Finite Group Databasebeta

← C151×#23616 #50328541

Subgroups — C151×#23616 #50328541

Order 38656.

1102 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C151C211yesmaximal, characteristic, complemented
2C2×#424×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C211yesmaximal, characteristic
4C2×#416×C151C211yesmaximal, characteristic
5#2317×C151C211yesmaximal, characteristic, complemented
6#2311×C151C211yesmaximal, characteristic
7#2068×C151C212yesmaximal, complemented
8#2067×C151C212yesmaximal, complemented
9#2066×C151C212yesmaximal, complemented
10#2065×C151C212yesmaximal, complemented
11C2×#340×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C23×C8×C151C2211yescharacteristic
15C2×#117×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19#428×C151—24no—
20C2×#107×C151C2212yes—
21C2×#106×C151C2212yes—
22#424×C151—24no—
23C2×C4⋊C8×C151C2212yes—
24C2×C4⋊C8×C151C2212yes—
25#417×C151—24no—
26#416×C151—24no—
27C2×#103×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2212yes—
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2212yes—
33#391×C151C2212yes—
34#390×C151C2212yes—
35#389×C151C2212yes—
36#389×C151C2212yes—
37#386×C151—22no—
38#385×C151—22no—
39#384×C151—21no—
40#382×C151—21no—
41#380×C151—21no—
42#380×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C2×#41×C151—22no—
46C2×#41×C151—22no—
47C2×#41×C151—22no—
48C2×#41×C151—22no—
49C2×#41×C151—22no—
50C2×#41×C151Q814yes—
51C22×Q8×C151C2311yescharacteristic
52C22×D4×C151—21no—
53C22×D4×C151C2311yescharacteristic
54C23×C4×C151—21no—
55C23×C4×C151—21no—
56C23×C4×C151—21no—
57C23×C4×C151C2311yescharacteristic
58C2×M16×C151—22no—
59C2×M16×C151—22no—
60C2×M16×C151D414yes—
61C22×C8×C151—22no—
62C22×C8×C151—22no—
63C22×C8×C151—22no—
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2312yes—
67#117×C151—22no—
68#117×C151—22no—
69#117×C151—22no—
70#117×C151D414yes—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151D411yescharacteristic
80C2×C4⋊C4×C151D411yescharacteristic
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151D412yes—
89C2×C42×C151—21no—
90C2×C42×C151C2312yes—
91#107×C151—24no—
92#106×C151—24no—
93C4⋊C8×C151—24no—
94C4⋊C8×C151—24no—
95#103×C151—24no—
96#103×C151—22no—
97#103×C151—22no—
98#102×C151—24no—
99#102×C151—22no—
100#102×C151—22no—
101#95×C151—22no—
102#95×C151—22no—
103#95×C151—22no—
104#95×C151—22no—
105C24×C151—21no—
106C24×C151C2×D411yescharacteristic
107#41×C151—28no—
108#41×C151—28no—
109#41×C151—44no—
110#41×C151—44no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151C2×Q812yes—
117C2×D4×C151—24no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—42no—
124C2×D4×C151—42no—
125C2×D4×C151C2×Q812yes—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—81no—
137C22×C4×C151—81no—
138C22×C4×C151—81no—
139C22×C4×C151—81no—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×Q812yes—
146C22×C4×C151#4112yes—
147C22×C4×C151#4112yes—
148C22×C4×C151#4112yes—
149C22×C4×C151C2411yescharacteristic
150M16×C151—28no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—44no—
160C2×C8×C151C2×D414yes—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151—42no—
171C4⋊C4×C151—82no—
172C4⋊C4×C151—82no—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D412yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—82no—
178C22⋊C4×C151—82no—
179C42×C151—24no—
180C42×C151—22no—
181C42×C151—22no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—22no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151#12112yes—
194C23×C151#12112yes—
195C23×C151C22⋊Q812yes—
196C23×C151C22×D411yescharacteristic
197Q8×C151—22no—
198Q8×C151—22no—
199Q8×C151—41no—
