Finite Group Databasebeta

← C22×#11071 #72316893

Subgroups — C22×#11071 #72316893

Order 1024.

29053 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#2905C211yesmaximal, characteristic, complemented
2C23×#407C212yesmaximal
3C22×#2280C211yesmaximal, characteristic
4C23×#344C212yesmaximal, complemented
5C22×#1742C211yesmaximal, characteristic, complemented
6C2×#11071C2124yesmaximal, direct product factor
7C26×C4C2211yescharacteristic
8C24×M16C2212yes—
9C24×M16C2212yes—
10C23×#117C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×#2905—212no—
13C2×#2905—26no—
14C2×#2905C22112yescomplemented
15C22×#424—24no—
16C22×#423—22no—
17C22×#407—216no—
18C22×#407—212no—
19C22×#407—216no—
20C22×#407C22124yes—
21C23×C22⋊C8—24no—
22C2×#2280—26no—
23C2×#2280—26no—
24C2×#2280C4112yes—
25C2×#2280C22112yes—
26C22×#381C412yes—
27C22×#380—22no—
28C22×#379C412yes—
29C22×C4×C22⋊C4—22no—
30C22×#344—216no—
31C22×#344C22124yescomplemented
32C2×#1742—26no—
33C2×#1742C22112yescomplemented
34C22×#343—22no—
35#11071C22164yesdirect product factor
36C27C2×C411yescharacteristic
37C25×C4—22no—
38C25×C4—28no—
39C25×C4—26no—
40C25×C4—21no—
41C25×C4—21no—
42C25×C4—23no—
43C25×C4—23no—
44C25×C4—24no—
45C25×C4—24no—
46C25×C4—22no—
47C25×C4—26no—
48C25×C4—28no—
49C25×C4C2×C411yescharacteristic
50C25×C4C2×C416yes—
51C25×C4D418yes—
52C25×C4Q818yes—
53C25×C4C2316yes—
54C25×C4C2311yescharacteristic
55C23×M16—28no—
56C23×M16—28no—
57C23×M16—28no—
58C23×M16—28no—
59C23×M16—26no—
60C23×M16—22no—
61C23×M16—22no—
62C23×M16—26no—
63C23×M16—26no—
64C23×M16—28no—
65C23×M16—22no—
66C23×M16—26no—
67C23×M16—22no—
68C23×M16—26no—
69C23×M16—28no—
70C23×M16—28no—
71C23×M16D4116yes—
72C23×M16D4112yes—
73C23×M16C23112yes—
74C23×M16C23112yes—
75C24×C8—22no—
76C24×C8D414yes—
77C22×#117—22no—
78C22×#117—26no—
79C22×#117—22no—
80C22×#117—26no—
81C22×#117—23no—
82C22×#117—23no—
83C22×#117—28no—
84C22×#117—28no—
85C22×#117C2×C416yes—
86C22×#117C2×C416yes—
87C22×#117D416yes—
88C22×#117D416yes—
89C22×#117C2316yes—
90C22×#117C2316yes—
91C23×C4⋊C4—21no—
92C23×C4⋊C4D412yes—
93C23×C22⋊C4—24no—
94C23×C22⋊C4C2×C412yes—
95C23×C22⋊C4C2×C412yes—
96C23×C42—21no—
97C23×C42D412yes—
98#2905—248no—
99#2905—248no—
100#2905—224no—
101#2905C23116yescomplemented
102C2×#424—248no—
103C2×#424—248no—
104C2×#423—224no—
105C2×#423—224no—
106C22×C4⋊C8—28no—
107C2×#407—2192no—
108C2×#407—296no—
109C2×#407—296no—
110C2×#407—248no—
111C2×#407C23132yes—
112C22×C22⋊C8—264no—
113C22×C22⋊C8—248no—
114#2280—248no—
115#2280—224no—
116#2280—224no—
117#2280C2×C4148yes—
118#2280C23116yes—
119C2×#381—212no—
120C2×#381C2×C4124yes—
121C2×#380—224no—
122C2×#380—224no—
123C2×#379—212no—
124C2×#379C2×C4124yes—
125C2×C4×C22⋊C4—224no—
126C2×C4×C22⋊C4—224no—
127C22×#95—24no—
128C2×#344—296no—
129C2×#344C23132yescomplemented
130#1742—224no—
131#1742C23116yescomplemented
132C2×#343—224no—
133C26—21no—
134C26—22no—
135C26—23no—
136C26—24no—
137C26—26no—
138C26—28no—
139C26—416no—
140C26C4⋊C418yes—
141C26C22×C416yes—
