Finite Group Databasebeta

← C151×#18623 #50323548

Subgroups — C151×#18623 #50323548

Order 38656.

970 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3C2×#494×C151C211yesmaximal, characteristic, complemented
4#3079×C151C211yesmaximal, characteristic
5#1633×C151C214yesmaximal, complemented
6#1632×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic
10C22×Q16×C151—22no—
11Q82×C151C2212yes—
12#557×C151—21no—
13#554×C151—22no—
14#554×C151C2212yes—
15D4×Q8×C151—22no—
16D4×Q8×C151—21no—
17#544×C151—22no—
18#544×C151—21no—
19#533×C151—21no—
20#533×C151C2211yescharacteristic
21C2×C4⋊Q8×C151—21no—
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#520×C151—21no—
25C4×#41×C151C2211yescharacteristic
26#500×C151—21no—
27#494×C151—22no—
28#494×C151C2214yes—
29#487×C151—21no—
30#484×C151—22no—
31#477×C151C2214yes—
32#477×C151C2212yes—
33#476×C151C2212yes—
34#475×C151—21no—
35#474×C151—21no—
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40C2×C4×C8×C151C2211yescharacteristic
41#333×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43Q8⋊C8×C151C2212yes—
44D4⋊C8×C151C2212yes—
45C2×#41×C151D411yescharacteristic
46C22×Q8×C151—22no—
47C22×Q8×C151—21no—
48C22×Q8×C151D412yes—
49C2×Q16×C151—28no—
50C2×Q16×C151—48no—
51C2×M16×C151—21no—
52C22×C8×C151—21no—
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—24no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D412yes—
66C4⋊Q8×C151C2312yes—
67C4⋊Q8×C151C2312yes—
68#125×C151—22no—
69#125×C151—24no—
70#125×C151—22no—
71#125×C151—21no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151—24no—
78C22⋊Q8×C151D412yes—
79C4×Q8×C151—22no—
80C4×Q8×C151—21no—
81C4×Q8×C151—22no—
82C4×Q8×C151—22no—
83C4×Q8×C151D411yescharacteristic
84C4×Q8×C151C2311yescharacteristic
85C4×Q8×C151C2312yes—
86C4×D4×C151—24no—
87C4×D4×C151—22no—
88C4×D4×C151—21no—
89C4×D4×C151—21no—
90C4×D4×C151D411yescharacteristic
91C4×D4×C151C2311yescharacteristic
92#117×C151—22no—
93#117×C151—21no—
94#117×C151—21no—
95#117×C151D411yescharacteristic
96C2×C4⋊C4×C151—22no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—22no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C42×C151—21no—
103C2×C42×C151C2311yescharacteristic
104#107×C151—22no—
105#107×C151—24no—
106#106×C151—22no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151C2312yes—
109C4⋊C8×C151C2312yes—
110#103×C151—22no—
111#103×C151—24no—
112#102×C151—22no—
113C22⋊C8×C151—21no—
114C4×C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151C2312yes—
117#41×C151—22no—
118#41×C151Q1614yescomplemented
119C2×Q8×C151—24no—
120C2×Q8×C151—22no—
121C2×Q8×C151—21no—
122C2×Q8×C151—22no—
123C2×Q8×C151—44no—
124C2×Q8×C151—44no—
125C2×Q8×C151—41no—
126C2×Q8×C151—84no—
127C2×Q8×C151C2×D412yes—
128C2×Q8×C151C2×D411yescharacteristic
129C2×Q8×C151C2×D414yes—
130C2×D4×C151—21no—
131C2×D4×C151C2×D411yescharacteristic
132C22×C4×C151—21no—
133C22×C4×C151—24no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—41no—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141Q16×C151—416no—
142M16×C151—42no—
143C2×C8×C151—24no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C4⋊C4×C151—24no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—41no—
165C4⋊C4×C151—41no—
166C4⋊C4×C151C2×D411yescharacteristic
167C4⋊C4×C151C2×D412yes—
168C4⋊C4×C151C2×D411yescharacteristic
169C22⋊C4×C151—24no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—21no—
172C22⋊C4×C151—21no—
173C22⋊C4×C151—21no—
174C42×C151—24no—
