Finite Group Databasebeta

← C2×#11120 #357787

Subgroups — C2×#11120 #357787

Order 512.

2726 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C22×#417C211yesmaximal, characteristic
4C22×#413C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic, complemented
6C22×#343C211yesmaximal, characteristic, complemented
7C2×#1736C211yesmaximal, characteristic, complemented
8#11120C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#430—24no—
17C2×#430—22no—
18C2×#430—24no—
19C2×#430C2214yescomplemented
20C22×#108—22no—
21C2×#421—24no—
22C2×#421—22no—
23C2×#421C418yescomplemented
24C2×#421C2214yes—
25C22×#104—22no—
26C2×#417—22no—
27C2×#417—22no—
28C2×#417—22no—
29C2×#417—22no—
30C2×#417—22no—
31C2×#417C2214yes—
32C22×#103—21no—
33C22×#102—21no—
34C2×#413—22no—
35C2×#413—24no—
36C2×#413—24no—
37C2×#413C2214yes—
38C22×#101—21no—
39C22×#100—21no—
40C2×#344—24no—
41C2×#344C2214yescomplemented
42C2×#343—22no—
43C2×#343—22no—
44C2×#343C2214yescomplemented
45#1736—22no—
46#1736C2214yescomplemented
47C2×#340—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—21no—
51C22×#41—21no—
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—22no—
59C22×#41—21no—
60C22×#41—21no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41—22no—
64C22×#41C2×C414yes—
65C22×#41D412yes—
66C22×#41Q814yes—
67C22×#41C2312yes—
68C23×Q8D411yescharacteristic
69C23×D4—21no—
70C23×D4D411yescharacteristic
71C24×C4—21no—
72C24×C4—21no—
73C24×C4C2311yescharacteristic
74C22×M16—22no—
75C22×M16—21no—
76C22×M16—22no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—21no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—21no—
93C22×M16—22no—
94C22×M16—21no—
95C22×M16—22no—
96C22×M16—22no—
97C22×M16—21no—
98C22×M16—21no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16C2×C414yes—
103C22×M16D414yes—
104C22×M16D414yes—
105C22×M16D412yes—
106C22×M16D412yes—
107C22×M16D412yes—
108C22×M16D414yes—
109C22×M16D412yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112C22×M16C2312yes—
113C22×M16C2312yes—
114C23×C8—21no—
115C23×C8—21no—
116C23×C8—21no—
117C23×C8—21no—
118C2×#117—22no—
119C2×#117—21no—
120C2×#117—22no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—22no—
124C2×#117C2×C414yes—
125C2×#117C2312yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4D412yes—
139C22×C4⋊C4D412yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4—21no—
142C22×C42—21no—
143#430—216no—
144#430—28no—
145#430—28no—
146C2×#108—216no—
147C2×#108—28no—
148#421—216no—
149#421—28no—
150#421C2×C4116yescomplemented
151C2×#104—216no—
152C2×#104—28no—
153#417—28no—
154#417—28no—
155#417—28no—
156#417—28no—
157C2×#103—24no—
158C2×#103—24no—
159C2×#103—24no—
160C2×#102—24no—
161C2×#102—24no—
162C2×#102—24no—
163#413—216no—
164#413—28no—
165#413—28no—
166C2×#101—28no—
167C2×#101—24no—
168C2×#100—28no—
169C2×#100—24no—
170#344—28no—
171#343—28no—
172#340—28no—
173C25—21no—
174C25#4111yescharacteristic
175C2×#41—24no—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—24no—
179C2×#41—24no—
180C2×#41—22no—
181C2×#41—22no—
182C2×#41—24no—
183C2×#41—24no—
184C2×#41—24no—
185C2×#41—24no—
186C2×#41—24no—