142C26C22×C411yescharacteristic
143C24×C4—21no—
144C24×C4—23no—
145C24×C4—24no—
146C24×C4—22no—
147C24×C4—26no—
148C24×C4—28no—
149C24×C4—26no—
150C24×C4—26no—
151C24×C4—212no—
152C24×C4—224no—
153C24×C4—212no—
154C24×C4—212no—
155C24×C4—224no—
156C24×C4—248no—
157C24×C4—216no—
158C24×C4—248no—
159C24×C4—28no—
160C24×C4—224no—
161C24×C4—28no—
162C24×C4—224no—
163C24×C4—28no—
164C24×C4—224no—
165C24×C4—28no—
166C24×C4—224no—
167C24×C4—216no—
168C24×C4—248no—
169C24×C4—216no—
170C24×C4—248no—
171C24×C4—216no—
172C24×C4—248no—
173C24×C4—212no—
174C24×C4—224no—
175C24×C4—212no—
176C24×C4—26no—
177C24×C4—26no—
178C24×C4—26no—
179C24×C4—26no—
180C24×C4—212no—
181C24×C4—212no—
182C24×C4—212no—
183C24×C4—212no—
184C24×C4—224no—
185C24×C4—22no—
186C24×C4—46no—
187C24×C4—46no—
188C24×C4—43no—
189C24×C4—41no—
190C24×C4—42no—
191C24×C4—46no—
192C24×C4—46no—
193C24×C4—46no—
194C24×C4—412no—
195C24×C4—48no—
196C24×C4—424no—
197C24×C4—48no—
198C24×C4—424no—
199C24×C4—46no—
200C24×C4—46no—
201C24×C4—43no—
202C24×C4—41no—
203C24×C4—48no—
204C24×C4—424no—
205C24×C4—48no—
206C24×C4—424no—
207C24×C4—412no—
208C24×C4—44no—
209C24×C4—48no—
210C24×C4—424no—
211C24×C4—412no—
212C24×C4—44no—
213C24×C4C22⋊C414yes—
214C24×C4C4⋊C418yes—
215C24×C4C4⋊C4148yes—
216C24×C4C22×C416yes—
217C24×C4C22×C4112yes—
218C24×C4C22×C413yes—
219C24×C4C2×D4124yes—
220C24×C4C2×D413yes—
221C24×C4C2×D411yescharacteristic
222C24×C4C2×D411yescharacteristic
223C24×C4C2×D413yes—
224C24×C4C2×D414yes—
225C24×C4C2×D416yes—
226C24×C4C2×D412yes—
227C24×C4C2×D418yes—
228C24×C4C2×Q8124yes—
229C24×C4C2×Q814yes—
230C24×C4#4114yes—
231C24×C4#4114yes—
232C24×C4#4112yes—
233C24×C4#4116yes—
234C24×C4#4118yes—
235C24×C4C2414yes—
236C24×C4C2413yes—
237C22×M16—248no—
238C22×M16—248no—
239C22×M16—212no—
240C22×M16—212no—
241C22×M16—224no—
242C22×M16—248no—
243C22×M16—224no—
244C22×M16—224no—
245C22×M16—224no—
246C22×M16—212no—
247C22×M16—212no—
248C22×M16—212no—
249C22×M16—212no—
250C22×M16—212no—
251C22×M16—224no—
252C22×M16—224no—
253C22×M16—216no—
254C22×M16—248no—
255C22×M16—216no—
256C22×M16—248no—
257C22×M16—212no—
258C22×M16—212no—
259C22×M16—212no—
260C22×M16—212no—
261C22×M16—224no—
262C22×M16—224no—
263C22×M16—48no—
264C22×M16—424no—
265C22×M16—46no—
266C22×M16—46no—
267C22×M16—412no—
268C22×M16—48no—
269C22×M16—424no—
270C22×M16—48no—
271C22×M16—424no—
272C22×M16—48no—
273C22×M16—424no—
274C22×M16—48no—
275C22×M16—424no—
276C22×M16—424no—
277C22×M16—424no—
278C22×M16—48no—
279C22×M16C2×D4148yes—
280C22×M16C2×D4124yes—
281C22×M16C2418yes—
282C22×M16C2418yes—
283C23×C8—216no—
284C23×C8—216no—
285C23×C8—212no—
286C23×C8—24no—
287C23×C8—216no—
288C23×C8—212no—
289C23×C8—42no—
290C23×C8—46no—
291C23×C8—48no—
292C23×C8C2×D4124yes—
293C2×#117—212no—
294C2×#117—212no—
295C2×#117—224no—
296C2×#117—212no—
297C2×#117—212no—
298C2×#117—212no—
299C2×#117—212no—
300C2×#117—224no—
301C2×#117—212no—
302C2×#117—212no—
303C2×#117—212no—
304C2×#117—212no—
305C2×#117—212no—
306C2×#117—212no—
307C2×#117—212no—