200Q8×C151—41no—
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—48no—
204D4×C151—41no—
205D4×C151—41no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—48no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—84no—
229C2×C4×C151—84no—
230C2×C4×C151#12114yes—
231C2×C4×C151#12112yes—
232C2×C4×C151#12112yes—
233C2×C4×C151C22⋊Q814yes—
234C2×C4×C151C22⋊Q814yes—
235C2×C4×C151C22⋊Q812yes—
236C2×C4×C151#12614yes—
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C22×D411yescharacteristic
239C2×C4×C151C22×Q811yescharacteristic
240C2×C4×C151C2×#4111yescharacteristic
241C2×C4×C151C2×#4111yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C8×C151—24no—
244C8×C151—41no—
245C8×C151—41no—
246C22×C151—22no—
247C22×C151—22no—
248C22×C151—22no—
249C22×C151—22no—
250C22×C151—22no—
251C22×C151—22no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—81no—
259C22×C151#39614yes—
260C22×C151C2×#12111yescharacteristic
261C22×C151C2×#12111yescharacteristic
262C22×C151C2×C22⋊Q811yescharacteristic
263C22×C151#57611yescharacteristic
264C22×C151#57711yescharacteristic
265C22×C151#57711yescharacteristic
266C22×C151#57811yescharacteristic
267C4×C151—42no—
268C4×C151—42no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—42no—
272C4×C151—82no—
273C4×C151—82no—
274C4×C151#39614yes—
275C4×C151C2×#12111yescharacteristic
276C4×C151C2×C22⋊Q811yescharacteristic
277C4×C151C2×C22⋊Q811yescharacteristic
278C4×C151C2×#12611yescharacteristic
279C2×C151—24no—
280C2×C151—82no—
281C2×C151C2×#39611yescharacteristic
282C2×C151#304511yescharacteristic
283C2×C151#304611yescharacteristic
284C2×C151#306211yescharacteristic
285C2×C151#306311yescharacteristic
286C2×C151#308311yescharacteristic
287C2×C151#308411yescharacteristic
288#23616C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#2361611yescharacteristic, direct product factor, Sylow
290C2×#428C2×C15111yescharacteristic, complemented
291C2×#424C2×C15111yescharacteristic, complemented
292C2×#417C2×C15111yescharacteristic
293C2×#416C2×C15111yescharacteristic
294#2317C2×C15111yescharacteristic, complemented
295#2311C2×C15111yescharacteristic
296#2068C2×C15112yescomplemented
297#2067C2×C15112yescomplemented
298#2066C2×C15112yescomplemented
299#2065C2×C15112yescomplemented
300C2×#340C2×C15111yescharacteristic, complemented
301C22×#41C22×C15111yescharacteristic
302C22×M16C22×C15111yescharacteristic
303C23×C8C22×C15111yescharacteristic
304C2×#117C22×C15111yescharacteristic
305C2×#117C22×C15111yescharacteristic
306C22×C4⋊C4C22×C15111yescharacteristic
307C22×C4⋊C4C22×C15111yescharacteristic
308#428—24no—
309C2×#107C22×C15112yes—
310C2×#106C22×C15112yes—
311#424—24no—
312C2×C4⋊C8C22×C15112yes—
313C2×C4⋊C8C22×C15112yes—
314#417—24no—
315#416—24no—
316C2×#103C22×C15111yescharacteristic
317C2×#103C22×C15112yes—
318C2×#103C22×C15111yescharacteristic
319C2×#102C22×C15111yescharacteristic
320C2×#102C22×C15112yes—
321C2×#102C22×C15111yescharacteristic
322#391C22×C15112yes—
323#390C22×C15112yes—
324#389C22×C15112yes—
325#389C22×C15112yes—
326#386—22no—
327#385—22no—
328#384—21no—
329#382—21no—
330#380—21no—
331#380—21no—
332#340C22×C15112yes—
333#340C22×C15112yes—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41Q8×C15114yes—
340C22×Q8C23×C15111yescharacteristic
341C22×D4—21no—
342C22×D4C23×C15111yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4C23×C15111yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16D4×C15114yes—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8C23×C15111yescharacteristic
354C22×C8C23×C15111yescharacteristic
355C22×C8C23×C15112yes—
356#117—22no—
357#117—22no—
358#117—22no—
