Finite Group Databasebeta

← C151×#13422 #50318347

Subgroups — C151×#13422 #50318347

Order 38656.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2669×C151C211yesmaximal, characteristic
2C2×#353×C151C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C151C211yesmaximal, characteristic, complemented
4#1889×C151C211yesmaximal, characteristic, complemented
5#1887×C151C211yesmaximal, characteristic, complemented
6#1867×C151C211yesmaximal, characteristic, complemented
7#1390×C151C211yesmaximal, characteristic, complemented
8C2×#127×C151C2211yescharacteristic
9C2×#121×C151—21no—
10C2×#120×C151—21no—
11C2×#120×C151C2211yescharacteristic
12#518×C151C2211yescharacteristic
13#418×C151—21no—
14C2×#100×C151C2211yescharacteristic
15C2×#99×C151C2211yescharacteristic
16C2×#99×C151C2211yescharacteristic
17#394×C151—21no—
18#392×C151—21no—
19#392×C151—21no—
20#388×C151—21no—
21#386×C151C2211yescharacteristic
22#385×C151—21no—
23#379×C151—21no—
24#353×C151—22no—
25AΣL(1,𝔽16)×C151—22no—
26#342×C151—21no—
27#342×C151—21no—
28#339×C151—21no—
29C25×C151D411yescharacteristic
30C22×D4×C151—21no—
31C22×D4×C151—21no—
32C22×D4×C151—21no—
33C22×D4×C151—21no—
34C22×D4×C151—21no—
35C22×D4×C151D411yescharacteristic
36C22×D4×C151C2311yescharacteristic
37C23×C4×C151D411yescharacteristic
38C2×M16×C151—21no—
39#127×C151—21no—
40#127×C151—21no—
41#127×C151—21no—
42#127×C151—21no—
43#121×C151—44no—
44#120×C151—21no—
45#120×C151—21no—
46#120×C151—21no—
47#120×C151—21no—
48#120×C151—44no—
49C4×D4×C151—41no—
50C4×D4×C151—41no—
51#117×C151—21no—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—41no—
54C2×C22⋊C4×C151—21no—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—21no—
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—21no—
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—21no—
61C2×C22⋊C4×C151—21no—
62C2×C22⋊C4×C151—21no—
63C2×C22⋊C4×C151—21no—
64C2×C22⋊C4×C151—41no—
65C2×C22⋊C4×C151—41no—
66C2×C22⋊C4×C151D411yescharacteristic
67C2×C22⋊C4×C151D411yescharacteristic
68C2×C42×C151D411yescharacteristic
69#102×C151—41no—
70#102×C151—41no—
71#100×C151—21no—
72#100×C151—21no—
73#99×C151—21no—
74#99×C151—21no—
75#99×C151—21no—
76#99×C151D412yescomplemented
77#95×C151—21no—
78#95×C151—21no—
79#95×C151—41no—
80C24×C151—21no—
81C24×C151—21no—
82C24×C151—21no—
83C24×C151—21no—
84C24×C151—41no—
85C24×C151—42no—
86C24×C151—41no—
87C24×C151—81no—
88C24×C151C2×D411yescharacteristic
89C24×C151C2×D411yescharacteristic
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—41no—
93C2×D4×C151—41no—
94C2×D4×C151—41no—
95C2×D4×C151—41no—
96C2×D4×C151—42no—
97C2×D4×C151—42no—
98C2×D4×C151—42no—
99C2×D4×C151—42no—
100C2×D4×C151—42no—
101C2×D4×C151—42no—
102C2×D4×C151—41no—
103C2×D4×C151—41no—
104C2×D4×C151—41no—
105C2×D4×C151—41no—
106C2×D4×C151—41no—
107C2×D4×C151—41no—
108C2×D4×C151—81no—
109C2×D4×C151—81no—
110C2×D4×C151—81no—
111C2×D4×C151—81no—
112C2×D4×C151—81no—
113C2×D4×C151—81no—
114C2×D4×C151C2×D411yescharacteristic
115C2×D4×C151#4111yescharacteristic
116C2×D4×C151#4111yescharacteristic
117C2×D4×C151#4111yescharacteristic
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—42no—
127C22×C4×C151—41no—
128C22×C4×C151—41no—
129C22×C4×C151—41no—
130C22×C4×C151C2×D411yescharacteristic
131M16×C151—41no—
132M16×C151—41no—
133C2×C8×C151—41no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151—82no—
138C22⋊C4×C151—24no—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—21no—
141C22⋊C4×C151—21no—
142C22⋊C4×C151—42no—
143C22⋊C4×C151—42no—
144C22⋊C4×C151—42no—
145C22⋊C4×C151—41no—
146C22⋊C4×C151—41no—
147C22⋊C4×C151—41no—
148C22⋊C4×C151—41no—
149C22⋊C4×C151—41no—
150C22⋊C4×C151—41no—
151C22⋊C4×C151—41no—
152C22⋊C4×C151—41no—
153C22⋊C4×C151—41no—
154C22⋊C4×C151—81no—
155C22⋊C4×C151—82no—
156C22⋊C4×C151—82no—
157C42×C151—21no—
158C42×C151—21no—
159C42×C151—41no—
160C23×C151—21no—
161C23×C151—21no—
162C23×C151—21no—
163C23×C151—21no—
164C23×C151—22no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—42no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—81no—
186C23×C151—82no—
187C23×C151—81no—
188C23×C151—82no—
189C23×C151—84no—
190C23×C151—81no—
191C23×C151#12011yescharacteristic
192C23×C151#12111yescharacteristic
193C23×C151#12111yescharacteristic
194C23×C151#12311yescharacteristic
195C23×C151#12411yescharacteristic
196D4×C151—41no—
197D4×C151—41no—
198D4×C151—41no—
199D4×C151—41no—
200D4×C151—42no—
201D4×C151—81no—
202D4×C151—82no—
203D4×C151—82no—
204D4×C151—82no—
205D4×C151—82no—
