Finite Group Databasebeta

← #15864403

Subgroups — #15864403

Order 3328.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719524C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic, complemented
3#13123355C211yesmaximal, characteristic, complemented
4#13123281C211yesmaximal, characteristic, complemented
5#13115200C218yesmaximal, complemented
6C2×#11718151C211yesmaximal, characteristic, complemented
7#13114562C211yesmaximal, characteristic, complemented
8C2×C13×#575C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C22×C13×#41C2211yescharacteristic
11C13×#575—22no—
12C13×#575—22no—
13C13×#575C414yescomplemented
14C13×#575C2214yes—
15C2×C13×#137—21no—
16C2×C13×#137C412yescomplemented
17C2×C13×AGL(1,ℤ/8)—21no—
18C2×C13×AGL(1,ℤ/8)C412yescomplemented
19C2×C13×#135—22no—
20C22×C13×M16C2211yescharacteristic
21#11719524—22no—
22#11719524—22no—
23#11719524—22no—
24#11719524C2214yescomplemented
25C2×#88202—22no—
26C2×#88202—22no—
27C2×#88180C2211yescharacteristic
28C22×#6099—22no—
29C22×#6099C2211yescharacteristic
30C22×#6099C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32#11718897—22no—
33#11718897C2214yescomplemented
34C2×#88077—22no—
35#11718895—22no—
36#11718895C2214yescomplemented
37#11718894C2214yescomplemented
38#11718893—22no—
39#11718886—21no—
40#11718876—21no—
41#11718868—22no—
42#11718151C2214yescomplemented
43#11718150C2214yescomplemented
44C2×C13×#41—21no—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C2×C13×#41—21no—
50C2×C13×#41—21no—
51C2×C13×#41—21no—
52C2×C13×#41—21no—
53C2×C13×#41—21no—
54C2×C13×#41—21no—
55C2×C13×#41—21no—
56C2×C13×#41—21no—
57C2×C13×#41—21no—
58C2×C13×#41—21no—
59C2×C13×#41—21no—
60C2×C13×#41C2×C412yes—
61C2×C13×#41C2×C412yes—
62C2×C13×#41C2×C412yes—
63C2×C13×#41D412yes—
64C2×C13×#41D412yes—
65C2×C13×#41D412yes—
66C2×C13×#41C2312yes—
67C2×C13×#41C2312yes—
68C22×Q8×C13C2×C411yescharacteristic
69C22×Q8×C13D411yescharacteristic
70C22×D4×C13—21no—
71C22×D4×C13—21no—
72C22×D4×C13C2×C411yescharacteristic
73C22×D4×C13D411yescharacteristic
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13C2311yescharacteristic
77C13×#137—24no—
78C13×#137—24no—
79C13×#137—24no—
80C13×#137C2×C418yescomplemented
81C13×AGL(1,ℤ/8)—24no—
82C13×AGL(1,ℤ/8)—24no—
83C13×AGL(1,ℤ/8)—24no—
84C13×AGL(1,ℤ/8)C2×C418yescomplemented
85C13×#135—28no—
86C13×#135—28no—
87C2×C13×Q16—22no—
88C2×C13×SD16—22no—
89C2×C13×SD16—22no—
90C2×C13×D8—22no—
91C2×C13×M16—21no—
92C2×C13×M16—21no—
93C2×C13×M16—21no—
94C2×C13×M16C2×C412yes—
95C2×C13×M16C2×C412yes—
96C2×C13×M16C2312yes—
97C22×C8×C13—21no—
98C2×C22⋊Dic13—21no—
99#88202—28no—
100#88202—28no—
101#88202—28no—
102#88202—28no—
103#88180—21no—
104#88180—21no—
105#88180—21no—
106#88180C2312yes—
107C2×C4⋊Dic13—21no—
108C2×C4×Dic13—21no—
109C2×#6099—24no—
110C2×#6099—28no—
111C2×#6099—21no—
112C2×#6099—21no—
113C2×#6099—21no—
114C2×#6099—21no—
115C2×#6099—21no—
116C2×#6099—21no—
117C2×#6099—21no—
118C2×#6099—28no—
119C2×#6099—21no—
120C2×#6099—21no—
121C2×#6099—21no—
122C2×#6099—21no—
123C2×#6099—21no—
124C2×#6099—21no—
125C2×#6099D412yes—
126C2×#6099D412yes—
127C2×#6099D412yes—
128C2×#6099C2312yes—
129C2×#6099C2312yes—
130C22×#1055—24no—
131C22×#1055—21no—
132C22×#1055D412yes—
133C22×#1055C2312yes—
134#88077—28no—
135#88075—24no—
136#88072—24no—
