Finite Group Databasebeta

← C2×#1390×C131 #45698456

Subgroups — C2×#1390×C131 #45698456

Order 33536.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C131C211yesmaximal, characteristic
2C22×#99×C131C211yesmaximal, characteristic
3C2×#386×C131C211yesmaximal, characteristic
4#1390×C131C214yesmaximal, direct product factor
5C23×D4×C131C2211yescharacteristic
6C24×C4×C131C411yescharacteristic, complemented
7C22×M16×C131—21no—
8C22×C22⋊C4×C131—21no—
9C22×C22⋊C4×C131—21no—
10C22×C22⋊C4×C131C411yescharacteristic, complemented
11C2×#100×C131—21no—
12C2×#100×C131—22no—
13C2×#100×C131C414yescomplemented
14C2×#100×C131C2212yes—
15C2×#99×C131—21no—
16C2×#99×C131—22no—
17C2×#99×C131C414yescomplemented
18C2×#99×C131C2212yes—
19#386×C131—21no—
20#386×C131—21no—
21#386×C131C412yescomplemented
22#386×C131C2212yes—
23C2×#95×C131—21no—
24C25×C131C2×C411yescharacteristic
25C25×C131D411yescharacteristic
26C22×D4×C131—42no—
27C22×D4×C131—41no—
28C22×D4×C131—41no—
29C22×D4×C131C2×C411yescharacteristic
30C22×D4×C131C2×C412yes—
31C22×D4×C131C2×C412yes—
32C22×D4×C131D411yescharacteristic
33C22×D4×C131D412yes—
34C22×D4×C131D411yescharacteristic
35C22×D4×C131Q812yes—
36C22×D4×C131C2311yescharacteristic
37C23×C4×C131—21no—
38C23×C4×C131—21no—
39C23×C4×C131—21no—
40C23×C4×C131—44no—
41C23×C4×C131—41no—
42C23×C4×C131—41no—
43C23×C4×C131—41no—
44C23×C4×C131C2×C412yescomplemented
45C23×C4×C131D411yescharacteristic
46C2×M16×C131—24no—
47C2×M16×C131—22no—
48C2×M16×C131—42no—
49C2×M16×C131—41no—
50C22×C8×C131—41no—
51C2×C22⋊C4×C131—24no—
52C2×C22⋊C4×C131—22no—
53C2×C22⋊C4×C131—22no—
54C2×C22⋊C4×C131—21no—
55C2×C22⋊C4×C131—22no—
56C2×C22⋊C4×C131—44no—
57C2×C22⋊C4×C131—41no—
58C2×C22⋊C4×C131—42no—
59C2×C22⋊C4×C131—42no—
60C2×C22⋊C4×C131C2×C412yescomplemented
61#100×C131—24no—
62#100×C131—22no—
63#100×C131C2×C414yescomplemented
64#99×C131—24no—
65#99×C131—22no—
66#99×C131C2×C414yescomplemented
67#95×C131—22no—
68#95×C131—22no—
69C24×C131—22no—
70C24×C131—21no—
71C24×C131—21no—
72C24×C131—21no—
73C24×C131—22no—
74C24×C131—21no—
75C24×C131—42no—
76C24×C131—42no—
77C24×C131—42no—
78C24×C131—42no—
79C24×C131C4212yes—
80C24×C131C22⋊C412yes—
81C24×C131C22⋊C411yescharacteristic
82C24×C131C22⋊C411yescharacteristic
83C24×C131C22⋊C411yescharacteristic
84C24×C131C4⋊C412yes—
85C24×C131C4⋊C412yes—
86C24×C131C22×C411yescharacteristic
87C24×C131C2×D411yescharacteristic
88C2×D4×C131—42no—
89C2×D4×C131—42no—
90C2×D4×C131—42no—
91C2×D4×C131—42no—
92C2×D4×C131—41no—
93C2×D4×C131—41no—
94C2×D4×C131—42no—
95C2×D4×C131—42no—
96C2×D4×C131—41no—
97C2×D4×C131—41no—
98C2×D4×C131—41no—
99C2×D4×C131—41no—
100C2×D4×C131—42no—
101C2×D4×C131—42no—
102C2×D4×C131—41no—
103C2×D4×C131—41no—
104C2×D4×C131C4212yes—
105C2×D4×C131C22⋊C412yes—
106C2×D4×C131C22⋊C412yes—
107C2×D4×C131C4⋊C412yes—
108C2×D4×C131C4⋊C412yes—
109C2×D4×C131C4⋊C412yes—
110C2×D4×C131C22×C411yescharacteristic
111C2×D4×C131C22×C411yescharacteristic
112C2×D4×C131C2×D411yescharacteristic
113C2×D4×C131C2×Q811yescharacteristic
