Finite Group Databasebeta

← C22×#11100 #72316989

Subgroups — C22×#11100 #72316989

Order 1024.

29701 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#2911C211yesmaximal, characteristic, complemented
2C23×#407C211yesmaximal, characteristic
3C22×#2280C212yesmaximal
4C22×#1733C212yesmaximal, complemented
5C23×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C2×#11100C2124yesmaximal, direct product factor
7C26×C4C2211yescharacteristic
8C24×M16C2211yescharacteristic
9C24×M16C2211yescharacteristic
10C23×#117C2212yes—
11C23×#117C2212yes—
12C2×#2911—26no—
13C2×#2911—212no—
14C2×#2911C22112yescomplemented
15C22×#428—24no—
16C22×#427—22no—
17C22×#407—28no—
18C22×#407—26no—
19C22×#407C4116yescomplemented
20C22×#407C22112yes—
21C23×C22⋊C8—22no—
22C2×#2280—212no—
23C2×#2280—212no—
24C2×#2280—212no—
25C2×#2280C22124yes—
26C22×#381—22no—
27C22×#380—24no—
28C22×#379—22no—
29C22×C4×C22⋊C4—24no—
30C2×#1733—212no—
31C2×#1733C22124yescomplemented
32C22×#339—24no—
33C22×H(3,ℤ/4)—28no—
34C22×H(3,ℤ/4)C22112yescomplemented
35#11100C22164yesdirect product factor
36C27D411yescharacteristic
37C25×C4—21no—
38C25×C4—24no—
39C25×C4—23no—
40C25×C4—22no—
41C25×C4—22no—
42C25×C4—26no—
43C25×C4—26no—
44C25×C4—21no—
45C25×C4—23no—
46C25×C4—24no—
47C25×C4—28no—
48C25×C4—28no—
49C25×C4C2×C418yes—
50C25×C4D411yescharacteristic
51C25×C4D416yes—
52C25×C4Q818yes—
53C25×C4C2316yes—
54C25×C4C2311yescharacteristic
55C23×M16—22no—
56C23×M16—26no—
57C23×M16—28no—
58C23×M16—24no—
59C23×M16—23no—
60C23×M16—22no—
61C23×M16—26no—
62C23×M16—28no—
63C23×M16C2×C418yes—
64C23×M16C2×C418yes—
65C23×M16D418yes—
66C23×M16D416yes—
67C23×M16C2316yes—
68C23×M16C2316yes—
69C24×C8—21no—
70C24×C8D412yes—
71C22×#117—26no—
72C22×#117—26no—
73C22×#117—26no—
74C22×#117—26no—
75C22×#117—22no—
76C22×#117—26no—
77C22×#117—22no—
78C22×#117—22no—
79C22×#117—26no—
80C22×#117—26no—
81C22×#117—22no—
82C22×#117—26no—
83C22×#117—28no—
84C22×#117—28no—
85C22×#117—28no—
86C22×#117—28no—
87C22×#117D4112yes—
88C22×#117D4112yes—
89C22×#117C23112yes—
90C22×#117C23112yes—
91C23×C4⋊C4—22no—
92C23×C4⋊C4D414yes—
93C23×C22⋊C4—28no—
94C23×C22⋊C4—22no—
95C23×C22⋊C4—22no—
96C23×C42—22no—
97C23×C42D414yes—
98#2911—248no—
99#2911—224no—
100#2911—248no—
101#2911C23116yescomplemented
102C2×#428—248no—
103C2×#428—248no—
104C2×#427—224no—
105C2×#427—224no—
106C22×#107—24no—
107C22×#106—24no—
108C2×#407—296no—
109C2×#407—248no—
110C2×#407—224no—
111C2×#407C2×C4196yescomplemented
112C2×#407C23116yes—
113C22×C22⋊C8—232no—
114C22×C22⋊C8—224no—
115#2280—296no—
116#2280—248no—
117#2280—248no—
118#2280—248no—
119#2280C23132yes—
120C2×#381—224no—
121C2×#381—224no—
122C2×#380—248no—
123C2×#380—248no—
124C2×#379—224no—
125C2×#379—224no—
126C2×C4×C22⋊C4—248no—
127C2×C4×C22⋊C4—248no—
128C22×#95—28no—
129#1733—248no—
130#1733C23132yescomplemented
131C2×#339—248no—
132C2×H(3,ℤ/4)—248no—
133C2×H(3,ℤ/4)C23116yescomplemented
134C26—22no—
135C26—21no—
136C26—26no—
137C26—23no—
138C26—24no—
139C26—28no—
140C26—416no—
141C26C4⋊C418yes—
142C26C2×D416yes—
143C26C2×D411yescharacteristic
