Finite Group Databasebeta

← #15890762

Subgroups — #15890762

Order 3328.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718785C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic, complemented
3#13123355C211yesmaximal, characteristic, complemented
4C2×#11718898C211yesmaximal, characteristic, complemented
5C2×#11718898C211yesmaximal, characteristic, complemented
6#13116113C214yesmaximal, complemented
7#13116106C214yesmaximal, complemented
8C2×#11718151C211yesmaximal, characteristic, complemented
9C2×C13×#575C211yesmaximal, characteristic
10C22×C13×#41C2211yescharacteristic
11C22×C13×#41C2211yescharacteristic
12C13×#575—22no—
13C13×#575—22no—
14C13×#575—22no—
15C13×#575—22no—
16C2×C13×#137—21no—
17C2×C13×#137C2212yes—
18C2×C13×AGL(1,ℤ/8)—21no—
19C2×C13×AGL(1,ℤ/8)C2212yes—
20C2×C13×#135—22no—
21C22×C13×M16C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C22×#6099C2211yescharacteristic
26#11718898—22no—
27#11718898—22no—
28#11718898—22no—
29#11718898C2214yes—
30#11718897—22no—
31#11718897C2214yes—
32C2×#88077—22no—
33#11718894—22no—
34#11718893—22no—
35C2×#88076—21no—
36C2×#88076C2212yescomplemented
37#11718886C2212yescomplemented
38C2×#88073—21no—
39C2×#88073C2212yescomplemented
40#11718876C2212yescomplemented
41#11718785—22no—
42#11718785C2214yescomplemented
43C2×#88062—22no—
44#11718151C2214yescomplemented
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×#41—21no—
61C2×C13×#41—21no—
62C2×C13×#41—21no—
63C2×C13×#41—21no—
64C2×C13×#41—21no—
65C2×C13×#41D412yes—
66C2×C13×#41D412yes—
67C2×C13×#41D412yes—
68C2×C13×#41C2312yes—
69C22×Q8×C13D411yescharacteristic
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13—21no—
72C22×D4×C13—21no—
73C22×D4×C13D411yescharacteristic
74C22×D4×C13C2311yescharacteristic
75C23×C4×C13—21no—
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C13×#137—24no—
79C13×#137—24no—
80C13×#137—24no—
81C13×#137—24no—
82C13×AGL(1,ℤ/8)—24no—
83C13×AGL(1,ℤ/8)—24no—
84C13×AGL(1,ℤ/8)—24no—
85C13×AGL(1,ℤ/8)—24no—
86C13×#135—28no—
87C13×#135—28no—
88C2×C13×Q16—22no—
89C2×C13×SD16—22no—
90C2×C13×SD16—22no—
91C2×C13×D8—22no—
92C2×C13×M16—21no—
93C2×C13×M16—21no—
94C2×C13×M16—21no—
95C2×C13×M16D412yes—
96C2×C13×M16D412yes—
97C2×C13×M16C2312yes—
98C22×C8×C13—21no—
99C2×C22⋊Dic13—21no—
100#88180—21no—
101#88180—21no—
102#88180—21no—
103#88180C2312yes—
104C2×C4⋊Dic13—21no—
105C2×C4×Dic13—21no—
106C2×#6099—21no—
107C2×#6099—21no—
108C2×#6099—21no—
109C2×#6099—21no—
110C2×#6099—21no—
111C2×#6099—21no—
112C2×#6099—21no—
113C2×#6099—21no—
114C2×#6099—21no—
115C2×#6099—21no—
116C2×#6099—21no—
117C2×#6099—21no—
118C2×#6099—21no—
119C2×#6099D412yes—
120C2×#6099D412yes—
121C2×#6099C2312yes—
122C2×#6099C2312yes—
123C2×#6099C2312yes—
124C22×#1055—21no—
125C22×#1055—21no—
126C22×#1055—21no—
127#88077—28no—
128#88076—24no—
129#88076—24no—
130#88075—24no—
131#88073—24no—
132#88073—24no—
133#88072—24no—
134#88062—28no—
135#23525—131nomaximal, Sylow
136C24×C13—21no—
137C24×C13—21no—
138C24×C13#4111yescharacteristic
139C13×#41—22no—
140C13×#41—22no—
141C13×#41—22no—
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—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—
165C13×#41—41no—
166C13×#41—41no—
167C13×#41—41no—
168C13×#41—41no—
169C13×#41—41no—
170C13×#41—41no—
171C2×Q8×C13—21no—
172C2×Q8×C13—21no—
173C2×Q8×C13—21no—
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×C13C2×D412yes—
182C2×Q8×C13C2×D412yes—
183C2×D4×C13—22no—
184C2×D4×C13—22no—
185C2×D4×C13—22no—
186C2×D4×C13—22no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—21no—
194C2×D4×C13—21no—
195C2×D4×C13—21no—
