Finite Group Databasebeta

← C151×#12693 #50317618

Subgroups — C151×#12693 #50317618

Order 38656.

1766 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 158 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
1C22×#127×C151C211yesmaximal, characteristic
2C2×#353×C151C214yesmaximal, complemented
3#1781×C151C212yesmaximal, complemented
4C23×D4×C151—22no—
5C23×D4×C151C411yescharacteristic, complemented
6C23×D4×C151C2211yescharacteristic
7C2×#127×C151—22no—
8C2×#127×C151—28no—
9C2×#127×C151C412yescomplemented
10C2×#127×C151C2212yes—
11C22×C42×C151C411yescharacteristic, complemented
12C2×#99×C151—22no—
13C2×#99×C151C2214yescomplemented
14#379×C151—22no—
15#353×C151—28no—
16C25×C151—21no—
17C25×C151D412yes—
18C22×D4×C151—216no—
19C22×D4×C151—24no—
20C22×D4×C151—24no—
21C22×D4×C151—21no—
22C22×D4×C151—24no—
23C22×D4×C151—24no—
24C22×D4×C151—42no—
25C22×D4×C151—42no—
26C22×D4×C151—42no—
27C22×D4×C151—416no—
28C22×D4×C151—42no—
29C22×D4×C151C2×C412yes—
30C22×D4×C151C2×C411yescharacteristic
31C22×D4×C151D412yes—
32C22×D4×C151C2311yescharacteristic
33C23×C4×C151—21no—
34C23×C4×C151C2×C411yescharacteristic
35#127×C151—216no—
36#127×C151—24no—
37#127×C151—24no—
38#127×C151—24no—
39#127×C151D418yes—
40C2×C22⋊C4×C151—24no—
41C2×C22⋊C4×C151—44no—
42C2×C42×C151—21no—
43C2×C42×C151—24no—
44C2×C42×C151C2×C412yes—
45#99×C151—28no—
46#99×C151—44no—
47C24×C151—24no—
48C24×C151—22no—
49C24×C151—24no—
50C24×C151—24no—
51C24×C151—42no—
52C24×C151—48no—
53C24×C151—48no—
54C24×C151—42no—
55C24×C151—42no—
56C24×C151C22⋊C412yes—
57C24×C151C22⋊C411yescharacteristic
58C24×C151C2×D412yes—
59C2×D4×C151—24no—
60C2×D4×C151—216no—
61C2×D4×C151—24no—
62C2×D4×C151—216no—
63C2×D4×C151—24no—
64C2×D4×C151—22no—
65C2×D4×C151—22no—
66C2×D4×C151—41no—
67C2×D4×C151—41no—
68C2×D4×C151—42no—
69C2×D4×C151—41no—
70C2×D4×C151—41no—
71C2×D4×C151—42no—
72C2×D4×C151—42no—
73C2×D4×C151—416no—
74C2×D4×C151—416no—
75C2×D4×C151—416no—
76C2×D4×C151—416no—
77C2×D4×C151—464no—
78C2×D4×C151—42no—
79C2×D4×C151—42no—
80C2×D4×C151C22⋊C414yescomplemented
81C2×D4×C151C2×D414yes—
82C22×C4×C151—24no—
83C22×C4×C151—28no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
86C22×C4×C151—22no—
87C22×C4×C151—22no—
88C22×C4×C151—44no—
89C22×C4×C151C22⋊C411yescharacteristic
90C22×C4×C151C22×C411yescharacteristic
91C22⋊C4×C151—44no—
92C22⋊C4×C151—44no—
93C22⋊C4×C151—88no—
94C42×C151—24no—
95C42×C151—22no—
96C42×C151C22⋊C414yescomplemented
97C23×C151—24no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—22no—
101C23×C151—22no—
102C23×C151—24no—
103C23×C151—22no—
104C23×C151—22no—
105C23×C151—22no—
106C23×C151—48no—
107C23×C151—44no—
108C23×C151—44no—
109C23×C151—416no—
110C23×C151—416no—
111C23×C151—48no—
112C23×C151—48no—
113C23×C151—48no—
114C23×C151—42no—
115C23×C151—42no—
116C23×C151—84no—
117C23×C151—88no—
118C23×C151—88no—
119C23×C151—84no—
120C23×C151—84no—
121C23×C151#9912yes—
122C23×C151C2×C22⋊C411yescharacteristic
123C23×C151#12014yes—
124D4×C151—44no—
125D4×C151—48no—
126D4×C151—44no—
127D4×C151—432no—
128D4×C151—432no—
129D4×C151—48no—
130D4×C151—44no—
131D4×C151—44no—
132C2×C4×C151—216no—
133C2×C4×C151—28no—
134C2×C4×C151—28no—
135C2×C4×C151—21no—
136C2×C4×C151—24no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—84no—
141C2×C4×C151—88no—
142C2×C4×C151#9912yes—
143C2×C4×C151C2×C22⋊C412yes—
144C22×C151—24no—
145C22×C151—24no—
146C22×C151—22no—
147C22×C151—22no—
148C22×C151—22no—
149C22×C151—24no—
150C22×C151—44no—
151C22×C151—44no—
152C22×C151—48no—
153C22×C151—44no—
154C22×C151—44no—
155C22×C151—42no—
156C22×C151—44no—
157C22×C151—82no—
158C22×C151—816no—
159C22×C151—82no—
160C22×C151—816no—
161C22×C151—84no—
162C22×C151—84no—
163C22×C151#35314yescomplemented
164C22×C151#37911yescharacteristic
165C22×C151C2×#9911yescharacteristic
166C22×C151C2×#9911yescharacteristic
167C4×C151—28no—
168C4×C151—22no—
169C4×C151—22no—
170C4×C151—164no—
171C2×C151—21no—
172C2×C151—24no—
173C2×C151—21no—
174C2×C151—44no—
175C2×C151—82no—
176C2×C151—84no—
177C2×C151#178111yescharacteristic
178C2×C151C2×#35312yes—