137C22⋊#1055—28no—
138#20939—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13—21no—
141C24×C13#4111yescharacteristic
142C13×#41—22no—
143C13×#41—22no—
144C13×#41—22no—
145C13×#41—22no—
146C13×#41—22no—
147C13×#41—22no—
148C13×#41—22no—
149C13×#41—22no—
150C13×#41—22no—
151C13×#41—22no—
152C13×#41—22no—
153C13×#41—22no—
154C13×#41—22no—
155C13×#41—22no—
156C13×#41—22no—
157C13×#41—22no—
158C13×#41—22no—
159C13×#41—22no—
160C13×#41—22no—
161C13×#41—22no—
162C13×#41—41no—
163C13×#41—41no—
164C13×#41—41no—
165C13×#41—41no—
166C13×#41—41no—
167C13×#41—41no—
168C13×#41—41no—
169C13×#41—41no—
170C13×#41C22⋊C414yes—
171C13×#41C22⋊C414yes—
172C13×#41C22×C414yes—
173C13×#41C2×D414yes—
174C2×Q8×C13—21no—
175C2×Q8×C13—21no—
176C2×Q8×C13—21no—
177C2×Q8×C13—21no—
178C2×Q8×C13—21no—
179C2×Q8×C13—21no—
180C2×Q8×C13—21no—
181C2×Q8×C13—21no—
182C2×Q8×C13C22⋊C412yes—
183C2×Q8×C13C22⋊C412yes—
184C2×Q8×C13C22×C412yes—
185C2×Q8×C13C2×D412yes—
186C2×D4×C13—22no—
187C2×D4×C13—22no—
188C2×D4×C13—22no—
189C2×D4×C13—22no—
190C2×D4×C13—22no—
191C2×D4×C13—22no—
192C2×D4×C13—22no—
193C2×D4×C13—22no—
194C2×D4×C13—21no—
195C2×D4×C13—21no—
196C2×D4×C13—21no—
197C2×D4×C13—21no—
198C2×D4×C13—21no—
199C2×D4×C13—21no—
200C2×D4×C13—21no—
201C2×D4×C13—21no—
202C2×D4×C13—41no—
203C2×D4×C13—41no—
204C2×D4×C13—41no—
205C2×D4×C13—41no—
206C2×D4×C13C22⋊C412yes—
207C2×D4×C13C22⋊C412yes—
208C2×D4×C13C22×C412yes—
209C2×D4×C13C2×D412yes—
210C22×C4×C13—21no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—22no—
214C22×C4×C13—22no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—21no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—41no—
221C22×C4×C13—41no—
222C22×C4×C13—41no—
223C22×C4×C13—41no—
224C22×C4×C13C22×C411yescharacteristic
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13#4111yescharacteristic
235C22×C4×C13#4111yescharacteristic
236C22×C4×C13#4111yescharacteristic
237C22×C4×C13C2411yescharacteristic
238C22×Dic13—41no—
239C13×Q16—28no—
240C13×SD16—28no—
241C13×SD16—28no—
242C13×D8—28no—
243C13×M16—22no—
244C13×M16—22no—
245C13×M16—22no—
246C13×M16C22×C414yes—
247C2×C8×C13—22no—
248C2×C8×C13—22no—
249C2×C8×C13—22no—
250C22⋊Dic13—22no—
251C22⋊Dic13—41no—
252C4⋊Dic13—22no—
253C4⋊Dic13—41no—
254C4×Dic13—22no—
255C4×Dic13—41no—
256#6099—216no—
257#6099—22no—
258#6099—22no—
259#6099—22no—
260#6099—22no—
261#6099—22no—
262#6099—22no—
263#6099—22no—
264#6099—41no—
265#6099—41no—
266#6099—41no—
267#6099—41no—
268#6099C2×D414yes—
269C2×#1055—216no—
270C2×#1055—22no—
271C2×#1055—22no—
272C2×#1055—22no—
273C2×#1055—22no—
274C2×#1055—22no—
275C2×#1055—22no—
276C2×#1055—22no—
277C2×#1055—22no—
278C2×#1055C2×D414yes—
279C2×#575D1311yescharacteristic
280C2×#568—131no—
281C2×#421—131no—
282#2896—131no—
283#2879—131no—
284#1881—138no—
285C2×#344—131no—
286#1738—131no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—81no—
294C23×C13—82no—
295C23×C13—82no—
296C23×C13C4×D411yescharacteristic
297C23×C13C4×D411yescharacteristic
298C23×C13#12111yescharacteristic
299C23×C13#12111yescharacteristic
300C23×C13#12311yescharacteristic
301C23×C13#12311yescharacteristic
302C23×C13C2×#4111yescharacteristic
303Q8×C13—22no—
304Q8×C13—22no—
305Q8×C13—22no—
306Q8×C13—22no—
307Q8×C13—22no—
308Q8×C13—41no—
309Q8×C13—41no—
310Q8×C13C2×C22⋊C414yes—
