Finite Group Databasebeta

← C151×#9307 #50314232

Subgroups — C151×#9307 #50314232

Order 38656.

464 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3077×C151C211yesmaximal, characteristic
2#2975×C151C211yesmaximal, characteristic
3#1804×C151C211yesmaximal, characteristic
4#1518×C151C211yesmaximal, characteristic, complemented
5#1481×C151C211yesmaximal, characteristic, complemented
6#1301×C151C211yesmaximal, characteristic, complemented
7#1286×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9C2×C4×D4×C151C2211yescharacteristic
10#478×C151—22no—
11#476×C151C412yescomplemented
12#474×C151C412yescomplemented
13#436×C151—22no—
14#436×C151—22no—
15#431×C151C2211yescharacteristic
16#431×C151C2211yescharacteristic
17#428×C151—21no—
18#423×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20#418×C151—21no—
21C2×#102×C151—21no—
22#407×C151—22no—
23#382×C151C2211yescharacteristic
24#340×C151—21no—
25#328×C151—22no—
26Q8⋊C8×C151—22no—
27C22×D4×C151D411yescharacteristic
28C23×C4×C151—21no—
29C2×M16×C151—21no—
30C2×M16×C151—24no—
31C22×C8×C151—21no—
32C4⋊Q8×C151C2×C411yescharacteristic
33C4⋊Q8×C151C2×C411yescharacteristic
34#125×C151—21no—
35C22⋊Q8×C151—21no—
36C22⋊Q8×C151—21no—
37C4×Q8×C151—21no—
38C4×Q8×C151—21no—
39C4×D4×C151—21no—
40C4×D4×C151—21no—
41C4×D4×C151C2×C412yes—
42C4×D4×C151D412yes—
43#117×C151—21no—
44C2×C4⋊C4×C151—21no—
45C2×C4⋊C4×C151D411yescharacteristic
46C2×C22⋊C4×C151—21no—
47C2×C42×C151C2311yescharacteristic
48#107×C151—22no—
49#106×C151—22no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55C4⋊C8×C151C2×C412yes—
56#102×C151—22no—
57#102×C151—22no—
58#102×C151—42no—
59C22⋊C8×C151—24no—
60C22⋊C8×C151—21no—
61C22⋊C8×C151D412yes—
62C4×C8×C151—21no—
63C4×C8×C151D412yes—
64#95×C151—21no—
65#95×C151—21no—
66C24×C151—21no—
67C2×Q8×C151—21no—
68C2×Q8×C151—21no—
69C2×D4×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—21no—
72C2×D4×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151C22⋊C412yes—
75C22×C4×C151—21no—
76C22×C4×C151—22no—
77C22×C4×C151—22no—
78C22×C4×C151—41no—
79C22×C4×C151—82no—
80C22×C4×C151C2×D411yescharacteristic
81C22×C4×C151C2×D411yescharacteristic
82C22×C4×C151#4111yescharacteristic
83M16×C151—41no—
84M16×C151—41no—
85M16×C151—84no—
86C2×C8×C151—22no—
87C2×C8×C151—22no—
88C2×C8×C151—22no—
89C2×C8×C151—41no—
90C2×C8×C151—41no—
91C2×C8×C151—41no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—21no—
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151—41no—
98C4⋊C4×C151—41no—
99C4⋊C4×C151—41no—
100C4⋊C4×C151—41no—
101C4⋊C4×C151C22⋊C412yes—
102C22⋊C4×C151—22no—
103C22⋊C4×C151—22no—
104C22⋊C4×C151—41no—
105C42×C151—41no—
106C42×C151C22×C411yescharacteristic
107C42×C151C2×D411yescharacteristic
108C42×C151C2×D411yescharacteristic
109C42×C151#4111yescharacteristic
110C23×C151—22no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151—81no—
114C23×C151—81no—
115C23×C151#12111yescharacteristic
116Q8×C151—42no—
117Q8×C151—81no—
118D4×C151—22no—
119D4×C151—22no—
120D4×C151—41no—
121D4×C151—41no—
122C2×C4×C151—22no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—44no—
126C2×C4×C151—41no—
127C2×C4×C151—41no—
128C2×C4×C151—82no—
129C2×C4×C151—81no—
130C2×C4×C151—81no—
131C2×C4×C151—81no—
132C2×C4×C151—81no—
133C2×C4×C151C2×C22⋊C411yescharacteristic
134C2×C4×C151C4×D411yescharacteristic
135C2×C4×C151C4×D411yescharacteristic
136C2×C4×C151#12011yescharacteristic
137C2×C4×C151#12111yescharacteristic
138C2×C4×C151#12311yescharacteristic
139C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C151#13711yescharacteristic
141C2×C4×C151#13711yescharacteristic
142C2×C4×C151#13711yescharacteristic
143C8×C151—42no—
144C8×C151—42no—
145C8×C151—42no—
146C8×C151—81no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—42no—
150C22×C151—42no—
151C22×C151—42no—
152C22×C151—82no—
153C22×C151—82no—
154C22×C151#38611yescharacteristic
155C22×C151#46811yescharacteristic
156C22×C151#47011yescharacteristic
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—42no—
162C4×C151—81no—
163C4×C151—81no—
164C4×C151—161no—
165C4×C151#41711yescharacteristic
