Finite Group Databasebeta

← #360299

Subgroups — #360299

Order 512.

2190 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2341C211yesmaximal, characteristic
2C2×#1923C211yesmaximal, characteristic, complemented
3C2×#1805C211yesmaximal, characteristic, complemented
4C2×#1788C211yesmaximal, characteristic
5C2×#1788C211yesmaximal, characteristic
6C2×C4×#103C211yesmaximal, characteristic, complemented
7#13875C211yesmaximal, characteristic, complemented
8#11200C211yesmaximal, characteristic, complemented
9#11199C211yesmaximal, characteristic, complemented
10#11076C211yesmaximal, characteristic, complemented
11#11051C211yesmaximal, characteristic, complemented
12#10931C211yesmaximal, characteristic, complemented
13#10925C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2341—24no—
32#2341C418yescomplemented
33C2×#390—21no—
34C2×#390—21no—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#382C2211yescharacteristic
38C2×#380—21no—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4—21no—
44C2×C4×C22⋊C4C2211yescharacteristic
45#1923—24no—
46#1805—24no—
47#1788—24no—
48#1788—24no—
49C4×#103—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1443—21no—
61#1440—21no—
62#1437—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65#1434—21no—
66C22×#41—22no—
67C22×#41—22no—
68C22×#41—22no—
69C22×#41—22no—
70C22×#41—22no—
71C22×#41—22no—
72C22×#41—22no—
73C22×#41—22no—
74C22×#41—22no—
75C22×#41—41no—
76C22×#41—41no—
77C22×#41—41no—
78C22×#41—41no—
79C22×#41C2×C414yes—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C2×C4×Q8—22no—
90C2×C4×Q8—22no—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8—22no—
95C2×C4×Q8—41no—
96C2×C4×Q8—41no—
97C2×C4×Q8—41no—
98C2×C4×Q8—41no—
99C2×C4×Q8C2×C414yes—
100C2×C4×Q8C2×C414yes—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4D411yescharacteristic
117C22×C22⋊C4D411yescharacteristic
118C22×C42—21no—
119C22×C42—21no—
120C22×C42—21no—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—41no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103D414yes—
137C2×#103D414yes—
138C2×#102—22no—
139C2×#102—22no—
140C2×#102—22no—
141C2×#102—22no—
142C2×#102—22no—
143C2×#102—22no—
144C2×#102—22no—
145C2×#102—22no—
146C2×#102—41no—
147C2×#102—41no—
148C2×#102—41no—
149C2×#102—41no—
150C2×C22⋊C8—22no—
151C2×C22⋊C8—22no—
152C2×C22⋊C8—22no—
153C2×C22⋊C8—22no—
154C2×C22⋊C8—41no—
155C2×C22⋊C8—41no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8—41no—
159#390—28no—
160#390—28no—
161#390—22no—
162#390—22no—
163#390C2×C414yes—
164#390C2×C414yes—
165#382—22no—
166#382—41no—
167#380—22no—
168#380—28no—
169#380—22no—
170#380—22no—
171#380—41no—
172#380—41no—
173#380C2×C414yes—
174C4×C4⋊C4—22no—
175C4×C4⋊C4—41no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4C2×C414yes—
178C4×C22⋊C4D414yes—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95D411yescharacteristic
190C2×#95D411yescharacteristic
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—41no—
196#340—41no—
197#340—41no—
198#340—41no—
199#336—22no—
200#336—22no—
201C25—21no—
202C25C2×D411yescharacteristic
203C2×#41—28no—
204C2×#41—28no—
205C2×#41—28no—
206C2×#41—28no—
207C2×#41—28no—
208C2×#41—28no—
209C2×#41—44no—
210C2×#41—44no—
211C2×#41—44no—
212C2×#41—44no—
213C2×#41—44no—
214C2×#41—44no—
215C2×#41—44no—
216C2×#41—44no—
217C2×#41—44no—
218C2×#41—44no—
219C2×#41—44no—
220C2×#41—44no—
221C2×#41—44no—
222C2×#41—44no—
223C2×#41—44no—
224C2×#41—44no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—44no—
229C2×#41—44no—
230C2×#41—44no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8C22×C412yes—
239C22×Q8C2×D412yes—
240C22×Q8C2×D412yes—
241C22×Q8#4112yes—
242C22×Q8#4112yes—
243C22×Q8#4112yes—
244C22×Q8#4112yes—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4C22×C412yes—
264C22×D4#4112yes—
265C22×D4#4112yes—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C22×C412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D412yes—
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8C2×D412yes—
327C22×C8C2×D412yes—
328C4×Q8—28no—
329C4×Q8—28no—
