Finite Group Databasebeta

← C151×#9745 #50314670

Subgroups — C151×#9745 #50314670

Order 38656.

442 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C151C211yesmaximal, characteristic
2#1988×C151C211yesmaximal, characteristic
3#1987×C151C211yesmaximal, characteristic
4#1770×C151C211yesmaximal, characteristic
5C2×#334×C151C211yesmaximal, characteristic
6C2×#333×C151C211yesmaximal, characteristic
7C2×#332×C151C211yesmaximal, characteristic
8C2×C4⋊Q8×C151C2211yescharacteristic
9C2×C4⋊Q8×C151C2211yescharacteristic
10#487×C151—22no—
11#487×C151C414yescomplemented
12C2×C4⋊C8×C151C2211yescharacteristic
13C2×C4⋊C8×C151C2211yescharacteristic
14C2×C4⋊C8×C151C2211yescharacteristic
15C2×#103×C151—21no—
16C2×#103×C151—21no—
17C2×#97×C151—21no—
18C2×C4×C8×C151C2211yescharacteristic
19C4×C4⋊C4×C151C2211yescharacteristic
20#340×C151—22no—
21#340×C151—22no—
22#336×C151—21no—
23#334×C151—22no—
24#333×C151—22no—
25#332×C151—22no—
26C22×Q8×C151—21no—
27C22×Q8×C151—21no—
28C22×C8×C151—21no—
29C22×C8×C151—21no—
30C22×C8×C151—21no—
31C22×C8×C151D411yescharacteristic
32C22×C8×C151D411yescharacteristic
33C4⋊Q8×C151—21no—
34C4⋊Q8×C151—21no—
35C4⋊Q8×C151—21no—
36C4⋊Q8×C151—21no—
37C4⋊Q8×C151—21no—
38C4⋊Q8×C151—21no—
39C4⋊Q8×C151C2×C412yes—
40C4⋊Q8×C151C2×C412yes—
41C2×C4⋊C4×C151—21no—
42C2×C4⋊C4×C151—21no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—21no—
45C2×C4⋊C4×C151D412yes—
46C2×C42×C151—21no—
47C2×C42×C151C2311yescharacteristic
48C4⋊C8×C151—21no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151D412yes—
54#103×C151—24no—
55#103×C151—24no—
56#97×C151—42no—
57C4×C8×C151C2×C412yes—
58C4×C8×C151D412yes—
59#95×C151—21no—
60C2×Q8×C151—22no—
61C2×Q8×C151—22no—
62C2×Q8×C151—41no—
63C2×Q8×C151—41no—
64C2×Q8×C151—41no—
65C2×Q8×C151—41no—
66C2×Q8×C151—41no—
67C2×Q8×C151—41no—
68C2×Q8×C151—82no—
69C22×C4×C151—22no—
70C22×C4×C151—41no—
71C22×C4×C151—41no—
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74C22×C4×C151#4111yescharacteristic
75C2×C8×C151—21no—
76C2×C8×C151—21no—
77C2×C8×C151—21no—
78C2×C8×C151—21no—
79C2×C8×C151—22no—
80C2×C8×C151—41no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151—42no—
85C2×C8×C151—42no—
86C2×C8×C151C22⋊C412yes—
87C2×C8×C151C22⋊C412yes—
88C4⋊C4×C151—22no—
89C4⋊C4×C151—22no—
90C4⋊C4×C151—22no—
91C4⋊C4×C151—22no—
92C4⋊C4×C151—22no—
93C4⋊C4×C151—22no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—41no—
98C42×C151—41no—
99C42×C151—41no—
100C42×C151C22×C411yescharacteristic
101C42×C151C2×D411yescharacteristic
102C42×C151C2×D411yescharacteristic
103C42×C151#4111yescharacteristic
104C23×C151#12111yescharacteristic
105Q8×C151—42no—
106Q8×C151—42no—
107Q8×C151—82no—
108Q8×C151—82no—
109Q8×C151—81no—
110Q8×C151—81no—
111C2×C4×C151—22no—
112C2×C4×C151—42no—
113C2×C4×C151—42no—
114C2×C4×C151—42no—
115C2×C4×C151—42no—
116C2×C4×C151—42no—
117C2×C4×C151—81no—
118C2×C4×C151—81no—
119C2×C4×C151—82no—
120C2×C4×C151C2×C22⋊C411yescharacteristic
121C2×C4×C151C4×D411yescharacteristic
122C2×C4×C151C4×D411yescharacteristic
123C2×C4×C151#12111yescharacteristic
124C2×C4×C151#12411yescharacteristic
125C2×C4×C151#12711yescharacteristic
126C2×C4×C151#13511yescharacteristic
127C2×C4×C151#13511yescharacteristic
128C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C151#13711yescharacteristic
130C2×C4×C151#13712yes—
131C2×C4×C151#13712yes—
132C8×C151—22no—
133C8×C151—22no—
134C8×C151—42no—
135C8×C151—81no—
136C8×C151—81no—
137C22×C151#39011yescharacteristic
138C22×C151#46311yescharacteristic
139C22×C151#46411yescharacteristic
140C22×C151#47012yes—
141C22×C151#47112yes—
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—82no—
145C4×C151—82no—
146C4×C151—82no—
147C4×C151#41611yescharacteristic
148C4×C151#41711yescharacteristic