179#12693C15111yesmaximal, characteristic, direct product factor, Sylow
180C151#1269311yescharacteristic, direct product factor, Sylow
181C22×#127C2×C15111yescharacteristic
182C2×#353C2×C15114yescomplemented
183#1781C2×C15112yescomplemented
184C23×D4—22no—
185C23×D4C4×C15111yescharacteristic, complemented
186C23×D4C22×C15111yescharacteristic
187C2×#127—22no—
188C2×#127—28no—
189C2×#127C4×C15112yescomplemented
190C2×#127C22×C15112yes—
191C22×C42C4×C15111yescharacteristic, complemented
192C2×#99—22no—
193C2×#99C22×C15114yescomplemented
194#379—22no—
195#353—28no—
196C25—21no—
197C25D4×C15112yes—
198C22×D4—216no—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—21no—
204C22×D4—42no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4—416no—
208C22×D4—42no—
209C22×D4C2×C4×C15111yescharacteristic
210C22×D4C2×C4×C15112yes—
211C22×D4D4×C15112yes—
212C22×D4C23×C15111yescharacteristic
213C23×C4—21no—
214C23×C4C2×C4×C15111yescharacteristic
215#127—216no—
216#127—24no—
217#127—24no—
218#127—24no—
219#127D4×C15118yes—
220C2×C22⋊C4—24no—
221C2×C22⋊C4—44no—
222C2×C42—21no—
223C2×C42—24no—
224C2×C42C2×C4×C15112yes—
225#99—28no—
226#99—44no—
227C24—24no—
228C24—22no—
229C24—24no—
230C24—24no—
231C24—42no—
232C24—48no—
233C24—48no—
234C24—42no—
235C24—42no—
236C24C22⋊C4×C15111yescharacteristic
237C24C22⋊C4×C15112yes—
238C24C2×D4×C15112yes—
239C2×D4—24no—
240C2×D4—216no—
241C2×D4—24no—
242C2×D4—216no—
243C2×D4—24no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—42no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—416no—
254C2×D4—416no—
255C2×D4—416no—
256C2×D4—416no—
257C2×D4—464no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4C22⋊C4×C15114yescomplemented
261C2×D4C2×D4×C15114yes—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—44no—
269C22×C4C22⋊C4×C15111yescharacteristic
270C22×C4C22×C4×C15111yescharacteristic
271C22⋊C4—44no—
272C22⋊C4—44no—
273C22⋊C4—88no—
274C42—24no—
275C42—22no—
276C42C22⋊C4×C15114yescomplemented
277C23—24no—
278C23—21no—
279C23—21no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—24no—
284C23—22no—
285C23—22no—
286C23—48no—
287C23—44no—
288C23—44no—
289C23—416no—
290C23—416no—
291C23—48no—
292C23—48no—
293C23—48no—
294C23—42no—
295C23—42no—
296C23—84no—
297C23—88no—
298C23—88no—
299C23—84no—
300C23—84no—
301C23#99×C15112yes—
302C23C2×C22⋊C4×C15111yescharacteristic
303C23#120×C15114yes—
304D4—44no—
305D4—48no—
306D4—44no—
307D4—432no—
308D4—432no—
309D4—48no—
310D4—44no—
311D4—44no—
312C2×C4—216no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—21no—
316C2×C4—24no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—84no—
321C2×C4—88no—
322C2×C4#99×C15112yes—
323C2×C4C2×C22⋊C4×C15112yes—
324C22—24no—
325C22—24no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—24no—
330C22—44no—
331C22—44no—
332C22—48no—
333C22—44no—
334C22—44no—
335C22—42no—
336C22—44no—
337C22—82no—
338C22—816no—
339C22—82no—
340C22—816no—
341C22—84no—
342C22—84no—
343C22#353×C15114yescomplemented
344C22#379×C15111yescharacteristic
345C22C2×#99×C15111yescharacteristic
346C22C2×#99×C15111yescharacteristic
347C4—28no—
348C4—22no—
349C4—22no—
350C4—164no—
351C2—21no—
352C2—24no—
353C2—21no—
354C2—44no—
355C2—82no—
356C2—84no—
357C2#1781×C15111yescharacteristic
358C2C2×#353×C15112yes—
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radicalC22×#127×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C23×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C151C2semidirect
3. #1781×C151C2semidirect
5. C23×D4×C151C4semidirect
9. C2×#127×C151C4semidirect
11. C22×C42×C151C4semidirect
13. C2×#99×C151C22semidirect
80. C2×D4×C151C22⋊C4semidirect
96. C42×C151C22⋊C4semidirect
163. C22×C151#353semidirect
179. #12693C151direct (N × H)
180. C151#12693direct (N × H)
182. C2×#353C2×C151semidirect
183. #1781C2×C151semidirect
185. C23×D4C4×C151semidirect
189. C2×#127C4×C151semidirect
191. C22×C42C4×C151semidirect
193. C2×#99C22×C151semidirect
260. C2×D4C22⋊C4×C151semidirect
276. C42C22⋊C4×C151semidirect
343. C22#353×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1512
C2×#353×C1512
#1781×C1512
#12693151