Finite Group Databasebeta

← C151×#18749 #50323674

Subgroups — C151×#18749 #50323674

Order 38656.

966 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2#3209×C151C211yesmaximal, characteristic, complemented
3#3104×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic
5#1644×C151C214yesmaximal, complemented
6#1632×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1487×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic
10#554×C151—22no—
11#554×C151—22no—
12#554×C151—22no—
13#554×C151C2214yes—
14#533×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—22no—
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×D4×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22C22×C4⋊C4×C151—21no—
23#494×C151C2212yescomplemented
24#487×C151C2212yescomplemented
25#484×C151—21no—
26#478×C151—22no—
27#477×C151C2212yescomplemented
28#476×C151C2212yes—
29#474×C151C2212yes—
30#462×C151—22no—
31#462×C151C2212yescomplemented
32#451×C151—21no—
33#451×C151—22no—
34C4×Q16×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#418×C151—21no—
40#333×C151C2214yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C22×Q8×C151D411yescharacteristic
44C22×Q8×C151D412yes—
45C22×D4×C151D411yescharacteristic
46C23×C4×C151—22no—
47C23×C4×C151—21no—
48C2×Q16×C151—22no—
49C2×Q16×C151—24no—
50C2×M16×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D412yes—
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2311yescharacteristic
56C4⋊Q8×C151C2312yes—
57#125×C151—24no—
58#125×C151—24no—
59#125×C151—21no—
60C22⋊Q8×C151—24no—
61C22⋊Q8×C151—28no—
62C22⋊Q8×C151—21no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151—24no—
65C22⋊Q8×C151—28no—
66C4×Q8×C151—21no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151D412yes—
71C4×Q8×C151C2312yes—
72C4×D4×C151—24no—
73C4×D4×C151—24no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151D412yes—
77C4×D4×C151C2312yes—
78#117×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—24no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—24no—
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D411yescharacteristic
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—22no—
93#107×C151—22no—
94#106×C151—22no—
95C4⋊C8×C151—21no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151C2312yes—
98C4⋊C8×C151C2312yes—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—24no—
102#102×C151—22no—
103#102×C151—22no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106C4×C8×C151—21no—
107C4×C8×C151C2312yes—
108C24×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—22no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—42no—
114C2×Q8×C151—82no—
115C2×Q8×C151C2×D412yes—
116C2×Q8×C151C2×D414yes—
117C2×D4×C151—21no—
118C2×D4×C151—22no—
119C2×D4×C151Q1614yescomplemented
120C2×D4×C151C2×D412yes—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—28no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—44no—
129C22×C4×C151—84no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133Q16×C151—44no—
134Q16×C151—84no—
135M16×C151—42no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C4⋊C4×C151—28no—
140C4⋊C4×C151—28no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151C2×D412yes—
156C4⋊C4×C151C2×D412yes—
157C22⋊C4×C151—28no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—22no—
160C22⋊C4×C151—41no—
161C42×C151—22no—
162C42×C151—22no—
163C42×C151—41no—
164C42×C151C2×D411yescharacteristic
165C42×C151C2×D411yescharacteristic
166C42×C151C2×D411yescharacteristic
167C42×C151C2411yescharacteristic
168C23×C151—22no—
169C23×C151—24no—
170C23×C151—42no—
171C23×C151—42no—
172C23×C151#12011yescharacteristic
173Q8×C151—22no—
174Q8×C151—22no—
175Q8×C151—44no—
176Q8×C151—42no—
177Q8×C151—42no—
178Q8×C151—42no—
179Q8×C151—82no—
180D4×C151—22no—
181D4×C151—24no—
182D4×C151C2×Q1614yes—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—24no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—41no—
189C2×C4×C151—44no—
190C2×C4×C151—42no—
191C2×C4×C151—44no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—44no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—88no—
198C2×C4×C151#12011yescharacteristic
199C2×C4×C151#12011yescharacteristic
200C2×C4×C151#12011yescharacteristic
201C2×C4×C151C2×Q1612yes—
202C2×C4×C151#13712yes—
203C2×C4×C151C22×D411yescharacteristic
204C2×C4×C151C22×D411yescharacteristic
205C2×C4×C151C22×D411yescharacteristic
206C8×C151—42no—
207C8×C151—42no—
208C8×C151—42no—
209C22×C151—21no—
210C22×C151—21no—
211C22×C151—24no—
212C22×C151—48no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151#45112yes—
216C22×C151C2×#12011yescharacteristic
217C4×C151—21no—
218C4×C151—21no—
219C4×C151—21no—
220C4×C151—42no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—44no—
224C4×C151—81no—
225C4×C151—81no—
226C4×C151#45112yes—
227C4×C151C22×Q1611yescharacteristic
228C4×C151C2×#13711yescharacteristic
229C4×C151#57512yes—
230C2×C151—22no—
231C2×C151—44no—
232C2×C151C2×#45111yescharacteristic
233C2×C151#300511yescharacteristic
234C2×C151#301911yescharacteristic
235#18749C15111yesmaximal, characteristic, direct product factor, Sylow
236C151#1874911yescharacteristic, direct product factor, Sylow
237C2×#554C2×C15111yescharacteristic
238#3209C2×C15111yescharacteristic, complemented
