Finite Group Databasebeta

← C151×#19317 #50324242

Subgroups — C151×#19317 #50324242

Order 38656.

598 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3139×C151C211yesmaximal, characteristic, complemented
2#3116×C151C211yesmaximal, characteristic
3#3079×C151C211yesmaximal, characteristic
4#2970×C151C211yesmaximal, characteristic
5#1704×C151C212yesmaximal, complemented
6#1700×C151C212yesmaximal, complemented
7#1683×C151C212yesmaximal, complemented
8#1679×C151C212yesmaximal, complemented
9#1569×C151C211yesmaximal, characteristic, complemented
10#1559×C151C211yesmaximal, characteristic, complemented
11#1556×C151C211yesmaximal, characteristic, complemented
12#533×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C4×#41×C151C2211yescharacteristic
15#491×C151—21no—
16#491×C151—21no—
17#487×C151C2212yes—
18#487×C151C2212yes—
19#485×C151—21no—
20#477×C151—21no—
21#477×C151C2211yescharacteristic
22#476×C151—21no—
23#476×C151C2211yescharacteristic
24#475×C151C2212yes—
25#474×C151C2212yes—
26#462×C151C2211yescharacteristic
27#461×C151C2211yescharacteristic
28#452×C151—21no—
29#446×C151C2212yes—
30#441×C151—21no—
31#440×C151—21no—
32#435×C151—22no—
33C8×D4×C151C2212yes—
34#432×C151—21no—
35#432×C151C2211yescharacteristic
36#432×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#419×C151—22no—
40#417×C151—21no—
41C4×M16×C151C2211yescharacteristic
42C2×#97×C151—21no—
43#335×C151C2212yes—
44#334×C151C2212yes—
45#333×C151C2212yes—
46#332×C151C2212yes—
47#332×C151C2212yes—
48#332×C151C2212yes—
49C2×#41×C151D411yescharacteristic
50C22×Q8×C151—21no—
51C2×Q16×C151—21no—
52C2×SD16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151D412yes—
55C22×C8×C151—22no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151C2311yescharacteristic
60C4⋊Q8×C151C2312yes—
61C4⋊Q8×C151C2311yescharacteristic
62#125×C151—21no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151—21no—
65C4×Q8×C151—21no—
66C4×Q8×C151—21no—
67C4×Q8×C151D411yescharacteristic
68C4×Q8×C151C2311yescharacteristic
69C4×D4×C151—21no—
70C4×D4×C151—21no—
71C4×D4×C151D411yescharacteristic
72C4×D4×C151C2311yescharacteristic
73#117×C151—21no—
74#117×C151—21no—
75#117×C151D411yescharacteristic
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C42×C151—21no—
79C2×C42×C151C2311yescharacteristic
80#107×C151—22no—
81#107×C151—21no—
82#106×C151—22no—
83#106×C151—21no—
84C4⋊C8×C151—22no—
85C4⋊C8×C151—21no—
86C4⋊C8×C151C2312yes—
87C4⋊C8×C151C2312yes—
88C4⋊C8×C151C2311yescharacteristic
89C4⋊C8×C151C2311yescharacteristic
90#103×C151—22no—
91#103×C151—22no—
92#103×C151—22no—
93#103×C151—22no—
94#103×C151—21no—
95#103×C151—21no—
96#103×C151—22no—
97#103×C151—21no—
98#102×C151—22no—
99#102×C151—21no—
100C22⋊C8×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—22no—
103#97×C151—22no—
104#97×C151—21no—
105#97×C151—21no—
106#97×C151D411yescharacteristic
107#97×C151D411yescharacteristic
108C4×C8×C151C2312yes—
109#41×C151—22no—
110#41×C151—41no—
111C2×Q8×C151—22no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—44no—
115C2×Q8×C151—41no—
116C2×Q8×C151C2×D411yescharacteristic
117C2×D4×C151—21no—
118C2×D4×C151C2×D411yescharacteristic
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—41no—
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151#4111yescharacteristic
126Q16×C151—42no—
127SD16×C151—42no—
128M16×C151—42no—
129M16×C151—42no—
130C2×C8×C151—22no—
131C2×C8×C151—21no—
132C2×C8×C151—21no—
133C2×C8×C151—22no—
134C2×C8×C151—44no—
135C2×C8×C151C2×D412yes—