308C2×#117—26no—
309C2×#117—26no—
310C2×#117—248no—
311C2×#117—224no—
312C2×#117—224no—
313C2×#117—424no—
314C2×#117—412no—
315C2×#117—412no—
316C2×#117C22⋊C4124yes—
317C2×#117C22×C4112yes—
318C2×#117C22×C4112yes—
319C2×#117C2×D4112yes—
320C2×#117C2×D4112yes—
321C2×#117C2414yes—
322C2×#117C2414yes—
323C22×C4⋊C4—24no—
324C22×C4⋊C4—212no—
325C22×C4⋊C4—26no—
326C22×C4⋊C4—26no—
327C22×C4⋊C4—48no—
328C22×C4⋊C4C22⋊C4112yes—
329C22×C4⋊C4C2×D4112yes—
330C22×C22⋊C4—24no—
331C22×C22⋊C4—212no—
332C22×C22⋊C4—216no—
333C22×C22⋊C4—26no—
334C22×C22⋊C4—248no—
335C22×C22⋊C4—432no—
336C22×C22⋊C4C22⋊C4112yes—
337C22×C22⋊C4C22×C4112yes—
338C22×C22⋊C4C22×C4112yes—
339C22×C42—26no—
340C22×C42—22no—
341C22×C42—22no—
342C22×C42—26no—
343C22×C42—26no—
344C22×C42—26no—
345C22×C42—44no—
346C22×C42—44no—
347C22×C42C22⋊C4112yes—
348C22×C42C2×D4112yes—
349#424—2192no—
350#424—264no—
351#423—296no—
352#423—232no—
353C2×C4⋊C8—296no—
354#407—2384no—
355#407—264no—
356#407—264no—
357C2×C22⋊C8—2384no—
358C2×C22⋊C8—264no—
359#381—248no—
360#381C22×C4132yes—
361#380—296no—
362#380—232no—
363#379—248no—
364#379C22×C4132yes—
365C4×C22⋊C4—296no—
366C4×C22⋊C4—232no—
367C2×#95—248no—
368#344—264no—
369#343—232no—
370C25—216no—
371C25—232no—
372C25—26no—
373C25—212no—
374C25—28no—
375C25—216no—
376C25—26no—
377C25—212no—
378C25—212no—
379C25—224no—
380C25—224no—
381C25—248no—
382C25—464no—
383C25—48no—
384C25—448no—
385C25—48no—
386C25—416no—
387C25—448no—
388C25—464no—
389C25—4128no—
390C25—496no—
391C25—46no—
392C25—43no—
393C25—46no—
394C25—41no—
395C25—48no—
396C25—424no—
397C25—44no—
398C25—412no—
399C25C2×C22⋊C411yescharacteristic
400C25C2×C22⋊C413yes—
401C25C2×C4⋊C4124yes—
402C25C2×C4⋊C414yes—
403C25#11714yes—
404C25C4×D412yes—
405C25C4×D416yes—
406C25C4×D418yes—
407C25C23×C414yes—
408C25C23×C413yes—
409C23×C4—26no—
410C23×C4—26no—
411C23×C4—212no—
412C23×C4—212no—
413C23×C4—212no—
414C23×C4—224no—
415C23×C4—28no—
416C23×C4—224no—
417C23×C4—216no—
418C23×C4—248no—
419C23×C4—24no—
420C23×C4—212no—
421C23×C4—212no—
422C23×C4—212no—
423C23×C4—224no—
424C23×C4—224no—
425C23×C4—224no—
426C23×C4—248no—
427C23×C4—248no—
428C23×C4—248no—
429C23×C4—224no—
430C23×C4—224no—
431C23×C4—224no—
432C23×C4—224no—
433C23×C4—224no—
434C23×C4—224no—
435C23×C4—224no—
436C23×C4—224no—
437C23×C4—248no—
438C23×C4—248no—
439C23×C4—248no—
440C23×C4—248no—
441C23×C4—248no—
442C23×C4—248no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—28no—
446C23×C4—28no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—28no—
450C23×C4—28no—
451C23×C4—248no—
452C23×C4—248no—
453C23×C4—296no—
454C23×C4—296no—
455C23×C4—296no—
456C23×C4—2192no—
457C23×C4—212no—
458C23×C4—46no—
459C23×C4—43no—
460C23×C4—46no—
461C23×C4—41no—
462C23×C4—48no—
463C23×C4—424no—
464C23×C4—44no—
465C23×C4—412no—
466C23×C4—46no—
467C23×C4—46no—
468C23×C4—412no—
469C23×C4—412no—
470C23×C4—412no—
471C23×C4—412no—
472C23×C4—412no—
473C23×C4—424no—
474C23×C4—424no—
475C23×C4—424no—
476C23×C4—424no—
477C23×C4—46no—