114C22×C4×C131—22no—
115C22×C4×C131—21no—
116C22×C4×C131—21no—
117C22×C4×C131—24no—
118C22×C4×C131—22no—
119C22×C4×C131—22no—
120C22×C4×C131—44no—
121C22×C4×C131—44no—
122C22×C4×C131—42no—
123C22×C4×C131—42no—
124C22×C4×C131—48no—
125C22×C4×C131—44no—
126C22×C4×C131—41no—
127C22×C4×C131—41no—
128C22×C4×C131—42no—
129C22×C4×C131—44no—
130C22×C4×C131—44no—
131C22×C4×C131—42no—
132C22×C4×C131—42no—
133C22×C4×C131—42no—
134C22×C4×C131—42no—
135C22×C4×C131—82no—
136C22×C4×C131—82no—
137C22×C4×C131C22⋊C411yescharacteristic
138C22×C4×C131C22⋊C412yes—
139C22×C4×C131C4⋊C412yes—
140C22×C4×C131C2×D411yescharacteristic
141M16×C131—24no—
142M16×C131—44no—
143M16×C131—42no—
144C2×C8×C131—44no—
145C2×C8×C131—42no—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—44no—
148C22⋊C4×C131—44no—
149C22⋊C4×C131—44no—
150C22⋊C4×C131—42no—
151C22⋊C4×C131—42no—
152C22⋊C4×C131—42no—
153C23×C131—22no—
154C23×C131—22no—
155C23×C131—22no—
156C23×C131—22no—
157C23×C131—22no—
158C23×C131—22no—
159C23×C131—22no—
160C23×C131—22no—
161C23×C131—21no—
162C23×C131—21no—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131—21no—
166C23×C131—21no—
167C23×C131—22no—
168C23×C131—22no—
169C23×C131—21no—
170C23×C131—21no—
171C23×C131—41no—
172C23×C131—41no—
173C23×C131—44no—
174C23×C131—41no—
175C23×C131—44no—
176C23×C131—41no—
177C23×C131—42no—
178C23×C131—42no—
179C23×C131—48no—
180C23×C131—41no—
181C23×C131—41no—
182C23×C131—41no—
183C23×C131—44no—
184C23×C131—44no—
185C23×C131—41no—
186C23×C131—42no—
187C23×C131—42no—
188C23×C131—42no—
189C23×C131—42no—
190C23×C131—81no—
191C23×C131—81no—
192C23×C131—84no—
193C23×C131#9512yes—
194C23×C131#9512yes—
195C23×C131#9512yes—
196C23×C131#9911yescharacteristic
197C23×C131#9912yes—
198C23×C131#9911yescharacteristic
199C23×C131C2×C4211yescharacteristic
200C23×C131C2×C22⋊C411yescharacteristic
201C23×C131C2×C22⋊C411yescharacteristic
202C23×C131C2×C4⋊C411yescharacteristic
203C23×C131C2×C4⋊C411yescharacteristic
204D4×C131—42no—
205D4×C131—42no—
206D4×C131—42no—
207D4×C131—42no—
208D4×C131—42no—
209D4×C131—42no—
210D4×C131—41no—
211D4×C131—41no—
212D4×C131—41no—
213D4×C131—41no—
214C2×C4×C131—22no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—22no—
218C2×C4×C131—21no—
219C2×C4×C131—21no—
220C2×C4×C131—21no—
221C2×C4×C131—21no—
222C2×C4×C131—24no—
223C2×C4×C131—42no—
224C2×C4×C131—44no—
225C2×C4×C131—48no—
226C2×C4×C131—44no—
227C2×C4×C131—44no—
228C2×C4×C131—42no—
229C2×C4×C131—44no—
230C2×C4×C131—44no—
231C2×C4×C131—42no—
232C2×C4×C131—42no—
233C2×C4×C131—42no—
234C2×C4×C131—84no—
235C2×C4×C131—82no—
236C2×C4×C131—82no—
237C2×C4×C131—88no—
238C2×C4×C131#9512yes—
239C2×C4×C131C2×C22⋊C411yescharacteristic
240C2×C4×C131C2×C4⋊C411yescharacteristic
241C8×C131—44no—
242C22×C131—21no—
243C22×C131—21no—
244C22×C131—21no—
245C22×C131—21no—
246C22×C131—24no—
247C22×C131—24no—
248C22×C131—21no—
249C22×C131—22no—
250C22×C131—22no—
251C22×C131—21no—
252C22×C131—21no—
253C22×C131—21no—
254C22×C131—42no—