136C2×C8×C151C2×D412yes—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—41no—
146C4⋊C4×C151—41no—
147C4⋊C4×C151—41no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151C2×D411yescharacteristic
150C4⋊C4×C151C2×D411yescharacteristic
151C22⋊C4×C151—21no—
152C22⋊C4×C151—21no—
153C22⋊C4×C151—21no—
154C22⋊C4×C151—41no—
155C42×C151—21no—
156C42×C151—21no—
157C42×C151—21no—
158C42×C151—41no—
159C42×C151C2×D411yescharacteristic
160C42×C151C2×D411yescharacteristic
161C42×C151#4111yescharacteristic
162C42×C151C2411yescharacteristic
163C23×C151—21no—
164C23×C151#12111yescharacteristic
165Q8×C151—21no—
166Q8×C151—21no—
167Q8×C151—41no—
168Q8×C151—44no—
169Q8×C151—41no—
170Q8×C151—81no—
171Q8×C151—82no—
172D4×C151—21no—
173D4×C151—42no—
174D4×C151#13712yes—
175C2×C4×C151—21no—
176C2×C4×C151—22no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—41no—
182C2×C4×C151—42no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—41no—
186C2×C4×C151—41no—
187C2×C4×C151—81no—
188C2×C4×C151—82no—
189C2×C4×C151#12111yescharacteristic
190C2×C4×C151#12111yescharacteristic
191C2×C4×C151#12111yescharacteristic
192C2×C4×C151C22×D411yescharacteristic
193C2×C4×C151C22×D411yescharacteristic
194C2×C4×C151C2×#4111yescharacteristic
195C8×C151—22no—
196C8×C151—22no—
197C8×C151—41no—
198C8×C151—42no—
199C8×C151—42no—
200C8×C151—41no—
201C22×C151—21no—
202C22×C151—21no—
203C22×C151—22no—
204C22×C151—21no—
205C22×C151—41no—
206C22×C151—41no—
207C22×C151C2×#12111yescharacteristic
208C4×C151—21no—
209C4×C151—21no—
210C4×C151—21no—
211C4×C151—21no—
212C4×C151—41no—
213C4×C151—41no—
214C4×C151—41no—
215C4×C151—82no—
216C4×C151—81no—
217C4×C151—81no—
218C4×C151C2×#13711yescharacteristic
219C4×C151#57512yes—
220C4×C151#57511yescharacteristic
221C2×C151—41no—
222C2×C151—42no—
223C2×C151#304011yescharacteristic
224C2×C151#305611yescharacteristic
225C2×C151#306911yescharacteristic
226#19317C15111yesmaximal, characteristic, direct product factor, Sylow
227C151#1931711yescharacteristic, direct product factor, Sylow
228#3139C2×C15111yescharacteristic, complemented
229#3116C2×C15111yescharacteristic
230#3079C2×C15111yescharacteristic
231#2970C2×C15111yescharacteristic
232#1704C2×C15112yescomplemented
233#1700C2×C15112yescomplemented
234#1683C2×C15112yescomplemented
235#1679C2×C15112yescomplemented
236#1569C2×C15111yescharacteristic, complemented
237#1559C2×C15111yescharacteristic, complemented
238#1556C2×C15111yescharacteristic, complemented
239#533C22×C15111yescharacteristic
240C2×C4⋊Q8C22×C15111yescharacteristic
241C4×#41C22×C15111yescharacteristic
242#491—21no—
243#491—21no—
244#487C22×C15112yes—
245#487C22×C15112yes—
246#485—21no—
247#477—21no—
248#477C22×C15111yescharacteristic
249#476—21no—
250#476C22×C15111yescharacteristic
251#475C22×C15112yes—
252#474C22×C15112yes—
253#462C22×C15111yescharacteristic
254#461C22×C15111yescharacteristic
255#452—21no—
256#446C22×C15112yes—
257#441—21no—
258#440—21no—
259#435—22no—
260C8×D4C22×C15112yes—
261#432—21no—
262#432C22×C15111yescharacteristic
263#432C22×C15111yescharacteristic
264#428—21no—
265#423C22×C15111yescharacteristic
266#419—22no—
267#417—21no—
268C4×M16C22×C15111yescharacteristic
269C2×#97—21no—
270#335C22×C15112yes—
271#334C22×C15112yes—
272#333C22×C15112yes—
273#332C22×C15112yes—
274#332C22×C15112yes—
275#332C22×C15112yes—
276C2×#41D4×C15111yescharacteristic
277C22×Q8—21no—
278C2×Q16—21no—
279C2×SD16—21no—
280C2×M16—21no—
281C2×M16D4×C15112yes—
282C22×C8—22no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C23×C15112yes—
