Finite Group Databasebeta

← #16015661

Subgroups — #16015661

Order 3328.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128165C211yesmaximal, characteristic
2C2×#11718898C211yesmaximal, characteristic, complemented
3#13116489C212yesmaximal, complemented
4#13116485C212yesmaximal, complemented
5#13116480C214yesmaximal, complemented
6#13116475C214yesmaximal, complemented
7C2×C13×#410C211yesmaximal, characteristic, complemented
8C22×C13×#41C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C2×C13×#117—21no—
11#11719538—21no—
12#11719538—21no—
13#11719537—21no—
14#11719537—21no—
15#11719535C411yescharacteristic, complemented
16#11719535C2211yescharacteristic
17#11719533C412yescomplemented
18#11719533C2212yes—
19#11719530C411yescharacteristic, complemented
20#11719530C2211yescharacteristic
21#11719521—21no—
22#11719510—21no—
23#11719509C412yescomplemented
24#11719509C2212yes—
25#11719496—21no—
26#11719496—21no—
27C2×#88180C411yescharacteristic, complemented
28C22×#6099—21no—
29C13×#410—21no—
30C13×#410—21no—
31C13×#410C2212yes—
32C13×#410C2212yes—
33C2×C13×#99—21no—
34C2×C13×#99C2212yes—
35#11718898—21no—
36#11718898—21no—
37#11718898C2212yes—
38#11718898C2212yes—
39C2×#88076—21no—
40C2×#88073C2212yes—
41#11718064C2218yescomplemented
42#11718063C2218yescomplemented
43C2×C13×#41—41no—
44C2×C13×#41—41no—
45C2×C13×#41—41no—
46C2×C13×#41—41no—
47C2×C13×#41C2×C411yescharacteristic
48C2×C13×#41C2×C411yescharacteristic
49C2×C13×#41D411yescharacteristic
50C2×C13×#41D411yescharacteristic
51C2×C13×#41D411yescharacteristic
52C2×C13×#41D411yescharacteristic
53C2×C13×#41C2311yescharacteristic
54C2×C13×#41C2311yescharacteristic
55C22×Q8×C13D411yescharacteristic
56C22×D4×C13C2×C411yescharacteristic
57C22×D4×C13D411yescharacteristic
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13C2×C411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13D411yescharacteristic
62C22×C22⋊D13C2×C412yes—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—21no—
66C2×#6127—21no—
67C2×#6127—41no—
68C2×#6127—41no—
69C2×#6127—41no—
70C2×#6127—41no—
71C22×D52C2×C411yescharacteristic, complemented
72C22×C4×D13C2×C412yescomplemented
73C22×Dic26C2×C411yescharacteristic, complemented
74C13×#117—22no—
75C13×#117—22no—
76C13×#117—41no—
77C13×#117—41no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C22⋊C4—22no—
80C2×C42×C13—41no—
81#88207—22no—
82#88207—22no—
83C2×C22⋊Dic13C2×C412yes—
84#88201—21no—
85#88201—21no—
86#88200—22no—
87#88200—22no—
88#88198—21no—
89#88198—21no—
90#88194—21no—
91#88194—21no—
92#88193—22no—
93#88193—22no—
94#88193—22no—
95#88193—22no—
96#88192—22no—
97#88192—22no—
98#88191C2×C412yes—
99#88191C2×C412yescomplemented
100#88191C2×C412yescomplemented
101#88191C2312yes—
102#88190—21no—
103#88190—21no—
104#88189C2×C412yes—
105#88189C2×C412yescomplemented
106#88189C2×C412yescomplemented
107#88189C2312yes—
108#88184—21no—