144C24×C4—22no—
145C24×C4—26no—
146C24×C4—21no—
147C24×C4—23no—
148C24×C4—24no—
149C24×C4—28no—
150C24×C4—28no—
151C24×C4—224no—
152C24×C4—28no—
153C24×C4—224no—
154C24×C4—216no—
155C24×C4—248no—
156C24×C4—216no—
157C24×C4—248no—
158C24×C4—212no—
159C24×C4—212no—
160C24×C4—224no—
161C24×C4—26no—
162C24×C4—26no—
163C24×C4—212no—
164C24×C4—224no—
165C24×C4—28no—
166C24×C4—224no—
167C24×C4—28no—
168C24×C4—224no—
169C24×C4—216no—
170C24×C4—248no—
171C24×C4—216no—
172C24×C4—248no—
173C24×C4—248no—
174C24×C4—26no—
175C24×C4—212no—
176C24×C4—26no—
177C24×C4—212no—
178C24×C4—212no—
179C24×C4—212no—
180C24×C4—212no—
181C24×C4—26no—
182C24×C4—26no—
183C24×C4—212no—
184C24×C4—224no—
185C24×C4—224no—
186C24×C4—24no—
187C24×C4—24no—
188C24×C4—41no—
189C24×C4—46no—
190C24×C4—43no—
191C24×C4—46no—
192C24×C4—46no—
193C24×C4—42no—
194C24×C4—46no—
195C24×C4—412no—
196C24×C4—46no—
197C24×C4—48no—
198C24×C4—424no—
199C24×C4—424no—
200C24×C4—48no—
201C24×C4—424no—
202C24×C4—48no—
203C24×C4—44no—
204C24×C4—412no—
205C24×C4—48no—
206C24×C4—424no—
207C24×C4—44no—
208C24×C4—412no—
209C24×C4—48no—
210C24×C4—424no—
211C24×C4—43no—
212C24×C4—46no—
213C24×C4—46no—
214C24×C4—41no—
215C24×C4C4⋊C418yes—
216C24×C4C4⋊C4148yes—
217C24×C4C22×C4124yes—
218C24×C4C22×C414yes—
219C24×C4C2×D416yes—
220C24×C4C2×D4112yes—
221C24×C4C2×D413yes—
222C24×C4C2×D411yescharacteristic
223C24×C4C2×D414yes—
224C24×C4C2×D413yes—
225C24×C4C2×D412yes—
226C24×C4C2×D416yes—
227C24×C4C2×D416yes—
228C24×C4C2×D412yes—
229C24×C4C2×Q8124yes—
230C24×C4C2×Q814yes—
231C24×C4#4113yes—
232C24×C4#4111yescharacteristic
233C24×C4#4114yes—
234C24×C4#4118yes—
235C24×C4#4118yes—
236C24×C4C2414yes—
237C24×C4C2413yes—
238C22×M16—216no—
239C22×M16—248no—
240C22×M16—212no—
241C22×M16—212no—
242C22×M16—216no—
243C22×M16—248no—
244C22×M16—224no—
245C22×M16—212no—
246C22×M16—212no—
247C22×M16—224no—
248C22×M16—224no—
249C22×M16—212no—
250C22×M16—26no—
251C22×M16—216no—
252C22×M16—248no—
253C22×M16—212no—
254C22×M16—212no—
255C22×M16—224no—
256C22×M16—424no—
257C22×M16—48no—
258C22×M16—412no—
259C22×M16—46no—
260C22×M16—46no—
261C22×M16C22⋊C4148yescomplemented
262C22×M16C22×C4124yes—
263C22×M16C22×C4124yes—
264C22×M16C2×D4124yes—
265C22×M16C2×D4112yes—
266C22×M16C2414yes—
267C22×M16C2414yes—
268C23×C8—22no—
269C23×C8—26no—
270C23×C8—28no—
271C23×C8—28no—
272C23×C8—26no—
273C23×C8—44no—
274C23×C8—43no—
275C23×C8—41no—
276C23×C8C22⋊C4116yescomplemented
277C23×C8C2×D4112yes—
278C2×#117—224no—
279C2×#117—224no—
280C2×#117—212no—
281C2×#117—212no—
282C2×#117—212no—
283C2×#117—212no—
284C2×#117—248no—
285C2×#117—248no—
286C2×#117—224no—
287C2×#117—224no—
288C2×#117—224no—
289C2×#117—224no—
290C2×#117—212no—
291C2×#117—212no—
292C2×#117—224no—
293C2×#117—212no—
294C2×#117—224no—
295C2×#117—212no—
296C2×#117—212no—
297C2×#117—212no—
298C2×#117—212no—
299C2×#117—212no—
300C2×#117—212no—
301C2×#117—212no—
302C2×#117—212no—
303C2×#117—212no—
304C2×#117—46no—
305C2×#117—412no—
306C2×#117—46no—
307C2×#117—46no—
308C2×#117—46no—
309C2×#117—412no—
310C2×#117—46no—
311C2×#117—46no—
