Finite Group Databasebeta

← C151×#9479 #50314404

Subgroups — C151×#9479 #50314404

Order 38656.

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

normal subgroups only

This group has 838 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#2404×C151C211yesmaximal, characteristic
2#2312×C151C211yesmaximal, characteristic, complemented
3#1789×C151C212yesmaximal, complemented
4#1462×C151C211yesmaximal, characteristic, complemented
5#1284×C151C212yesmaximal, complemented
6C22×#41×C151C2211yescharacteristic
7C2×#120×C151—21no—
8C22×C22⋊C4×C151C2211yescharacteristic
9C2×#104×C151—24no—
10#407×C151C2212yes—
11#393×C151C412yescomplemented
12#392×C151C412yescomplemented
13#388×C151—24no—
14#386×C151—21no—
15#386×C151—22no—
16#381×C151C2211yescharacteristic
17#380×C151—21no—
18#379×C151—21no—
19C4×C22⋊C4×C151C2212yes—
20#323×C151—22no—
21C25×C151D411yescharacteristic
22C2×#41×C151—22no—
23C2×#41×C151—22no—
24C2×#41×C151—44no—
25C22×Q8×C151C2×C411yescharacteristic
26C22×D4×C151—22no—
27C22×D4×C151—21no—
28C22×D4×C151C2×C411yescharacteristic
29C23×C4×C151—21no—
30C23×C4×C151D411yescharacteristic
31C23×C4×C151C2311yescharacteristic
32C2×M16×C151—22no—
33#120×C151—44no—
34C2×C4⋊C4×C151—22no—
35C2×C22⋊C4×C151—22no—
36C2×C22⋊C4×C151—22no—
37C2×C22⋊C4×C151—22no—
38C2×C22⋊C4×C151—22no—
39C2×C22⋊C4×C151—22no—
40C2×C22⋊C4×C151—22no—
41C2×C22⋊C4×C151—22no—
42C2×C22⋊C4×C151—21no—
43C2×C22⋊C4×C151C2×C412yes—
44C2×C22⋊C4×C151D412yes—
45C2×C42×C151D414yescomplemented
46#104×C151—48no—
47C22⋊C8×C151—22no—
48C22⋊C8×C151—22no—
49#95×C151—22no—
50#95×C151—22no—
51#95×C151—22no—
52#95×C151—21no—
53#95×C151C2×C412yes—
54C24×C151—21no—
55C24×C151—21no—
56C24×C151—21no—
57C24×C151—42no—
58C24×C151—42no—
59C24×C151—81no—
60C24×C151C22⋊C412yes—
61C24×C151C2×D411yescharacteristic
62#41×C151—28no—
63#41×C151—44no—
64#41×C151—44no—
65#41×C151—44no—
66C2×Q8×C151—22no—
67C2×Q8×C151—42no—
68C2×D4×C151—24no—
69C2×D4×C151—22no—
70C2×D4×C151—42no—
71C2×D4×C151—42no—
72C2×D4×C151—41no—
73C2×D4×C151—41no—
74C2×D4×C151—44no—
75C2×D4×C151—44no—
76C2×D4×C151—82no—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151—22no—
81C22×C4×C151—24no—
82C22×C4×C151—42no—
83C22×C4×C151—42no—
84C22×C4×C151—42no—
85C22×C4×C151—42no—
86C22×C4×C151—81no—
87C22×C4×C151C22⋊C412yes—
88C22×C4×C151C22×C411yescharacteristic
89C22×C4×C151C2×D412yes—
90C22×C4×C151C2×D411yescharacteristic
91C22×C4×C151#4112yes—
92M16×C151—44no—
93C2×C8×C151—42no—
94C4⋊C4×C151—82no—
95C22⋊C4×C151—24no—
96C22⋊C4×C151—24no—
97C22⋊C4×C151—44no—
98C22⋊C4×C151—44no—
99C22⋊C4×C151—42no—
100C22⋊C4×C151—82no—
101C22⋊C4×C151—82no—
102C22⋊C4×C151—82no—
103C42×C151—44no—
104C23×C151—22no—
105C23×C151—22no—
106C23×C151—22no—
107C23×C151—22no—
108C23×C151—22no—
109C23×C151—22no—
110C23×C151—41no—
111C23×C151—42no—
112C23×C151—42no—
113C23×C151—42no—
114C23×C151—42no—
115C23×C151—42no—
116C23×C151—42no—
117C23×C151—41no—
118C23×C151—41no—
119C23×C151—42no—
120C23×C151—42no—
121C23×C151—81no—
122C23×C151—81no—
123C23×C151—88no—
124C23×C151C2×C22⋊C411yescharacteristic
125C23×C151#12011yescharacteristic
126C23×C151#12311yescharacteristic
127Q8×C151—24no—
128Q8×C151—42no—
129D4×C151—24no—
130D4×C151—42no—
131D4×C151—44no—
132D4×C151—44no—
133D4×C151—88no—
134C2×C4×C151—24no—
135C2×C4×C151—22no—
136C2×C4×C151—22no—
137C2×C4×C151—41no—
138C2×C4×C151—42no—
139C2×C4×C151—41no—
140C2×C4×C151—48no—
141C2×C4×C151—41no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151—42no—
145C2×C4×C151—42no—
146C2×C4×C151—44no—
147C2×C4×C151—44no—
148C2×C4×C151—42no—
149C2×C4×C151—42no—
150C2×C4×C151—44no—
151C2×C4×C151—81no—
152C2×C4×C151C4×D412yes—
153C2×C4×C151#12112yes—
154C8×C151—82no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—44no—
163C22×C151—44no—
164C22×C151—44no—
165C22×C151—42no—
166C22×C151—42no—
167C22×C151—42no—
168C22×C151—42no—
169C22×C151—82no—
170C22×C151—82no—
171C22×C151—84no—
172C22×C151—84no—
173C22×C151—81no—
174C22×C151—81no—
175C22×C151#38611yescharacteristic
176C22×C151#42112yes—