109#88184—21no—
110#88184—21no—
111#88184—21no—
112#88183—22no—
113#88183—22no—
114C4×C22⋊D13—22no—
115C4×C22⋊D13—22no—
116C4×C22⋊D13—22no—
117C4×C22⋊D13—22no—
118#88180—21no—
119#88180—21no—
120#88180C2×C411yescharacteristic, complemented
121#88180C2×C411yescharacteristic, complemented
122#88180C2×C412yescomplemented
123C2×C4⋊Dic13—21no—
124#88178—21no—
125#88178—21no—
126#88178—21no—
127#88178—21no—
128C2×C4×Dic13—21no—
129C2×#6099—22no—
130C2×#6099—22no—
131C2×#6099—22no—
132C2×#6099—41no—
133C2×#6099—41no—
134C2×#6099—41no—
135C22×#1055—41no—
136C13×#99—22no—
137C13×#99—22no—
138C13×#99—22no—
139C13×#99C2314yes—
140#88076—22no—
141#88076—22no—
142#88073—22no—
143#88073C2314yes—
144#33347—131nomaximal, Sylow
145C24×C13C22⋊C411yescharacteristic
146C24×C13C22×C411yescharacteristic
147C24×C13C2×D411yescharacteristic
148C23×D13C22×C412yes—
149C13×#41—41no—
150C13×#41—41no—
151C13×#41—41no—
152C13×#41—41no—
153C13×#41—41no—
154C13×#41—41no—
155C13×#41—41no—
156C13×#41—41no—
157C13×#41—41no—
158C13×#41—41no—
159C13×#41—41no—
160C13×#41—41no—
161C13×#41—41no—
162C13×#41—41no—
163C13×#41—41no—
164C13×#41—41no—
165C2×Q8×C13—41no—
166C2×Q8×C13—41no—
167C2×Q8×C13C22⋊C411yescharacteristic
168C2×Q8×C13C22⋊C411yescharacteristic
169C2×Q8×C13C2×D411yescharacteristic
170C2×Q8×C13C2×D411yescharacteristic
171C2×D4×C13—41no—
172C2×D4×C13—41no—
173C2×D4×C13—41no—
174C2×D4×C13—41no—
175C2×D4×C13—41no—
176C2×D4×C13—41no—
177C2×D4×C13C22⋊C411yescharacteristic
178C2×D4×C13C22⋊C411yescharacteristic
179C2×D4×C13C22⋊C411yescharacteristic
180C2×D4×C13C22⋊C411yescharacteristic
181C2×D4×C13C22×C411yescharacteristic
182C2×D4×C13C22×C411yescharacteristic
183C2×D4×C13C22×C411yescharacteristic
184C2×D4×C13C2×D411yescharacteristic
185C2×D4×C13C2×D411yescharacteristic
186C2×D4×C13C2×D411yescharacteristic
187C2×D4×C13C2×D411yescharacteristic
188C2×D4×C13C2411yescharacteristic
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—42no—
202C22×C4×C13C22⋊C411yescharacteristic
203C22×C4×C13C22⋊C411yescharacteristic
204C22×C4×C13C22⋊C411yescharacteristic
205C22×C4×C13C22⋊C411yescharacteristic
206C22×C4×C13C22⋊C411yescharacteristic
207C22×C4×C13C22⋊C411yescharacteristic
208C22×C4×C13C22⋊C411yescharacteristic
209C22×C4×C13C22⋊C411yescharacteristic
210C22×C4×C13C22⋊C411yescharacteristic
211C22×C4×C13C22×C411yescharacteristic
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C2×C22⋊D13—22no—
219C2×C22⋊D13—22no—
220C2×C22⋊D13—22no—
221C2×C22⋊D13—22no—
222C2×C22⋊D13—22no—
223C2×C22⋊D13—22no—
224C2×C22⋊D13—42no—
225C2×C22⋊D13—42no—
226C22×Dic13—22no—
227C22×Dic13C22×C412yes—
228#6127—42no—
229#6127—42no—
230#6127—42no—
231#6127—42no—
232#6127—42no—
233#6127—42no—
234#6127—41no—
235#6127—41no—
236#6127—41no—
237#6127—41no—
238C2×D52—21no—
239C2×D52—21no—
240C2×D52—41no—
241C2×D52—41no—
242C2×C4×D13—22no—
243C2×C4×D13—22no—
244C2×C4×D13—42no—
245C2×C4×D13—42no—
