Finite Group Databasebeta

← C151×#12703 #50317628

Subgroups — C151×#12703 #50317628

Order 38656.

1154 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 150 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×#535×C151C211yesmaximal, characteristic
2C2×#355×C151C214yesmaximal, complemented
3#1785×C151C212yesmaximal, complemented
4C22×#41×C151C2211yescharacteristic
5C23×D4×C151C411yescharacteristic
6#535×C151—28no—
7C2×#127×C151C412yes—
8C2×#124×C151C2212yes—
9C2×#121×C151—22no—
10C2×#120×C151—22no—
11C2×#117×C151C411yescharacteristic
12C2×#101×C151C2214yescomplemented
13C2×#100×C151—22no—
14#407×C151—22no—
15#355×C151—28no—
16C25×C151—21no—
17C2×#41×C151—24no—
18C2×#41×C151—42no—
19C2×#41×C151—42no—
20C22×Q8×C151C2311yescharacteristic
21C22×D4×C151—24no—
22C22×D4×C151—21no—
23C22×D4×C151—24no—
24C22×D4×C151—42no—
25C22×D4×C151—42no—
26C22×D4×C151C2×C412yes—
27C22×D4×C151C2×C411yescharacteristic
28C22×D4×C151D412yes—
29C23×C4×C151C2×C411yescharacteristic
30C23×C4×C151D412yes—
31C2×M16×C151—24no—
32#127×C151—24no—
33#127×C151—24no—
34#124×C151—24no—
35#124×C151D418yes—
36#121×C151—216no—
37#120×C151—216no—
38#117×C151—24no—
39C2×C4⋊C4×C151—21no—
40C2×C22⋊C4×C151—24no—
41C2×C22⋊C4×C151—21no—
42C2×C42×C151C2×C412yes—
43#101×C151—28no—
44#100×C151—44no—
45C22⋊C8×C151—44no—
46C24×C151—24no—
47C24×C151—22no—
48C24×C151—42no—
49C24×C151—42no—
50C24×C151—84no—
51C24×C151C22⋊C412yes—
52C24×C151C22⋊C411yescharacteristic
53#41×C151—416no—
54C2×Q8×C151—41no—
55C2×Q8×C151—41no—
56C2×Q8×C151C2×D414yes—
57C2×D4×C151—24no—
58C2×D4×C151—24no—
59C2×D4×C151—216no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—24no—
63C2×D4×C151—41no—
64C2×D4×C151—41no—
65C2×D4×C151—42no—
66C2×D4×C151—42no—
67C2×D4×C151—42no—
68C2×D4×C151—416no—
69C2×D4×C151—42no—
70C2×D4×C151—42no—
71C2×D4×C151—88no—
72C2×D4×C151C22⋊C414yes—
73C22×C4×C151—22no—
74C22×C4×C151—22no—
75C22×C4×C151—22no—
76C22×C4×C151—22no—
77C22×C4×C151—24no—
78C22×C4×C151—24no—
79C22×C4×C151—42no—
80C22×C4×C151C22⋊C411yescharacteristic
81C22×C4×C151C22×C411yescharacteristic
82C22×C4×C151C2×D412yes—
83M16×C151—44no—
84M16×C151—44no—
85C2×C8×C151—44no—
86C4⋊C4×C151—24no—
87C22⋊C4×C151—24no—
88C22⋊C4×C151—216no—
89C42×C151—22no—
90C42×C151C22⋊C414yes—
91C23×C151—21no—
92C23×C151—21no—
93C23×C151—24no—
94C23×C151—22no—
95C23×C151—22no—
96C23×C151—22no—
97C23×C151—42no—
98C23×C151—44no—
99C23×C151—48no—
100C23×C151—48no—
101C23×C151—42no—
102C23×C151—42no—
103C23×C151—88no—
104C23×C151—88no—
105C23×C151—88no—
106C23×C151#9912yes—
107C23×C151C2×C22⋊C411yescharacteristic
108Q8×C151—44no—
109D4×C151—48no—
110D4×C151—44no—
111D4×C151—44no—
112D4×C151—48no—
113D4×C151—44no—
114D4×C151—816no—
115C2×C4×C151—28no—
116C2×C4×C151—21no—
117C2×C4×C151—22no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—22no—
121C2×C4×C151—21no—
122C2×C4×C151—24no—
123C2×C4×C151—48no—
124C2×C4×C151—44no—
125C2×C4×C151#9912yes—
126C2×C4×C151C2×C22⋊C412yes—
127C2×C4×C151#12014yes—
128C8×C151—84no—
129C22×C151—22no—
130C22×C151—22no—
131C22×C151—42no—
132C22×C151—42no—
133C22×C151—44no—
134C22×C151—48no—
135C22×C151—42no—
136C22×C151—44no—
137C22×C151—42no—
138C22×C151—44no—
139C22×C151—82no—
140C22×C151—84no—
141C22×C151—816no—
142C22×C151—84no—
143C22×C151#37911yescharacteristic
144C22×C151C2×#9911yescharacteristic
145C22×C151C2×#9911yescharacteristic
146C4×C151—24no—
147C4×C151—22no—
148C4×C151—22no—
149C4×C151—44no—
150C2×C151—21no—
151C2×C151—21no—
