Finite Group Databasebeta

← C151×#19290 #50324215

Subgroups — C151×#19290 #50324215

Order 38656.

586 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C151C211yesmaximal, characteristic
2#3113×C151C212yesmaximal
3C2×#446×C151C211yesmaximal, characteristic
4#1700×C151C214yesmaximal, complemented
5#1694×C151C212yesmaximal, complemented
6#1690×C151C212yesmaximal, complemented
7#1568×C151C211yesmaximal, characteristic
8#1552×C151C212yesmaximal
9#533×C151C2212yes—
10C2×C4×Q8×C151C2211yescharacteristic
11#500×C151C2211yescharacteristic
12#494×C151C2211yescharacteristic
13#487×C151C2212yes—
14#483×C151—22no—
15#475×C151C2214yes—
16#467×C151—21no—
17#467×C151—21no—
18#462×C151C2214yes—
19#451×C151—22no—
20#446×C151—21no—
21#446×C151—21no—
22#446×C151C2212yes—
23#446×C151C2212yes—
24#441×C151—24no—
25C4×Q16×C151—21no—
26C4×Q16×C151—21no—
27#432×C151C2212yes—
28C2×C4⋊C8×C151—21no—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#97×C151—21no—
31C2×C4×C8×C151C2211yescharacteristic
32#335×C151C2212yes—
33#334×C151C2212yes—
34#332×C151C2214yes—
35#332×C151C2214yes—
36C22×Q8×C151D411yescharacteristic
37C2×Q16×C151—21no—
38C2×Q16×C151—21no—
39C2×Q16×C151—24no—
40C22×C8×C151—21no—
41C22×C8×C151D411yescharacteristic
42C22×C8×C151D411yescharacteristic
43C4⋊Q8×C151C2312yes—
44C4⋊Q8×C151C2312yes—
45#125×C151—22no—
46C22⋊Q8×C151—22no—
47C22⋊Q8×C151—22no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—22no—
51C4×Q8×C151—22no—
52C4×Q8×C151D412yes—
53C4×Q8×C151C2312yes—
54#117×C151—22no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C42×C151—21no—
58C2×C42×C151C2311yescharacteristic
59#107×C151—21no—
60#107×C151—21no—
61#106×C151—24no—
62C4⋊C8×C151—22no—
63C4⋊C8×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151C2312yes—
66C4⋊C8×C151C2314yes—
67#103×C151—22no—
68#103×C151—22no—
69#103×C151—24no—
70#103×C151—24no—
71C22⋊C8×C151—22no—
72#97×C151—22no—
73#97×C151—22no—
74#97×C151—22no—
75C4×C8×C151D411yescharacteristic
76C4×C8×C151D411yescharacteristic
77C4×C8×C151C2311yescharacteristic
78C4×C8×C151C2311yescharacteristic
79C2×Q8×C151—21no—
80C2×Q8×C151—22no—
81C2×Q8×C151—22no—
82C2×Q8×C151—42no—
83C2×Q8×C151C2×D412yes—
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151C2×D411yescharacteristic
87C22×C4×C151C2×D411yescharacteristic
88C22×C4×C151#4111yescharacteristic
89Q16×C151—42no—
90Q16×C151—48no—
91Q16×C151—42no—
92C2×C8×C151—22no—
93C2×C8×C151—22no—
94C2×C8×C151—24no—
95C2×C8×C151—41no—
96C2×C8×C151—42no—
97C2×C8×C151C2×D411yescharacteristic
98C2×C8×C151C2×D411yescharacteristic
99C2×C8×C151C2×D411yescharacteristic
100C2×C8×C151C2×D411yescharacteristic
101C4⋊C4×C151—22no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151—22no—
104C4⋊C4×C151—22no—
105C4⋊C4×C151—22no—
106C4⋊C4×C151—22no—
107C4⋊C4×C151—22no—
108C4⋊C4×C151—42no—
109C4⋊C4×C151—42no—
110C4⋊C4×C151C2×D412yes—
111C22⋊C4×C151—42no—
112C42×C151—22no—
113C42×C151—22no—
114C42×C151—42no—
115C42×C151C2×D411yescharacteristic
116C42×C151C2×D411yescharacteristic
117C42×C151#4111yescharacteristic
118C42×C151C2411yescharacteristic
119C23×C151#12111yescharacteristic
120Q8×C151—24no—
121Q8×C151—42no—
122Q8×C151—42no—
123Q8×C151—42no—
124Q8×C151—44no—
125C2×C4×C151—22no—
126C2×C4×C151—21no—
127C2×C4×C151—22no—
128C2×C4×C151—21no—
129C2×C4×C151—22no—
130C2×C4×C151—22no—
131C2×C4×C151—42no—
132C2×C4×C151—42no—
133C2×C4×C151—42no—
134C2×C4×C151—42no—
135C2×C4×C151#12111yescharacteristic
136C2×C4×C151#12111yescharacteristic
137C2×C4×C151#12111yescharacteristic
138C2×C4×C151C22×D411yescharacteristic
139C2×C4×C151C22×D411yescharacteristic
140C2×C4×C151C2×#4111yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C8×C151—21no—
144C8×C151—42no—
145C8×C151—44no—
146C8×C151#13712yes—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151#47312yes—
150C22×C151C2×#12111yescharacteristic
151C4×C151—21no—
152C4×C151—21no—
153C4×C151—21no—
154C4×C151—21no—
155C4×C151—42no—
156C4×C151—42no—
157C4×C151—82no—
158C4×C151—82no—
159C4×C151C2×#13711yescharacteristic
160C4×C151#57511yescharacteristic
161C4×C151#57512yes—
162C2×C151—22no—
