Finite Group Databasebeta

← C151×#18364 #50323289

Subgroups — C151×#18364 #50323289

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2#3236×C151C212yesmaximal, complemented
3#2633×C151C211yesmaximal, characteristic
4#1614×C151C214yesmaximal, complemented
5#1608×C151C214yesmaximal, complemented
6#1515×C151C212yesmaximal, complemented
7#1466×C151C211yesmaximal, characteristic
8#554×C151—22no—
9#554×C151—24no—
10D4×Q8×C151—22no—
11#544×C151—21no—
12#543×C151C2214yes—
13#533×C151C2212yes—
14C2×#125×C151C2211yescharacteristic
15C2×C22⋊Q8×C151—22no—
16#518×C151—21no—
17C2×C4×D4×C151C2211yescharacteristic
18#501×C151—22no—
19#491×C151—22no—
20#484×C151C2214yes—
21#483×C151C2214yes—
22#479×C151—24no—
23#432×C151C2212yes—
24#399×C151C2212yes—
25#398×C151—21no—
26#397×C151C2212yes—
27#394×C151—21no—
28#385×C151—22no—
29#383×C151C2211yescharacteristic
30#328×C151C2218yes—
31#323×C151C2214yes—
32C22×Q8×C151—22no—
33C22×D4×C151D411yescharacteristic
34C23×C4×C151D412yes—
35C4⋊Q8×C151—24no—
36C4⋊Q8×C151D412yes—
37C4⋊Q8×C151D412yes—
38#125×C151—24no—
39#125×C151—22no—
40#125×C151—22no—
41#125×C151—22no—
42C22⋊Q8×C151—24no—
43C22⋊Q8×C151—24no—
44C22⋊Q8×C151—22no—
45C22⋊Q8×C151—24no—
46C22⋊Q8×C151—28no—
47C22⋊Q8×C151—28no—
48C22⋊Q8×C151C2314yes—
49C4×Q8×C151—22no—
50C4×Q8×C151D414yes—
51C4×D4×C151—24no—
52C4×D4×C151—24no—
53C4×D4×C151—22no—
54C4×D4×C151—22no—
55#117×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151D411yescharacteristic
62C2×C4⋊C4×C151C2311yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151C2312yes—
68C2×C42×C151C2311yescharacteristic
69#107×C151—24no—
70#106×C151—24no—
71C4⋊C8×C151—22no—
72#103×C151—24no—
73#103×C151—24no—
74C22⋊C8×C151C2314yes—
75#97×C151—22no—
76#95×C151—21no—
77#95×C151—21no—
78#95×C151—22no—
79#95×C151C2312yes—
80C24×C151C2×D412yes—
81C2×Q8×C151—24no—
82C2×Q8×C151—22no—
83C2×Q8×C151—84no—
84C2×Q8×C151C2×D414yes—
85C2×D4×C151—24no—
86C2×D4×C151—22no—
87C22×C4×C151—24no—
88C22×C4×C151—24no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—82no—
95C22×C4×C151C2×D411yescharacteristic
96C22×C4×C151C2×D412yes—
97C22×C4×C151C2×D411yescharacteristic
98C22×C4×C151C2411yescharacteristic
99C2×C8×C151—24no—
100C4⋊C4×C151—24no—
101C4⋊C4×C151—28no—
102C4⋊C4×C151—22no—
103C4⋊C4×C151—24no—
104C4⋊C4×C151—22no—
105C4⋊C4×C151—22no—
106C4⋊C4×C151—22no—
107C4⋊C4×C151—24no—
108C4⋊C4×C151—22no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—41no—
111C4⋊C4×C151—42no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—82no—
114C4⋊C4×C151C2×D414yes—
115C22⋊C4×C151—28no—
116C22⋊C4×C151—24no—
117C22⋊C4×C151—24no—
118C22⋊C4×C151—44no—
119C22⋊C4×C151—82no—
120C42×C151—24no—
121C42×C151C2×D412yes—
122C42×C151C2×D412yes—
123C23×C151—22no—
124C23×C151—22no—
125C23×C151—42no—
126C23×C151—42no—
127C23×C151#13714yes—
128C23×C151C22×D411yescharacteristic
129Q8×C151—44no—
130Q8×C151—44no—
131Q8×C151—84no—
132D4×C151—28no—
133C2×C4×C151—22no—
134C2×C4×C151—24no—
135C2×C4×C151—22no—
136C2×C4×C151—24no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—44no—
140C2×C4×C151—42no—
141C2×C4×C151—41no—
142C2×C4×C151—42no—
143C2×C4×C151—41no—
144C2×C4×C151—42no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151—82no—
150C2×C4×C151—84no—
151C2×C4×C151—84no—
152C2×C4×C151#12011yescharacteristic
153C2×C4×C151#12012yes—
154C2×C4×C151#12011yescharacteristic
155C2×C4×C151C22×D412yes—
156C8×C151—44no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—24no—
160C22×C151—44no—
161C22×C151—42no—
162C22×C151—42no—
163C22×C151—82no—
164C22×C151C2×#12011yescharacteristic
165C22×C151C2×#13712yes—
166C4×C151—22no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—22no—
170C4×C151—42no—
171C4×C151—44no—
172C4×C151—44no—
173C4×C151—82no—
174C4×C151—81no—
175C4×C151—81no—