246C2×Dic26—21no—
247C2×Dic26—21no—
248C2×Dic26—41no—
249C2×Dic26—41no—
250C13×C4⋊C4—42no—
251C13×C4⋊C4—42no—
252C13×C22⋊C4—24no—
253C13×C22⋊C4—42no—
254C42×C13—42no—
255C42×C13—42no—
256C22⋊Dic13—22no—
257C22⋊Dic13—22no—
258C22⋊Dic13—22no—
259C22⋊Dic13—22no—
260C22⋊Dic13—22no—
261C22⋊Dic13C22×C412yes—
262C22⋊Dic13C22×C412yes—
263#6103—22no—
264#6103—22no—
265#6103—22no—
266#6103—22no—
267C4⋊Dic13—21no—
268C4⋊Dic13—21no—
269C4⋊Dic13—22no—
270#6101—22no—
271#6101—22no—
272#6101—22no—
273#6101—22no—
274C4×Dic13—22no—
275C4×Dic13—21no—
276C4×Dic13—21no—
277#6099—24no—
278#6099—42no—
279#6099—42no—
280#6099—42no—
281C2×#1055—42no—
282C2×#1055—42no—
283C2×#1055—42no—
284#3449—131no—
285C2×#413—131no—
286C2×#410D1311yescharacteristic, complemented
287#2123—132no—
288#2122—132no—
289#2121—134no—
290#2120—134no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—81no—
298C23×C13—81no—
299C23×C13—81no—
300C23×C13C2×C22⋊C411yescharacteristic
301C23×C13C2×C22⋊C411yescharacteristic
302C23×C13C2×C22⋊C411yescharacteristic
303C23×C13C2×C22⋊C411yescharacteristic
304C23×C13C2×C22⋊C411yescharacteristic
305C23×C13C23×C411yescharacteristic
306C23×C13C22×D411yescharacteristic
307C22×D13—22no—
308C22×D13—42no—
309C22×D13—82no—
310Q8×C13—41no—
311Q8×C13—41no—
312Q8×C13—41no—
313Q8×C13—41no—
314D4×C13—41no—
315D4×C13—41no—
316D4×C13—41no—
317D4×C13—41no—
318D4×C13—41no—
319D4×C13—41no—
320D4×C13—41no—
321D4×C13—41no—
322D4×C13—41no—
323D4×C13—41no—
324D4×C13—41no—
325D4×C13—41no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
337C2×C4×C13—21no—
338C2×C4×C13—21no—
339C2×C4×C13—21no—
340C2×C4×C13—21no—
341C2×C4×C13—21no—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—21no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—21no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—44no—
357C2×C4×C13—84no—
358C2×C4×C13#9911yescharacteristic
359C2×C4×C13#9911yescharacteristic
360C2×C4×C13#9911yescharacteristic
361C2×C4×C13#9911yescharacteristic
362C2×C4×C13C2×C22⋊C411yescharacteristic
363C2×C4×C13C2×C22⋊C411yescharacteristic
364C2×C4×C13C2×C22⋊C411yescharacteristic
365C2×C4×C13C2×C22⋊C411yescharacteristic
366C2×C4×C13C2×C22⋊C411yescharacteristic
367C2×C4×C13C2×C22⋊C411yescharacteristic
368C2×C4×C13C2×C22⋊C411yescharacteristic
369C2×C4×C13C22×D411yescharacteristic
370C22⋊D13—44no—
371C22⋊D13—42no—
372C22⋊D13—42no—
373C22⋊D13—82no—
374C22⋊D13—82no—
375C22⋊D13—82no—
376C22⋊D13—82no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—42no—
381C2×Dic13—82no—
382D52—42no—
383D52—41no—
384D52—41no—
385C4×D13—44no—
386C4×D13—42no—
387C4×D13—42no—
388Dic26—42no—
389Dic26—41no—
390Dic26—41no—
391#1055—44no—
392C22×#41—131no—
393C22×#41C2×D1311yescharacteristic
394C22×M16—261no—
395#537—261no—
396#537—261no—
397#536—131no—
398#536—131no—
399#536—261no—
400#535—131no—
401#535—131no—
402#535—261no—
403#534—132no—
404#534—132no—