311D4×C13—24no—
312D4×C13—24no—
313D4×C13—24no—
314D4×C13—24no—
315D4×C13—22no—
316D4×C13—22no—
317D4×C13—22no—
318D4×C13—22no—
319D4×C13—22no—
320D4×C13—42no—
321D4×C13—42no—
322D4×C13—42no—
323D4×C13—42no—
324D4×C13—41no—
325D4×C13—41no—
326D4×C13C2×C22⋊C414yes—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—24no—
331C2×C4×C13—24no—
332C2×C4×C13—24no—
333C2×C4×C13—24no—
334C2×C4×C13—22no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13C2×C22⋊C411yescharacteristic
342C2×C4×C13C2×C22⋊C411yescharacteristic
343C2×C4×C13C2×C22⋊C411yescharacteristic
344C2×C4×C13C2×C22⋊C411yescharacteristic
345C2×C4×C13C4×D411yescharacteristic
346C2×C4×C13C4×D411yescharacteristic
347C2×C4×C13C4×D411yescharacteristic
348C2×C4×C13C4×D411yescharacteristic
349C2×C4×C13C4×D411yescharacteristic
350C2×C4×C13C4×D411yescharacteristic
351C2×C4×C13#12011yescharacteristic
352C2×C4×C13#12011yescharacteristic
353C2×C4×C13#12011yescharacteristic
354C2×C4×C13#12011yescharacteristic
355C2×C4×C13#12111yescharacteristic
356C2×C4×C13#12111yescharacteristic
357C2×C4×C13#12111yescharacteristic
358C2×C4×C13#12111yescharacteristic
359C2×C4×C13#12111yescharacteristic
360C2×C4×C13#12111yescharacteristic
361C2×C4×C13#12311yescharacteristic
362C2×C4×C13#12311yescharacteristic
363C2×C4×C13C23×C411yescharacteristic
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C22×D411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C2×#4111yescharacteristic
369C2×Dic13—42no—
370C2×Dic13—82no—
371C8×C13—24no—
372#1055—24no—
373#1055—24no—
374#1055—42no—
375C22×#41C2×D1311yescharacteristic
376C22×#41C2×D1311yescharacteristic
377#575—22no—
378#575—22no—
379#575Dic1314yescomplemented
380#575C2×D1314yes—
381C2×#137—21no—
382C2×#137Dic1312yescomplemented
383C2×AGL(1,ℤ/8)—21no—
384C2×AGL(1,ℤ/8)Dic1312yescomplemented
385C2×#135—22no—
386#568—134no—
387#568—262no—
388#568—262no—
389#568—262no—
390C2×#131—262no—
391C2×#131—262no—
392C22×M16—131no—
393C22×M16—131no—
394C22×M16—131no—
395C22×M16—262no—
396C22×M16C2×D1311yescharacteristic
397C2×#117—131no—
398#421—134no—
399#421—262no—
400C2×#104—262no—
401#419—261no—
402#418—261no—
403#417—262no—
404#416—134no—
405#408—134no—
406#408—262no—
407#407—262no—
408#344—134no—
409#341—134no—
410C22×C13—24no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—41no—
414C22×C13—41no—
415C22×C13—41no—
416C22×C13—41no—
417C22×C13—41no—
418C22×C13—44no—
419C22×C13—44no—
420C22×C13—42no—
421C22×C13—82no—
422C22×C13—82no—
423C22×C13—82no—
424C22×C13—82no—
425C22×C13#38611yescharacteristic
426C22×C13#38611yescharacteristic
427C22×C13#38611yescharacteristic
428C22×C13#38611yescharacteristic
429C22×C13C2×C4×D411yescharacteristic
430C22×C13C2×#12111yescharacteristic
431C22×C13C2×#12311yescharacteristic
432C4×C13—24no—
433C4×C13—42no—
434C4×C13#38611yescharacteristic
435C4×C13#38611yescharacteristic
436C4×C13#38611yescharacteristic
437C4×C13#38611yescharacteristic
438C4×C13C22×C22⋊C411yescharacteristic
439C4×C13C2×C4×D411yescharacteristic
440C4×C13C2×#12011yescharacteristic
441C4×C13C2×#12111yescharacteristic
442Dic13—82no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×Dic1312yes—
460C2×#41C2×Dic1312yes—
461C2×#41C2×Dic1312yes—
462C2×#41C22⋊D1312yes—
463C2×#41C22⋊D1312yes—
464C2×#41C22⋊D1312yes—