255C22×C131—42no—
256C22×C131—41no—
257C22×C131—41no—
258C22×C131—41no—
259C22×C131—41no—
260C22×C131—42no—
261C22×C131—42no—
262C22×C131—44no—
263C22×C131—44no—
264C22×C131—41no—
265C22×C131—41no—
266C22×C131—41no—
267C22×C131—41no—
268C22×C131—41no—
269C22×C131—41no—
270C22×C131—41no—
271C22×C131—41no—
272C22×C131—44no—
273C22×C131—44no—
274C22×C131—44no—
275C22×C131—44no—
276C22×C131—81no—
277C22×C131—81no—
278C22×C131—82no—
279C22×C131—82no—
280C22×C131#34212yes—
281C22×C131#34212yes—
282C22×C131AΣL(1,𝔽16)12yes—
283C22×C131#35212yes—
284C22×C131C2×#9511yescharacteristic
285C22×C131C2×#9911yescharacteristic
286C22×C131C2×#9911yescharacteristic
287C4×C131—21no—
288C4×C131—22no—
289C4×C131—21no—
290C4×C131—44no—
291C4×C131—82no—
292C4×C131—84no—
293C2×C131—21no—
294C2×C131—21no—
295C2×C131—22no—
296C2×C131—41no—
297C2×C131—42no—
298C2×C131—41no—
299C2×C131—41no—
300C2×C131—42no—
301C2×C131—41no—
302C2×C131#139014yesdirect product factor
303C2×C131C2×#34211yescharacteristic
304C2×C131C2×AΣL(1,𝔽16)11yescharacteristic
305C2×C131C2×#35211yescharacteristic
306C2×#1390C13111yesmaximal, characteristic, direct product factor, Sylow
307C131C2×#139011yescharacteristic, direct product factor, Sylow
308C22×#100C2×C13111yescharacteristic
309C22×#99C2×C13111yescharacteristic
310C2×#386C2×C13111yescharacteristic
311#1390C2×C13114yesdirect product factor
312C23×D4C22×C13111yescharacteristic
313C24×C4C4×C13111yescharacteristic, complemented
314C22×M16—21no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4—21no—
317C22×C22⋊C4C4×C13111yescharacteristic, complemented
318C2×#100—21no—
319C2×#100—22no—
320C2×#100C4×C13114yescomplemented
321C2×#100C22×C13112yes—
322C2×#99—21no—
323C2×#99—22no—
324C2×#99C4×C13114yescomplemented
325C2×#99C22×C13112yes—
326#386—21no—
327#386—21no—
328#386C4×C13112yescomplemented
329#386C22×C13112yes—
330C2×#95—21no—
331C25C2×C4×C13111yescharacteristic
332C25D4×C13111yescharacteristic
333C22×D4—41no—
334C22×D4—42no—
335C22×D4—41no—
336C22×D4C2×C4×C13111yescharacteristic
337C22×D4C2×C4×C13112yes—
338C22×D4C2×C4×C13112yes—
339C22×D4D4×C13111yescharacteristic
340C22×D4D4×C13112yes—
341C22×D4D4×C13111yescharacteristic
342C22×D4Q8×C13112yes—
343C22×D4C23×C13111yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C13112yescomplemented
352C23×C4D4×C13111yescharacteristic
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—41no—
356C2×M16—42no—
357C22×C8—41no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4C2×C4×C13112yescomplemented
368#100—24no—
369#100—22no—
370#100C2×C4×C13114yescomplemented
371#99—24no—
372#99—22no—
373#99C2×C4×C13114yescomplemented
374#95—22no—
375#95—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C42×C13112yes—
387C24C22⋊C4×C13111yescharacteristic
388C24C22⋊C4×C13111yescharacteristic
389C24C22⋊C4×C13112yes—
390C24C22⋊C4×C13111yescharacteristic
391C24C4⋊C4×C13112yes—
392C24C4⋊C4×C13112yes—
393C24C22×C4×C13111yescharacteristic
394C24C2×D4×C13111yescharacteristic