312C2×#117—412no—
313C2×#117—424no—
314C2×#117—424no—
315C2×#117—424no—
316C2×#117—424no—
317C2×#117—46no—
318C2×#117—412no—
319C2×#117—46no—
320C2×#117C2×D4124yes—
321C2×#117C2×D4124yes—
322C2×#117C2418yes—
323C2×#117C2418yes—
324C22×C4⋊C4—24no—
325C22×C4⋊C4—212no—
326C22×C4⋊C4—212no—
327C22×C4⋊C4—24no—
328C22×C4⋊C4—212no—
329C22×C4⋊C4—212no—
330C22×C4⋊C4—212no—
331C22×C4⋊C4—48no—
332C22×C4⋊C4—48no—
333C22×C4⋊C4C2×D4124yes—
334C22×C22⋊C4—296no—
335C22×C22⋊C4—212no—
336C22×C22⋊C4—212no—
337C22×C22⋊C4—212no—
338C22×C22⋊C4—212no—
339C22×C22⋊C4—464no—
340C22×C22⋊C4—42no—
341C22×C22⋊C4—46no—
342C22×C22⋊C4—42no—
343C22×C22⋊C4—46no—
344C22×C22⋊C4—48no—
345C22×C22⋊C4—48no—
346C22×C42—216no—
347C22×C42—216no—
348C22×C42—212no—
349C22×C42—212no—
350C22×C42—212no—
351C22×C42—42no—
352C22×C42—46no—
353C22×C42—46no—
354C22×C42—42no—
355C22×C42C2×D4124yes—
356#428—2192no—
357#428—264no—
358#427—296no—
359#427—232no—
360C2×#107—248no—
361C2×#106—248no—
362#407—2192no—
363#407—232no—
364#407C22×C4164yescomplemented
365C2×C22⋊C8—2192no—
366C2×C22⋊C8—232no—
367#381—296no—
368#381—232no—
369#380—2192no—
370#380—264no—
371#379—296no—
372#379—232no—
373C4×C22⋊C4—2192no—
374C4×C22⋊C4—264no—
375C2×#95—296no—
376#339—264no—
377H(3,ℤ/4)—232no—
378C25—232no—
379C25—216no—
380C25—212no—
381C25—26no—
382C25—28no—
383C25—216no—
384C25—212no—
385C25—26no—
386C25—212no—
387C25—224no—
388C25—224no—
389C25—248no—
390C25—464no—
391C25—48no—
392C25—448no—
393C25—416no—
394C25—48no—
395C25—496no—
396C25—464no—
397C25—448no—
398C25—4128no—
399C25—43no—
400C25—46no—
401C25—46no—
402C25—41no—
403C25—48no—
404C25—424no—
405C25—44no—
406C25—412no—
407C25C2×C4⋊C4124yes—
408C25C2×C4⋊C414yes—
409C25#12012yes—
410C25#12016yes—
411C25#12111yescharacteristic
412C25#12113yes—
413C25#12114yes—
414C25#12318yes—
415C25C22×D414yes—
416C25C22×D413yes—
417C23×C4—212no—
418C23×C4—212no—
419C23×C4—26no—
420C23×C4—26no—
421C23×C4—212no—
422C23×C4—224no—
423C23×C4—28no—
424C23×C4—224no—
425C23×C4—216no—
426C23×C4—248no—
427C23×C4—224no—
428C23×C4—224no—
429C23×C4—224no—
430C23×C4—224no—
431C23×C4—248no—
432C23×C4—248no—
433C23×C4—248no—
434C23×C4—248no—
435C23×C4—224no—
436C23×C4—224no—
437C23×C4—212no—
438C23×C4—212no—
439C23×C4—224no—
440C23×C4—224no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—248no—
445C23×C4—248no—
446C23×C4—248no—
447C23×C4—248no—
448C23×C4—248no—
449C23×C4—28no—
450C23×C4—28no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—28no—
456C23×C4—28no—
457C23×C4—248no—
458C23×C4—248no—
459C23×C4—296no—
460C23×C4—296no—
461C23×C4—296no—
462C23×C4—2192no—
463C23×C4—224no—
464C23×C4—224no—
465C23×C4—43no—
466C23×C4—46no—
467C23×C4—46no—
468C23×C4—41no—
469C23×C4—48no—
470C23×C4—424no—
471C23×C4—44no—
472C23×C4—412no—
473C23×C4—46no—
474C23×C4—412no—
475C23×C4—46no—
476C23×C4—412no—
477C23×C4—412no—
478C23×C4—412no—
479C23×C4—412no—
480C23×C4—424no—
481C23×C4—424no—
482C23×C4—424no—
483C23×C4—424no—
484C23×C4—424no—
485C23×C4—424no—
486C23×C4—412no—
487C23×C4—412no—
488C23×C4—424no—
489C23×C4—424no—
490C23×C4—412no—