196C2×D4×C13—21no—
197C2×D4×C13—41no—
198C2×D4×C13—41no—
199C2×D4×C13—41no—
200C2×D4×C13—41no—
201C2×D4×C13—41no—
202C2×D4×C13—41no—
203C2×D4×C13—41no—
204C2×D4×C13—41no—
205C2×D4×C13C2×D412yes—
206C2×D4×C13C2×D412yes—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—22no—
212C22×C4×C13—22no—
213C22×C4×C13—41no—
214C22×C4×C13—41no—
215C22×C4×C13—41no—
216C22×C4×C13—41no—
217C22×C4×C13—41no—
218C22×C4×C13—41no—
219C22×C4×C13—41no—
220C22×C4×C13—41no—
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13#4111yescharacteristic
230C22×C4×C13#4111yescharacteristic
231C22×C4×C13#4111yescharacteristic
232C22×C4×C13#4111yescharacteristic
233C22×C4×C13#4111yescharacteristic
234C22×C4×C13C2411yescharacteristic
235C22×Dic13—41no—
236C13×Q16—28no—
237C13×SD16—28no—
238C13×SD16—28no—
239C13×D8—28no—
240C13×M16—22no—
241C13×M16—22no—
242C13×M16—22no—
243C13×M16C2×D414yes—
244C2×C8×C13—22no—
245C2×C8×C13—22no—
246C2×C8×C13—22no—
247C22⋊Dic13—22no—
248C22⋊Dic13—41no—
249C4⋊Dic13—22no—
250C4⋊Dic13—41no—
251C4×Dic13—22no—
252C4×Dic13—41no—
253#6099—22no—
254#6099—22no—
255#6099—22no—
256#6099—22no—
257#6099—22no—
258#6099—22no—
259#6099—22no—
260#6099—41no—
261#6099—41no—
262#6099—41no—
263#6099—41no—
264#6099C2×D414yes—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055—22no—
270C2×#1055—41no—
271C2×#1055—41no—
272C2×#1055—41no—
273C2×#1055—41no—
274C2×#575D1311yescharacteristic
275C2×#430—131no—
276C2×#421—131no—
277#2896—131no—
278C2×#413—131no—
279C2×#413—131no—
280#2049—134no—
281#2048—134no—
282C2×#344—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—81no—
290C23×C13—82no—
291C23×C13—82no—
292C23×C13#12111yescharacteristic
293C23×C13#12111yescharacteristic
294C23×C13#12311yescharacteristic
295C23×C13#12311yescharacteristic
296C23×C13#12411yescharacteristic
297C23×C13#12411yescharacteristic
298C23×C13C2×#4111yescharacteristic
299Q8×C13—22no—
300Q8×C13—22no—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—41no—
304Q8×C13—41no—
305Q8×C13—41no—
306Q8×C13—41no—
307D4×C13—22no—
308D4×C13—22no—
309D4×C13—22no—
310D4×C13—22no—
311D4×C13—42no—
312D4×C13—42no—
313D4×C13—42no—
314D4×C13—42no—
315D4×C13—42no—
316D4×C13—42no—
317D4×C13—42no—
318D4×C13—42no—
319D4×C13—41no—
320D4×C13—41no—
321D4×C13—41no—
322D4×C13—41no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13#12011yescharacteristic
338C2×C4×C13#12011yescharacteristic
339C2×C4×C13#12011yescharacteristic
340C2×C4×C13#12011yescharacteristic
341C2×C4×C13#12111yescharacteristic
342C2×C4×C13#12111yescharacteristic
343C2×C4×C13#12111yescharacteristic
344C2×C4×C13#12111yescharacteristic
345C2×C4×C13#12111yescharacteristic
346C2×C4×C13#12111yescharacteristic
347C2×C4×C13#12111yescharacteristic
348C2×C4×C13#12111yescharacteristic
349C2×C4×C13#12111yescharacteristic
350C2×C4×C13#12111yescharacteristic
351C2×C4×C13#12311yescharacteristic
352C2×C4×C13#12311yescharacteristic
353C2×C4×C13#12311yescharacteristic
354C2×C4×C13#12311yescharacteristic
355C2×C4×C13#12311yescharacteristic
356C2×C4×C13#12311yescharacteristic
357C2×C4×C13#12411yescharacteristic
358C2×C4×C13#12411yescharacteristic
359C2×C4×C13C22×D411yescharacteristic
360C2×C4×C13C22×D411yescharacteristic
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C2×#4111yescharacteristic
364C2×C4×C13C2×#4111yescharacteristic
365C2×Dic13—42no—
366C2×Dic13—82no—
367C8×C13—24no—
368#1055—24no—
369#1055—42no—
370#1055—42no—
371C22×#41C2×D1311yescharacteristic
372C22×#41C2×D1311yescharacteristic
373#575—22no—
374#575—22no—
375#575—22no—
376#575—22no—
377C2×#137—21no—
378C2×#137C2×D1312yes—
379C2×AGL(1,ℤ/8)—21no—