206D4×C151—84no—
207D4×C151—82no—
208D4×C151—82no—
209D4×C151—84no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—81no—
229C2×C4×C151—81no—
230C2×C4×C151—81no—
231C2×C4×C151—81no—
232C2×C4×C151—81no—
233C2×C4×C151—81no—
234C2×C4×C151—81no—
235C2×C4×C151—81no—
236C2×C4×C151—81no—
237C2×C4×C151—81no—
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12311yescharacteristic
240C8×C151—81no—
241C22×C151—21no—
242C22×C151—21no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—21no—
247C22×C151—41no—
248C22×C151—41no—
249C22×C151—41no—
250C22×C151—41no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—44no—
258C22×C151—42no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—81no—
264C22×C151—81no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151—82no—
268C22×C151—82no—
269C22×C151—82no—
270C22×C151—81no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151#39411yescharacteristic
276C22×C151B(4,𝔽2)11yescharacteristic
277C22×C151#45811yescharacteristic
278C4×C151—21no—
279C4×C151—21no—
280C4×C151—42no—
281C4×C151—42no—
282C4×C151—81no—
283C4×C151—81no—
284C4×C151—82no—
285C4×C151—81no—
286C4×C151—81no—
287C4×C151—161no—
288C2×C151—21no—
289C2×C151—21no—
290C2×C151—41no—
291C2×C151—41no—
292C2×C151—41no—
293C2×C151—41no—
294C2×C151—82no—
295C2×C151—161no—
296C2×C151#204411yescharacteristic
297C2×C151#219611yescharacteristic
298C2×C151#220011yescharacteristic
299#13422C15111yesmaximal, characteristic, direct product factor, Sylow
300C151#1342211yescharacteristic, direct product factor, Sylow
301#2669C2×C15111yescharacteristic
302C2×#353C2×C15111yescharacteristic, complemented
303C2×AΣL(1,𝔽16)C2×C15111yescharacteristic, complemented
304#1889C2×C15111yescharacteristic, complemented
305#1887C2×C15111yescharacteristic, complemented
306#1867C2×C15111yescharacteristic, complemented
307#1390C2×C15111yescharacteristic, complemented
308C2×#127C22×C15111yescharacteristic
309C2×#121—21no—
310C2×#120—21no—
311C2×#120C22×C15111yescharacteristic
312#518C22×C15111yescharacteristic
313#418—21no—
314C2×#100C22×C15111yescharacteristic
315C2×#99C22×C15111yescharacteristic
316C2×#99C22×C15111yescharacteristic
317#394—21no—
318#392—21no—
319#392—21no—
320#388—21no—
321#386C22×C15111yescharacteristic
322#385—21no—
323#379—21no—
324#353—22no—
325AΣL(1,𝔽16)—22no—
326#342—21no—
327#342—21no—
328#339—21no—
329C25D4×C15111yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C15111yescharacteristic
336C22×D4C23×C15111yescharacteristic
337C23×C4D4×C15111yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C15111yescharacteristic
367C2×C22⋊C4D4×C15111yescharacteristic
368C2×C42D4×C15111yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C15112yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C15111yescharacteristic
389C24C2×D4×C15111yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C15111yescharacteristic
415C2×D4#41×C15111yescharacteristic
416C2×D4#41×C15111yescharacteristic
417C2×D4#41×C15111yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C15111yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C15111yescharacteristic
492C23#121×C15111yescharacteristic
493C23#121×C15111yescharacteristic
494C23#123×C15111yescharacteristic
495C23#124×C15111yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C15111yescharacteristic
539C2×C4#123×C15111yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#394×C15111yescharacteristic
576C22B(4,𝔽2)×C15111yescharacteristic
577C22#458×C15111yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2#2044×C15111yescharacteristic
597C2#2196×C15111yescharacteristic
598C2#2200×C15111yescharacteristic
subgroupG/H
center, socleC22×C151B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C151
prime radical#2669×C151C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C151 ◁ C22×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C151C2semidirect
3. C2×AΣL(1,𝔽16)×C151C2semidirect
4. #1889×C151C2semidirect
5. #1887×C151C2semidirect
6. #1867×C151C2semidirect
7. #1390×C151C2semidirect
76. #99×C151D4semidirect
299. #13422C151direct (N × H)
300. C151#13422direct (N × H)
302. C2×#353C2×C151semidirect
303. C2×AΣL(1,𝔽16)C2×C151semidirect
304. #1889C2×C151semidirect
305. #1887C2×C151semidirect
306. #1867C2×C151semidirect
307. #1390C2×C151semidirect
376. #99D4×C151semidirect

Maximal subgroups

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

subgroupindex
#2669×C1512
C2×#353×C1512
C2×AΣL(1,𝔽16)×C1512
#1889×C1512
#1887×C1512
#1867×C1512
#1390×C1512
#13422151