491C23×C4—412no—
492C23×C4—424no—
493C23×C4—424no—
494C23×C4—46no—
495C23×C4—412no—
496C23×C4—46no—
497C23×C4—424no—
498C23×C4—48no—
499C23×C4—448no—
500C23×C4—448no—
501C23×C4—448no—
502C23×C4—448no—
503C23×C4—448no—
504C23×C4—496no—
505C23×C4—416no—
506C23×C4—424no—
507C23×C4—48no—
508C23×C4—448no—
509C23×C4—448no—
510C23×C4—46no—
511C23×C4—412no—
512C23×C4—424no—
513C23×C4—46no—
514C23×C4—424no—
515C23×C4—412no—
516C23×C4—412no—
517C23×C4—448no—
518C23×C4—424no—
519C23×C4—448no—
520C23×C4—48no—
521C23×C4—448no—
522C23×C4—448no—
523C23×C4—496no—
524C23×C4—448no—
525C23×C4—448no—
526C23×C4—448no—
527C23×C4—496no—
528C23×C4—416no—
529C23×C4—424no—
530C23×C4—424no—
531C23×C4—448no—
532C23×C4—424no—
533C23×C4—448no—
534C23×C4—448no—
535C23×C4—48no—
536C23×C4—432no—
537C23×C4—432no—
538C23×C4—412no—
539C23×C4—44no—
540C23×C4—416no—
541C23×C4C2×C22⋊C414yes—
542C23×C4C2×C22⋊C4112yes—
543C23×C4C2×C4⋊C4124yes—
544C23×C4C2×C4⋊C4148yes—
545C23×C4C2×C4⋊C4112yes—
546C23×C4#11714yes—
547C23×C4#117112yes—
548C23×C4C4×D418yes—
549C23×C4C4×D4124yes—
550C23×C4C4×D4124yes—
551C23×C4C4×D418yes—
552C23×C4#12011yescharacteristic
553C23×C4#12016yes—
554C23×C4#12013yes—
555C23×C4#12016yes—
556C23×C4#12016yes—
557C23×C4#120112yes—
558C23×C4#12016yes—
559C23×C4#12118yes—
560C23×C4#121124yes—
561C23×C4#12116yes—
562C23×C4#12112yes—
563C23×C4#12116yes—
564C23×C4#121112yes—
565C23×C4#12116yes—
566C23×C4#121124yes—
567C23×C4#12118yes—
568C23×C4#12113yes—
569C23×C4#12113yes—
570C23×C4#12116yes—
571C23×C4#121112yes—
572C23×C4C22⋊Q8112yes—
573C23×C4C22⋊Q814yes—
574C23×C4C22⋊Q814yes—
575C23×C4C22⋊Q8112yes—
576C23×C4C22⋊Q818yes—
577C23×C4C22⋊Q8124yes—
578C23×C4C22⋊Q8124yes—
579C23×C4C22⋊Q818yes—
580C23×C4#12314yes—
581C23×C4#123112yes—
582C23×C4#123124yes—
583C23×C4#12318yes—
584C23×C4#123124yes—
585C23×C4#12418yes—
586C23×C4#124124yes—
587C23×C4#12414yes—
588C23×C4#124112yes—
589C23×C4#12618yes—
590C23×C4#126124yes—
591C23×C4#12713yes—
592C23×C4#12716yes—
593C23×C4#12716yes—
594C23×C4#12711yescharacteristic
595C23×C4C23×C418yes—
596C23×C4C23×C416yes—
597C23×C4C22×D414yes—
598C23×C4C22×D413yes—
599C23×C4C22×D413yes—
600C23×C4C22×D416yes—
601C23×C4C22×D413yes—
602C23×C4C22×D416yes—
603C23×C4C22×D416yes—
604C23×C4C22×D416yes—
605C23×C4C22×D416yes—
606C23×C4C22×Q818yes—
607C23×C4C22×Q816yes—
608C23×C4C2×#4113yes—
609C23×C4C2×#4113yes—
610C23×C4C2×#4116yes—
611C23×C4C2×#41112yes—
612C23×C4C2×#41112yes—
613C23×C4C2511yescharacteristic
614C2×M16—248no—
615C2×M16—248no—
616C2×M16—224no—
617C2×M16—248no—
618C2×M16—248no—
619C2×M16—224no—
620C2×M16—28no—
621C2×M16—28no—
622C2×M16—296no—
623C2×M16—296no—
624C2×M16—224no—
625C2×M16—24no—
626C2×M16—248no—
627C2×M16—248no—
628C2×M16—28no—
629C2×M16—28no—
630C2×M16—424no—
631C2×M16—424no—
632C2×M16—412no—
633C2×M16—412no—
634C2×M16—448no—
635C2×M16—448no—
636C2×M16C2×C22⋊C4148yescomplemented
637C2×M16C23×C418yes—
638C2×M16C23×C418yes—
639C2×M16C22×D418yes—
640C22×C8—212no—
641C22×C8—212no—
642C22×C8—224no—
643C22×C8—216no—
644C22×C8—248no—
645C22×C8—224no—
646C22×C8—24no—