380C2×AGL(1,ℤ/8)C2×D1312yes—
381C2×#135—22no—
382C22×M16—131no—
383C22×M16—131no—
384C22×M16—131no—
385C22×M16C2×D1311yescharacteristic
386C2×#117—131no—
387#430—134no—
388#430—262no—
389C2×#108—262no—
390#421—134no—
391#421—262no—
392C2×#104—262no—
393#419—132no—
394#418—132no—
395#417—262no—
396#416—262no—
397#413—134no—
398#413—262no—
399#413—262no—
400#413—262no—
401C2×#101—132no—
402C2×#101—261no—
403C2×#100—132no—
404C2×#100—261no—
405#344—134no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—41no—
412C22×C13—41no—
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—82no—
416C22×C13—82no—
417C22×C13—82no—
418C22×C13—82no—
419C22×C13—82no—
420C22×C13—82no—
421C22×C13#39411yescharacteristic
422C22×C13#39411yescharacteristic
423C22×C13#39411yescharacteristic
424C22×C13#39411yescharacteristic
425C22×C13C2×#12111yescharacteristic
426C22×C13C2×#12311yescharacteristic
427C22×C13C2×#12411yescharacteristic
428C4×C13—42no—
429C4×C13—42no—
430C4×C13#39411yescharacteristic
431C4×C13#39411yescharacteristic
432C4×C13#39411yescharacteristic
433C4×C13#39411yescharacteristic
434C4×C13C2×#12011yescharacteristic
435C4×C13C2×#12111yescharacteristic
436C4×C13C2×#12111yescharacteristic
437C4×C13C2×#12311yescharacteristic
438Dic13—82no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
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×#41C22⋊D1312yes—
460C2×#41C22⋊D1312yes—
461C2×#41C22⋊D1312yes—
462C2×#41C22×D1312yes—
463C22×Q8C22⋊D1311yescharacteristic
464C22×Q8C22×D1311yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C22⋊D1311yescharacteristic
468C22×D4C22×D1311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C22×D1311yescharacteristic
472#137—24no—
473#137—24no—
474#137—24no—
475#137—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)—24no—
478AGL(1,ℤ/8)—24no—
479AGL(1,ℤ/8)—24no—
480#135—28no—
481#135—28no—
482C2×Q16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×D8—22no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—132no—
490C2×M16—132no—
491C2×M16—132no—
492C2×M16—132no—
493C2×M16—132no—
494C2×M16—261no—
495C2×M16—261no—
496C2×M16—261no—
497C2×M16—261no—
498C2×M16—261no—
499C2×M16—261no—
500C2×M16—261no—
501C2×M16—261no—
502C2×M16—261no—
503C2×M16—261no—
504C2×M16—261no—
505C2×M16—261no—
506C2×M16—261no—
507C2×M16C22⋊D1312yes—
508C2×M16C22⋊D1312yes—
509C2×M16C22×D1312yes—
510C22×C8—21no—
511C22×C8—261no—
512C22×C8—261no—
513C22×C8—261no—
514#117—132no—
515#117—261no—
516#117—261no—
517#117—261no—
518C2×C4⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C42—261no—
521#108—268no—
522#104—268no—
523#103—264no—
524#102—264no—
525#101—264no—
526#101—264no—
527#100—264no—
528#100—264no—
529C2×C13—21no—
530C2×C13—21no—
531C2×C13—21no—
532C2×C13—21no—
533C2×C13—21no—
534C2×C13—21no—
535C2×C13—21no—
536C2×C13—82no—
537C2×C13—82no—
538C2×C13C2×#39411yescharacteristic
539C24—21no—
540C24—21no—
541C24#612911yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
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—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×C22⋊D1312yes—
585C2×Q8C2×C22⋊D1312yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4C2×C22⋊D1312yes—
609C2×D4C2×C22⋊D1312yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—521no—
625C22×C4D4×D1311yescharacteristic
626C22×C4D4×D1311yescharacteristic
627C22×C4#612911yescharacteristic
628C22×C4#612911yescharacteristic
629C22×C4#612911yescharacteristic
630C22×C4#612911yescharacteristic
631C22×C4#612911yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C2×C22⋊D1311yescharacteristic
635C22×C4C2×C22⋊D1311yescharacteristic
