Finite Group Databasebeta

← C151×#18411 #50323336

Subgroups — C151×#18411 #50323336

Order 38656.

870 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3502×C151C211yesmaximal, characteristic
2#3230×C151C212yesmaximal
3#2568×C151C211yesmaximal, characteristic
4#1617×C151C218yesmaximal
5#1503×C151C212yesmaximal
6#1461×C151C211yesmaximal, characteristic
7Q82×C151—22no—
8#557×C151—22no—
9#557×C151—24no—
10#544×C151—21no—
11#544×C151C2214yes—
12#533×C151—22no—
13#533×C151C2212yes—
14C2×C4⋊Q8×C151C2211yescharacteristic
15#519×C151—21no—
16C2×C4×Q8×C151C2211yescharacteristic
17#500×C151—22no—
18#487×C151—22no—
19#484×C151C2218yes—
20#477×C151—24no—
21#431×C151C2212yes—
22#400×C151C2214yes—
23#391×C151—21no—
24#391×C151—22no—
25#382×C151—21no—
26C4×C4⋊C4×C151C2211yescharacteristic
27#328×C151C2218yes—
28#324×C151C2214yes—
29C22×Q8×C151—21no—
30C22×Q8×C151D411yescharacteristic
31C4⋊Q8×C151—22no—
32C4⋊Q8×C151—22no—
33C4⋊Q8×C151—24no—
34C4⋊Q8×C151—28no—
35C4⋊Q8×C151—22no—
36C4⋊Q8×C151—22no—
37C4⋊Q8×C151D412yes—
38C4⋊Q8×C151D412yes—
39#125×C151—24no—
40#125×C151—24no—
41#125×C151—28no—
42#125×C151—22no—
43C22⋊Q8×C151—22no—
44C22⋊Q8×C151—24no—
45C22⋊Q8×C151C2314yes—
46C4×Q8×C151—24no—
47C4×Q8×C151—24no—
48C4×Q8×C151—24no—
49C4×Q8×C151—24no—
50C4×Q8×C151—22no—
51C4×Q8×C151—22no—
52C4×Q8×C151—22no—
53C4×Q8×C151D414yes—
54#117×C151—24no—
55#117×C151—22no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C4⋊C4×C151C2312yes—
60C2×C4⋊C4×C151C2312yes—
61C2×C42×C151—21no—
62C2×C42×C151D412yes—
63C2×C42×C151C2311yescharacteristic
64#107×C151—28no—
65C4⋊C8×C151—22no—
66#103×C151—28no—
67C22⋊C8×C151C2314yes—
68C4×C8×C151—22no—
69#95×C151—24no—
70#95×C151—24no—
71#95×C151C2312yes—
72C2×Q8×C151—24no—
73C2×Q8×C151—22no—
74C2×Q8×C151—22no—
75C2×Q8×C151—22no—
76C2×Q8×C151—44no—
77C2×Q8×C151—41no—
78C2×Q8×C151—41no—
79C2×Q8×C151Q1614yes—
80C2×Q8×C151C2×D414yes—
81C22×C4×C151—22no—
82C22×C4×C151—22no—
83C22×C4×C151C2×D411yescharacteristic
84C22×C4×C151C2×D412yes—
85C22×C4×C151C2×D412yes—
86C22×C4×C151C2×D411yescharacteristic
87C22×C4×C151C2411yescharacteristic
88C2×C8×C151—24no—
89C4⋊C4×C151—24no—
90C4⋊C4×C151—24no—
91C4⋊C4×C151—24no—
92C4⋊C4×C151—28no—
93C4⋊C4×C151—22no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—22no—
96C4⋊C4×C151—22no—
97C4⋊C4×C151—24no—
98C4⋊C4×C151—24no—
99C4⋊C4×C151—24no—
100C4⋊C4×C151—24no—
101C4⋊C4×C151—42no—
102C4⋊C4×C151—42no—
103C4⋊C4×C151C2×D414yes—
104C22⋊C4×C151—24no—
105C42×C151—28no—
106C42×C151—22no—
107C42×C151—22no—
108C42×C151—24no—
109C42×C151—42no—
110C42×C151C2×D412yes—
111C42×C151C2×D412yes—
112C23×C151C22×D411yescharacteristic
113Q8×C151—28no—
114Q8×C151—44no—
115Q8×C151—44no—
116Q8×C151—82no—
117Q8×C151—84no—
118Q8×C151—82no—
119C2×C4×C151—22no—
120C2×C4×C151—22no—
121C2×C4×C151—22no—
122C2×C4×C151—24no—
123C2×C4×C151—22no—
124C2×C4×C151—24no—
125C2×C4×C151—41no—
126C2×C4×C151—42no—
127C2×C4×C151—44no—
128C2×C4×C151—42no—
129C2×C4×C151—42no—
130C2×C4×C151—42no—
131C2×C4×C151—42no—
132C2×C4×C151#12011yescharacteristic
133C2×C4×C151#12012yes—
134C2×C4×C151#12011yescharacteristic
135C2×C4×C151C2×Q1614yes—
136C2×C4×C151C2×Q1612yes—
137C2×C4×C151#13712yes—
138C2×C4×C151C22×D412yes—
139C8×C151—44no—
140C22×C151—21no—
141C22×C151—21no—
142C22×C151C2×#12011yescharacteristic
143C22×C151C22×Q1611yescharacteristic
144C22×C151C2×#13711yescharacteristic
145C4×C151—24no—
146C4×C151—21no—
147C4×C151—22no—
148C4×C151—44no—
149C4×C151—42no—