647C22×C8—412no—
648C22×C8—46no—
649C22×C8—46no—
650C22×C8—424no—
651C22×C8—48no—
652C22×C8C2×C22⋊C4148yescomplemented
653C22×C8C22×D418yes—
654#117—248no—
655#117—248no—
656#117—28no—
657#117—28no—
658#117—28no—
659#117—28no—
660#117—224no—
661#117—224no—
662#117—224no—
663#117—224no—
664#117—28no—
665#117—28no—
666#117—28no—
667#117—28no—
668#117—412no—
669#117—412no—
670#117—412no—
671#117—412no—
672#117—424no—
673#117—424no—
674#117—412no—
675#117—412no—
676#117—424no—
677#117—424no—
678#117—412no—
679#117—412no—
680#117—424no—
681#117—424no—
682#117—424no—
683#117—424no—
684#117—496no—
685C2×C4⋊C4—224no—
686C2×C4⋊C4—224no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—224no—
690C2×C4⋊C4—224no—
691C2×C4⋊C4—28no—
692C2×C4⋊C4—424no—
693C2×C4⋊C4—424no—
694C2×C4⋊C4—412no—
695C2×C4⋊C4—412no—
696C2×C4⋊C4—424no—
697C2×C4⋊C4—448no—
698C2×C4⋊C4C22×D4116yes—
699C2×C22⋊C4—2128no—
700C2×C22⋊C4—224no—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—28no—
703C2×C22⋊C4—28no—
704C2×C22⋊C4—4384no—
705C2×C22⋊C4—412no—
706C2×C22⋊C4—412no—
707C2×C22⋊C4—412no—
708C2×C22⋊C4—412no—
709C2×C22⋊C4—424no—
710C2×C22⋊C4—424no—
711C2×C22⋊C4—412no—
712C2×C22⋊C4—412no—
713C2×C22⋊C4—424no—
714C2×C22⋊C4—448no—
715C2×C42—248no—
716C2×C42—248no—
717C2×C42—224no—
718C2×C42—224no—
719C2×C42—28no—
720C2×C42—412no—
721C2×C42—412no—
722C2×C42—412no—
723C2×C42—412no—
724C2×C42—412no—
725C2×C42—412no—
726C2×C42—424no—
727C2×C42—448no—
728C2×C42C22×D4116yes—
729#107—264no—
730#106—264no—
731C22⋊C8—2128no—
732#95—2128no—
733C24—216no—
734C24—28no—
735C24—296no—
736C24—264no—
737C24—2128no—
738C24—248no—
739C24—28no—
740C24—24no—
741C24—224no—
742C24—248no—
743C24—24no—
744C24—28no—
745C24—224no—
746C24—248no—
747C24—416no—
748C24—496no—
749C24—424no—
750C24—416no—
751C24—412no—
752C24—432no—
753C24—412no—
754C24—416no—
755C24—4128no—
756C24—432no—
757C24—464no—
758C24—464no—
759C24—448no—
760C24—496no—
761C24—424no—
762C24—448no—
763C24—496no—
764C24—496no—
765C24—448no—
766C24—4192no—
767C24—4192no—
768C24—4384no—
769C24—496no—
770C24—4384no—
771C24—4192no—
772C24—46no—
773C24—412no—
774C24—46no—
775C24—424no—
776C24—424no—
777C24—412no—
778C24—412no—
779C24—424no—
780C24—448no—
781C24—448no—
782C24—48no—
783C24—416no—
784C24#38014yes—
785C24#380112yes—
786C24#38518yes—
787C24#385124yes—
788C24#39213yes—
789C24#39216yes—
790C24#39216yes—
791C24#39211yescharacteristic
792C24#39418yes—
793C24#394124yes—
794C24#39714yes—
795C24#397112yes—
796C24C22×C4⋊C418yes—
797C24C22×C4⋊C416yes—
798C24C2×#12016yes—
799C24C2×#12016yes—
800C24C2×#12113yes—
801C24C2×#12113yes—
802C24C2×#12116yes—
803C24C2×#123112yes—
804C24C23×D411yescharacteristic
805C22×C4—28no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—224no—
810C22×C4—224no—
811C22×C4—248no—
812C22×C4—248no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—216no—
816C22×C4—216no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—216no—
820C22×C4—216no—
821C22×C4—248no—
822C22×C4—248no—
823C22×C4—296no—
824C22×C4—296no—
825C22×C4—216no—
826C22×C4—216no—
827C22×C4—46no—