478C23×C4—46no—
479C23×C4—412no—
480C23×C4—424no—
481C23×C4—424no—
482C23×C4—424no—
483C23×C4—424no—
484C23×C4—412no—
485C23×C4—412no—
486C23×C4—424no—
487C23×C4—424no—
488C23×C4—412no—
489C23×C4—412no—
490C23×C4—412no—
491C23×C4—46no—
492C23×C4—46no—
493C23×C4—412no—
494C23×C4—412no—
495C23×C4—424no—
496C23×C4—424no—
497C23×C4—448no—
498C23×C4—448no—
499C23×C4—496no—
500C23×C4—424no—
501C23×C4—424no—
502C23×C4—448no—
503C23×C4—48no—
504C23×C4—448no—
505C23×C4—424no—
506C23×C4—448no—
507C23×C4—448no—
508C23×C4—424no—
509C23×C4—448no—
510C23×C4—48no—
511C23×C4—448no—
512C23×C4—416no—
513C23×C4—448no—
514C23×C4—448no—
515C23×C4—496no—
516C23×C4—448no—
517C23×C4—448no—
518C23×C4—448no—
519C23×C4—496no—
520C23×C4—416no—
521C23×C4—448no—
522C23×C4—424no—
523C23×C4—448no—
524C23×C4—48no—
525C23×C4—448no—
526C23×C4—424no—
527C23×C4—448no—
528C23×C4—48no—
529C23×C4—416no—
530C23×C4—416no—
531C23×C4—48no—
532C23×C4C2×C22⋊C4124yes—
533C23×C4C2×C22⋊C413yes—
534C23×C4C2×C22⋊C416yes—
535C23×C4C2×C22⋊C413yes—
536C23×C4C2×C4⋊C4124yes—
537C23×C4C2×C4⋊C4148yes—
538C23×C4C2×C4⋊C4112yes—
539C23×C4#117112yes—
540C23×C4C4×D416yes—
541C23×C4C4×D4112yes—
542C23×C4C4×D416yes—
543C23×C4C4×D4124yes—
544C23×C4#12018yes—
545C23×C4#120124yes—
546C23×C4#12016yes—
547C23×C4#12016yes—
548C23×C4#12013yes—
549C23×C4#12011yescharacteristic
550C23×C4#12114yes—
551C23×C4#121112yes—
552C23×C4#12114yes—
553C23×C4#121112yes—
554C23×C4#12112yes—
555C23×C4#12116yes—
556C23×C4#12116yes—
557C23×C4#12116yes—
558C23×C4#121112yes—
559C23×C4#12118yes—
560C23×C4#121124yes—
561C23×C4#12118yes—
562C23×C4#121124yes—
563C23×C4C22⋊Q8112yes—
564C23×C4C22⋊Q814yes—
565C23×C4C22⋊Q814yes—
566C23×C4C22⋊Q8112yes—
567C23×C4C22⋊Q8124yes—
568C23×C4C22⋊Q818yes—
569C23×C4C22⋊Q818yes—
570C23×C4C22⋊Q8124yes—
571C23×C4#12318yes—
572C23×C4#123124yes—
573C23×C4#12316yes—
574C23×C4#12316yes—
575C23×C4#12311yescharacteristic
576C23×C4#12313yes—
577C23×C4#12318yes—
578C23×C4#123124yes—
579C23×C4#12418yes—
580C23×C4#124124yes—
581C23×C4#124112yes—
582C23×C4#12414yes—
583C23×C4#12618yes—
584C23×C4#126124yes—
585C23×C4#127112yes—
586C23×C4#12714yes—
587C23×C4C23×C414yes—
588C23×C4C23×C413yes—
589C23×C4C22×D418yes—
590C23×C4C22×D413yes—
591C23×C4C22×D413yes—
592C23×C4C22×D413yes—
593C23×C4C22×D413yes—
594C23×C4C22×D416yes—
595C23×C4C22×D416yes—
596C23×C4C22×D416yes—
597C23×C4C22×D4112yes—
598C23×C4C22×Q818yes—
599C23×C4C22×Q816yes—
600C23×C4C2×#4116yes—
601C23×C4C2×#4116yes—
602C23×C4C2×#4116yes—
603C23×C4C2×#4116yes—
604C23×C4C2×#41112yes—
605C23×C4C2511yescharacteristic
606C2×M16—248no—
607C2×M16—248no—
608C2×M16—224no—
609C2×M16—224no—
610C2×M16—248no—
611C2×M16—28no—
612C2×M16—28no—
613C2×M16—28no—
614C2×M16—28no—
615C2×M16—28no—
616C2×M16—28no—
617C2×M16—28no—
618C2×M16—248no—
619C2×M16—248no—
620C2×M16—248no—
621C2×M16—248no—
622C2×M16—28no—
623C2×M16—28no—
624C2×M16—28no—
625C2×M16—28no—
626C2×M16—424no—
627C2×M16—424no—
628C2×M16—424no—
629C2×M16—424no—
630C2×M16—424no—
631C2×M16—424no—