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—24no—
190C2×#41—22no—
191C2×#41—22no—
192C2×#41—22no—
193C2×#41—22no—
194C2×#41—24no—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—24no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—22no—
209C2×#41—22no—
210C2×#41—22no—
211C2×#41—22no—
212C2×#41—42no—
213C2×#41—42no—
214C2×#41—41no—
215C2×#41—41no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41—42no—
220C2×#41—41no—
221C2×#41—41no—
222C2×#41—42no—
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—42no—
226C2×#41—42no—
227C2×#41—41no—
228C2×#41—41no—
229C2×#41—42no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41—41no—
234C2×#41—41no—
235C2×#41—42no—
236C2×#41—42no—
237C2×#41—42no—
238C2×#41—42no—
239C2×#41—42no—
240C2×#41C4⋊C418yes—
241C2×#41C22×C414yes—
242C2×#41C2×Q814yes—
243C22×Q8—22no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8C4⋊C414yes—
252C22×Q8C2×D412yes—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—22no—
264C22×D4—21no—
265C22×D4—41no—
266C22×D4—41no—
267C22×D4—41no—
268C22×D4—41no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4C4⋊C414yes—
272C22×D4C2×D412yes—
273C23×C4—21no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4—41no—
290C23×C4—41no—
291C23×C4—41no—
292C23×C4—84no—
293C23×C4C22×C412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D412yes—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×Q812yes—
306C23×C4#4112yes—
307C23×C4#4111yescharacteristic
308C23×C4#4111yescharacteristic
309C23×C4#4112yes—
310C23×C4#4111yescharacteristic
311C23×C4#4111yescharacteristic
312C23×C4#4111yescharacteristic
313C23×C4#4112yes—
314C23×C4C2411yescharacteristic
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—24no—
338C2×M16—24no—
339C2×M16—24no—
340C2×M16—24no—
341C2×M16—24no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16—24no—
345C2×M16—24no—
346C2×M16—24no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—41no—
360C2×M16—41no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—41no—
364C2×M16—41no—
365C2×M16—42no—
366C2×M16—42no—
367C2×M16—42no—
368C2×M16—42no—
369C2×M16—42no—
370C2×M16—42no—
371C2×M16—42no—
372C2×M16—42no—
373C2×M16—42no—
374C2×M16—42no—
375C2×M16—42no—
376C2×M16—42no—
377C2×M16—42no—
378C2×M16—42no—
379C2×M16C22⋊C418yes—
380C2×M16C22⋊C418yes—
381C2×M16C22×C414yes—
382C2×M16C2×D414yes—
383C2×M16C2×D414yes—
384C2×M16C2×D414yes—
385C2×M16C2×D414yes—
386C2×M16C2×D414yes—
387C22×C8—24no—
388C22×C8—24no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—24no—
395C22×C8—24no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—41no—
400C22×C8—41no—
401C22×C8—42no—
402C22×C8—42no—
403C22×C8—41no—
404C22×C8—41no—
405C22×C8—42no—
406C22×C8—42no—
407#117—24no—
408#117—22no—
409#117—24no—
410#117—22no—
411#117—24no—
412#117—22no—
413#117—42no—
414#117—42no—
415#117—42no—
416#117C22×C414yes—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4C2×D414yes—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—41no—
452C2×C22⋊C4—42no—
453C2×C42—24no—
454C2×C42—22no—
455C2×C42—42no—
456C2×C42—41no—
457#108—232no—
458#104—232no—
459#103—216no—