405#532—261no—
406#532—261no—
407#525—132no—
408#525—132no—
409#525—261no—
410#525—261no—
411C2×#117—21no—
412C2×#117—131no—
413#413—132no—
414#413—132no—
415#413—261no—
416#413—261no—
417C2×#101—261no—
418C2×#100—132no—
419#410—21no—
420#410—21no—
421#410C2×D1312yes—
422#410C2×D1312yes—
423C2×#99—21no—
424C2×#99C2×D1312yes—
425#352—138no—
426AΣL(1,𝔽16)—138no—
427C22×C13—21no—
428C22×C13—21no—
429C22×C13—21no—
430C22×C13—21no—
431C22×C13—21no—
432C22×C13—21no—
433C22×C13—41no—
434C22×C13—41no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13—41no—
438C22×C13—41no—
439C22×C13—41no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—81no—
443C22×C13—81no—
444C22×C13—81no—
445C22×C13—81no—
446C22×C13C2×#9911yescharacteristic
447C22×C13C2×#9911yescharacteristic
448C22×C13C22×C22⋊C411yescharacteristic
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—84no—
453C4×C13—21no—
454C4×C13—21no—
455C4×C13—21no—
456C4×C13—21no—
457C4×C13—21no—
458C4×C13—21no—
459C4×C13—84no—
460C4×C13C2×#9911yescharacteristic
461C4×C13C2×#9911yescharacteristic
462C4×C13C2×#9911yescharacteristic
463C4×C13C2×#9911yescharacteristic
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467C2×#41—41no—
468C2×#41—41no—
469C2×#41—41no—
470C2×#41—41no—
471C2×#41—261no—
472C2×#41—261no—
473C2×#41—261no—
474C2×#41—261no—
475C2×#41—521no—
476C2×#41—521no—
477C2×#41—521no—
478C2×#41—521no—
479C2×#41C4×D1311yescharacteristic
480C2×#41C4×D1311yescharacteristic
481C2×#41D5211yescharacteristic
482C2×#41D5211yescharacteristic
483C2×#41C22⋊D1311yescharacteristic
484C2×#41C22⋊D1311yescharacteristic
485C2×#41C22×D1311yescharacteristic
486C2×#41C22×D1311yescharacteristic
487C22×Q8—131no—
488C22×Q8D5211yescharacteristic
489C22×D4—132no—
490C22×D4—131no—
491C22×D4C4×D1311yescharacteristic
492C22×D4C22⋊D1311yescharacteristic
493C22×D4C22×D1311yescharacteristic
494C23×C4—132no—
495C23×C4C4×D1311yescharacteristic
496C23×C4D5211yescharacteristic
497C23×C4C22⋊D1311yescharacteristic
498C2×M16—262no—
499C2×M16—262no—
500C2×M16—262no—
501C2×M16—521no—
502C2×M16—521no—
503C2×M16—521no—
504C22×C8—521no—
505C4⋊Q8—261no—
506C4⋊Q8—261no—
507#127—261no—
508#127—261no—
509#124—261no—
510#124—261no—
511#124—261no—
512#124—261no—
513#123—132no—
514#123—132no—
515#123—132no—
516#123—132no—
517#123—262no—
518#123—262no—
519C22⋊Q8—262no—
520C22⋊Q8—262no—
521C22⋊Q8—261no—
522C22⋊Q8—261no—
523C22⋊Q8—261no—
524C22⋊Q8—261no—
525#121—262no—
526#121—262no—
527#121—262no—
528#121—262no—
529#121—262no—
530#121—262no—
531#121—261no—
532#121—261no—
533#121—261no—
534#121—261no—
535#120—132no—
536#120—132no—
537#120—132no—
538#120—132no—
539#120—262no—
540#120—262no—
541C4×D4—262no—
542C4×D4—262no—
543C4×D4—262no—
544C4×D4—262no—
545#117—22no—
546#117—22no—
547#117—41no—
548#117—41no—
549#117—132no—
550#117—131no—
551#117—131no—
552#117—261no—