176C2×C151—22no—
177C2×C151—44no—
178C2×C151#300411yescharacteristic
179C2×C151#301911yescharacteristic
180C2×C151#302811yescharacteristic
181#18364C15111yesmaximal, characteristic, direct product factor, Sylow
182C151#1836411yescharacteristic, direct product factor, Sylow
183#3501C2×C15111yescharacteristic
184#3236C2×C15112yescomplemented
185#2633C2×C15111yescharacteristic
186#1614C2×C15114yescomplemented
187#1608C2×C15114yescomplemented
188#1515C2×C15112yescomplemented
189#1466C2×C15111yescharacteristic
190#554—22no—
191#554—24no—
192D4×Q8—22no—
193#544—21no—
194#543C22×C15114yes—
195#533C22×C15112yes—
196C2×#125C22×C15111yescharacteristic
197C2×C22⋊Q8—22no—
198#518—21no—
199C2×C4×D4C22×C15111yescharacteristic
200#501—22no—
201#491—22no—
202#484C22×C15114yes—
203#483C22×C15114yes—
204#479—24no—
205#432C22×C15112yes—
206#399C22×C15112yes—
207#398—21no—
208#397C22×C15112yes—
209#394—21no—
210#385—22no—
211#383C22×C15111yescharacteristic
212#328C22×C15118yes—
213#323C22×C15114yes—
214C22×Q8—22no—
215C22×D4D4×C15111yescharacteristic
216C23×C4D4×C15112yes—
217C4⋊Q8—24no—
218C4⋊Q8D4×C15112yes—
219C4⋊Q8D4×C15112yes—
220#125—24no—
221#125—22no—
222#125—22no—
223#125—22no—
224C22⋊Q8—24no—
225C22⋊Q8—24no—
226C22⋊Q8—28no—
227C22⋊Q8—22no—
228C22⋊Q8—24no—
229C22⋊Q8—28no—
230C22⋊Q8C23×C15114yes—
231C4×Q8—22no—
232C4×Q8D4×C15114yes—
233C4×D4—24no—
234C4×D4—24no—
235C4×D4—22no—
236C4×D4—22no—
237#117—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4D4×C15111yescharacteristic
244C2×C4⋊C4C23×C15111yescharacteristic
245C2×C4⋊C4C23×C15111yescharacteristic
246C2×C22⋊C4—24no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4C23×C15112yes—
250C2×C42C23×C15111yescharacteristic
251#107—24no—
252#106—24no—
253C4⋊C8—22no—
254#103—24no—
255#103—24no—
256C22⋊C8C23×C15114yes—
257#97—22no—
258#95—21no—
259#95—21no—
260#95—22no—
261#95C23×C15112yes—
262C24C2×D4×C15112yes—
263C2×Q8—24no—
264C2×Q8—22no—
265C2×Q8—84no—
266C2×Q8C2×D4×C15114yes—
267C2×D4—24no—
268C2×D4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—82no—
277C22×C4C2×D4×C15111yescharacteristic
278C22×C4C2×D4×C15112yes—
279C22×C4C2×D4×C15111yescharacteristic
280C22×C4C24×C15111yescharacteristic
281C2×C8—24no—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—22no—
285C4⋊C4—24no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—82no—
296C4⋊C4C2×D4×C15114yes—
297C22⋊C4—28no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—44no—
301C22⋊C4—82no—
302C42—24no—
303C42C2×D4×C15112yes—
304C42C2×D4×C15112yes—
305C23—22no—
306C23—22no—
307C23—42no—
308C23—42no—
309C23#137×C15114yes—
310C23C22×D4×C15111yescharacteristic
311Q8—44no—
312Q8—44no—
313Q8—84no—
314D4—28no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—84no—
333C2×C4—84no—
334C2×C4#120×C15112yes—
335C2×C4#120×C15111yescharacteristic
336C2×C4#120×C15111yescharacteristic
337C2×C4C22×D4×C15112yes—
338C8—44no—
339C22—21no—
340C22—21no—
341C22—24no—
342C22—44no—
343C22—42no—
344C22—42no—
345C22—82no—
346C22C2×#120×C15111yescharacteristic
347C22C2×#137×C15112yes—
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—42no—
353C4—44no—
354C4—44no—
355C4—82no—
356C4—81no—
357C4—81no—
358C2—22no—
359C2—44no—
360C2#3004×C15111yescharacteristic
361C2#3019×C15111yescharacteristic
362C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
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
2. #3236×C151C2semidirect
4. #1614×C151C2semidirect
5. #1608×C151C2semidirect
6. #1515×C151C2semidirect
181. #18364C151direct (N × H)
182. C151#18364direct (N × H)
184. #3236C2×C151semidirect
186. #1614C2×C151semidirect
187. #1608C2×C151semidirect
188. #1515C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
#3236×C1512
#2633×C1512
#1614×C1512
#1608×C1512
#1515×C1512
#1466×C1512
#18364151