828C22×C4—412no—
829C22×C4—46no—
830C22×C4—424no—
831C22×C4—424no—
832C22×C4—412no—
833C22×C4—412no—
834C22×C4—424no—
835C22×C4—448no—
836C22×C4—448no—
837C22×C4—48no—
838C22×C4—412no—
839C22×C4—424no—
840C22×C4—412no—
841C22×C4—448no—
842C22×C4—424no—
843C22×C4—424no—
844C22×C4—448no—
845C22×C4—448no—
846C22×C4—448no—
847C22×C4—448no—
848C22×C4—448no—
849C22×C4—448no—
850C22×C4—424no—
851C22×C4—424no—
852C22×C4—448no—
853C22×C4—424no—
854C22×C4—424no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—496no—
866C22×C4—4192no—
867C22×C4—4192no—
868C22×C4—496no—
869C22×C4—448no—
870C22×C4—448no—
871C22×C4—496no—
872C22×C4—424no—
873C22×C4—424no—
874C22×C4—448no—
875C22×C4—448no—
876C22×C4—448no—
877C22×C4—448no—
878C22×C4—448no—
879C22×C4—424no—
880C22×C4—424no—
881C22×C4—448no—
882C22×C4—496no—
883C22×C4—496no—
884C22×C4—424no—
885C22×C4—424no—
886C22×C4—448no—
887C22×C4—864no—
888C22×C4—848no—
889C22×C4—816no—
890C22×C4#380112yes—
891C22×C4#380112yes—
892C22×C4#380124yes—
893C22×C4#385124yes—
894C22×C4#385124yes—
895C22×C4#385148yes—
896C22×C4#386112yes—
897C22×C4#38614yes—
898C22×C4#386124yes—
899C22×C4#386124yes—
900C22×C4#388124yes—
901C22×C4#388124yes—
902C22×C4#388124yes—
903C22×C4#388148yes—
904C22×C4#38818yes—
905C22×C4#390112yes—
906C22×C4#39014yes—
907C22×C4#390124yes—
908C22×C4#390124yes—
909C22×C4#39213yes—
910C22×C4#39216yes—
911C22×C4#392112yes—
912C22×C4#39213yes—
913C22×C4#392112yes—
914C22×C4#39216yes—
915C22×C4#39216yes—
916C22×C4#393124yes—
917C22×C4#393112yes—
918C22×C4#393124yes—
919C22×C4#39314yes—
920C22×C4#394124yes—
921C22×C4#394124yes—
922C22×C4#394148yes—
923C22×C4#396124yes—
924C22×C4#396124yes—
925C22×C4#396124yes—
926C22×C4#396148yes—
927C22×C4#39618yes—
928C22×C4#397112yes—
929C22×C4#397112yes—
930C22×C4#397124yes—
931C22×C4#399112yes—
932C22×C4#399124yes—
933C22×C4#399124yes—
934C22×C4#39914yes—
935C22×C4C22×C22⋊C416yes—
936C22×C4C22×C22⋊C416yes—
937C22×C4C22×C4⋊C418yes—
938C22×C4C22×C4⋊C416yes—
939C22×C4C2×#11716yes—
940C22×C4C2×#11716yes—
941C22×C4C2×C4×D4112yes—
942C22×C4C2×C4×D4112yes—
943C22×C4C2×C4×D4112yes—
944C22×C4C2×C4×D4112yes—
945C22×C4C2×#12016yes—
946C22×C4C2×#12016yes—
947C22×C4C2×#12013yes—
948C22×C4C2×#12016yes—
949C22×C4C2×#12013yes—
950C22×C4C2×#12113yes—
951C22×C4C2×#12113yes—
952C22×C4C2×#12116yes—
953C22×C4C2×#12116yes—
954C22×C4C2×#12116yes—
955C22×C4C2×#12116yes—
956C22×C4C2×#12116yes—
957C22×C4C2×#121112yes—
958C22×C4C2×#121112yes—
959C22×C4C2×#121112yes—
960C22×C4C2×#121112yes—
961C22×C4C2×C22⋊Q8112yes—
962C22×C4C2×C22⋊Q8112yes—
963C22×C4C2×C22⋊Q816yes—
964C22×C4C2×C22⋊Q816yes—
965C22×C4C2×C22⋊Q816yes—
966C22×C4C2×C22⋊Q816yes—
967C22×C4C2×C22⋊Q8112yes—
968C22×C4C2×C22⋊Q8112yes—
969C22×C4C2×#123112yes—
970C22×C4C2×#123112yes—
971C22×C4C2×#123112yes—
972C22×C4C2×#12316yes—
973C22×C4C2×#12316yes—
974C22×C4C2×#124112yes—
975C22×C4C2×#124112yes—
976C22×C4C2×#12416yes—
977C22×C4C2×#12416yes—
978C22×C4C2×#126112yes—
979C22×C4C2×#126112yes—
980C22×C4C2×#12713yes—
981C22×C4C2×#12716yes—
982C22×C4C2×#12713yes—
983C22×C4C24×C411yescharacteristic