239#3104C2×C15111yescharacteristic, complemented
240#3077C2×C15111yescharacteristic
241#1644C2×C15114yescomplemented
242#1632C2×C15114yescomplemented
243#1548C2×C15111yescharacteristic, complemented
244#1487C2×C15111yescharacteristic, complemented
245#1478C2×C15111yescharacteristic
246#554—22no—
247#554—22no—
248#554—22no—
249#554C22×C15114yes—
250#533C22×C15111yescharacteristic
251C2×C4⋊Q8C22×C15111yescharacteristic
252C2×#125—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—22no—
255C2×C4×Q8C22×C15111yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C22×C15111yescharacteristic
258C22×C4⋊C4—21no—
259#494C22×C15112yescomplemented
260#487C22×C15112yescomplemented
261#484—21no—
262#478—22no—
263#477C22×C15112yescomplemented
264#476C22×C15112yes—
265#474C22×C15112yes—
266#462—22no—
267#462C22×C15112yescomplemented
268#451—21no—
269#451—22no—
270C4×Q16—22no—
271#431C22×C15111yescharacteristic
272#431C22×C15111yescharacteristic
273#428—21no—
274#423C22×C15111yescharacteristic
275#418—21no—
276#333C22×C15114yescomplemented
277Q8⋊C8C22×C15114yescomplemented
278D4⋊C8C22×C15114yes—
279C22×Q8D4×C15111yescharacteristic
280C22×Q8D4×C15112yes—
281C22×D4D4×C15111yescharacteristic
282C23×C4—22no—
283C23×C4—21no—
284C2×Q16—22no—
285C2×Q16—24no—
286C2×M16—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8D4×C15112yes—
290C4⋊Q8C23×C15111yescharacteristic
291C4⋊Q8C23×C15111yescharacteristic
292C4⋊Q8C23×C15112yes—
293#125—24no—
294#125—24no—
295#125—21no—
296C22⋊Q8—24no—
297C22⋊Q8—28no—
298C22⋊Q8—24no—
299C22⋊Q8—28no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C15112yes—
307C4×Q8C23×C15112yes—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4D4×C15112yes—
313C4×D4C23×C15112yes—
314#117—21no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4D4×C15111yescharacteristic
323C2×C4⋊C4D4×C15111yescharacteristic
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C42—21no—
327C2×C42C23×C15111yescharacteristic
328#107—22no—
329#107—22no—
330#106—22no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8C23×C15112yes—
334C4⋊C8C23×C15112yes—
335#103—22no—
336#103—24no—
337#103—22no—
338#102—22no—
339#102—22no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C4×C8—21no—
343C4×C8C23×C15112yes—
344C24—21no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×Q8—82no—
351C2×Q8C2×D4×C15112yes—
352C2×Q8C2×D4×C15114yes—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4Q16×C15114yescomplemented
356C2×D4C2×D4×C15112yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—28no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—44no—
365C22×C4—84no—
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C2×D4×C15111yescharacteristic
369Q16—44no—
370Q16—84no—
371M16—42no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C4⋊C4—28no—
376C4⋊C4—28no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C15112yes—
392C4⋊C4C2×D4×C15112yes—
393C22⋊C4—28no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—41no—
397C42—22no—
398C42—22no—
399C42—41no—
400C42C2×D4×C15111yescharacteristic
401C42C2×D4×C15111yescharacteristic
402C42C2×D4×C15111yescharacteristic
403C42C24×C15111yescharacteristic
404C23—24no—
405C23—22no—
406C23—42no—
407C23—42no—
408C23#120×C15111yescharacteristic
409Q8—22no—
410Q8—22no—
411Q8—44no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415Q8—82no—
416D4—24no—
417D4—22no—
418D4C2×Q16×C15114yes—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—88no—
434C2×C4#120×C15111yescharacteristic
435C2×C4#120×C15111yescharacteristic
436C2×C4#120×C15111yescharacteristic
437C2×C4C2×Q16×C15112yes—
438C2×C4#137×C15112yes—
439C2×C4C22×D4×C15111yescharacteristic
440C2×C4C22×D4×C15111yescharacteristic
441C2×C4C22×D4×C15111yescharacteristic
442C8—42no—
443C8—42no—
444C8—42no—
445C22—21no—
446C22—21no—
447C22—24no—
448C22—48no—
449C22—42no—
450C22—42no—
451C22#451×C15112yes—
452C22C2×#120×C15111yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—44no—
460C4—81no—
461C4—81no—
462C4#451×C15112yes—
463C4C22×Q16×C15111yescharacteristic
464C4C2×#137×C15111yescharacteristic
465C4#575×C15112yes—
466C2—22no—
467C2—44no—
468C2C2×#451×C15111yescharacteristic
469C2#3005×C15111yescharacteristic
470C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×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
2. #3209×C151C2semidirect
3. #3104×C151C2semidirect
5. #1644×C151C2semidirect
6. #1632×C151C2semidirect
7. #1548×C151C2semidirect
8. #1487×C151C2semidirect
23. #494×C151C22semidirect
24. #487×C151C22semidirect
27. #477×C151C22semidirect
31. #462×C151C22semidirect
40. #333×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
119. C2×D4×C151Q16semidirect
235. #18749C151direct (N × H)
236. C151#18749direct (N × H)
238. #3209C2×C151semidirect
239. #3104C2×C151semidirect
241. #1644C2×C151semidirect
242. #1632C2×C151semidirect
243. #1548C2×C151semidirect
244. #1487C2×C151semidirect
259. #494C22×C151semidirect
260. #487C22×C151semidirect
263. #477C22×C151semidirect
267. #462C22×C151semidirect
276. #333C22×C151semidirect
277. Q8⋊C8C22×C151semidirect
355. C2×D4Q16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
#3209×C1512
#3104×C1512
#3077×C1512
#1644×C1512
#1632×C1512
#1548×C1512
#1487×C1512
#1478×C1512
#18749151