465C2×#41C22×D1312yes—
466C2×#41C22×D1312yes—
467C22×Q8C2×Dic1311yescharacteristic
468C22×Q8C22⋊D1311yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4C2×Dic1311yescharacteristic
472C22×D4C22⋊D1311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4C22×D1311yescharacteristic
476#137—24no—
477#137—24no—
478#137—24no—
479#137C2×Dic1318yescomplemented
480AGL(1,ℤ/8)—24no—
481AGL(1,ℤ/8)—24no—
482AGL(1,ℤ/8)—24no—
483AGL(1,ℤ/8)C2×Dic1318yescomplemented
484#135—28no—
485#135—28no—
486C2×Q16—22no—
487C2×SD16—22no—
488C2×SD16—22no—
489C2×D8—22no—
490#131—268no—
491#131—268no—
492#131—268no—
493#131—268no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—132no—
498C2×M16—132no—
499C2×M16—132no—
500C2×M16—132no—
501C2×M16—132no—
502C2×M16—268no—
503C2×M16—264no—
504C2×M16—268no—
505C2×M16—261no—
506C2×M16—261no—
507C2×M16—261no—
508C2×M16—261no—
509C2×M16—261no—
510C2×M16—261no—
511C2×M16—261no—
512C2×M16—261no—
513C2×M16—261no—
514C2×M16—261no—
515C2×M16—261no—
516C2×M16—261no—
517C2×M16—261no—
518C2×M16C2×Dic1312yes—
519C2×M16C2×Dic1312yes—
520C2×M16C22×D1312yes—
521C22×C8—21no—
522C22×C8—132no—
523C22×C8—132no—
524C22×C8—264no—
525C22×C8—261no—
526#117—132no—
527#117—261no—
528#117—261no—
529#117—261no—
530C2×C4⋊C4—261no—
531C2×C22⋊C4—261no—
532C2×C42—261no—
533#104—268no—
534#103—264no—
535#102—264no—
536C22⋊C8—268no—
537C2×C13—21no—
538C2×C13—21no—
539C2×C13—21no—
540C2×C13—21no—
541C2×C13—21no—
542C2×C13—21no—
543C2×C13—21no—
544C2×C13—44no—
545C2×C13—82no—
546C2×C13C2×#38611yescharacteristic
547C24—21no—
548C24—21no—
549C24#612911yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41C22⋊Dic1314yes—
579#41C22⋊Dic1314yes—
580#41C22×Dic1314yes—
581#41C2×C22⋊D1314yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8C22⋊Dic1312yes—
591C2×Q8C22⋊Dic1312yes—
592C2×Q8C22×Dic1312yes—
593C2×Q8C2×C22⋊D1312yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4C22⋊Dic1312yes—
615C2×D4C22⋊Dic1312yes—
616C2×D4C22×Dic1312yes—
617C2×D4C2×C22⋊D1312yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—521no—
633C22×C4D4×D1311yescharacteristic
634C22×C4D4×D1311yescharacteristic
635C22×C4D4×D1311yescharacteristic
636C22×C4D4×D1311yescharacteristic
637C22×C4#612911yescharacteristic
638C22×C4#612911yescharacteristic
639C22×C4#612911yescharacteristic
640C22×C4C22×Dic1311yescharacteristic
641C22×C4C22×Dic1311yescharacteristic
642C22×C4C2×C22⋊D1311yescharacteristic
643C22×C4C2×C22⋊D1311yescharacteristic
644C22×C4C2×C22⋊D1311yescharacteristic
645C22×C4C2×C22⋊D1311yescharacteristic
646C22×C4C23×D1311yescharacteristic
647Q16—28no—
648SD16—28no—
649SD16—28no—
650D8—28no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—134no—
655M16—2616no—
656M16—262no—
657M16—262no—
658M16—262no—
659M16—262no—
660M16—262no—
661M16—262no—
662M16—262no—
663M16—521no—
664M16—521no—
665M16—521no—
666M16—521no—
667M16C22×Dic1314yes—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—134no—
672C2×C8—2616no—
673C2×C8—262no—
674C2×C8—262no—
675C2×C8—262no—
676C2×C8—262no—
677C2×C8—262no—
678C2×C8—262no—
679C2×C8—262no—
680C2×C8—262no—
681C4⋊C4—262no—
682C4⋊C4—521no—
683C22⋊C4—262no—
684C22⋊C4—521no—
685C42—262no—
686C42—521no—
687C13#2093911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—82no—
696C23—82no—
697C23D4×Dic1311yescharacteristic