149C4×C151#44112yes—
150C4×C151#46311yescharacteristic
151C4×C151#46411yescharacteristic
152C4×C151#49711yescharacteristic
153C4×C151#49711yescharacteristic
154C2×C151#170312yes—
155C2×C151#170412yes—
156C2×C151#197111yescharacteristic
157C2×C151#197711yescharacteristic
158C2×C151#198311yescharacteristic
159#9745C15111yesmaximal, characteristic, direct product factor, Sylow
160C151#974511yescharacteristic, direct product factor, Sylow
161C2×#487C2×C15111yescharacteristic
162#1988C2×C15111yescharacteristic
163#1987C2×C15111yescharacteristic
164#1770C2×C15111yescharacteristic
165C2×#334C2×C15111yescharacteristic
166C2×#333C2×C15111yescharacteristic
167C2×#332C2×C15111yescharacteristic
168C2×C4⋊Q8C22×C15111yescharacteristic
169C2×C4⋊Q8C22×C15111yescharacteristic
170#487—22no—
171#487C4×C15114yescomplemented
172C2×C4⋊C8C22×C15111yescharacteristic
173C2×C4⋊C8C22×C15111yescharacteristic
174C2×C4⋊C8C22×C15111yescharacteristic
175C2×#103—21no—
176C2×#103—21no—
177C2×#97—21no—
178C2×C4×C8C22×C15111yescharacteristic
179C4×C4⋊C4C22×C15111yescharacteristic
180#340—22no—
181#340—22no—
182#336—21no—
183#334—22no—
184#333—22no—
185#332—22no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8D4×C15111yescharacteristic
192C22×C8D4×C15111yescharacteristic
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8C2×C4×C15112yes—
200C4⋊Q8C2×C4×C15112yes—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4D4×C15112yes—
206C2×C42—21no—
207C2×C42C23×C15111yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8D4×C15112yes—
214#103—24no—
215#103—24no—
216#97—42no—
217C4×C8C2×C4×C15112yes—
218C4×C8D4×C15112yes—
219#95—21no—
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—82no—
229C22×C4—22no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4C2×D4×C15111yescharacteristic
233C22×C4C2×D4×C15111yescharacteristic
234C22×C4#41×C15111yescharacteristic
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8C22⋊C4×C15112yes—
247C2×C8C22⋊C4×C15112yes—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C42—41no—
259C42—41no—
260C42C22×C4×C15111yescharacteristic
261C42C2×D4×C15111yescharacteristic
262C42C2×D4×C15111yescharacteristic
263C42#41×C15111yescharacteristic
264C23#121×C15111yescharacteristic
265Q8—42no—
266Q8—42no—
267Q8—82no—
268Q8—82no—
269Q8—81no—
270Q8—81no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—82no—
280C2×C4C2×C22⋊C4×C15111yescharacteristic
281C2×C4C4×D4×C15111yescharacteristic
282C2×C4C4×D4×C15111yescharacteristic
283C2×C4#121×C15111yescharacteristic
284C2×C4#124×C15111yescharacteristic
285C2×C4#127×C15111yescharacteristic
286C2×C4#135×C15111yescharacteristic
287C2×C4#135×C15111yescharacteristic
288C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
289C2×C4#137×C15111yescharacteristic
290C2×C4#137×C15112yes—
291C2×C4#137×C15112yes—
292C8—22no—
293C8—22no—
294C8—42no—
295C8—81no—
296C8—81no—
297C22#390×C15111yescharacteristic
298C22#463×C15111yescharacteristic
299C22#464×C15111yescharacteristic
300C22#470×C15112yes—
301C22#471×C15112yes—
302C4—21no—
303C4—21no—
304C4—82no—
305C4—82no—
306C4—82no—
307C4#416×C15111yescharacteristic
308C4#417×C15111yescharacteristic
309C4#441×C15112yes—
310C4#463×C15111yescharacteristic
311C4#464×C15111yescharacteristic
312C4#497×C15111yescharacteristic
313C4#497×C15111yescharacteristic
314C2#1703×C15112yes—
315C2#1704×C15112yes—
316C2#1971×C15111yescharacteristic
317C2#1977×C15111yescharacteristic
318C2#1983×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
11. #487×C151C4semidirect
159. #9745C151direct (N × H)
160. C151#9745direct (N × H)
171. #487C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#487×C1512
#1988×C1512
#1987×C1512
#1770×C1512
C2×#334×C1512
C2×#333×C1512
C2×#332×C1512
#9745151