287C4⋊Q8C23×C15111yescharacteristic
288C4⋊Q8C23×C15111yescharacteristic
289#125—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8D4×C15111yescharacteristic
295C4×Q8C23×C15111yescharacteristic
296C4×D4—21no—
297C4×D4—21no—
298C4×D4D4×C15111yescharacteristic
299C4×D4C23×C15111yescharacteristic
300#117—21no—
301#117—21no—
302#117D4×C15111yescharacteristic
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42—21no—
306C2×C42C23×C15111yescharacteristic
307#107—22no—
308#107—21no—
309#106—22no—
310#106—21no—
311C4⋊C8—22no—
312C4⋊C8—21no—
313C4⋊C8C23×C15112yes—
314C4⋊C8C23×C15111yescharacteristic
315C4⋊C8C23×C15111yescharacteristic
316C4⋊C8C23×C15112yes—
317#103—22no—
318#103—21no—
319#103—22no—
320#103—22no—
321#103—22no—
322#103—22no—
323#103—21no—
324#103—21no—
325#102—22no—
326#102—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—22no—
330#97—22no—
331#97—21no—
332#97—21no—
333#97D4×C15111yescharacteristic
334#97D4×C15111yescharacteristic
335C4×C8C23×C15112yes—
336#41—22no—
337#41—41no—
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—44no—
342C2×Q8—41no—
343C2×Q8C2×D4×C15111yescharacteristic
344C2×D4—21no—
345C2×D4C2×D4×C15111yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4C2×D4×C15111yescharacteristic
351C22×C4C2×D4×C15111yescharacteristic
352C22×C4#41×C15111yescharacteristic
353Q16—42no—
354SD16—42no—
355M16—42no—
356M16—42no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—44no—
362C2×C8C2×D4×C15112yes—
363C2×C8C2×D4×C15112yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C2×D4×C15111yescharacteristic
377C4⋊C4C2×D4×C15111yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—41no—
382C42—21no—
383C42—21no—
384C42—21no—
385C42—41no—
386C42C2×D4×C15111yescharacteristic
387C42C2×D4×C15111yescharacteristic
388C42#41×C15111yescharacteristic
389C42C24×C15111yescharacteristic
390C23—21no—
391C23#121×C15111yescharacteristic
392Q8—21no—
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—44no—
397Q8—81no—
398Q8—82no—
399D4—21no—
400D4—42no—
401D4#137×C15112yes—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4#121×C15111yescharacteristic
417C2×C4#121×C15111yescharacteristic
418C2×C4#121×C15111yescharacteristic
419C2×C4C22×D4×C15111yescharacteristic
420C2×C4C22×D4×C15111yescharacteristic
421C2×C4C2×#41×C15111yescharacteristic
422C8—22no—
423C8—22no—
424C8—41no—
425C8—42no—
426C8—42no—
427C8—41no—
428C22—21no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22C2×#121×C15111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4C2×#137×C15111yescharacteristic
446C4#575×C15112yes—
447C4#575×C15111yescharacteristic
448C2—41no—
449C2—42no—
450C2#3040×C15111yescharacteristic
451C2#3056×C15111yescharacteristic
452C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#41×C151D4
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
1. #3139×C151C2semidirect
5. #1704×C151C2semidirect
6. #1700×C151C2semidirect
7. #1683×C151C2semidirect
8. #1679×C151C2semidirect
9. #1569×C151C2semidirect
10. #1559×C151C2semidirect
11. #1556×C151C2semidirect
226. #19317C151direct (N × H)
227. C151#19317direct (N × H)
228. #3139C2×C151semidirect
232. #1704C2×C151semidirect
233. #1700C2×C151semidirect
234. #1683C2×C151semidirect
235. #1679C2×C151semidirect
236. #1569C2×C151semidirect
237. #1559C2×C151semidirect
238. #1556C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3139×C1512
#3116×C1512
#3079×C1512
#2970×C1512
#1704×C1512
#1700×C1512
#1683×C1512
#1679×C1512
#1569×C1512
#1559×C1512
#1556×C1512
#19317151