Finite Group Databasebeta

← C151×#18363 #50323288

Subgroups — C151×#18363 #50323288

Order 38656.

1202 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3496×C151C211yesmaximal, characteristic
2#3234×C151C212yesmaximal, complemented
3#2633×C151C211yesmaximal, characteristic, complemented
4#1613×C151C214yesmaximal, complemented
5#1607×C151C214yesmaximal, complemented
6#1514×C151C212yesmaximal, complemented
7#1466×C151C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C151—21no—
9#547×C151—22no—
10#546×C151—24no—
11D42×C151—22no—
12#537×C151—21no—
13#534×C151C2214yes—
14#532×C151C2212yes—
15C2×#125×C151C2211yescharacteristic, complemented
16C2×#121×C151—22no—
17C2×C4×D4×C151C2211yescharacteristic
18#501×C151—22no—
19#490×C151—22no—
20#481×C151C2214yescomplemented
21#480×C151C2214yescomplemented
22#478×C151—24no—
23#432×C151C2212yescomplemented
24#399×C151C2212yescomplemented
25#398×C151—21no—
26#397×C151C2212yescomplemented
27#394×C151—21no—
28#385×C151—22no—
29#383×C151C2211yescharacteristic, complemented
30#327×C151C2218yescomplemented
31#323×C151C2214yescomplemented
32H(5,𝔽2)×C151—48no—
33C2×#41×C151—24no—
34C2×#41×C151—22no—
35C22×D4×C151—24no—
36C22×D4×C151—22no—
37C22×D4×C151—24no—
38C22×D4×C151D411yescharacteristic
39C23×C4×C151D412yes—
40C4⋊Q8×C151D412yes—
41#127×C151D412yes—
42#125×C151—22no—
43#125×C151—22no—
44#124×C151—22no—
45#123×C151—28no—
46C22⋊Q8×C151—24no—
47#121×C151—24no—
48#121×C151—24no—
49#121×C151—24no—
50#121×C151—22no—
51#121×C151—24no—
52#121×C151C2314yes—
53#120×C151—28no—
54C4×D4×C151—22no—
55C4×D4×C151—22no—
56C4×D4×C151—22no—
57C4×D4×C151D414yes—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—22no—
68C2×C22⋊C4×C151C2312yes—
69C2×C42×C151C2311yescharacteristic
70#107×C151—24no—
71#106×C151—24no—
72C4⋊C8×C151—22no—
73#102×C151—24no—
74#102×C151—24no—
75C22⋊C8×C151C2314yes—
76#97×C151—22no—
77#95×C151—21no—
78#95×C151—21no—
79#95×C151—22no—
80#95×C151C2312yes—
81C24×C151—24no—
82C24×C151C2×D412yes—
83#41×C151—48no—
84#41×C151—416no—
85C2×Q8×C151—22no—
86C2×D4×C151—24no—
87C2×D4×C151—28no—
88C2×D4×C151—24no—
89C2×D4×C151—24no—
90C2×D4×C151—22no—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151—416no—
94C2×D4×C151—48no—
95C2×D4×C151—48no—
96C2×D4×C151—84no—
97C2×D4×C151C2×D414yes—
98C22×C4×C151—24no—
99C22×C4×C151—22no—
100C22×C4×C151—24no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—82no—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2×D412yes—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2411yescharacteristic
110C2×C8×C151—24no—
111C4⋊C4×C151—24no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—22no—
114C4⋊C4×C151—22no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—42no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—82no—
120C4⋊C4×C151C2×D414yes—
121C22⋊C4×C151—28no—
122C22⋊C4×C151—24no—
123C22⋊C4×C151—24no—
124C22⋊C4×C151—24no—
125C22⋊C4×C151—44no—
126C22⋊C4×C151—82no—
127C42×C151C2×D412yes—
128C42×C151C2×D412yes—
129C23×C151—22no—
130C23×C151—22no—
131C23×C151—24no—
132C23×C151—42no—