152C2×C151—42no—
153C2×C151—82no—
154C2×C151—84no—
155C2×C151#178111yescharacteristic
156C2×C151#213412yes—
157#12703C15111yesmaximal, characteristic, direct product factor, Sylow
158C151#1270311yescharacteristic, direct product factor, Sylow
159C2×#535C2×C15111yescharacteristic
160C2×#355C2×C15114yescomplemented
161#1785C2×C15112yescomplemented
162C22×#41C22×C15111yescharacteristic
163C23×D4C4×C15111yescharacteristic
164#535—28no—
165C2×#127C4×C15112yes—
166C2×#124C22×C15112yes—
167C2×#121—22no—
168C2×#120—22no—
169C2×#117C4×C15111yescharacteristic
170C2×#101C22×C15114yescomplemented
171C2×#100—22no—
172#407—22no—
173#355—28no—
174C25—21no—
175C2×#41—24no—
176C2×#41—42no—
177C2×#41—42no—
178C22×Q8C23×C15111yescharacteristic
179C22×D4—24no—
180C22×D4—24no—
181C22×D4—21no—
182C22×D4—42no—
183C22×D4—42no—
184C22×D4C2×C4×C15111yescharacteristic
185C22×D4C2×C4×C15112yes—
186C22×D4D4×C15112yes—
187C23×C4C2×C4×C15111yescharacteristic
188C23×C4D4×C15112yes—
189C2×M16—24no—
190#127—24no—
191#127—24no—
192#124—24no—
193#124D4×C15118yes—
194#121—216no—
195#120—216no—
196#117—24no—
197C2×C4⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—24no—
200C2×C42C2×C4×C15112yes—
201#101—28no—
202#100—44no—
203C22⋊C8—44no—
204C24—24no—
205C24—22no—
206C24—42no—
207C24—42no—
208C24—84no—
209C24C22⋊C4×C15112yes—
210C24C22⋊C4×C15111yescharacteristic
211#41—416no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C2×D4×C15114yes—
215C2×D4—24no—
216C2×D4—24no—
217C2×D4—216no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—24no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—416no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—88no—
230C2×D4C22⋊C4×C15114yes—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—42no—
238C22×C4C22⋊C4×C15111yescharacteristic
239C22×C4C22×C4×C15111yescharacteristic
240C22×C4C2×D4×C15112yes—
241M16—44no—
242M16—44no—
243C2×C8—44no—
244C4⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—216no—
247C42—22no—
248C42C22⋊C4×C15114yes—
249C23—21no—
250C23—21no—
251C23—24no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—42no—
256C23—44no—
257C23—48no—
258C23—48no—
259C23—42no—
260C23—42no—
261C23—88no—
262C23—88no—
263C23—88no—
264C23#99×C15112yes—
265C23C2×C22⋊C4×C15111yescharacteristic
266Q8—44no—
267D4—48no—
268D4—44no—
269D4—48no—
270D4—44no—
271D4—44no—
272D4—816no—
273C2×C4—28no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—24no—
281C2×C4—48no—
282C2×C4—44no—
283C2×C4#99×C15112yes—
284C2×C4C2×C22⋊C4×C15112yes—
285C2×C4#120×C15114yes—
286C8—84no—
287C22—22no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—48no—
293C22—42no—
294C22—44no—
295C22—42no—
296C22—44no—
297C22—82no—
298C22—84no—
299C22—816no—
300C22—84no—
301C22#379×C15111yescharacteristic
302C22C2×#99×C15111yescharacteristic
303C22C2×#99×C15111yescharacteristic
304C4—24no—
305C4—22no—
306C4—22no—
307C4—44no—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—82no—
312C2—84no—
313C2#1781×C15111yescharacteristic
314C2#2134×C15112yes—
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC22×Q8C23×C151
prime radicalC2×#535×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#355×C151C2semidirect
3. #1785×C151C2semidirect
12. C2×#101×C151C22semidirect
157. #12703C151direct (N × H)
158. C151#12703direct (N × H)
160. C2×#355C2×C151semidirect
161. #1785C2×C151semidirect
170. C2×#101C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1512
C2×#355×C1512
#1785×C1512
#12703151