698C23D4×Dic1311yescharacteristic
699C23#8818911yescharacteristic
700C23#8818911yescharacteristic
701C23#8819311yescharacteristic
702C23#8819311yescharacteristic
703C23C2×#612911yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8C2×C22⋊Dic1314yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4C2×C22⋊Dic1314yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—522no—
743C2×C4—1042no—
744C2×C4D4×Dic1311yescharacteristic
745C2×C4D4×Dic1311yescharacteristic
746C2×C4D4×Dic1311yescharacteristic
747C2×C4D4×Dic1311yescharacteristic
748C2×C4D4×Dic1311yescharacteristic
749C2×C4D4×Dic1311yescharacteristic
750C2×C4#8818911yescharacteristic
751C2×C4#8818911yescharacteristic
752C2×C4#8819111yescharacteristic
753C2×C4#8819111yescharacteristic
754C2×C4#8819111yescharacteristic
755C2×C4#8819111yescharacteristic
756C2×C4#8819311yescharacteristic
757C2×C4#8819311yescharacteristic
758C2×C4#8819311yescharacteristic
759C2×C4#8819311yescharacteristic
760C2×C4#8819311yescharacteristic
761C2×C4#8819311yescharacteristic
762C2×C4C2×C22⋊Dic1311yescharacteristic
763C2×C4C2×C22⋊Dic1311yescharacteristic
764C2×C4C2×C22⋊Dic1311yescharacteristic
765C2×C4C2×C22⋊Dic1311yescharacteristic
766C2×C4C2×D4×D1311yescharacteristic
767C2×C4C2×D4×D1311yescharacteristic
768C2×C4C2×#612911yescharacteristic
769C2×C4C23×Dic1311yescharacteristic
770C2×C4C22×C22⋊D1311yescharacteristic
771C2×C4C22×C22⋊D1311yescharacteristic
772C8—24no—
773C8—264no—
774C8—264no—
775C8—522no—
776C22—24no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22#1171888111yescharacteristic
792C22#1171888111yescharacteristic
793C22#1171888111yescharacteristic
794C22#1171888111yescharacteristic
795C22C2×D4×Dic1311yescharacteristic
796C22C2×#8818911yescharacteristic
797C22C2×#8819311yescharacteristic
798C4—24no—
799C4—42no—
800C4—1042no—
801C4#1171888111yescharacteristic
802C4#1171888111yescharacteristic
803C4#1171888111yescharacteristic
804C4#1171888111yescharacteristic
805C4C2×D4×Dic1311yescharacteristic
806C4C2×#8819111yescharacteristic
807C4C2×#8819311yescharacteristic
808C4C22×C22⋊Dic1311yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—44no—
817C2—82no—
818C2C2×#1171888111yescharacteristic
subgroupG/H
centerC4C2×#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#575C2
socleC2×C13C2×#386
cosocleC22×C4×C13C24
hypercenterC2×#575D13
hypocenterC13#20939
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#11719524C2semidirect
2. C2×#11718897C2semidirect
3. #13123355C2semidirect
4. #13123281C2semidirect
5. #13115200C2semidirect
6. C2×#11718151C2semidirect
7. #13114562C2semidirect
13. C13×#575C4semidirect
16. C2×C13×#137C4semidirect
18. C2×C13×AGL(1,ℤ/8)C4semidirect
24. #11719524C22semidirect
33. #11718897C22semidirect
36. #11718895C22semidirect
37. #11718894C22semidirect
42. #11718151C22semidirect
43. #11718150C22semidirect
80. C13×#137C2×C4semidirect
84. C13×AGL(1,ℤ/8)C2×C4semidirect
379. #575Dic13semidirect
382. C2×#137Dic13semidirect
384. C2×AGL(1,ℤ/8)Dic13semidirect
479. #137C2×Dic13semidirect
483. AGL(1,ℤ/8)C2×Dic13semidirect
687. C13#20939semidirect

Maximal subgroups

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

subgroupindex
C2×#117195242
C2×#117188972
#131233552
#131232812
#131152002
C2×#117181512
#131145622
C2×C13×#5752
#2093913