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C42×C13112yes—
412C2×D4C22⋊C4×C13112yes—
413C2×D4C22⋊C4×C13112yes—
414C2×D4C4⋊C4×C13112yes—
415C2×D4C4⋊C4×C13112yes—
416C2×D4C4⋊C4×C13112yes—
417C2×D4C22×C4×C13111yescharacteristic
418C2×D4C22×C4×C13111yescharacteristic
419C2×D4C2×D4×C13111yescharacteristic
420C2×D4C2×Q8×C13111yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C22⋊C4×C13111yescharacteristic
445C22×C4C22⋊C4×C13112yes—
446C22×C4C4⋊C4×C13112yes—
447C22×C4C2×D4×C13111yescharacteristic
448M16—24no—
449M16—42no—
450M16—44no—
451C2×C8—42no—
452C2×C8—44no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—42no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23—41no—
479C23—41no—
480C23—44no—
481C23—41no—
482C23—44no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—84no—
500C23#95×C13112yes—
501C23#95×C13112yes—
502C23#95×C13112yes—
503C23#99×C13111yescharacteristic
504C23#99×C13112yes—
505C23#99×C13111yescharacteristic
506C23C2×C42×C13111yescharacteristic
507C23C2×C22⋊C4×C13111yescharacteristic
508C23C2×C22⋊C4×C13111yescharacteristic
509C23C2×C4⋊C4×C13111yescharacteristic
510C23C2×C4⋊C4×C13111yescharacteristic
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4#95×C13112yes—
546C2×C4C2×C22⋊C4×C13111yescharacteristic
547C2×C4C2×C4⋊C4×C13111yescharacteristic
548C8—44no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—81no—
584C22—81no—
585C22—82no—
586C22—82no—
587C22#342×C13112yes—
588C22#342×C13112yes—
589C22AΣL(1,𝔽16)×C13112yes—
590C22#352×C13112yes—
591C22C2×#95×C13111yescharacteristic
592C22C2×#99×C13111yescharacteristic
593C22C2×#99×C13111yescharacteristic
594C4—21no—
595C4—22no—
596C4—21no—
597C4—44no—
598C4—82no—
599C4—84no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—42no—
605C2—41no—
606C2—41no—
607C2—42no—
608C2—41no—
609C2#1390×C13114yesdirect product factor
610C2C2×#342×C13111yescharacteristic
611C2C2×AΣL(1,𝔽16)×C13111yescharacteristic
612C2C2×#352×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#99
commutatorC23C2×C42×C131
Frattini, cosocleC22×D4C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C131 ◁ C23×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1390×C131C2direct (N × H)
6. C24×C4×C131C4semidirect
10. C22×C22⋊C4×C131C4semidirect
13. C2×#100×C131C4semidirect
17. C2×#99×C131C4semidirect
21. #386×C131C4semidirect
44. C23×C4×C131C2×C4semidirect
60. C2×C22⋊C4×C131C2×C4semidirect
63. #100×C131C2×C4semidirect
66. #99×C131C2×C4semidirect
302. C2×C131#1390direct (N × H)
306. C2×#1390C131direct (N × H)
307. C131C2×#1390direct (N × H)
311. #1390C2×C131direct (N × H)
313. C24×C4C4×C131semidirect
317. C22×C22⋊C4C4×C131semidirect
320. C2×#100C4×C131semidirect
324. C2×#99C4×C131semidirect
328. #386C4×C131semidirect
351. C23×C4C2×C4×C131semidirect
367. C2×C22⋊C4C2×C4×C131semidirect
370. #100C2×C4×C131semidirect
373. #99C2×C4×C131semidirect
609. C2#1390×C131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#100×C1312
C22×#99×C1312
C2×#386×C1312
#1390×C1312
C2×#1390131