553#117—261no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—261no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—132no—
558C2×C42—41no—
559C2×C42—261no—
560#101—262no—
561#101—262no—
562#100—134no—
563#100—262no—
564#99—22no—
565#99—22no—
566#99—22no—
567#99C22×D1314yes—
568C2×C13—21no—
569C2×C13—21no—
570C2×C13—21no—
571C2×C13—41no—
572C2×C13—41no—
573C2×C13—41no—
574C2×C13—41no—
575C2×C13—41no—
576C2×C13—41no—
577C2×C13C22×#9911yescharacteristic
578D13—82no—
579C24—132no—
580C24#610311yescharacteristic
581C24C2×C4×D1311yescharacteristic
582C24C2×C22⋊D1311yescharacteristic
583#41—41no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—522no—
600#41—522no—
601#41—522no—
602#41—522no—
603#41—522no—
604#41—522no—
605#41—521no—
606#41—521no—
607#41—521no—
608#41—521no—
609C2×Q8—41no—
610C2×Q8—41no—
611C2×Q8—261no—
612C2×Q8—261no—
613C2×Q8—521no—
614C2×Q8—521no—
615C2×Q8#610311yescharacteristic
616C2×Q8#610311yescharacteristic
617C2×Q8C2×D5211yescharacteristic
618C2×Q8C2×D5211yescharacteristic
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—262no—
626C2×D4—262no—
627C2×D4—262no—
628C2×D4—262no—
629C2×D4—262no—
630C2×D4—262no—
631C2×D4—261no—
632C2×D4—261no—
633C2×D4—521no—
634C2×D4—521no—
635C2×D4—522no—
636C2×D4—522no—
637C2×D4#610311yescharacteristic
638C2×D4#610311yescharacteristic
639C2×D4#610311yescharacteristic
640C2×D4#610311yescharacteristic
641C2×D4C2×C4×D1311yescharacteristic
642C2×D4C2×C4×D1311yescharacteristic
643C2×D4C2×C4×D1311yescharacteristic
644C2×D4C2×D5211yescharacteristic
645C2×D4C2×C22⋊D1311yescharacteristic
646C2×D4C2×C22⋊D1311yescharacteristic
647C2×D4C2×C22⋊D1311yescharacteristic
648C2×D4C23×D1311yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—132no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—522no—
667C22×C4—522no—
668C22×C4#610311yescharacteristic
669C22×C4#610311yescharacteristic
670C22×C4#610311yescharacteristic
671C22×C4#610311yescharacteristic
672C22×C4#610311yescharacteristic
673C22×C4#610311yescharacteristic
674C22×C4#610311yescharacteristic
675C22×C4#610311yescharacteristic
676C22×C4#610311yescharacteristic
677C22×C4C2×C4×D1311yescharacteristic
678C22×C4C2×C4×D1311yescharacteristic
679C22×C4C2×D5211yescharacteristic
680C22×C4C2×D5211yescharacteristic
681C22×C4C2×D5211yescharacteristic
682C22×C4C2×C22⋊D1311yescharacteristic
683C22×C4C2×C22⋊D1311yescharacteristic
684M16—264no—
685M16—522no—
686M16—522no—
687M16—522no—
688C2×C8—522no—
689C2×C8—522no—
690C2×C8—522no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—262no—
694C4⋊C4—261no—
695C4⋊C4—261no—
696C4⋊C4—262no—
697C4⋊C4—262no—
698C4⋊C4—262no—
699C4⋊C4—262no—
700C22⋊C4—24no—
701C22⋊C4—42no—
702C22⋊C4—132no—
703C22⋊C4—132no—
704C22⋊C4—262no—
705C22⋊C4—262no—
706C22⋊C4—262no—
707C22⋊C4—262no—
708C22⋊C4—262no—
709C22⋊C4—262no—
710C22⋊C4—262no—
711C22⋊C4—262no—
712C22⋊C4—262no—
713C42—42no—
714C42—42no—
715C42—262no—
716C42—261no—
