Finite Group Databasebeta

← C151×#9964 #50314889

Subgroups — C151×#9964 #50314889

Order 38656.

944 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 138 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×#448×C151C212yesmaximal, complemented
2#2656×C151C211yesmaximal, characteristic
3C2×#327×C151C212yesmaximal, complemented
4#1446×C151C211yesmaximal, characteristic, complemented
5#1280×C151C211yesmaximal, characteristic, complemented
6C23×Q8×C151C2211yescharacteristic
7C22×SD16×C151—22no—
8C2×#121×C151—22no—
9C2×#121×C151C2212yes—
10#448×C151—24no—
11#448×C151—24no—
12C2×#103×C151—22no—
13C2×C22⋊C8×C151C2212yes—
14#399×C151—22no—
15#392×C151—22no—
16C2×#95×C151—22no—
17C2×#95×C151C2211yescharacteristic
18C2×#95×C151C2211yescharacteristic
19#327×C151—24no—
20C22×Q8×C151—22no—
21C22×Q8×C151—22no—
22C22×Q8×C151—21no—
23C22×Q8×C151—44no—
24C22×Q8×C151D412yescomplemented
25C22×D4×C151—22no—
26C22×D4×C151—22no—
27C22×D4×C151D412yes—
28C23×C4×C151—21no—
29C23×C4×C151—21no—
30C23×C4×C151D412yes—
31C23×C4×C151C2311yescharacteristic
32C2×SD16×C151—28no—
33C2×SD16×C151—48no—
34C22×C8×C151—22no—
35#121×C151—22no—
36#121×C151—22no—
37#121×C151—22no—
38#121×C151—22no—
39#121×C151—44no—
40#121×C151—44no—
41C2×C4⋊C4×C151—22no—
42C2×C4⋊C4×C151D412yes—
43C2×C22⋊C4×C151—24no—
44C2×C22⋊C4×C151—22no—
45#103×C151—28no—
46C22⋊C8×C151—22no—
47C22⋊C8×C151D414yescomplemented
48#95×C151—22no—
49#95×C151—22no—
50#95×C151—44no—
51C24×C151—22no—
52C24×C151C2×D411yescharacteristic
53C2×Q8×C151—28no—
54C2×Q8×C151—24no—
55C2×Q8×C151—44no—
56C2×Q8×C151—44no—
57C2×Q8×C151—44no—
58C2×Q8×C151—48no—
59C2×Q8×C151—42no—
60C2×D4×C151—22no—
61C2×D4×C151—22no—
62C2×D4×C151—44no—
63C2×D4×C151—44no—
64C2×D4×C151—42no—
65C2×D4×C151—42no—
66C2×D4×C151—44no—
67C2×D4×C151—44no—
68C2×D4×C151—82no—
69C2×D4×C151—82no—
70C22×C4×C151—24no—
71C22×C4×C151—22no—
72C22×C4×C151—22no—
73C22×C4×C151—22no—
74C22×C4×C151—22no—
75C22×C4×C151—22no—
76C22×C4×C151—42no—
77C22×C4×C151—42no—
78C22×C4×C151—41no—
79C22×C4×C151—41no—
80C22×C4×C151—42no—
81C22×C4×C151—42no—
82C22×C4×C151—42no—
83C22×C4×C151—41no—
84C22×C4×C151—41no—
85C22×C4×C151—42no—
86C22×C4×C151SD1614yescomplemented
87C22×C4×C151C2×D412yes—
88C22×C4×C151C2×D411yescharacteristic
89C22×C4×C151C2×D412yes—
90C22×C4×C151#4111yescharacteristic
91SD16×C151—416no—
92C2×C8×C151—24no—
93C2×C8×C151—44no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—22no—
96C4⋊C4×C151—44no—
97C22⋊C4×C151—48no—
98C22⋊C4×C151—42no—
99C22⋊C4×C151—42no—
100C23×C151—21no—
101C23×C151—21no—
102C23×C151—22no—
103C23×C151—42no—
104C23×C151—44no—
105C23×C151—42no—
106C23×C151—42no—
107C23×C151—44no—
108C23×C151#12011yescharacteristic
109C23×C151#12111yescharacteristic
110C23×C151#12711yescharacteristic
111C23×C151C2×SD1612yes—
112C23×C151AGL(1,ℤ/8)12yes—
113Q8×C151—28no—
114Q8×C151—44no—
115Q8×C151—48no—
116D4×C151—44no—
117D4×C151—82no—
118D4×C151—88no—
119D4×C151—84no—
120D4×C151—82no—
121D4×C151—82no—
122C2×C4×C151—24no—
123C2×C4×C151—24no—
124C2×C4×C151—24no—
125C2×C4×C151—41no—
126C2×C4×C151—42no—
127C2×C4×C151—41no—
128C2×C4×C151—42no—
129C2×C4×C151—44no—
130C2×C4×C151—42no—
131C2×C4×C151—42no—
132C2×C4×C151—44no—
133C2×C4×C151—42no—
134C2×C4×C151—44no—
135C2×C4×C151—44no—
136C2×C4×C151—42no—
137C2×C4×C151—42no—
138C2×C4×C151—44no—
139C2×C4×C151—82no—
140C2×C4×C151—82no—
141C2×C4×C151—81no—
142C2×C4×C151—81no—
143C2×C4×C151#12012yes—
144C2×C4×C151#12112yes—
145C8×C151—44no—
146C22×C151—22no—
147C22×C151—22no—
148C22×C151—22no—
149C22×C151—22no—
150C22×C151—21no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—84no—
155C22×C151—84no—
156C22×C151—82no—
157C22×C151—82no—
158C22×C151—82no—
159C22×C151#39211yescharacteristic
160C22×C151#45012yes—
161C22×C151#45511yescharacteristic
162C22×C151#45611yescharacteristic
163C22×C151B(4,𝔽2)12yes—
164C22×C151#46012yes—
165C22×C151#49211yescharacteristic
166C22×C151#49611yescharacteristic
167C4×C151—22no—
168C4×C151—22no—