166C4×C151#41911yescharacteristic
167C4×C151#46811yescharacteristic
168C4×C151#47011yescharacteristic
169C2×C151—21no—
170C2×C151—21no—
171C2×C151—82no—
172C2×C151#188111yescharacteristic
173C2×C151#189411yescharacteristic
174C2×C151#190411yescharacteristic
175#9307C15111yesmaximal, characteristic, direct product factor, Sylow
176C151#930711yescharacteristic, direct product factor, Sylow
177#3077C2×C15111yescharacteristic
178#2975C2×C15111yescharacteristic
179#1804C2×C15111yescharacteristic
180#1518C2×C15111yescharacteristic, complemented
181#1481C2×C15111yescharacteristic, complemented
182#1301C2×C15111yescharacteristic, complemented
183#1286C2×C15111yescharacteristic, complemented
184#533C22×C15111yescharacteristic
185C2×C4×D4C22×C15111yescharacteristic
186#478—22no—
187#476C4×C15112yescomplemented
188#474C4×C15112yescomplemented
189#436—22no—
190#436—22no—
191#431C22×C15111yescharacteristic
192#431C22×C15111yescharacteristic
193#428—21no—
194#423C22×C15111yescharacteristic
195C2×C4⋊C8C22×C15111yescharacteristic
196#418—21no—
197C2×#102—21no—
198#407—22no—
199#382C22×C15111yescharacteristic
200#340—21no—
201#328—22no—
202Q8⋊C8—22no—
203C22×D4D4×C15111yescharacteristic
204C23×C4—21no—
205C2×M16—21no—
206C2×M16—24no—
207C22×C8—21no—
208C4⋊Q8C2×C4×C15111yescharacteristic
209C4⋊Q8C2×C4×C15111yescharacteristic
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4C2×C4×C15112yes—
218C4×D4D4×C15112yes—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4×C15111yescharacteristic
222C2×C22⋊C4—21no—
223C2×C42C23×C15111yescharacteristic
224#107—22no—
225#106—22no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8C2×C4×C15112yes—
232#102—22no—
233#102—22no—
234#102—42no—
235C22⋊C8—24no—
236C22⋊C8—21no—
237C22⋊C8D4×C15112yes—
238C4×C8—21no—
239C4×C8D4×C15112yes—
240#95—21no—
241#95—21no—
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4C22⋊C4×C15112yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—82no—
256C22×C4C2×D4×C15111yescharacteristic
257C22×C4C2×D4×C15111yescharacteristic
258C22×C4#41×C15111yescharacteristic
259M16—41no—
260M16—41no—
261M16—84no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4C22⋊C4×C15112yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C42—41no—
282C42C22×C4×C15111yescharacteristic
283C42C2×D4×C15111yescharacteristic
284C42C2×D4×C15111yescharacteristic
285C42#41×C15111yescharacteristic
286C23—22no—
287C23—41no—
288C23—41no—
289C23—81no—
290C23—81no—
291C23#121×C15111yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—22no—
295D4—22no—
296D4—41no—
297D4—41no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—82no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×C22⋊C4×C15111yescharacteristic
310C2×C4C4×D4×C15111yescharacteristic
311C2×C4C4×D4×C15111yescharacteristic
312C2×C4#120×C15111yescharacteristic
313C2×C4#121×C15111yescharacteristic
314C2×C4#123×C15111yescharacteristic
315C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
316C2×C4#137×C15111yescharacteristic
317C2×C4#137×C15111yescharacteristic
318C2×C4#137×C15111yescharacteristic
319C8—42no—
320C8—42no—
321C8—42no—
322C8—81no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#386×C15111yescharacteristic
331C22#468×C15111yescharacteristic
332C22#470×C15111yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4#417×C15111yescharacteristic
342C4#419×C15111yescharacteristic
343C4#468×C15111yescharacteristic
344C4#470×C15111yescharacteristic
345C2—21no—
346C2—21no—
347C2—82no—
348C2#1881×C15111yescharacteristic
349C2#1894×C15111yescharacteristic
350C2#1904×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1518×C151C2semidirect
5. #1481×C151C2semidirect
6. #1301×C151C2semidirect
7. #1286×C151C2semidirect
11. #476×C151C4semidirect
12. #474×C151C4semidirect
175. #9307C151direct (N × H)
176. C151#9307direct (N × H)
180. #1518C2×C151semidirect
181. #1481C2×C151semidirect
182. #1301C2×C151semidirect
183. #1286C2×C151semidirect
187. #476C4×C151semidirect
188. #474C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3077×C1512
#2975×C1512
#1804×C1512
#1518×C1512
#1481×C1512
#1301×C1512
#1286×C1512
#9307151