460#102—216no—
461#101—216no—
462#100—216no—
463C24—22no—
464C24—24no—
465C24—42no—
466C24—42no—
467C24—41no—
468C24—41no—
469C24—42no—
470C24—82no—
471C24—82no—
472C24C4×D412yes—
473C24#12111yescharacteristic
474C24#12111yescharacteristic
475C24C22⋊Q812yes—
476C24#12311yescharacteristic
477C24#12311yescharacteristic
478C24#12411yescharacteristic
479C24#12411yescharacteristic
480C24#12412yes—
481C24#12612yes—
482C24C2×#4111yescharacteristic
483#41—24no—
484#41—24no—
485#41—24no—
486#41—24no—
487#41—24no—
488#41—24no—
489#41—24no—
490#41—24no—
491#41—28no—
492#41—28no—
493#41—28no—
494#41—28no—
495#41—42no—
496#41—42no—
497#41—42no—
498#41—42no—
499#41—42no—
500#41—42no—
501#41—42no—
502#41—42no—
503#41—44no—
504#41—44no—
505#41—44no—
506#41—44no—
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513#41—44no—
514#41—44no—
515#41—44no—
516#41—44no—
517#41—44no—
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—22no—
524C2×Q8—24no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—24no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8—42no—
540C2×Q8C2×C4⋊C414yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—28no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4C2×C4⋊C414yes—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4C2×C22⋊C412yes—
619C22×C4C2×C22⋊C412yes—
620C22×C4C2×C4⋊C412yes—
621C22×C4C2×C4⋊C412yes—
622C22×C4#11712yes—
623C22×C4#11712yes—
624C22×C4C4×D412yes—
625C22×C4C4×D412yes—
626C22×C4C4×D412yes—
627C22×C4C4×D412yes—
628C22×C4C4×D412yes—
629C22×C4C4×D412yes—
630C22×C4C4×D412yes—
631C22×C4#12011yescharacteristic
632C22×C4#12011yescharacteristic
633C22×C4#12011yescharacteristic
634C22×C4#12011yescharacteristic
635C22×C4#12012yes—
636C22×C4#12012yes—
637C22×C4#12012yes—
638C22×C4#12012yes—
639C22×C4#12112yes—
640C22×C4#12112yes—
641C22×C4#12111yescharacteristic
642C22×C4#12111yescharacteristic
643C22×C4#12111yescharacteristic
644C22×C4#12111yescharacteristic
645C22×C4#12112yes—
646C22×C4#12112yes—
647C22×C4#12111yescharacteristic
648C22×C4#12111yescharacteristic
649C22×C4#12111yescharacteristic
650C22×C4#12111yescharacteristic
651C22×C4#12112yes—
652C22×C4#12112yes—
653C22×C4#12112yes—
654C22×C4#12112yes—
655C22×C4#12112yes—
656C22×C4#12112yes—
657C22×C4#12111yescharacteristic
658C22×C4#12111yescharacteristic
659C22×C4C22⋊Q812yes—
660C22×C4C22⋊Q812yes—
661C22×C4C22⋊Q812yes—
662C22×C4C22⋊Q812yes—
663C22×C4C22⋊Q812yes—
664C22×C4C22⋊Q812yes—
665C22×C4C22⋊Q812yes—
666C22×C4C22⋊Q812yes—
667C22×C4C22⋊Q812yes—
668C22×C4C22⋊Q812yes—
669C22×C4C22⋊Q812yes—
670C22×C4#12312yes—
671C22×C4#12312yes—
672C22×C4#12312yes—
673C22×C4#12312yes—
674C22×C4#12311yescharacteristic
675C22×C4#12311yescharacteristic
676C22×C4#12311yescharacteristic
677C22×C4#12311yescharacteristic
678C22×C4#12312yes—
679C22×C4#12312yes—
680C22×C4#12311yescharacteristic
681C22×C4#12311yescharacteristic
682C22×C4#12412yes—
683C22×C4#12412yes—
684C22×C4#12411yescharacteristic
685C22×C4#12411yescharacteristic
686C22×C4#12412yes—
687C22×C4#12612yes—
688C22×C4#12612yes—
689C22×C4#12612yes—
690C22×C4#12712yes—
691C22×C4#12712yes—
692C22×C4C23×C411yescharacteristic