984C22×C4C23×D411yescharacteristic
985C22×C4C23×D411yescharacteristic
986C22×C4C23×D412yes—
987C22×C4C23×D412yes—
988C22×C4C23×Q811yescharacteristic
989C22×C4C22×#4111yescharacteristic
990C22×C4C22×#4111yescharacteristic
991C22×C4C22×#4112yes—
992C22×C4C22×#4112yes—
993M16—216no—
994M16—216no—
995M16—296no—
996M16—216no—
997M16—48no—
998M16—448no—
999C2×C8—28no—
1000C2×C8—28no—
1001C2×C8—248no—
1002C2×C8—248no—
1003C2×C8—28no—
1004C2×C8—44no—
1005C2×C8—44no—
1006C2×C8—424no—
1007C2×C8—424no—
1008C2×C8C22×C22⋊C4116yescomplemented
1009C4⋊C4—216no—
1010C4⋊C4—216no—
1011C4⋊C4—424no—
1012C4⋊C4—424no—
1013C4⋊C4—448no—
1014C4⋊C4—48no—
1015C4⋊C4—48no—
1016C22⋊C4—4256no—
1017C22⋊C4—424no—
1018C22⋊C4—424no—
1019C22⋊C4—448no—
1020C22⋊C4—48no—
1021C22⋊C4—48no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C42—216no—
1025C42—216no—
1026C42—424no—
1027C42—424no—
1028C42—448no—
1029C42—48no—
1030C42—48no—
1031C23—232no—
1032C23—216no—
1033C23—232no—
1034C23—216no—
1035C23—224no—
1036C23—224no—
1037C23—212no—
1038C23—212no—
1039C23—232no—
1040C23—296no—
1041C23—2192no—
1042C23—216no—
1043C23—28no—
1044C23—216no—
1045C23—412no—
1046C23—416no—
1047C23—412no—
1048C23—412no—
1049C23—46no—
1050C23—424no—
1051C23—42no—
1052C23—424no—
1053C23—448no—
1054C23—412no—
1055C23—448no—
1056C23—424no—
1057C23—4192no—
1058C23—448no—
1059C23—496no—
1060C23—496no—
1061C23—4384no—
1062C23—4192no—
1063C23—416no—
1064C23—496no—
1065C23—48no—
1066C23—448no—
1067C23—416no—
1068C23—432no—
1069C23—496no—
1070C23—4192no—
1071C23—4192no—
1072C23—496no—
1073C23—4384no—
1074C23—424no—
1075C23—448no—
1076C23—424no—
1077C23—464no—
1078C23—448no—
1079C23—44no—
1080C23—48no—
1081C23—44no—
1082C23#1439112yes—
1083C23#1439124yes—
1084C23#1439124yes—
1085C23#143914yes—
1086C23#201018yes—
1087C23C2×#38016yes—
1088C23C2×#38016yes—
1089C23C2×#385112yes—
1090C23C2×#385112yes—
1091C23C2×#39213yes—
1092C23C2×#39216yes—
1093C23C2×#39213yes—
1094C23C2×#394112yes—
1095C23C2×#394112yes—
1096C23C2×#39716yes—
1097C23C2×#39716yes—
1098C23C23×C4⋊C411yescharacteristic
1099C23C22×#12012yes—
1100C23C22×#12111yescharacteristic
1101C23C22×#12111yescharacteristic
1102C23C22×#12312yes—
1103C2×C4—28no—
1104C2×C4—216no—
1105C2×C4—424no—
1106C2×C4—448no—
1107C2×C4—424no—
1108C2×C4—44no—
1109C2×C4—48no—
1110C2×C4—44no—
1111C2×C4—448no—
1112C2×C4—496no—
1113C2×C4—448no—
1114C2×C4—48no—
1115C2×C4—416no—
1116C2×C4—48no—
1117C2×C4—48no—
1118C2×C4—416no—
1119C2×C4—48no—
1120C2×C4—432no—
1121C2×C4—432no—
1122C2×C4—416no—
1123C2×C4—416no—
1124C2×C4—896no—
1125C2×C4—848no—
1126C2×C4—848no—
1127C2×C4#1439124yes—
1128C2×C4#1439148yes—
1129C2×C4#1439148yes—
1130C2×C4#1439124yes—
1131C2×C4#1439112yes—
1132C2×C4#1439112yes—
1133C2×C4#1439124yes—
1134C2×C4C2×#38016yes—
1135C2×C4C2×#38016yes—
1136C2×C4C2×#385112yes—
1137C2×C4C2×#385112yes—
1138C2×C4C2×#38616yes—
1139C2×C4C2×#38616yes—
1140C2×C4C2×#386112yes—
1141C2×C4C2×#388112yes—
1142C2×C4C2×#388112yes—
1143C2×C4C2×#388112yes—
1144C2×C4C2×#388112yes—
1145C2×C4C2×#39016yes—
1146C2×C4C2×#39016yes—