150C4×C151—44no—
151C4×C151—82no—
152C4×C151—82no—
153C4×C151#45114yes—
154C4×C151#45412yes—
155C2×C151—21no—
156C2×C151—21no—
157C2×C151C2×#45111yescharacteristic
158C2×C151C2×#45411yescharacteristic
159C2×C151#302811yescharacteristic
160#18411C15111yesmaximal, characteristic, direct product factor, Sylow
161C151#1841111yescharacteristic, direct product factor, Sylow
162#3502C2×C15111yescharacteristic
163#3230C2×C15112yes—
164#2568C2×C15111yescharacteristic
165#1617C2×C15118yes—
166#1503C2×C15112yes—
167#1461C2×C15111yescharacteristic
168Q82—22no—
169#557—22no—
170#557—24no—
171#544—21no—
172#544C22×C15114yes—
173#533—22no—
174#533C22×C15112yes—
175C2×C4⋊Q8C22×C15111yescharacteristic
176#519—21no—
177C2×C4×Q8C22×C15111yescharacteristic
178#500—22no—
179#487—22no—
180#484C22×C15118yes—
181#477—24no—
182#431C22×C15112yes—
183#400C22×C15114yes—
184#391—21no—
185#391—22no—
186#382—21no—
187C4×C4⋊C4C22×C15111yescharacteristic
188#328C22×C15118yes—
189#324C22×C15114yes—
190C22×Q8—21no—
191C22×Q8D4×C15111yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—24no—
195C4⋊Q8—28no—
196C4⋊Q8—22no—
197C4⋊Q8—22no—
198C4⋊Q8D4×C15112yes—
199C4⋊Q8D4×C15112yes—
200#125—24no—
201#125—24no—
202#125—28no—
203#125—22no—
204C22⋊Q8—22no—
205C22⋊Q8—24no—
206C22⋊Q8C23×C15114yes—
207C4×Q8—24no—
208C4×Q8—24no—
209C4×Q8—24no—
210C4×Q8—24no—
211C4×Q8—22no—
212C4×Q8—22no—
213C4×Q8—22no—
214C4×Q8D4×C15114yes—
215#117—24no—
216#117—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4D4×C15111yescharacteristic
220C2×C4⋊C4C23×C15112yes—
221C2×C4⋊C4C23×C15112yes—
222C2×C42—21no—
223C2×C42D4×C15112yes—
224C2×C42C23×C15111yescharacteristic
225#107—28no—
226C4⋊C8—22no—
227#103—28no—
228C22⋊C8C23×C15114yes—
229C4×C8—22no—
230#95—24no—
231#95—24no—
232#95C23×C15112yes—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8Q16×C15114yes—
241C2×Q8C2×D4×C15114yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×D4×C15111yescharacteristic
245C22×C4C2×D4×C15112yes—
246C22×C4C2×D4×C15112yes—
247C22×C4C2×D4×C15111yescharacteristic
248C22×C4C24×C15111yescharacteristic
249C2×C8—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—28no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4C2×D4×C15114yes—
265C22⋊C4—24no—
266C42—28no—
267C42—22no—
268C42—22no—
269C42—24no—
270C42—42no—
271C42C2×D4×C15112yes—
272C42C2×D4×C15112yes—
273C23C22×D4×C15111yescharacteristic
274Q8—28no—
275Q8—44no—
276Q8—44no—
277Q8—82no—
278Q8—84no—
279Q8—82no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4#120×C15111yescharacteristic
294C2×C4#120×C15112yes—
295C2×C4#120×C15111yescharacteristic
296C2×C4C2×Q16×C15114yes—
297C2×C4C2×Q16×C15112yes—
298C2×C4#137×C15112yes—
299C2×C4C22×D4×C15112yes—
300C8—44no—
301C22—21no—
302C22—21no—
303C22C2×#120×C15111yescharacteristic
304C22C22×Q16×C15111yescharacteristic
305C22C2×#137×C15111yescharacteristic
306C4—24no—
307C4—21no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—44no—
312C4—82no—
313C4—82no—
314C4#451×C15114yes—
315C4#454×C15112yes—
316C2—21no—
317C2—21no—
318C2C2×#451×C15111yescharacteristic
319C2C2×#454×C15111yescharacteristic
320C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×C151C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
160. #18411C151direct (N × H)
161. C151#18411direct (N × H)

Maximal subgroups

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

subgroupindex
#3502×C1512
#3230×C1512
#2568×C1512
#1617×C1512
#1503×C1512
#1461×C1512
#18411151