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D411yescharacteristic
695C22×C4C22×D411yescharacteristic
696C22×C4C22×D411yescharacteristic
697C22×C4C22×D411yescharacteristic
698C22×C4C22×D411yescharacteristic
699C22×C4C22×D411yescharacteristic
700C22×C4C22×Q811yescharacteristic
701C22×C4C2×#4111yescharacteristic
702C22×C4C2×#4111yescharacteristic
703C22×C4C2×#4111yescharacteristic
704C22×C4C2×#4111yescharacteristic
705C22×C4C2×#4111yescharacteristic
706M16—24no—
707M16—24no—
708M16—24no—
709M16—28no—
710M16—28no—
711M16—24no—
712M16—24no—
713M16—24no—
714M16—24no—
715M16—24no—
716M16—24no—
717M16—42no—
718M16—42no—
719M16—42no—
720M16—42no—
721M16—42no—
722M16—42no—
723M16—44no—
724M16—44no—
725M16—44no—
726M16—44no—
727M16—44no—
728M16—44no—
729M16C2×C22⋊C418yes—
730C2×C8—24no—
731C2×C8—24no—
732C2×C8—24no—
733C2×C8—28no—
734C2×C8—28no—
735C2×C8—24no—
736C2×C8—24no—
737C2×C8—24no—
738C2×C8—42no—
739C2×C8—42no—
740C2×C8—42no—
741C2×C8—42no—
742C2×C8—42no—
743C2×C8—42no—
744C2×C8—44no—
745C2×C8—44no—
746C2×C8—44no—
747C2×C8—44no—
748C2×C8—44no—
749C2×C8—44no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—42no—
754C4⋊C4—42no—
755C4⋊C4—42no—
756C4⋊C4—44no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C22⋊C4—24no—
762C22⋊C4—42no—
763C22⋊C4—44no—
764C42—24no—
765C42—42no—
766C42—44no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—44no—
779C23—41no—
780C23—44no—
781C23—41no—
782C23—44no—
783C23—41no—
784C23—44no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—44no—
789C23—44no—
790C23—88no—
791C23—82no—
792C23—82no—
793C23—88no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23#38512yes—
799C23#38512yes—
800C23#38812yes—
801C23#38812yes—
802C23#39012yes—
803C23#39012yes—
804C23#39312yes—
805C23#39312yes—
806C23#39411yescharacteristic
807C23#39411yescharacteristic
808C23#39411yescharacteristic
809C23#39411yescharacteristic
810C23#39612yes—
811C23#39612yes—
812C23#39712yes—
813C23#39712yes—
814C23C2×C4×D411yescharacteristic
815C23C2×#12111yescharacteristic
816C23C2×C22⋊Q811yescharacteristic
817C23C2×#12311yescharacteristic
818C23C2×#12411yescharacteristic
819C23C2×#12411yescharacteristic
820C23C2×#12611yescharacteristic
821Q8—24no—
822Q8—24no—
823Q8—42no—
824Q8—42no—
825Q8—44no—
826Q8—44no—
827D4—24no—
828D4—24no—
829D4—44no—
830D4—44no—
831D4—48no—
832D4—48no—
833D4—44no—
834D4—44no—
835D4—42no—
836D4—42no—
837D4—44no—
838D4—44no—
839C2×C4—24no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—88no—
853C2×C4—82no—
854C2×C4—82no—
855C2×C4—84no—
856C2×C4—84no—
857C2×C4—84no—
858C2×C4—84no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—84no—
862C2×C4#38012yes—
863C2×C4#38012yes—
864C2×C4#38012yes—
865C2×C4#38012yes—
866C2×C4#38512yes—
867C2×C4#38512yes—
868C2×C4#38512yes—
869C2×C4#38512yes—
870C2×C4#38512yes—
871C2×C4#38512yes—
872C2×C4#38612yes—
873C2×C4#38612yes—
874C2×C4#38612yes—
875C2×C4#38612yes—
876C2×C4#38812yes—
877C2×C4#38812yes—
878C2×C4#38812yes—
879C2×C4#38812yes—
880C2×C4#38812yes—
881C2×C4#38812yes—
882C2×C4#39012yes—
883C2×C4#39012yes—
884C2×C4#39212yes—
885C2×C4#39212yes—
886C2×C4#39212yes—