359#117D4×C15114yes—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4D4×C15111yescharacteristic
369C2×C4⋊C4D4×C15111yescharacteristic
370C2×C4⋊C4C23×C15112yes—
371C2×C4⋊C4C23×C15112yes—
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4D4×C15112yes—
378C2×C42—21no—
379C2×C42C23×C15112yes—
380#107—24no—
381#106—24no—
382C4⋊C8—24no—
383C4⋊C8—24no—
384#103—24no—
385#103—22no—
386#103—22no—
387#102—24no—
388#102—22no—
389#102—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394C24—21no—
395C24C2×D4×C15111yescharacteristic
396#41—28no—
397#41—28no—
398#41—44no—
399#41—44no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8C2×Q8×C15112yes—
406C2×D4—24no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4C2×Q8×C15112yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4C2×D4×C15112yes—
430C22×C4C2×D4×C15112yes—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15112yes—
433C22×C4C2×D4×C15112yes—
434C22×C4C2×Q8×C15112yes—
435C22×C4#41×C15112yes—
436C22×C4#41×C15112yes—
437C22×C4#41×C15112yes—
438C22×C4C24×C15111yescharacteristic
439M16—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—44no—
449C2×C8C2×D4×C15114yes—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—82no—
461C4⋊C4—82no—
462C4⋊C4C2×D4×C15112yes—
463C4⋊C4C2×D4×C15112yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—82no—
467C22⋊C4—82no—
468C42—24no—
469C42—22no—
470C42—22no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23#121×C15112yes—
483C23#121×C15112yes—
484C23C22⋊Q8×C15112yes—
485C23C22×D4×C15111yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490D4—22no—
491D4—22no—
492D4—48no—
493D4—41no—
494D4—41no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4#121×C15112yes—
520C2×C4#121×C15112yes—
521C2×C4#121×C15114yes—
522C2×C4C22⋊Q8×C15112yes—
523C2×C4C22⋊Q8×C15114yes—
524C2×C4C22⋊Q8×C15114yes—
525C2×C4#126×C15114yes—
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×Q8×C15111yescharacteristic
529C2×C4C2×#41×C15111yescharacteristic
530C2×C4C2×#41×C15111yescharacteristic
531C2×C4C2×#41×C15111yescharacteristic
532C8—24no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22#396×C15114yes—
549C22C2×#121×C15111yescharacteristic
550C22C2×#121×C15111yescharacteristic
551C22C2×C22⋊Q8×C15111yescharacteristic
552C22#576×C15111yescharacteristic
553C22#577×C15111yescharacteristic
554C22#577×C15111yescharacteristic
555C22#578×C15111yescharacteristic
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—82no—
562C4—82no—
563C4#396×C15114yes—
564C4C2×#121×C15111yescharacteristic
565C4C2×C22⋊Q8×C15111yescharacteristic
566C4C2×C22⋊Q8×C15111yescharacteristic
567C4C2×#126×C15111yescharacteristic
568C2—24no—
569C2—82no—
570C2C2×#396×C15111yescharacteristic
571C2#3045×C15111yescharacteristic
572C2#3046×C15111yescharacteristic
573C2#3062×C15111yescharacteristic
574C2#3063×C15111yescharacteristic
575C2#3083×C15111yescharacteristic
576C2#3084×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#428×C151C2semidirect
2. C2×#424×C151C2semidirect
5. #2317×C151C2semidirect
7. #2068×C151C2semidirect
8. #2067×C151C2semidirect
9. #2066×C151C2semidirect
10. #2065×C151C2semidirect
11. C2×#340×C151C2semidirect
288. #23616C151direct (N × H)
289. C151#23616direct (N × H)
290. C2×#428C2×C151semidirect
291. C2×#424C2×C151semidirect
294. #2317C2×C151semidirect
296. #2068C2×C151semidirect
297. #2067C2×C151semidirect
298. #2066C2×C151semidirect
299. #2065C2×C151semidirect
300. C2×#340C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1512
C2×#424×C1512
C2×#417×C1512
C2×#416×C1512
#2317×C1512
#2311×C1512
#2068×C1512
#2067×C1512
#2066×C1512
#2065×C1512
C2×#340×C1512
#23616151