Finite Group Databasebeta

← C151×#18768 #50323693

Subgroups — C151×#18768 #50323693

Order 38656.

976 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C151C211yesmaximal, characteristic, complemented
2#3206×C151C211yesmaximal, characteristic
3#3103×C151C211yesmaximal, characteristic
4#3037×C151C211yesmaximal, characteristic
5#1645×C151C214yesmaximal, complemented
6#1623×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1487×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C2×#137×C151—21no—
11Q82×C151—22no—
12Q82×C151—22no—
13Q82×C151—22no—
14Q82×C151C2214yes—
15#532×C151C2211yescharacteristic
16C2×C4⋊Q8×C151—22no—
17C2×C4⋊Q8×C151—21no—
18C2×C4⋊Q8×C151—21no—
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151—21no—
21C2×C4×Q8×C151—21no—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24#492×C151C2212yes—
25#487×C151C2212yes—
26#481×C151—21no—
27#475×C151C2212yes—
28#464×C151—22no—
29#462×C151C2212yes—
30#461×C151—22no—
31#460×C151C2212yes—
32#460×C151C2212yes—
33#448×C151—21no—
34#448×C151—22no—
35C4×SD16×C151—22no—
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40#333×C151C2214yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—22no—
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151D411yescharacteristic
47C22×Q8×C151D412yes—
48#137×C151—44no—
49C2×Q16×C151—22no—
50C2×SD16×C151—22no—
51C2×SD16×C151—22no—
52C2×SD16×C151—24no—
53C2×M16×C151—21no—
54C4⋊Q8×C151—24no—
55C4⋊Q8×C151—24no—
56C4⋊Q8×C151—28no—
57C4⋊Q8×C151—24no—
58C4⋊Q8×C151—24no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—28no—
62C4⋊Q8×C151D412yes—
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2312yes—
65#127×C151C2311yescharacteristic
66#124×C151—21no—
67#121×C151—21no—
68#121×C151—21no—
69C4×Q8×C151—24no—
70C4×Q8×C151—24no—
71C4×Q8×C151—21no—
72C4×Q8×C151—21no—
73C4×Q8×C151—21no—
74C4×Q8×C151—21no—
75C4×Q8×C151—24no—
76C4×Q8×C151—24no—
77C4×Q8×C151D412yes—
78C4×Q8×C151D412yes—
79C4×Q8×C151C2312yes—
80C4×Q8×C151C2312yes—
81C4×D4×C151—21no—
82C4×D4×C151—21no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C42×C151—22no—
92C2×C42×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#106×C151—22no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—22no—
101#103×C151—22no—
102#103×C151—24no—
103#102×C151—22no—
104#102×C151—22no—
105C22⋊C8×C151—21no—
106C22⋊C8×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151C2312yes—
109#41×C151—42no—
110#41×C151—42no—
111C2×Q8×C151—24no—
112C2×Q8×C151—28no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—21no—
118C2×Q8×C151—82no—
119C2×Q8×C151—84no—
120C2×Q8×C151SD1614yescomplemented
121C2×Q8×C151C2×D412yes—
122C2×Q8×C151C2×D412yes—
123C2×Q8×C151C2×D414yes—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—41no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—41no—
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D411yescharacteristic
136C22×C4×C151C2×D411yescharacteristic
137Q16×C151—44no—
138SD16×C151—44no—
139SD16×C151—44no—
140SD16×C151—84no—
141M16×C151—42no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C4⋊C4×C151—28no—
146C4⋊C4×C151—28no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151C2×D412yes—
160C4⋊C4×C151C2×D412yes—
161C22⋊C4×C151—41no—
162C22⋊C4×C151—41no—
163C42×C151—28no—
164C42×C151—22no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—22no—
168C42×C151C2×D411yescharacteristic
