Finite Group Databasebeta

← C151×#9176 #50314101

Subgroups — C151×#9176 #50314101

Order 38656.

490 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3078×C151C211yesmaximal, characteristic
2#2351×C151C211yesmaximal, characteristic
3#1518×C151C211yesmaximal, characteristic
4#1503×C151C211yesmaximal, characteristic
5#1479×C151C211yesmaximal, characteristic
6#1303×C151C211yesmaximal, characteristic
7#1286×C151C211yesmaximal, characteristic
8#533×C151C2211yescharacteristic
9C2×C4×Q8×C151—21no—
10C2×C4×Q8×C151C2211yescharacteristic
11#479×C151—22no—
12#477×C151C412yescomplemented
13#475×C151C412yescomplemented
14#431×C151C2211yescharacteristic
15#431×C151C2211yescharacteristic
16#428×C151—21no—
17#423×C151C2211yescharacteristic
18#419×C151—21no—
19#389×C151—21no—
20#389×C151—22no—
21#382×C151—21no—
22#382×C151C2211yescharacteristic
23C4×C4⋊C4×C151—21no—
24C4×C4⋊C4×C151C2211yescharacteristic
25#328×C151—21no—
26#328×C151—21no—
27#328×C151—22no—
28Q8⋊C8×C151—22no—
29C22×Q8×C151D411yescharacteristic
30C2×M16×C151—21no—
31C4⋊Q8×C151C2×C411yescharacteristic
32C4⋊Q8×C151C2×C411yescharacteristic
33#125×C151—21no—
34C22⋊Q8×C151—21no—
35C22⋊Q8×C151—21no—
36C4×Q8×C151—21no—
37C4×Q8×C151—21no—
38C4×Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151—42no—
41C4×Q8×C151—42no—
42C4×Q8×C151C2×C412yes—
43C4×Q8×C151D412yes—
44#117×C151—21no—
45C2×C4⋊C4×C151—21no—
46C2×C4⋊C4×C151—22no—
47C2×C4⋊C4×C151—22no—
48C2×C4⋊C4×C151—21no—
49C2×C4⋊C4×C151—21no—
50C2×C4⋊C4×C151D411yescharacteristic
51C2×C42×C151—21no—
52C2×C42×C151—22no—
53C2×C42×C151—21no—
54C2×C42×C151C2311yescharacteristic
55#107×C151—22no—
56#106×C151—22no—
57C4⋊C8×C151—21no—
58C4⋊C8×C151—21no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151C2×C412yes—
61#103×C151—22no—
62#103×C151—22no—
63C22⋊C8×C151—21no—
64C22⋊C8×C151—21no—
65C4×C8×C151—21no—
66C4×C8×C151—21no—
67#95×C151—22no—
68#95×C151—21no—
69#95×C151D411yescharacteristic
70#95×C151D411yescharacteristic
71#95×C151D412yes—
72C2×Q8×C151—21no—
73C2×Q8×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—21no—
76C2×Q8×C151—21no—
77C2×Q8×C151C22⋊C412yes—
78C2×Q8×C151SD1612yes—
79C2×Q8×C151Q1612yes—
80C22×C4×C151—21no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—21no—
84C22×C4×C151—22no—
85C22×C4×C151C2×D411yescharacteristic
86C22×C4×C151C2×D411yescharacteristic
87C22×C4×C151C2×D411yescharacteristic
88M16×C151—41no—
89M16×C151—41no—
90C2×C8×C151—22no—
91C2×C8×C151—41no—
92C2×C8×C151—41no—
93C4⋊C4×C151—22no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—21no—
100C4⋊C4×C151—42no—
101C4⋊C4×C151—44no—
102C4⋊C4×C151—44no—
103C4⋊C4×C151—41no—
104C4⋊C4×C151—41no—
105C4⋊C4×C151—41no—
106C4⋊C4×C151—41no—
107C4⋊C4×C151C22⋊C412yes—
108C22⋊C4×C151—41no—
109C42×C151—22no—
110C42×C151—22no—
111C42×C151—44no—
112C42×C151—41no—
113C42×C151—41no—
114C42×C151—41no—
115C42×C151C22×C411yescharacteristic
116C42×C151C2×D411yescharacteristic
117C42×C151#4111yescharacteristic
118C42×C151#4111yescharacteristic
119C23×C151#12011yescharacteristic
120Q8×C151—22no—
121Q8×C151—22no—
122Q8×C151—22no—
123Q8×C151—81no—
124Q8×C151—81no—
125Q8×C151#10314yes—
126C2×C4×C151—22no—
127C2×C4×C151—22no—
128C2×C4×C151—22no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—42no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—42no—
138C2×C4×C151—41no—
139C2×C4×C151—42no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151C2×C22⋊C411yescharacteristic
145C2×C4×C151C4×D411yescharacteristic
146C2×C4×C151C4×D411yescharacteristic
147C2×C4×C151#12111yescharacteristic
148C2×C4×C151#12111yescharacteristic
149C2×C4×C151#12311yescharacteristic
150C2×C4×C151C2×SD1611yescharacteristic
151C2×C4×C151C2×Q1611yescharacteristic
152C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C151#13711yescharacteristic
154C8×C151—42no—
155C8×C151—81no—
156C8×C151—81no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151#38611yescharacteristic
160C22×C151#45011yescharacteristic
161C22×C151#45111yescharacteristic
162C4×C151—24no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—42no—
168C4×C151—42no—
169C4×C151—82no—
170C4×C151—81no—
171C4×C151—81no—