632C2×M16—424no—
633C2×M16—424no—
634C2×M16—412no—
635C2×M16—412no—
636C2×M16—424no—
637C2×M16—424no—
638C2×M16—424no—
639C2×M16—424no—
640C2×M16—424no—
641C2×M16—448no—
642C2×M16—448no—
643C2×M16—496no—
644C2×M16—448no—
645C2×M16—448no—
646C2×M16—496no—
647C2×M16C22×D4116yes—
648C22×C8—248no—
649C22×C8—248no—
650C22×C8—224no—
651C22×C8—224no—
652C22×C8—248no—
653C22×C8—28no—
654C22×C8—412no—
655C22×C8—412no—
656C22×C8—424no—
657C22×C8—416no—
658C22×C8—448no—
659C22×C8—448no—
660C22×C8—416no—
661C22×C8C22×D4116yes—
662#117—224no—
663#117—224no—
664#117—224no—
665#117—224no—
666#117—224no—
667#117—224no—
668#117—28no—
669#117—28no—
670#117—248no—
671#117—248no—
672#117—248no—
673#117—28no—
674#117—28no—
675#117—424no—
676#117—412no—
677#117—412no—
678#117—448no—
679C2×C4⋊C4—224no—
680C2×C4⋊C4—224no—
681C2×C4⋊C4—224no—
682C2×C4⋊C4—224no—
683C2×C4⋊C4—212no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—424no—
686C2×C4⋊C4—424no—
687C2×C4⋊C4C2×C22⋊C4124yes—
688C2×C4⋊C4C22×D418yes—
689C2×C22⋊C4—224no—
690C2×C22⋊C4—224no—
691C2×C22⋊C4—224no—
692C2×C22⋊C4—224no—
693C2×C22⋊C4—248no—
694C2×C22⋊C4—212no—
695C2×C22⋊C4—264no—
696C2×C22⋊C4—4192no—
697C2×C22⋊C4—424no—
698C2×C22⋊C4C2×C22⋊C4124yes—
699C2×C22⋊C4C23×C418yes—
700C2×C22⋊C4C23×C418yes—
701C2×C42—212no—
702C2×C42—212no—
703C2×C42—212no—
704C2×C42—212no—
705C2×C42—212no—
706C2×C42—212no—
707C2×C42—224no—
708C2×C42—212no—
709C2×C42—24no—
710C2×C42—412no—
711C2×C42—412no—
712C2×C42—424no—
713C2×C42C2×C22⋊C4124yes—
714C2×C42C22×D418yes—
715C4⋊C8—2128no—
716C22⋊C8—2256no—
717#95—264no—
718C24—28no—
719C24—216no—
720C24—248no—
721C24—264no—
722C24—2128no—
723C24—296no—
724C24—24no—
725C24—28no—
726C24—224no—
727C24—248no—
728C24—24no—
729C24—28no—
730C24—224no—
731C24—248no—
732C24—412no—
733C24—416no—
734C24—496no—
735C24—416no—
736C24—432no—
737C24—424no—
738C24—412no—
739C24—416no—
740C24—464no—
741C24—432no—
742C24—464no—
743C24—4128no—
744C24—424no—
745C24—448no—
746C24—448no—
747C24—496no—
748C24—448no—
749C24—496no—
750C24—4192no—
751C24—496no—
752C24—4192no—
753C24—4384no—
754C24—496no—
755C24—4384no—
756C24—4192no—
757C24—416no—
758C24—424no—
759C24—448no—
760C24—448no—
761C24—48no—
762C24—412no—
763C24—46no—
764C24—46no—
765C24—424no—
766C24—424no—
767C24—412no—
768C24—412no—
769C24#38014yes—
770C24#380112yes—
771C24#38518yes—
772C24#385124yes—
773C24#38616yes—
774C24#38613yes—
775C24#38616yes—
776C24#38611yescharacteristic
777C24#38818yes—
778C24#388124yes—
779C24#39014yes—
780C24#390112yes—
781C24C22×C22⋊C413yes—
782C24C22×C22⋊C413yes—
783C24C22×C4⋊C418yes—
784C24C22×C4⋊C416yes—
785C24C2×#11716yes—
786C24C2×C4×D416yes—
787C24C2×C4×D416yes—
788C24C2×C4×D4112yes—
789C24C24×C411yescharacteristic
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—224no—
795C22×C4—224no—
796C22×C4—248no—
797C22×C4—248no—
798C22×C4—224no—
799C22×C4—224no—
800C22×C4—216no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—216no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—248no—