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2411yescharacteristic
172C23×C151—41no—
173C23×C151#12011yescharacteristic
174Q8×C151—24no—
175Q8×C151—22no—
176Q8×C151—22no—
177Q8×C151—24no—
178Q8×C151—44no—
179Q8×C151—41no—
180Q8×C151—41no—
181Q8×C151—82no—
182Q8×C151—88no—
183Q8×C151C2×SD1614yes—
184Q8×C151#13714yescomplemented
185D4×C151—42no—
186D4×C151—41no—
187D4×C151—41no—
188D4×C151—42no—
189D4×C151—82no—
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—24no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—41no—
199C2×C4×C151—44no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—41no—
203C2×C4×C151—82no—
204C2×C4×C151#12011yescharacteristic
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151#12011yescharacteristic
207C2×C4×C151C2×SD1612yes—
208C2×C4×C151#13712yes—
209C2×C4×C151C22×D411yescharacteristic
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C22×D411yescharacteristic
212C8×C151—42no—
213C8×C151—42no—
214C8×C151—42no—
215C22×C151—21no—
216C22×C151—21no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151#44812yes—
221C22×C151C2×#12011yescharacteristic
222C4×C151—24no—
223C4×C151—24no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—21no—
227C4×C151—44no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—81no—
231C4×C151#44812yes—
232C4×C151C22×SD1611yescharacteristic
233C4×C151C2×#13711yescharacteristic
234C4×C151C2×#13712yes—
235C2×C151—22no—
236C2×C151—161no—
237C2×C151C2×#44811yescharacteristic
238C2×C151#300411yescharacteristic
239C2×C151#301911yescharacteristic
240#18768C15111yesmaximal, characteristic, direct product factor, Sylow
241C151#1876811yescharacteristic, direct product factor, Sylow
242C2×Q82C2×C15111yescharacteristic, complemented
243#3206C2×C15111yescharacteristic
244#3103C2×C15111yescharacteristic
245#3037C2×C15111yescharacteristic
246#1645C2×C15114yescomplemented
247#1623C2×C15114yescomplemented
248#1548C2×C15111yescharacteristic, complemented
249#1487C2×C15111yescharacteristic, complemented
250#1479C2×C15111yescharacteristic, complemented
251C2×#137—21no—
252Q82—22no—
253Q82—22no—
254Q82—22no—
255Q82C22×C15114yes—
256#532C22×C15111yescharacteristic
257C2×C4⋊Q8—22no—
258C2×C4⋊Q8—21no—
259C2×C4⋊Q8—21no—
260C2×C4⋊Q8C22×C15111yescharacteristic
261C2×C4×Q8—21no—
262C2×C4×Q8—21no—
263C2×C4×Q8C22×C15111yescharacteristic
264C2×C4×Q8C22×C15111yescharacteristic
265#492C22×C15112yes—
266#487C22×C15112yes—
267#481—21no—
268#475C22×C15112yes—
269#464—22no—
270#462C22×C15112yes—
271#461—22no—
272#460C22×C15112yes—
273#460C22×C15112yes—
274#448—21no—
275#448—22no—
276C4×SD16—22no—
277#431C22×C15111yescharacteristic
278#431C22×C15111yescharacteristic
279#423C22×C15111yescharacteristic
280#417—21no—
281#333C22×C15114yes—
282Q8⋊C8C22×C15114yes—
283Q8⋊C8C22×C15114yes—
284C2×#41—21no—
285C22×Q8—22no—
286C22×Q8D4×C15111yescharacteristic
287C22×Q8D4×C15111yescharacteristic
288C22×Q8D4×C15112yes—
289#137—44no—
290C2×Q16—22no—
291C2×SD16—22no—
292C2×SD16—22no—
293C2×SD16—24no—
294C2×M16—21no—
295C4⋊Q8—28no—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8—28no—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C15112yes—
304C4⋊Q8C23×C15111yescharacteristic
305C4⋊Q8C23×C15112yes—
306#127C23×C15111yescharacteristic
307#124—21no—
308#121—21no—
309#121—21no—
310C4×Q8—24no—
