49311yescharacteristic
143C4×C151#49611yescharacteristic
144C2×C151—22no—
145C2×C151—84no—
146C2×C151—161no—
147C2×C151#201012yes—
148C2×C151#201111yescharacteristic
149#10012C15111yesmaximal, characteristic, direct product factor, Sylow
150C151#1001211yescharacteristic, direct product factor, Sylow
151#3100C2×C15112yescomplemented
152#2397C2×C15111yescharacteristic, complemented
153#1963C2×C15111yescharacteristic, complemented
154#1486C2×C15112yescomplemented
155#1274C2×C15111yescharacteristic, complemented
156#532C22×C15111yescharacteristic
157C2×C4×D4—22no—
158C2×C4×D4C22×C15112yes—
159#480—22no—
160#474—22no—
161#459—22no—
162#447—22no—
163C4×D8—24no—
164#431C22×C15112yes—
165#423C22×C15111yescharacteristic
166C2×#104—22no—
167#399—22no—
168#392—22no—
169#376C22×C15111yescharacteristic
170D4⋊C8—24no—
171C2×#41—21no—
172C22×D4—22no—
173C22×D4D4×C15112yes—
174C23×C4—22no—
175C2×D8—24no—
176C2×M16—21no—
177C4⋊Q8D4×C15111yescharacteristic, complemented
178#127D4×C15111yescharacteristic, complemented
179#124—21no—
180#121—22no—
181C4×D4—22no—
182C4×D4—22no—
183C4×D4—22no—
184C4×D4—22no—
185C4×D4—22no—
186C4×D4—44no—
187C4×D4—44no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4D4×C15112yes—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—22no—
192C2×C42D4×C15112yes—
193C2×C42C23×C15111yescharacteristic
194#107—24no—
195C4⋊C8—22no—
196C4⋊C8—22no—
197#104—44no—
198#102—24no—
199#102—24no—
200C22⋊C8—22no—
201C4×C8D4×C15114yescomplemented
202#95—22no—
203C24—22no—
204#41—42no—
205#41—42no—
206C2×Q8—21no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—21no—
211C2×D4—44no—
212C2×D4—44no—
213C2×D4—48no—
214C2×D4—41no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—41no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4C2×D4×C15112yes—
223C22×C4C2×D4×C15111yescharacteristic
224D8—48no—
225M16—42no—
226C2×C8—24no—
227C2×C8—41no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—44no—
232C22⋊C4—48no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C42—22no—
237C42D8×C15114yescomplemented
238C42C2×D4×C15111yescharacteristic
239C42C2×D4×C15112yes—
240C42#41×C15111yescharacteristic
241C23—24no—
242C23—44no—
243C23—42no—
244C23—42no—
245C23—44no—
246C23—41no—
247C23#120×C15111yescharacteristic
248Q8—42no—
249D4—24no—
250D4—24no—
251D4—42no—
252D4—42no—
253D4—44no—
254D4—416no—
255D4—42no—
256D4—82no—
257C2×C4—24no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—84no—
264C2×C4—82no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4—81no—
268C2×C4#120×C15112yes—
269C2×C4#121×C15112yes—
270C2×C4#121×C15111yescharacteristic
271C2×C4#127×C15111yescharacteristic
272C2×C4C2×D8×C15112yes—
273C2×C4AGL(1,ℤ/8)×C15112yes—
274C8—44no—
275C8—81no—
276C22—22no—
277C22—48no—
278C22—44no—
279C22—84no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—81no—
284C22#392×C15111yescharacteristic
285C22#447×C15112yes—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—82no—
290C4—81no—
291C4#459×C15112yes—
292C4#493×C15111yescharacteristic
293C4#496×C15111yescharacteristic
294C2—22no—
295C2—84no—
296C2—161no—
297C2#2010×C15112yes—
298C2#2011×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#127
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#392
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3100×C151C2semidirect
2. #2397×C151C2semidirect
3. #1963×C151C2semidirect
4. #1486×C151C2semidirect
5. #1274×C151C2semidirect
27. C4⋊Q8×C151D4semidirect
28. #127×C151D4semidirect
51. C4×C8×C151D4semidirect
87. C42×C151D8semidirect
149. #10012C151direct (N × H)
150. C151#10012direct (N × H)
151. #3100C2×C151semidirect
152. #2397C2×C151semidirect
153. #1963C2×C151semidirect
154. #1486C2×C151semidirect
155. #1274C2×C151semidirect
177. C4⋊Q8D4×C151semidirect
178. #127D4×C151semidirect
201. C4×C8D4×C151semidirect
237. C42D8×C151semidirect

Maximal subgroups

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

subgroupindex
#3100×C1512
#2397×C1512
#1963×C1512
#1486×C1512
#1274×C1512
#10012151