177C22×C151B(4,𝔽2)12yes—
178C4×C151—22no—
179C4×C151—22no—
180C4×C151—42no—
181C4×C151—42no—
182C4×C151—84no—
183C4×C151—82no—
184C2×C151—22no—
185C2×C151—22no—
186C2×C151—41no—
187C2×C151—82no—
188C2×C151—82no—
189C2×C151#188911yescharacteristic
190C2×C151#189711yescharacteristic
191C2×C151#191111yescharacteristic
192#9479C15111yesmaximal, characteristic, direct product factor, Sylow
193C151#947911yescharacteristic, direct product factor, Sylow
194#2404C2×C15111yescharacteristic
195#2312C2×C15111yescharacteristic, complemented
196#1789C2×C15112yescomplemented
197#1462C2×C15111yescharacteristic, complemented
198#1284C2×C15112yescomplemented
199C22×#41C22×C15111yescharacteristic
200C2×#120—21no—
201C22×C22⋊C4C22×C15111yescharacteristic
202C2×#104—24no—
203#407C22×C15112yes—
204#393C4×C15112yescomplemented
205#392C4×C15112yescomplemented
206#388—24no—
207#386—21no—
208#386—22no—
209#381C22×C15111yescharacteristic
210#380—21no—
211#379—21no—
212C4×C22⋊C4C22×C15112yes—
213#323—22no—
214C25D4×C15111yescharacteristic
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—44no—
218C22×Q8C2×C4×C15111yescharacteristic
219C22×D4—21no—
220C22×D4—22no—
221C22×D4C2×C4×C15111yescharacteristic
222C23×C4—21no—
223C23×C4D4×C15111yescharacteristic
224C23×C4C23×C15111yescharacteristic
225C2×M16—22no—
226#120—44no—
227C2×C4⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4C2×C4×C15112yes—
237C2×C22⋊C4D4×C15112yes—
238C2×C42D4×C15114yescomplemented
239#104—48no—
240C22⋊C8—22no—
241C22⋊C8—22no—
242#95—22no—
243#95—22no—
244#95—22no—
245#95—21no—
246#95C2×C4×C15112yes—
247C24—21no—
248C24—21no—
249C24—21no—
250C24—42no—
251C24—42no—
252C24—81no—
253C24C22⋊C4×C15112yes—
254C24C2×D4×C15111yescharacteristic
255#41—28no—
256#41—44no—
257#41—44no—
258#41—44no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×D4—24no—
262C2×D4—22no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—82no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—81no—
280C22×C4C22⋊C4×C15112yes—
281C22×C4C22×C4×C15111yescharacteristic
282C22×C4C2×D4×C15112yes—
283C22×C4C2×D4×C15111yescharacteristic
284C22×C4#41×C15112yes—
285M16—44no—
286C2×C8—42no—
287C4⋊C4—82no—
288C22⋊C4—24no—
289C22⋊C4—24no—
290C22⋊C4—44no—
291C22⋊C4—42no—
292C22⋊C4—44no—
293C22⋊C4—82no—
294C22⋊C4—82no—
295C22⋊C4—82no—
296C42—44no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—41no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—41no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—88no—
317C23C2×C22⋊C4×C15111yescharacteristic
318C23#120×C15111yescharacteristic
319C23#123×C15111yescharacteristic
320Q8—24no—
321Q8—42no—
322D4—24no—
323D4—42no—
324D4—44no—
325D4—44no—
326D4—88no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—48no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—81no—
345C2×C4C4×D4×C15112yes—
346C2×C4#121×C15112yes—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22—44no—
357C22—44no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—82no—
363C22—84no—
364C22—82no—
365C22—84no—
366C22—81no—
367C22—81no—
368C22#386×C15111yescharacteristic
369C22#421×C15112yes—
370C22B(4,𝔽2)×C15112yes—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—42no—
375C4—82no—
376C4—84no—
377C2—22no—
378C2—22no—
379C2—41no—
380C2—82no—
381C2—82no—
382C2#1889×C15111yescharacteristic
383C2#1897×C15111yescharacteristic
384C2#1911×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radical#2404×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2312×C151C2semidirect
3. #1789×C151C2semidirect
4. #1462×C151C2semidirect
5. #1284×C151C2semidirect
11. #393×C151C4semidirect
12. #392×C151C4semidirect
45. C2×C42×C151D4semidirect
192. #9479C151direct (N × H)
193. C151#9479direct (N × H)
195. #2312C2×C151semidirect
196. #1789C2×C151semidirect
197. #1462C2×C151semidirect
198. #1284C2×C151semidirect
204. #393C4×C151semidirect
205. #392C4×C151semidirect
238. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
#2404×C1512
#2312×C1512
#1789×C1512
#1462×C1512
#1284×C1512
#9479151