133C23×C151—42no—
134C23×C151—48no—
135C23×C151—84no—
136C23×C151—84no—
137C23×C151AGL(1,ℤ/8)14yes—
138C23×C151C22×D411yescharacteristic
139Q8×C151—44no—
140D4×C151—28no—
141D4×C151—44no—
142D4×C151—44no—
143D4×C151—44no—
144D4×C151—416no—
145D4×C151—48no—
146D4×C151—84no—
147C2×C4×C151—22no—
148C2×C4×C151—24no—
149C2×C4×C151—22no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—48no—
153C2×C4×C151—44no—
154C2×C4×C151—48no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—42no—
158C2×C4×C151—41no—
159C2×C4×C151—42no—
160C2×C4×C151—41no—
161C2×C4×C151—41no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—82no—
165C2×C4×C151#12012yes—
166C2×C4×C151#12011yescharacteristic
167C2×C4×C151#12011yescharacteristic
168C2×C4×C151C22×D412yes—
169C8×C151—44no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—24no—
173C22×C151—44no—
174C22×C151—42no—
175C22×C151—42no—
176C22×C151—44no—
177C22×C151—44no—
178C22×C151—44no—
179C22×C151—82no—
180C22×C151—168no—
181C22×C151C2×#12011yescharacteristic
182C22×C151C2×AGL(1,ℤ/8)12yes—
183C4×C151—22no—
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—22no—
187C4×C151—44no—
188C4×C151—42no—
189C4×C151—82no—
190C4×C151—81no—
191C4×C151—81no—
192C2×C151—22no—
193C2×C151—44no—
194C2×C151—84no—
195C2×C151#300311yescharacteristic
196C2×C151#301911yescharacteristic
197C2×C151#302811yescharacteristic
198#18363C15111yesmaximal, characteristic, direct product factor, Sylow
199C151#1836311yescharacteristic, direct product factor, Sylow
200#3496C2×C15111yescharacteristic
201#3234C2×C15112yescomplemented
202#2633C2×C15111yescharacteristic, complemented
203#1613C2×C15114yescomplemented
204#1607C2×C15114yescomplemented
205#1514C2×C15112yescomplemented
206#1466C2×C15111yescharacteristic, complemented
207C2×H(5,𝔽2)—21no—
208#547—22no—
209#546—24no—
210D42—22no—
211#537—21no—
212#534C22×C15114yes—
213#532C22×C15112yes—
214C2×#125C22×C15111yescharacteristic, complemented
215C2×#121—22no—
216C2×C4×D4C22×C15111yescharacteristic
217#501—22no—
218#490—22no—
219#481C22×C15114yescomplemented
220#480C22×C15114yescomplemented
221#478—24no—
222#432C22×C15112yescomplemented
223#399C22×C15112yescomplemented
224#398—21no—
225#397C22×C15112yescomplemented
226#394—21no—
227#385—22no—
228#383C22×C15111yescharacteristic, complemented
229#327C22×C15118yescomplemented
230#323C22×C15114yescomplemented
231H(5,𝔽2)—48no—
232C2×#41—24no—
233C2×#41—22no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4D4×C15111yescharacteristic
238C23×C4D4×C15112yes—
239C4⋊Q8D4×C15112yes—
240#127D4×C15112yes—
241#125—22no—
242#125—22no—
243#124—22no—
244#123—28no—
245C22⋊Q8—24no—
246#121—24no—
247#121—24no—
248#121—24no—
249#121—22no—
250#121—24no—
251#121C23×C15114yes—
252#120—28no—
253C4×D4—22no—
254C4×D4—22no—
255C4×D4—22no—
256C4×D4D4×C15114yes—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4D4×C15111yescharacteristic
262C2×C4⋊C4C23×C15111yescharacteristic
263C2×C4⋊C4C23×C15111yescharacteristic
264C2×C22⋊C4—24no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4C23×C15112yes—