330C4×Q8—44no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C2×D412yes—
377C2×C4⋊C4C2×D412yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—81no—
396C2×C22⋊C4—81no—
397C2×C22⋊C4—81no—
398C2×C22⋊C4—81no—
399C2×C22⋊C4—81no—
400C2×C22⋊C4—81no—
401C2×C22⋊C4—81no—
402C2×C22⋊C4—81no—
403C2×C22⋊C4C22⋊C414yes—
404C2×C22⋊C4C22⋊C414yes—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—81no—
422C2×C42C22×C412yes—
423C2×C42C22×C412yes—
424C2×C42C2×D412yes—
425C2×C42C2×D412yes—
426C4⋊C8—44no—
427#103—28no—
428#103—28no—
429#103—44no—
430#103—44no—
431#102—44no—
432#102—44no—
433#102—44no—
434#102—44no—
435C22⋊C8—44no—
436C22⋊C8—44no—
437C4×C8—44no—
438#95—24no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—81no—
446#95—81no—
447#95—81no—
448#95C22⋊C414yes—
449#95C22⋊C414yes—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—41no—
473C24—41no—
474C24—41no—
475C24—41no—
476C24—41no—
477C24—41no—
478C24—41no—
479C24C2×C22⋊C412yes—
480C24C22×D411yescharacteristic
481#41—416no—
482#41—416no—
483#41—416no—
484#41—416no—
485#41—416no—
486#41—416no—
487#41—416no—
488#41—416no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8#11714yes—
511C2×Q8C4×D414yes—
512C2×Q8C4×D414yes—
513C2×Q8#12114yes—
514C2×Q8#12314yes—
515C2×Q8#12414yes—
516C2×Q8#12614yes—
517C2×D4—216no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4#11714yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—216no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
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—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4C2×C22⋊C412yes—
665C22×C4C2×C22⋊C412yes—
666C22×C4C2×C22⋊C412yes—
667C22×C4C2×C22⋊C412yes—
668C22×C4C2×C22⋊C412yes—
669C22×C4#13512yes—
670C22×C4#13512yes—
671C22×C4C23×C411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D411yescharacteristic
674C22×C4C22×D411yescharacteristic
675C22×C4C2×#4111yescharacteristic
676C22×C4C2×#4111yescharacteristic
677C22×C4C2×#4111yescharacteristic
678C22×C4C2×#4111yescharacteristic
679C22×C4C2×#4111yescharacteristic
680C22×C4C2×#4111yescharacteristic
681C22×C4H(5,𝔽2)11yescharacteristic
682C22×C4H(5,𝔽2)11yescharacteristic
683C22×C4H(5,𝔽2)11yescharacteristic
684C22×C4H(5,𝔽2)11yescharacteristic
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—41no—
703C2×C8—41no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—41no—
707C2×C8—41no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—41no—
711C2×C8—41no—
712C2×C8—41no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—41no—
724C4⋊C4—41no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—41no—
728C4⋊C4—41no—
729C4⋊C4—41no—
730C4⋊C4—41no—
731C4⋊C4—41no—
732C4⋊C4—41no—
733C4⋊C4—41no—
734C4⋊C4—41no—
735C4⋊C4—41no—
736C4⋊C4—41no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C22⋊C4—28no—
740C22⋊C4—44no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—84no—
744C22⋊C4—84no—
745C22⋊C4—84no—
746C22⋊C4—84no—
747C22⋊C4—84no—
748C42—22no—
749C42—22no—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—48no—
757C42—48no—
758C42—84no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—41no—
778C23—42no—
779C23—41no—
780C23—42no—
781C23—41no—
782C23—42no—
783C23—41no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—41no—
795C23—42no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—81no—
814C23—81no—
815C23—81no—
816C23—81no—
817C23—81no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23—81no—
826C23—81no—
827C23—81no—
828C23—81no—
829C23C22×C22⋊C411yescharacteristic
830C23#52511yescharacteristic
831C23#52511yescharacteristic
832C23D4211yescharacteristic
833C23D4211yescharacteristic
834C23#54611yescharacteristic
835C23#54611yescharacteristic
836C23C2×#13511yescharacteristic
837C23C2×#13511yescharacteristic
838C23#57511yescharacteristic
839C23#57511yescharacteristic
840C23#57611yescharacteristic
841C23#57711yescharacteristic
842C23#57711yescharacteristic
843C23#57811yescharacteristic
844Q8—24no—
845Q8—24no—
846Q8—24no—
847Q8—24no—
848Q8—24no—
849Q8—24no—
850Q8—24no—
851Q8#38818yes—
852D4—24no—
853D4—24no—
854D4—432no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—432no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—81no—