169C4×C151—44no—
170C4×C151—44no—
171C4×C151—82no—
172C4×C151—82no—
173C2×C151—21no—
174C2×C151—22no—
175C2×C151—21no—
176C2×C151—162no—
177C2×C151#160112yes—
178C2×C151#160412yes—
179C2×C151#200711yescharacteristic
180C2×C151#201411yescharacteristic
181C2×C151#202111yescharacteristic
182#9964C15111yesmaximal, characteristic, direct product factor, Sylow
183C151#996411yescharacteristic, direct product factor, Sylow
184C2×#448C2×C15112yescomplemented
185#2656C2×C15111yescharacteristic
186C2×#327C2×C15112yescomplemented
187#1446C2×C15111yescharacteristic, complemented
188#1280C2×C15111yescharacteristic, complemented
189C23×Q8C22×C15111yescharacteristic
190C22×SD16—22no—
191C2×#121—22no—
192C2×#121C22×C15112yes—
193#448—24no—
194#448—24no—
195C2×#103—22no—
196C2×C22⋊C8C22×C15112yes—
197#399—22no—
198#392—22no—
199C2×#95—22no—
200C2×#95C22×C15111yescharacteristic
201C2×#95C22×C15111yescharacteristic
202#327—24no—
203C22×Q8—21no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—44no—
207C22×Q8D4×C15112yescomplemented
208C22×D4—22no—
209C22×D4—22no—
210C22×D4D4×C15112yes—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4D4×C15112yes—
214C23×C4C23×C15111yescharacteristic
215C2×SD16—28no—
216C2×SD16—48no—
217C22×C8—22no—
218#121—22no—
219#121—22no—
220#121—22no—
221#121—22no—
222#121—44no—
223#121—44no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4D4×C15112yes—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—22no—
228#103—28no—
229C22⋊C8—22no—
230C22⋊C8D4×C15114yescomplemented
231#95—22no—
232#95—22no—
233#95—44no—
234C24—22no—
235C24C2×D4×C15111yescharacteristic
236C2×Q8—28no—
237C2×Q8—24no—
238C2×Q8—44no—
239C2×Q8—44no—
240C2×Q8—44no—
241C2×Q8—48no—
242C2×Q8—42no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—82no—
252C2×D4—82no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4SD16×C15114yescomplemented
270C22×C4C2×D4×C15112yes—
271C22×C4C2×D4×C15111yescharacteristic
272C22×C4C2×D4×C15112yes—
273C22×C4#41×C15111yescharacteristic
274SD16—416no—
275C2×C8—24no—
276C2×C8—44no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—44no—
280C22⋊C4—48no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C23—21no—
284C23—21no—
285C23—22no—
286C23—42no—
287C23—44no—
288C23—42no—
289C23—42no—
290C23—44no—
291C23#120×C15111yescharacteristic
292C23#121×C15111yescharacteristic
293C23#127×C15111yescharacteristic
294C23C2×SD16×C15112yes—
295C23AGL(1,ℤ/8)×C15112yes—
296Q8—28no—
297Q8—44no—
298Q8—48no—
299D4—44no—
300D4—82no—
301D4—88no—
302D4—84no—
303D4—82no—
304D4—82no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4#120×C15112yes—
327C2×C4#121×C15112yes—
328C8—44no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—84no—
338C22—84no—
339C22—82no—
340C22—82no—
341C22—82no—
342C22#392×C15111yescharacteristic
343C22#450×C15112yes—
344C22#455×C15111yescharacteristic
345C22#456×C15111yescharacteristic
346C22B(4,𝔽2)×C15112yes—
347C22#460×C15112yes—
348C22#492×C15111yescharacteristic
349C22#496×C15111yescharacteristic
350C4—22no—
351C4—22no—
352C4—44no—
353C4—44no—
354C4—82no—
355C4—82no—
356C2—21no—
357C2—22no—
358C2—21no—
359C2—162no—
360C2#1601×C15112yes—
361C2#1604×C15112yes—
362C2#2007×C15111yescharacteristic
363C2#2014×C15111yescharacteristic
364C2#2021×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC23×C4C23×C151
prime radical#2656×C151C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#448×C151C2semidirect
3. C2×#327×C151C2semidirect
4. #1446×C151C2semidirect
5. #1280×C151C2semidirect
24. C22×Q8×C151D4semidirect
47. C22⋊C8×C151D4semidirect
86. C22×C4×C151SD16semidirect
182. #9964C151direct (N × H)
183. C151#9964direct (N × H)
184. C2×#448C2×C151semidirect
186. C2×#327C2×C151semidirect
187. #1446C2×C151semidirect
188. #1280C2×C151semidirect
207. C22×Q8D4×C151semidirect
230. C22⋊C8D4×C151semidirect
269. C22×C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1512
#2656×C1512
C2×#327×C1512
#1446×C1512
#1280×C1512
#9964151