268C2×C42C23×C15111yescharacteristic
269#107—24no—
270#106—24no—
271C4⋊C8—22no—
272#102—24no—
273#102—24no—
274C22⋊C8C23×C15114yes—
275#97—22no—
276#95—21no—
277#95—21no—
278#95—22no—
279#95C23×C15112yes—
280C24—24no—
281C24C2×D4×C15112yes—
282#41—48no—
283#41—416no—
284C2×Q8—22no—
285C2×D4—24no—
286C2×D4—28no—
287C2×D4—24no—
288C2×D4—24no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—416no—
293C2×D4—48no—
294C2×D4—48no—
295C2×D4—84no—
296C2×D4C2×D4×C15114yes—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—82no—
305C22×C4C2×D4×C15111yescharacteristic
306C22×C4C2×D4×C15112yes—
307C22×C4C2×D4×C15111yescharacteristic
308C22×C4C24×C15111yescharacteristic
309C2×C8—24no—
310C4⋊C4—24no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—82no—
319C4⋊C4C2×D4×C15114yes—
320C22⋊C4—28no—
321C22⋊C4—24no—
322C22⋊C4—24no—
323C22⋊C4—24no—
324C22⋊C4—44no—
325C22⋊C4—82no—
326C42C2×D4×C15112yes—
327C42C2×D4×C15112yes—
328C23—22no—
329C23—22no—
330C23—24no—
331C23—42no—
332C23—42no—
333C23—48no—
334C23—84no—
335C23—84no—
336C23AGL(1,ℤ/8)×C15114yes—
337C23C22×D4×C15111yescharacteristic
338Q8—44no—
339D4—28no—
340D4—44no—
341D4—44no—
342D4—44no—
343D4—416no—
344D4—48no—
345D4—84no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—44no—
352C2×C4—48no—
353C2×C4—48no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4#120×C15111yescharacteristic
365C2×C4#120×C15111yescharacteristic
366C2×C4#120×C15112yes—
367C2×C4C22×D4×C15112yes—
368C8—44no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—44no—
373C22—42no—
374C22—42no—
375C22—44no—
376C22—44no—
377C22—44no—
378C22—82no—
379C22—168no—
380C22C2×#120×C15111yescharacteristic
381C22C2×AGL(1,ℤ/8)×C15112yes—
382C4—22no—
383C4—21no—
384C4—21no—
385C4—22no—
386C4—44no—
387C4—42no—
388C4—82no—
389C4—81no—
390C4—81no—
391C2—22no—
392C2—44no—
393C2—84no—
394C2#3003×C15111yescharacteristic
395C2#3019×C15111yescharacteristic
396C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3496×C151C2
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. #3234×C151C2semidirect
3. #2633×C151C2semidirect
4. #1613×C151C2semidirect
5. #1607×C151C2semidirect
6. #1514×C151C2semidirect
7. #1466×C151C2semidirect
15. C2×#125×C151C22semidirect
20. #481×C151C22semidirect
21. #480×C151C22semidirect
23. #432×C151C22semidirect
24. #399×C151C22semidirect
26. #397×C151C22semidirect
29. #383×C151C22semidirect
30. #327×C151C22semidirect
31. #323×C151C22semidirect
198. #18363C151direct (N × H)
199. C151#18363direct (N × H)
201. #3234C2×C151semidirect
202. #2633C2×C151semidirect
203. #1613C2×C151semidirect
204. #1607C2×C151semidirect
205. #1514C2×C151semidirect
206. #1466C2×C151semidirect
214. C2×#125C22×C151semidirect
219. #481C22×C151semidirect
220. #480C22×C151semidirect
222. #432C22×C151semidirect
223. #399C22×C151semidirect
225. #397C22×C151semidirect
228. #383C22×C151semidirect
229. #327C22×C151semidirect
230. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3496×C1512
#3234×C1512
#2633×C1512
#1613×C1512
#1607×C1512
#1514×C1512
#1466×C1512
#18363151