175C42×C151—21no—
176C42×C151—21no—
177C42×C151—21no—
178C42×C151—22no—
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2411yescharacteristic
183C23×C151—21no—
184C23×C151#12011yescharacteristic
185Q8×C151—21no—
186Q8×C151—24no—
187Q8×C151—44no—
188Q8×C151—44no—
189Q8×C151—44no—
190Q8×C151—42no—
191Q8×C151—84no—
192Q8×C151—82no—
193Q8×C151C2×Q1612yescomplemented
194D4×C151—24no—
195D4×C151—21no—
196D4×C151C2×Q1612yescomplemented
197C2×C4×C151—21no—
198C2×C4×C151—22no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—21no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—21no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—82no—
210C2×C4×C151—84no—
211C2×C4×C151—82no—
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151C2×Q1612yes—
216C2×C4×C151#13712yes—
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C22×D411yescharacteristic
220C8×C151—24no—
221C8×C151—42no—
222C8×C151—42no—
223C22×C151—21no—
224C22×C151—21no—
225C22×C151—22no—
226C22×C151—41no—
227C22×C151—41no—
228C22×C151#45112yes—
229C22×C151C2×#12011yescharacteristic
230C4×C151—22no—
231C4×C151—21no—
232C4×C151—21no—
233C4×C151—41no—
234C4×C151—42no—
235C4×C151—41no—
236C4×C151—44no—
237C4×C151—42no—
238C4×C151—82no—
239C4×C151#45112yes—
240C4×C151#45312yes—
241C4×C151C22×Q1611yescharacteristic
242C4×C151C2×#13711yescharacteristic
243C4×C151#57812yes—
244C2×C151—22no—
245C2×C151—42no—
246C2×C151C2×#45111yescharacteristic
247C2×C151#301111yescharacteristic
248C2×C151C2×#45311yescharacteristic
249#18623C15111yesmaximal, characteristic, direct product factor, Sylow
250C151#1862311yescharacteristic, direct product factor, Sylow
251#3503C2×C15111yescharacteristic
252#3230C2×C15111yescharacteristic, complemented
253C2×#494C2×C15111yescharacteristic, complemented
254#3079C2×C15111yescharacteristic
255#1633C2×C15114yescomplemented
256#1632C2×C15114yescomplemented
257#1548C2×C15111yescharacteristic, complemented
258#1493C2×C15111yescharacteristic, complemented
259#1476C2×C15111yescharacteristic
260C22×Q16—22no—
261Q82C22×C15112yes—
262#557—21no—
263#554—22no—
264#554C22×C15112yes—
265D4×Q8—22no—
266D4×Q8—21no—
267#544—22no—
268#544—21no—
269#533—21no—
270#533C22×C15111yescharacteristic
271C2×C4⋊Q8—21no—
272C2×C4⋊Q8C22×C15111yescharacteristic
273C2×C4⋊Q8C22×C15111yescharacteristic
274#520—21no—
275C4×#41C22×C15111yescharacteristic
276#500—21no—
277#494—22no—
278#494C22×C15114yes—
279#487—21no—
280#484—22no—
281#477C22×C15112yes—
282#477C22×C15114yes—
283#476C22×C15112yes—
284#475—21no—
285#474—21no—
286#431C22×C15111yescharacteristic
287#428—21no—
288#423C22×C15111yescharacteristic
289#417—21no—
290C2×C4×C8C22×C15111yescharacteristic
291#333C22×C15114yes—
292Q8⋊C8C22×C15114yes—
293Q8⋊C8C22×C15112yes—
294D4⋊C8C22×C15112yes—
295C2×#41D4×C15111yescharacteristic
296C22×Q8—22no—
297C22×Q8—21no—
298C22×Q8D4×C15112yes—
299C2×Q16—28no—
300C2×Q16—48no—
301C2×M16—21no—
302C22×C8—21no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—24no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8D4×C15112yes—
314C4⋊Q8D4×C15111yescharacteristic
315C4⋊Q8D4×C15111yescharacteristic
316C4⋊Q8C23×C15112yes—
317C4⋊Q8C23×C15112yes—
318#125—22no—
319#125—24no—
320#125—22no—
321#125—21no—
322C22⋊Q8—22no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8—21no—
328C22⋊Q8D4×C15112yes—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—21no—
333C4×Q8D4×C15111yescharacteristic
334C4×Q8C23×C15111yescharacteristic