809C22×C4—248no—
810C22×C4—296no—
811C22×C4—296no—
812C22×C4—28no—
813C22×C4—416no—
814C22×C4—448no—
815C22×C4—424no—
816C22×C4—448no—
817C22×C4—48no—
818C22×C4—412no—
819C22×C4—46no—
820C22×C4—46no—
821C22×C4—424no—
822C22×C4—424no—
823C22×C4—412no—
824C22×C4—412no—
825C22×C4—424no—
826C22×C4—448no—
827C22×C4—424no—
828C22×C4—424no—
829C22×C4—448no—
830C22×C4—424no—
831C22×C4—448no—
832C22×C4—448no—
833C22×C4—448no—
834C22×C4—448no—
835C22×C4—448no—
836C22×C4—448no—
837C22×C4—448no—
838C22×C4—448no—
839C22×C4—424no—
840C22×C4—448no—
841C22×C4—424no—
842C22×C4—424no—
843C22×C4—448no—
844C22×C4—424no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—496no—
856C22×C4—496no—
857C22×C4—4192no—
858C22×C4—4192no—
859C22×C4—448no—
860C22×C4—448no—
861C22×C4—496no—
862C22×C4—412no—
863C22×C4—412no—
864C22×C4—424no—
865C22×C4—448no—
866C22×C4—448no—
867C22×C4—424no—
868C22×C4—424no—
869C22×C4—448no—
870C22×C4—448no—
871C22×C4—424no—
872C22×C4—824no—
873C22×C4—832no—
874C22×C4#380112yes—
875C22×C4#380112yes—
876C22×C4#380124yes—
877C22×C4#385124yes—
878C22×C4#385124yes—
879C22×C4#385148yes—
880C22×C4#38616yes—
881C22×C4#38613yes—
882C22×C4#38613yes—
883C22×C4#38616yes—
884C22×C4#38616yes—
885C22×C4#386112yes—
886C22×C4#386112yes—
887C22×C4#388124yes—
888C22×C4#388124yes—
889C22×C4#388148yes—
890C22×C4#390112yes—
891C22×C4#390112yes—
892C22×C4#390124yes—
893C22×C4#39214yes—
894C22×C4#392124yes—
895C22×C4#392112yes—
896C22×C4#392124yes—
897C22×C4#393124yes—
898C22×C4#393112yes—
899C22×C4#393124yes—
900C22×C4#39314yes—
901C22×C4#394124yes—
902C22×C4#39418yes—
903C22×C4#394124yes—
904C22×C4#394124yes—
905C22×C4#394148yes—
906C22×C4#396124yes—
907C22×C4#396124yes—
908C22×C4#396124yes—
909C22×C4#396148yes—
910C22×C4#39618yes—
911C22×C4#397124yes—
912C22×C4#397112yes—
913C22×C4#397124yes—
914C22×C4#39714yes—
915C22×C4#399124yes—
916C22×C4#399112yes—
917C22×C4#399124yes—
918C22×C4#39914yes—
919C22×C4C22×C22⋊C4116yes—
920C22×C4C22×C22⋊C413yes—
921C22×C4C22×C22⋊C413yes—
922C22×C4C22×C4⋊C418yes—
923C22×C4C22×C4⋊C416yes—
924C22×C4C2×#11716yes—
925C22×C4C2×C4×D416yes—
926C22×C4C2×C4×D416yes—
927C22×C4C2×C4×D4112yes—
928C22×C4C2×#12013yes—
929C22×C4C2×#12013yes—
930C22×C4C2×#12016yes—
931C22×C4C2×#120112yes—
932C22×C4C2×#120112yes—
933C22×C4C2×#121112yes—
934C22×C4C2×#121112yes—
935C22×C4C2×#12116yes—
936C22×C4C2×#12116yes—
937C22×C4C2×#12116yes—
938C22×C4C2×#12116yes—
939C22×C4C2×#12116yes—
940C22×C4C2×#12116yes—
941C22×C4C2×#12116yes—
942C22×C4C2×#12116yes—
943C22×C4C2×#121112yes—
944C22×C4C2×#121112yes—
945C22×C4C2×C22⋊Q8112yes—
946C22×C4C2×C22⋊Q8112yes—
947C22×C4C2×C22⋊Q816yes—
948C22×C4C2×C22⋊Q816yes—
949C22×C4C2×C22⋊Q816yes—
950C22×C4C2×C22⋊Q816yes—
951C22×C4C2×C22⋊Q8112yes—
952C22×C4C2×C22⋊Q8112yes—
953C22×C4C2×#123112yes—
954C22×C4C2×#123112yes—
955C22×C4C2×#123112yes—
956C22×C4C2×#123112yes—
957C22×C4C2×#12313yes—
958C22×C4C2×#12313yes—
959C22×C4C2×#12316yes—
960C22×C4C2×#124112yes—
961C22×C4C2×#124112yes—
962C22×C4C2×#12416yes—