717C42—261no—
718C13#3334711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—262no—
729C23—522no—
730C23—1042no—
731C23C2×#610311yescharacteristic
732C23C2×#610311yescharacteristic
733C23C2×#610311yescharacteristic
734C23C2×#610311yescharacteristic
735C23C2×#610311yescharacteristic
736C23C22×C4×D1311yescharacteristic
737C23C22×C22⋊D1311yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—522no—
743Q8—521no—
744Q8—521no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—522no—
758D4—524no—
759D4—522no—
760D4—522no—
761D4—521no—
762D4—521no—
763D4—1042no—
764D4—1042no—
765D4—1042no—
766D4—1042no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—44no—
798C2×C4—84no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—524no—
803C2×C4—522no—
804C2×C4—522no—
805C2×C4—522no—
806C2×C4—1042no—
807C2×C4#8804611yescharacteristic
808C2×C4#8804611yescharacteristic
809C2×C4#8804611yescharacteristic
810C2×C4#8804611yescharacteristic
811C2×C4C2×#610311yescharacteristic
812C2×C4C2×#610311yescharacteristic
813C2×C4C2×#610311yescharacteristic
814C2×C4C2×#610311yescharacteristic
815C2×C4C2×#610311yescharacteristic
816C2×C4C2×#610311yescharacteristic
817C2×C4C2×#610311yescharacteristic
818C2×C4C22×D5211yescharacteristic
819C8—524no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—522no—
840C22—522no—
841C22—522no—
842C22—1044no—
843C22C2×#8804611yescharacteristic
844C22C2×#8804611yescharacteristic
845C22C22×#610311yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—84no—
853C4—522no—
854C4—522no—
855C4—522no—
856C4C2×#8804611yescharacteristic
857C4C2×#8804611yescharacteristic
858C4C2×#8804611yescharacteristic
859C4C2×#8804611yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—1042no—
870C2C22×#8804611yescharacteristic
subgroupG/H
centerC4C2×#88046
commutatorC23×C13C23×C4
FrattiniC2×D4C23×D13
FittingC2×C13×#410C2
socleC2×C13C22×#99
prime radical#13128165C2
cosocleC2×D4×C13C24
hypercenterC2×#410D13
hypocenterC13#33347
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#11718898C2semidirect
3. #13116489C2semidirect
4. #13116485C2semidirect
5. #13116480C2semidirect
6. #13116475C2semidirect
7. C2×C13×#410C2semidirect
9. C22×#6127C4semidirect
15. #11719535C4semidirect
17. #11719533C4semidirect
19. #11719530C4semidirect
23. #11719509C4semidirect
27. C2×#88180C4semidirect
41. #11718064C22semidirect
42. #11718063C22semidirect
71. C22×D52C2×C4semidirect
72. C22×C4×D13C2×C4semidirect
73. C22×Dic26C2×C4semidirect
99. #88191C2×C4semidirect
100. #88191C2×C4semidirect
105. #88189C2×C4semidirect
106. #88189C2×C4semidirect
120. #88180C2×C4semidirect
121. #88180C2×C4semidirect
122. #88180C2×C4semidirect
286. C2×#410D13semidirect
718. C13#33347semidirect

Maximal subgroups

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

subgroupindex
#131281652
C2×#117188982
#131164892
#131164852
#131164802
#131164752
C2×C13×#4102
#3334713