335C4×Q8C23×C15112yes—
336C4×D4—24no—
337C4×D4—22no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4D4×C15111yescharacteristic
341C4×D4C23×C15111yescharacteristic
342#117—22no—
343#117—21no—
344#117—21no—
345#117D4×C15111yescharacteristic
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C42—21no—
353C2×C42C23×C15111yescharacteristic
354#107—22no—
355#107—24no—
356#106—22no—
357C4⋊C8—21no—
358C4⋊C8C23×C15112yes—
359C4⋊C8C23×C15112yes—
360#103—22no—
361#103—24no—
362#102—22no—
363C22⋊C8—21no—
364C4×C8—21no—
365C4×C8—21no—
366C4×C8C23×C15112yes—
367#41—22no—
368#41Q16×C15114yescomplemented
369C2×Q8—24no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—44no—
374C2×Q8—44no—
375C2×Q8—41no—
376C2×Q8—84no—
377C2×Q8C2×D4×C15112yes—
378C2×Q8C2×D4×C15111yescharacteristic
379C2×Q8C2×D4×C15114yes—
380C2×D4—21no—
381C2×D4C2×D4×C15111yescharacteristic
382C22×C4—21no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—41no—
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C2×D4×C15111yescharacteristic
390C22×C4C2×D4×C15111yescharacteristic
391Q16—416no—
392M16—42no—
393C2×C8—24no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4C2×D4×C15111yescharacteristic
417C4⋊C4C2×D4×C15112yes—
418C4⋊C4C2×D4×C15111yescharacteristic
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C42—24no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—22no—
429C42C2×D4×C15111yescharacteristic
430C42C2×D4×C15111yescharacteristic
431C42C2×D4×C15111yescharacteristic
432C42C24×C15111yescharacteristic
433C23—21no—
434C23#120×C15111yescharacteristic
435Q8—21no—
436Q8—24no—
437Q8—44no—
438Q8—44no—
439Q8—44no—
440Q8—42no—
441Q8—84no—
442Q8—82no—
443Q8C2×Q16×C15112yescomplemented
444D4—24no—
445D4—21no—
446D4C2×Q16×C15112yescomplemented
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—82no—
460C2×C4—84no—
461C2×C4—82no—
462C2×C4#120×C15111yescharacteristic
463C2×C4#120×C15111yescharacteristic
464C2×C4#120×C15111yescharacteristic
465C2×C4C2×Q16×C15112yes—
466C2×C4#137×C15112yes—
467C2×C4C22×D4×C15111yescharacteristic
468C2×C4C22×D4×C15111yescharacteristic
469C2×C4C22×D4×C15111yescharacteristic
470C8—24no—
471C8—42no—
472C8—42no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—41no—
477C22—41no—
478C22#451×C15112yes—
479C22C2×#120×C15111yescharacteristic
480C4—22no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—42no—
485C4—41no—
486C4—44no—
487C4—42no—
488C4—82no—
489C4#451×C15112yes—
490C4#453×C15112yes—
491C4C22×Q16×C15111yescharacteristic
492C4C2×#137×C15111yescharacteristic
493C4#578×C15112yes—
494C2—22no—
495C2—42no—
496C2C2×#451×C15111yescharacteristic
497C2#3011×C15111yescharacteristic
498C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
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
2. #3230×C151C2semidirect
3. C2×#494×C151C2semidirect
5. #1633×C151C2semidirect
6. #1632×C151C2semidirect
7. #1548×C151C2semidirect
8. #1493×C151C2semidirect
118. #41×C151Q16semidirect
193. Q8×C151C2×Q16semidirect
196. D4×C151C2×Q16semidirect
249. #18623C151direct (N × H)
250. C151#18623direct (N × H)
252. #3230C2×C151semidirect
253. C2×#494C2×C151semidirect
255. #1633C2×C151semidirect
256. #1632C2×C151semidirect
257. #1548C2×C151semidirect
258. #1493C2×C151semidirect
368. #41Q16×C151semidirect
443. Q8C2×Q16×C151semidirect
446. D4C2×Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3230×C1512
C2×#494×C1512
#3079×C1512
#1633×C1512
#1632×C1512
#1548×C1512
#1493×C1512
#1476×C1512
#18623151