963C22×C4C2×#12416yes—
964C22×C4C2×#126112yes—
965C22×C4C2×#126112yes—
966C22×C4C2×#12716yes—
967C22×C4C2×#12716yes—
968C22×C4C23×D412yes—
969C22×C4C23×D411yescharacteristic
970C22×C4C23×D412yes—
971C22×C4C23×D411yescharacteristic
972C22×C4C23×D411yescharacteristic
973C22×C4C23×Q811yescharacteristic
974C22×C4C22×#4111yescharacteristic
975C22×C4C22×#4112yes—
976C22×C4C22×#4111yescharacteristic
977C22×C4C22×#4112yes—
978M16—216no—
979M16—216no—
980M16—448no—
981M16—448no—
982M16—448no—
983M16—448no—
984M16—48no—
985M16—48no—
986M16—48no—
987M16—48no—
988M16—48no—
989M16—48no—
990C2×C8—216no—
991C2×C8—216no—
992C2×C8—216no—
993C2×C8—216no—
994C2×C8—448no—
995C2×C8—448no—
996C2×C8—448no—
997C2×C8—448no—
998C2×C8—48no—
999C2×C8—48no—
1000C4⋊C4—216no—
1001C4⋊C4—248no—
1002C4⋊C4—48no—
1003C4⋊C4—424no—
1004C22⋊C4—216no—
1005C22⋊C4—248no—
1006C22⋊C4—216no—
1007C22⋊C4—4128no—
1008C22⋊C4—424no—
1009C42—28no—
1010C42—28no—
1011C42—224no—
1012C42—224no—
1013C42—44no—
1014C42—44no—
1015C42—424no—
1016C23—216no—
1017C23—216no—
1018C23—232no—
1019C23—232no—
1020C23—212no—
1021C23—212no—
1022C23—224no—
1023C23—224no—
1024C23—216no—
1025C23—296no—
1026C23—2192no—
1027C23—232no—
1028C23—28no—
1029C23—216no—
1030C23—46no—
1031C23—412no—
1032C23—416no—
1033C23—412no—
1034C23—424no—
1035C23—412no—
1036C23—42no—
1037C23—424no—
1038C23—448no—
1039C23—412no—
1040C23—448no—
1041C23—424no—
1042C23—496no—
1043C23—448no—
1044C23—496no—
1045C23—4192no—
1046C23—4384no—
1047C23—4192no—
1048C23—48no—
1049C23—448no—
1050C23—416no—
1051C23—496no—
1052C23—416no—
1053C23—432no—
1054C23—496no—
1055C23—4192no—
1056C23—4384no—
1057C23—4192no—
1058C23—496no—
1059C23—424no—
1060C23—448no—
1061C23—424no—
1062C23—464no—
1063C23—44no—
1064C23—48no—
1065C23—448no—
1066C23—44no—
1067C23#1439124yes—
1068C23#1439112yes—
1069C23#1439124yes—
1070C23#143914yes—
1071C23#189118yes—
1072C23C2×#38016yes—
1073C23C2×#38016yes—
1074C23C2×#385112yes—
1075C23C2×#385112yes—
1076C23C2×#38616yes—
1077C23C2×#38613yes—
1078C23C2×#38613yes—
1079C23C2×#388112yes—
1080C23C2×#388112yes—
1081C23C2×#39016yes—
1082C23C2×#39016yes—
1083C23C23×C22⋊C411yescharacteristic
1084C23C23×C4⋊C411yescharacteristic
1085C23C22×#11711yescharacteristic
1086C23C22×C4×D412yes—
1087C23C22×C4×D412yes—
1088C2×C4—28no—
1089C2×C4—216no—
1090C2×C4—216no—
1091C2×C4—448no—
1092C2×C4—424no—
1093C2×C4—424no—
1094C2×C4—44no—
1095C2×C4—48no—
1096C2×C4—448no—
1097C2×C4—44no—
1098C2×C4—448no—
1099C2×C4—496no—
1100C2×C4—448no—
1101C2×C4—48no—
1102C2×C4—48no—
1103C2×C4—416no—
1104C2×C4—416no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—416no—
1108C2×C4—416no—
1109C2×C4—48no—
1110C2×C4—824no—
1111C2×C4—848no—
1112C2×C4#1439124yes—
1113C2×C4#1439124yes—
1114C2×C4#1439148yes—
1115C2×C4#1439148yes—
1116C2×C4#1439112yes—
1117C2×C4#1439112yes—
1118C2×C4#1439124yes—
1119C2×C4C2×#38016yes—
1120C2×C4C2×#38016yes—
1121C2×C4C2×#385112yes—
1122C2×C4C2×#385112yes—
1123C2×C4C2×#38613yes—
1124C2×C4C2×#38613yes—
1125C2×C4C2×#38616yes—