1147C2×C4C2×#390112yes—
1148C2×C4C2×#39213yes—
1149C2×C4C2×#39216yes—
1150C2×C4C2×#39213yes—
1151C2×C4C2×#393112yes—
1152C2×C4C2×#39316yes—
1153C2×C4C2×#39316yes—
1154C2×C4C2×#394112yes—
1155C2×C4C2×#394112yes—
1156C2×C4C2×#396112yes—
1157C2×C4C2×#396112yes—
1158C2×C4C2×#396112yes—
1159C2×C4C2×#396112yes—
1160C2×C4C2×#39716yes—
1161C2×C4C2×#39716yes—
1162C2×C4C2×#399112yes—
1163C2×C4C2×#39916yes—
1164C2×C4C2×#39916yes—
1165C2×C4C23×C22⋊C411yescharacteristic
1166C2×C4C22×#11711yescharacteristic
1167C2×C4C22×C4×D412yes—
1168C2×C4C22×C4×D412yes—
1169C2×C4C22×#12011yescharacteristic
1170C2×C4C22×#12112yes—
1171C2×C4C22×#12112yes—
1172C2×C4C22×#12112yes—
1173C2×C4C22×C22⋊Q812yes—
1174C2×C4C22×C22⋊Q811yescharacteristic
1175C2×C4C22×C22⋊Q811yescharacteristic
1176C2×C4C22×C22⋊Q812yes—
1177C2×C4C22×#12311yescharacteristic
1178C2×C4C22×#12312yes—
1179C2×C4C22×#12412yes—
1180C2×C4C22×#12411yescharacteristic
1181C2×C4C22×#12612yes—
1182C2×C4C22×#12711yescharacteristic
1183C8—216no—
1184C8—48no—
1185C22—224no—
1186C22—212no—
1187C22—224no—
1188C22—212no—
1189C22—248no—
1190C22—224no—
1191C22—24no—
1192C22—212no—
1193C22—22no—
1194C22—26no—
1195C22—216no—
1196C22—232no—
1197C22—412no—
1198C22—46no—
1199C22—41no—
1200C22—41no—
1201C22—42no—
1202C22—424no—
1203C22—46no—
1204C22—412no—
1205C22—432no—
1206C22—48no—
1207C22—416no—
1208C22—4192no—
1209C22—496no—
1210C22—416no—
1211C22—496no—
1212C22—48no—
1213C22—416no—
1214C22#11100116yesdirect product factor
1215C22C2×#143916yes—
1216C22C2×#1439112yes—
1217C22C2×#143916yes—
1218C22C2×#2010112yes—
1219C22C22×#38011yescharacteristic
1220C22C22×#38512yes—
1221C22C22×#39211yescharacteristic
1222C22C22×#39412yes—
1223C22C22×#39711yescharacteristic
1224C4—48no—
1225C4—816no—
1226C4—816no—
1227C4C2×#143916yes—
1228C4C2×#1439112yes—
1229C4C2×#143916yes—
1230C4C22×#38611yescharacteristic
1231C4C22×#38812yes—
1232C4C22×#39011yescharacteristic
1233C4C22×#39311yescharacteristic
1234C4C22×#39612yes—
1235C4C22×#39911yescharacteristic
1236C2—22no—
1237C2—21no—
1238C2—22no—
1239C2—212no—
1240C2—26no—
1241C2—21no—
1242C2—416no—
1243C2C2×#11100112yesdirect product factor
1244C2C22×#143911yescharacteristic
1245C2C22×#201012yes—
subgroupG/H
centerC23×C4#127
commutatorC22×C4C24×C4
Frattini, cosocleC23×C4C25
socleC24#392
prime radicalC27D4
LCSG ▷ C22×C4 ▷ 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×#2911C2semidirect
4. C22×#1733C2semidirect
5. C23×H(3,ℤ/4)C2semidirect
6. C2×#11100C2direct (N × H)
14. C2×#2911C22semidirect
19. C22×#407C4semidirect
31. C2×#1733C22semidirect
34. C22×H(3,ℤ/4)C22semidirect
35. #11100C22direct (N × H)
101. #2911C23semidirect
111. C2×#407C2×C4semidirect
130. #1733C23semidirect
133. C2×H(3,ℤ/4)C23semidirect
261. C22×M16C22⋊C4semidirect
276. C23×C8C22⋊C4semidirect
364. #407C22×C4semidirect
636. C2×M16C2×C22⋊C4semidirect
652. C22×C8C2×C22⋊C4semidirect
1008. C2×C8C22×C22⋊C4semidirect
1214. C22#11100direct (N × H)
1243. C2C2×#11100direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#29112
C23×#4072
C22×#22802
C22×#17332
C23×H(3,ℤ/4)2
C2×#111002