163C2×C151#303711yescharacteristic
164C2×C151#305411yescharacteristic
165C2×C151C2×#47311yescharacteristic
166#19290C15111yesmaximal, characteristic, direct product factor, Sylow
167C151#1929011yescharacteristic, direct product factor, Sylow
168#3170C2×C15111yescharacteristic
169#3113C2×C15112yes—
170C2×#446C2×C15111yescharacteristic
171#1700C2×C15114yescomplemented
172#1694C2×C15112yescomplemented
173#1690C2×C15112yescomplemented
174#1568C2×C15111yescharacteristic
175#1552C2×C15112yes—
176#533C22×C15112yes—
177C2×C4×Q8C22×C15111yescharacteristic
178#500C22×C15111yescharacteristic
179#494C22×C15111yescharacteristic
180#487C22×C15112yes—
181#483—22no—
182#475C22×C15114yes—
183#467—21no—
184#467—21no—
185#462C22×C15114yes—
186#451—22no—
187#446—21no—
188#446—21no—
189#446C22×C15112yes—
190#446C22×C15112yes—
191#441—24no—
192C4×Q16—21no—
193C4×Q16—21no—
194#432C22×C15112yes—
195C2×C4⋊C8—21no—
196C2×C4⋊C8C22×C15111yescharacteristic
197C2×#97—21no—
198C2×C4×C8C22×C15111yescharacteristic
199#335C22×C15112yes—
200#334C22×C15112yes—
201#332C22×C15114yes—
202#332C22×C15114yes—
203C22×Q8D4×C15111yescharacteristic
204C2×Q16—24no—
205C2×Q16—21no—
206C2×Q16—21no—
207C22×C8—21no—
208C22×C8D4×C15111yescharacteristic
209C22×C8D4×C15111yescharacteristic
210C4⋊Q8C23×C15112yes—
211C4⋊Q8C23×C15112yes—
212#125—22no—
213C22⋊Q8—22no—
214C22⋊Q8—22no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—22no—
218C4×Q8—22no—
219C4×Q8D4×C15112yes—
220C4×Q8C23×C15112yes—
221#117—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C15111yescharacteristic
224C2×C42—21no—
225C2×C42C23×C15111yescharacteristic
226#107—21no—
227#107—21no—
228#106—24no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—21no—
232C4⋊C8C23×C15112yes—
233C4⋊C8C23×C15114yes—
234#103—24no—
235#103—22no—
236#103—22no—
237#103—24no—
238C22⋊C8—22no—
239#97—22no—
240#97—22no—
241#97—22no—
242C4×C8D4×C15111yescharacteristic
243C4×C8D4×C15111yescharacteristic
244C4×C8C23×C15111yescharacteristic
245C4×C8C23×C15111yescharacteristic
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—42no—
250C2×Q8C2×D4×C15112yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C2×D4×C15111yescharacteristic
254C22×C4C2×D4×C15111yescharacteristic
255C22×C4#41×C15111yescharacteristic
256Q16—42no—
257Q16—48no—
258Q16—42no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—24no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8C2×D4×C15111yescharacteristic
265C2×C8C2×D4×C15111yescharacteristic
266C2×C8C2×D4×C15111yescharacteristic
267C2×C8C2×D4×C15111yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4C2×D4×C15112yes—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42C2×D4×C15111yescharacteristic
283C42C2×D4×C15111yescharacteristic
284C42#41×C15111yescharacteristic
285C42C24×C15111yescharacteristic
286C23#121×C15111yescharacteristic
287Q8—24no—
288Q8—42no—
289Q8—42no—
290Q8—42no—
291Q8—44no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4#121×C15111yescharacteristic
303C2×C4#121×C15111yescharacteristic
304C2×C4#121×C15111yescharacteristic
305C2×C4C22×D4×C15111yescharacteristic
306C2×C4C22×D4×C15111yescharacteristic
307C2×C4C2×#41×C15111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—42no—
312C8—44no—
313C8#137×C15112yes—
314C22—21no—
315C22—21no—
316C22#473×C15112yes—
317C22C2×#121×C15111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—42no—
323C4—42no—
324C4—82no—
325C4—82no—
326C4C2×#137×C15111yescharacteristic
327C4#575×C15111yescharacteristic
328C4#575×C15112yes—
329C2—22no—
330C2#3037×C15111yescharacteristic
331C2#3054×C15111yescharacteristic
332C2C2×#473×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC23×C151#121
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. #1700×C151C2semidirect
5. #1694×C151C2semidirect
6. #1690×C151C2semidirect
166. #19290C151direct (N × H)
167. C151#19290direct (N × H)
171. #1700C2×C151semidirect
172. #1694C2×C151semidirect
173. #1690C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3170×C1512
#3113×C1512
C2×#446×C1512
#1700×C1512
#1694×C1512
#1690×C1512
#1568×C1512
#1552×C1512
#19290151