636C22×C4C2×C22⋊D1311yescharacteristic
637C22×C4C2×C22⋊D1311yescharacteristic
638C22×C4C23×D1311yescharacteristic
639Q16—28no—
640SD16—28no—
641SD16—28no—
642D8—28no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—134no—
647M16—262no—
648M16—262no—
649M16—262no—
650M16—262no—
651M16—262no—
652M16—262no—
653M16—262no—
654M16—521no—
655M16—521no—
656M16—521no—
657M16—521no—
658M16C2×C22⋊D1314yes—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—262no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—262no—
667C2×C8—521no—
668C2×C8—521no—
669C2×C8—521no—
670C2×C8—521no—
671C4⋊C4—262no—
672C4⋊C4—521no—
673C22⋊C4—262no—
674C22⋊C4—521no—
675C42—262no—
676C42—521no—
677C13#2352511yescharacteristic, complemented, Sylow
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—82no—
686C23—82no—
687C23#8818911yescharacteristic
688C23#8818911yescharacteristic
689C23#8819011yescharacteristic
690C23#8819011yescharacteristic
691C23#8819311yescharacteristic
692C23#8819311yescharacteristic
693C23C2×#612911yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—522no—
733C2×C4—1042no—
734C2×C4#8818911yescharacteristic
735C2×C4#8818911yescharacteristic
736C2×C4#8818911yescharacteristic
737C2×C4#8818911yescharacteristic
738C2×C4#8818911yescharacteristic
739C2×C4#8818911yescharacteristic
740C2×C4#8819011yescharacteristic
741C2×C4#8819011yescharacteristic
742C2×C4#8819211yescharacteristic
743C2×C4#8819211yescharacteristic
744C2×C4#8819211yescharacteristic
745C2×C4#8819211yescharacteristic
746C2×C4#8819311yescharacteristic
747C2×C4#8819311yescharacteristic
748C2×C4#8819311yescharacteristic
749C2×C4#8819311yescharacteristic
750C2×C4#8819311yescharacteristic
751C2×C4#8819311yescharacteristic
752C2×C4#8820711yescharacteristic
753C2×C4#8820711yescharacteristic
754C2×C4#8820711yescharacteristic
755C2×C4#8820711yescharacteristic
756C2×C4C2×D4×D1311yescharacteristic
757C2×C4C2×#612911yescharacteristic
758C2×C4C2×#612911yescharacteristic
759C2×C4C22×C22⋊D1311yescharacteristic
760C2×C4C22×C22⋊D1311yescharacteristic
761C2×C4C22×C22⋊D1311yescharacteristic
762C8—24no—
763C8—264no—
764C8—522no—
765C8—522no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22#1171888311yescharacteristic
782C22#1171888311yescharacteristic
783C22#1171888311yescharacteristic
784C22#1171888311yescharacteristic
785C22C2×#8818911yescharacteristic
786C22C2×#8819011yescharacteristic
787C22C2×#8819311yescharacteristic
788C4—42no—
789C4—42no—
790C4—1042no—
791C4#1171888311yescharacteristic
792C4#1171888311yescharacteristic
793C4#1171888311yescharacteristic
794C4#1171888311yescharacteristic
795C4C2×#8818911yescharacteristic
796C4C2×#8819211yescharacteristic
797C4C2×#8819311yescharacteristic
798C4C2×#8820711yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—82no—
808C2C2×#1171888311yescharacteristic
subgroupG/H
centerC4#11718883
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#575C2
socleC2×C13C2×#394
hypercenterC2×#575D13
hypocenterC13#23525
LCSG ▷ C22×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×#11718785C2semidirect
2. C2×#11718897C2semidirect
3. #13123355C2semidirect
4. C2×#11718898C2semidirect
5. C2×#11718898C2semidirect
6. #13116113C2semidirect
7. #13116106C2semidirect
8. C2×#11718151C2semidirect
36. C2×#88076C22semidirect
37. #11718886C22semidirect
39. C2×#88073C22semidirect
40. #11718876C22semidirect
42. #11718785C22semidirect
44. #11718151C22semidirect
677. C13#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#117187852
C2×#117188972
#131233552
C2×#117188982
#131161132
#131161062
C2×#117181512
C2×C13×#5752
#2352513