924C2×C4—81no—
925C2×C4—81no—
926C2×C4—81no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—81no—
952C2×C4—81no—
953C2×C4#41614yes—
954C2×C4C2×#11711yescharacteristic
955C2×C4C2×#11711yescharacteristic
956C2×C4C2×C4×D411yescharacteristic
957C2×C4C2×C4×D411yescharacteristic
958C2×C4#51811yescharacteristic
959C2×C4#51811yescharacteristic
960C2×C4C2×#12111yescharacteristic
961C2×C4C2×#12311yescharacteristic
962C2×C4#52511yescharacteristic
963C2×C4#52511yescharacteristic
964C2×C4C2×#12411yescharacteristic
965C2×C4C2×#12611yescharacteristic
966C2×C4#53811yescharacteristic
967C2×C4#53811yescharacteristic
968C2×C4#53811yescharacteristic
969C2×C4#53811yescharacteristic
970C2×C4D4211yescharacteristic
971C2×C4D4211yescharacteristic
972C2×C4#54611yescharacteristic
973C2×C4#54611yescharacteristic
974C2×C4#54611yescharacteristic
975C2×C4#54611yescharacteristic
976C2×C4#54611yescharacteristic
977C2×C4#54611yescharacteristic
978C2×C4#55111yescharacteristic
979C2×C4#55111yescharacteristic
980C2×C4#55111yescharacteristic
981C2×C4#55111yescharacteristic
982C8—42no—
983C8—42no—
984C8—81no—
985C8—81no—
986C22—42no—
987C22—44no—
988C22—42no—
989C22—44no—
990C22—44no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—81no—
997C22—82no—
998C22—81no—
999C22—82no—
1000C22—81no—
1001C22—82no—
1002C22—81no—
1003C22—82no—
1004C22—81no—
1005C22—82no—
1006C22—81no—
1007C22—82no—
1008C22—81no—
1009C22—82no—
1010C22—81no—
1011C22—82no—
1012C22—82no—
1013C22—82no—
1014C22—82no—
1015C22—82no—
1016C22#228011yescharacteristic
1017C22D4×C22⋊C411yescharacteristic
1018C22D4×C22⋊C411yescharacteristic
1019C22#241811yescharacteristic
1020C22#242411yescharacteristic
1021C22#247211yescharacteristic
1022C22#248011yescharacteristic
1023C22C2×#41611yescharacteristic
1024C22#289611yescharacteristic
1025C22#289711yescharacteristic
1026C22#289811yescharacteristic
1027C22#310211yescharacteristic
1028C22#310211yescharacteristic
1029C22#310211yescharacteristic
1030C22#310211yescharacteristic
1031C22#311911yescharacteristic
1032C22#312011yescharacteristic
1033C22#312411yescharacteristic
1034C22#312511yescharacteristic
1035C22#326811yescharacteristic
1036C22#327111yescharacteristic
1037C22#327511yescharacteristic
1038C22#327711yescharacteristic
1039C22#328211yescharacteristic
1040C22#328411yescharacteristic
1041C22#328511yescharacteristic
1042C22#328711yescharacteristic
1043C22#330011yescharacteristic
1044C22#330111yescharacteristic
1045C22#330411yescharacteristic
1046C22#330511yescharacteristic
1047C22#330911yescharacteristic
1048C22#331711yescharacteristic
1049C22#332611yescharacteristic
1050C22#332711yescharacteristic
1051C4—28no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—82no—
1058C4—82no—
1059C4—82no—
1060C4—82no—
1061C4—161no—
1062C4—161no—
1063C4C2×#38811yescharacteristic
1064C4#231211yescharacteristic
1065C4#234211yescharacteristic
1066C4#234211yescharacteristic
1067C4#241811yescharacteristic
1068C4#242411yescharacteristic
1069C4#247211yescharacteristic
1070C4#248011yescharacteristic
1071C2—82no—
1072C2—84no—
1073C2#1387311yescharacteristic
1074C2#2073611yescharacteristic
1075C2#2074611yescharacteristic
1076C2#2241611yescharacteristic
1077C2#2241811yescharacteristic
1078C2#2242211yescharacteristic
1079C2#2242911yescharacteristic
1080C2#2490011yescharacteristic
1081C2#2490811yescharacteristic
1082C2#2515511yescharacteristic
1083C2#2516311yescharacteristic
1084C2#2723411yescharacteristic
1085C2#2723611yescharacteristic
1086C2#2753011yescharacteristic
1087C2#2753211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1923C2semidirect
3. C2×#1805C2semidirect
6. C2×C4×#103C2semidirect
7. #13875C2semidirect
8. #11200C2semidirect
9. #11199C2semidirect
10. #11076C2semidirect
11. #11051C2semidirect
12. #10931C2semidirect
13. #10925C2semidirect
14. #10789C2semidirect
15. #10789C2semidirect
32. #2341C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23412
C2×#19232
C2×#18052
C2×#17882
C2×C4×#1032
#138752
#112002
#111992
#110762
#110512
#109312
#109252
#107892