1126C2×C4C2×#388112yes—
1127C2×C4C2×#388112yes—
1128C2×C4C2×#39016yes—
1129C2×C4C2×#39016yes—
1130C2×C4C2×#39216yes—
1131C2×C4C2×#392112yes—
1132C2×C4C2×#39216yes—
1133C2×C4C2×#39316yes—
1134C2×C4C2×#393112yes—
1135C2×C4C2×#39316yes—
1136C2×C4C2×#394112yes—
1137C2×C4C2×#394112yes—
1138C2×C4C2×#394112yes—
1139C2×C4C2×#394112yes—
1140C2×C4C2×#396112yes—
1141C2×C4C2×#396112yes—
1142C2×C4C2×#396112yes—
1143C2×C4C2×#396112yes—
1144C2×C4C2×#39716yes—
1145C2×C4C2×#397112yes—
1146C2×C4C2×#39716yes—
1147C2×C4C2×#39916yes—
1148C2×C4C2×#399112yes—
1149C2×C4C2×#39916yes—
1150C2×C4C22×#12011yescharacteristic
1151C2×C4C22×#12012yes—
1152C2×C4C22×#12112yes—
1153C2×C4C22×#12111yescharacteristic
1154C2×C4C22×#12111yescharacteristic
1155C2×C4C22×#12112yes—
1156C2×C4C22×#12112yes—
1157C2×C4C22×C22⋊Q812yes—
1158C2×C4C22×C22⋊Q811yescharacteristic
1159C2×C4C22×C22⋊Q811yescharacteristic
1160C2×C4C22×C22⋊Q812yes—
1161C2×C4C22×#12312yes—
1162C2×C4C22×#12312yes—
1163C2×C4C22×#12311yescharacteristic
1164C2×C4C22×#12412yes—
1165C2×C4C22×#12411yescharacteristic
1166C2×C4C22×#12612yes—
1167C2×C4C22×#12711yescharacteristic
1168C8—416no—
1169C8—416no—
1170C22—212no—
1171C22—212no—
1172C22—224no—
1173C22—224no—
1174C22—248no—
1175C22—224no—
1176C22—22no—
1177C22—26no—
1178C22—24no—
1179C22—212no—
1180C22—216no—
1181C22—232no—
1182C22—41no—
1183C22—41no—
1184C22—42no—
1185C22—424no—
1186C22—46no—
1187C22—412no—
1188C22—412no—
1189C22—46no—
1190C22—416no—
1191C22—48no—
1192C22—416no—
1193C22—496no—
1194C22—4192no—
1195C22—432no—
1196C22—496no—
1197C22—416no—
1198C22—48no—
1199C22#11071116yesdirect product factor
1200C22C2×#1439112yes—
1201C22C2×#143916yes—
1202C22C2×#143916yes—
1203C22C2×#1891112yes—
1204C22C22×#38011yescharacteristic
1205C22C22×#38512yes—
1206C22C22×#38611yescharacteristic
1207C22C22×#38812yes—
1208C22C22×#39011yescharacteristic
1209C4—416no—
1210C4—48no—
1211C4—88no—
1212C4C2×#143916yes—
1213C4C2×#1439112yes—
1214C4C2×#143916yes—
1215C4C22×#39211yescharacteristic
1216C4C22×#39311yescharacteristic
1217C4C22×#39412yes—
1218C4C22×#39612yes—
1219C4C22×#39711yescharacteristic
1220C4C22×#39911yescharacteristic
1221C2—21no—
1222C2—21no—
1223C2—22no—
1224C2—26no—
1225C2—212no—
1226C2—22no—
1227C2—416no—
1228C2C2×#11071112yesdirect product factor
1229C2C22×#143911yescharacteristic
1230C2C22×#189112yes—
subgroupG/H
centerC23×C4#120
commutatorC24C24×C4
Frattini, cosocleC23×C4C25
socleC24#386
prime radicalC27C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C25×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#2905C2semidirect
4. C23×#344C2semidirect
5. C22×#1742C2semidirect
6. C2×#11071C2direct (N × H)
14. C2×#2905C22semidirect
31. C22×#344C22semidirect
33. C2×#1742C22semidirect
35. #11071C22direct (N × H)
101. #2905C23semidirect
129. C2×#344C23semidirect
131. #1742C23semidirect
1199. C22#11071direct (N × H)
1228. C2C2×#11071direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#29052
C23×#4072
C22×#22802
C23×#3442
C22×#17422
C2×#110712