172C4×C151—81no—
173C4×C151C2×#10311yescharacteristic
174C4×C151#41711yescharacteristic
175C4×C151#48311yescharacteristic
176C4×C151#48411yescharacteristic
177C2×C151—21no—
178C2×C151—21no—
179C2×C151#187211yescharacteristic
180C2×C151#190511yescharacteristic
181C2×C151#190611yescharacteristic
182#9176C15111yesmaximal, characteristic, direct product factor, Sylow
183C151#917611yescharacteristic, direct product factor, Sylow
184#3078C2×C15111yescharacteristic
185#2351C2×C15111yescharacteristic
186#1518C2×C15111yescharacteristic
187#1503C2×C15111yescharacteristic
188#1479C2×C15111yescharacteristic
189#1303C2×C15111yescharacteristic
190#1286C2×C15111yescharacteristic
191#533C22×C15111yescharacteristic
192C2×C4×Q8—21no—
193C2×C4×Q8C22×C15111yescharacteristic
194#479—22no—
195#477C4×C15112yescomplemented
196#475C4×C15112yescomplemented
197#431C22×C15111yescharacteristic
198#431C22×C15111yescharacteristic
199#428—21no—
200#423C22×C15111yescharacteristic
201#419—21no—
202#389—21no—
203#389—22no—
204#382—21no—
205#382C22×C15111yescharacteristic
206C4×C4⋊C4—21no—
207C4×C4⋊C4C22×C15111yescharacteristic
208#328—21no—
209#328—21no—
210#328—22no—
211Q8⋊C8—22no—
212C22×Q8D4×C15111yescharacteristic
213C2×M16—21no—
214C4⋊Q8C2×C4×C15111yescharacteristic
215C4⋊Q8C2×C4×C15111yescharacteristic
216#125—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—42no—
224C4×Q8—42no—
225C4×Q8C2×C4×C15112yes—
226C4×Q8D4×C15112yes—
227#117—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C15111yescharacteristic
234C2×C42—21no—
235C2×C42—22no—
236C2×C42—21no—
237C2×C42C23×C15111yescharacteristic
238#107—22no—
239#106—22no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8C2×C4×C15112yes—
244#103—22no—
245#103—22no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250#95—22no—
251#95—21no—
252#95D4×C15111yescharacteristic
253#95D4×C15111yescharacteristic
254#95D4×C15112yes—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8C22⋊C4×C15112yes—
261C2×Q8SD16×C15112yes—
262C2×Q8Q16×C15112yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4C2×D4×C15111yescharacteristic
269C22×C4C2×D4×C15111yescharacteristic
270C22×C4C2×D4×C15111yescharacteristic
271M16—41no—
272M16—41no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—44no—
284C4⋊C4—42no—
285C4⋊C4—44no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C15112yes—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42—44no—
295C42—41no—
296C42—41no—
297C42—41no—
298C42C22×C4×C15111yescharacteristic
299C42C2×D4×C15111yescharacteristic
300C42#41×C15111yescharacteristic
301C42#41×C15111yescharacteristic
302C23#120×C15111yescharacteristic
303Q8—22no—
304Q8—22no—
305Q8—22no—
306Q8—81no—
307Q8—81no—
308Q8#103×C15114yes—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4C2×C22⋊C4×C15111yescharacteristic
328C2×C4C4×D4×C15111yescharacteristic
329C2×C4C4×D4×C15111yescharacteristic
330C2×C4#121×C15111yescharacteristic
331C2×C4#121×C15111yescharacteristic
332C2×C4#123×C15111yescharacteristic
333C2×C4C2×SD16×C15111yescharacteristic
334C2×C4C2×Q16×C15111yescharacteristic
335C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
336C2×C4#137×C15111yescharacteristic
337C8—42no—
338C8—81no—
339C8—81no—
340C22—21no—
341C22—21no—
342C22#386×C15111yescharacteristic
343C22#450×C15111yescharacteristic
344C22#451×C15111yescharacteristic
345C4—24no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—42no—
352C4—82no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4C2×#103×C15111yescharacteristic
357C4#417×C15111yescharacteristic
358C4#483×C15111yescharacteristic
359C4#484×C15111yescharacteristic
360C2—21no—
361C2—21no—
362C2#1872×C15111yescharacteristic
363C2#1905×C15111yescharacteristic
364C2#1906×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151#120
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
12. #477×C151C4semidirect
13. #475×C151C4semidirect
182. #9176C151direct (N × H)
183. C151#9176direct (N × H)
195. #477C4×C151semidirect
196. #475C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3078×C1512
#2351×C1512
#1518×C1512
#1503×C1512
#1479×C1512
#1303×C1512
#1286×C1512
#9176151