887C2×C4#39212yes—
888C2×C4#39312yes—
889C2×C4#39312yes—
890C2×C4#39412yes—
891C2×C4#39412yes—
892C2×C4#39412yes—
893C2×C4#39412yes—
894C2×C4#39411yescharacteristic
895C2×C4#39411yescharacteristic
896C2×C4#39411yescharacteristic
897C2×C4#39411yescharacteristic
898C2×C4#39612yes—
899C2×C4#39612yes—
900C2×C4#39612yes—
901C2×C4#39612yes—
902C2×C4#39612yes—
903C2×C4#39612yes—
904C2×C4#39712yes—
905C2×C4#39712yes—
906C2×C4#39912yes—
907C2×C4#39912yes—
908C2×C4#39912yes—
909C2×C4#39912yes—
910C2×C4C22×C22⋊C411yescharacteristic
911C2×C4C22×C4⋊C411yescharacteristic
912C2×C4C2×#11711yescharacteristic
913C2×C4C2×C4×D411yescharacteristic
914C2×C4C2×C4×D411yescharacteristic
915C2×C4C2×C4×D411yescharacteristic
916C2×C4C2×#12011yescharacteristic
917C2×C4C2×#12011yescharacteristic
918C2×C4C2×#12011yescharacteristic
919C2×C4C2×#12111yescharacteristic
920C2×C4C2×#12111yescharacteristic
921C2×C4C2×#12111yescharacteristic
922C2×C4C2×#12111yescharacteristic
923C2×C4C2×#12111yescharacteristic
924C2×C4C2×#12111yescharacteristic
925C2×C4C2×#12111yescharacteristic
926C2×C4C2×C22⋊Q811yescharacteristic
927C2×C4C2×C22⋊Q811yescharacteristic
928C2×C4C2×C22⋊Q811yescharacteristic
929C2×C4C2×C22⋊Q811yescharacteristic
930C2×C4C2×C22⋊Q811yescharacteristic
931C2×C4C2×#12311yescharacteristic
932C2×C4C2×#12311yescharacteristic
933C2×C4C2×#12311yescharacteristic
934C2×C4C2×#12311yescharacteristic
935C2×C4C2×#12411yescharacteristic
936C2×C4C2×#12611yescharacteristic
937C2×C4C2×#12711yescharacteristic
938C8—28no—
939C8—44no—
940C8—44no—
941C8—44no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—44no—
971C22—84no—
972C22—84no—
973C22—88no—
974C22—88no—
975C22—82no—
976C22—82no—
977C22#143912yes—
978C22#143912yes—
979C22#143912yes—
980C22#143912yes—
981C22#204812yes—
982C22#204912yes—
983C22C2×#38511yescharacteristic
984C22C2×#38811yescharacteristic
985C22C2×#39011yescharacteristic
986C22C2×#39311yescharacteristic
987C22C2×#39411yescharacteristic
988C22C2×#39611yescharacteristic
989C22C2×#39711yescharacteristic
990C4—44no—
991C4—84no—
992C4—84no—
993C4#143912yes—
994C4#143912yes—
995C4#143912yes—
996C4#143912yes—
997C4C2×#38011yescharacteristic
998C4C2×#38511yescharacteristic
999C4C2×#38611yescharacteristic
1000C4C2×#38811yescharacteristic
1001C4C2×#39211yescharacteristic
1002C4C2×#39411yescharacteristic
1003C4C2×#39611yescharacteristic
1004C4C2×#39911yescharacteristic
1005C2—21no—
1006C2—21no—
1007C2—22no—
1008C2—21no—
1009C2—21no—
1010C2—21no—
1011C2—22no—
1012C2—22no—
1013C2—21no—
1014C2—84no—
1015C2#1112014yesdirect product factor
1016C2C2×#143911yescharacteristic
1017C2C2×#204811yescharacteristic
1018C2C2×#204911yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#430C2semidirect
5. C22×#344C2semidirect
6. C22×#343C2semidirect
7. C2×#1736C2semidirect
8. #11120C2direct (N × H)
19. C2×#430C22semidirect
23. C2×#421C4semidirect
41. C2×#344C22semidirect
44. C2×#343C22semidirect
46. #1736C22semidirect
150. #421C2×C4semidirect
1015. C2#11120direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4302
C22×#4212
C22×#4172
C22×#4132
C22×#3442
C22×#3432
C2×#17362
#111202