311C4×Q8—24no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8D4×C15112yes—
319C4×Q8D4×C15112yes—
320C4×Q8C23×C15112yes—
321C4×Q8C23×C15112yes—
322C4×D4—21no—
323C4×D4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C15111yescharacteristic
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C42—22no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42C23×C15111yescharacteristic
336#106—22no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C15112yes—
340C4⋊C8C23×C15112yes—
341#103—22no—
342#103—24no—
343#103—22no—
344#102—22no—
345#102—22no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C4×C8—21no—
349C4×C8C23×C15112yes—
350#41—42no—
351#41—42no—
352C2×Q8—24no—
353C2×Q8—28no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—82no—
360C2×Q8—84no—
361C2×Q8SD16×C15114yescomplemented
362C2×Q8C2×D4×C15112yes—
363C2×Q8C2×D4×C15112yes—
364C2×Q8C2×D4×C15114yes—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4C2×D4×C15111yescharacteristic
376C22×C4C2×D4×C15111yescharacteristic
377C22×C4C2×D4×C15111yescharacteristic
378Q16—44no—
379SD16—44no—
380SD16—44no—
381SD16—84no—
382M16—42no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C4⋊C4—28no—
387C4⋊C4—28no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4C2×D4×C15112yes—
401C4⋊C4C2×D4×C15112yes—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C42—28no—
405C42—22no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42C2×D4×C15111yescharacteristic
410C42C2×D4×C15111yescharacteristic
411C42C2×D4×C15111yescharacteristic
412C42C24×C15111yescharacteristic
413C23—41no—
414C23#120×C15111yescharacteristic
415Q8—24no—
416Q8—24no—
417Q8—22no—
418Q8—22no—
419Q8—44no—
420Q8—41no—
421Q8—41no—
422Q8—82no—
423Q8—88no—
424Q8C2×SD16×C15114yes—
425Q8#137×C15114yescomplemented
426D4—42no—
427D4—41no—
428D4—42no—
429D4—41no—
430D4—82no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—82no—
445C2×C4#120×C15111yescharacteristic
446C2×C4#120×C15111yescharacteristic
447C2×C4#120×C15111yescharacteristic
448C2×C4C2×SD16×C15112yes—
449C2×C4#137×C15112yes—
450C2×C4C22×D4×C15111yescharacteristic
451C2×C4C22×D4×C15111yescharacteristic
452C2×C4C22×D4×C15111yescharacteristic
453C8—42no—
454C8—42no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#448×C15112yes—
462C22C2×#120×C15111yescharacteristic
463C4—24no—
464C4—24no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—81no—
472C4#448×C15112yes—
473C4C22×SD16×C15111yescharacteristic
474C4C2×#137×C15111yescharacteristic
475C4C2×#137×C15112yes—
476C2—22no—
477C2—161no—
478C2C2×#448×C15111yescharacteristic
479C2#3004×C15111yescharacteristic
480C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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. C2×Q82×C151C2semidirect
5. #1645×C151C2semidirect
6. #1623×C151C2semidirect
7. #1548×C151C2semidirect
8. #1487×C151C2semidirect
9. #1479×C151C2semidirect
120. C2×Q8×C151SD16semidirect
184. Q8×C151#137semidirect
240. #18768C151direct (N × H)
241. C151#18768direct (N × H)
242. C2×Q82C2×C151semidirect
246. #1645C2×C151semidirect
247. #1623C2×C151semidirect
248. #1548C2×C151semidirect
249. #1487C2×C151semidirect
250. #1479C2×C151semidirect
361. C2×Q8SD16×C151semidirect
425. Q8#137×C151semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1512
#3206×C1512
#3103×C1512
#3037×C1512
#1645×C1512
#1623×C1512
#1548×C1512
#1487×C1512
#1479×C1512
#18768151