Finite Group Databasebeta

← C2×#11065 #357722

Subgroups — C2×#11065 #357722

Order 512.

2710 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C22×#408C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic, complemented
6C22×#341C211yesmaximal, characteristic, complemented
7C2×#1735C211yesmaximal, characteristic, complemented
8#11065C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2905—22no—
17#2905—22no—
18#2905—22no—
19#2905C2214yescomplemented
20C2×#424—22no—
21C2×#424—22no—
22C2×#423—22no—
23C2×#421—24no—
24C2×#421—22no—
25C2×#421—24no—
26C2×#421C2214yes—
27C22×#104—22no—
28#2896—22no—
29#2896—22no—
30#2896C414yescomplemented
31#2896C2214yes—
32C2×#417—22no—
33C2×#419C412yescomplemented
34C2×#418C412yescomplemented
35C2×#416—22no—
36C2×#408—24no—
37C2×#408—22no—
38C2×#408—24no—
39C2×#408C2214yes—
40C22×C22⋊C8—22no—
41C2×#344—24no—
42C2×#344C2214yescomplemented
43C2×#341—24no—
44C2×#341C2214yescomplemented
45#1735—22no—
46#1735C2214yescomplemented
47C2×#340—22no—
48C22×#41—22no—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—22no—
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—21no—
61C22×#41—21no—
62C22×#41—22no—
63C22×#41—22no—
64C22×#41C2×C412yes—
65C22×#41D414yes—
66C22×#41Q814yes—
67C22×#41C2312yes—
68C23×Q8C2×C411yescharacteristic
69C23×D4—21no—
70C23×D4C2×C411yescharacteristic
71C24×C4—21no—
72C24×C4C2311yescharacteristic
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—22no—
93C22×M16—22no—
94C22×M16—22no—
95C22×M16C2×C412yes—
96C22×M16C2×C412yes—
97C22×M16D412yes—
98C22×M16D412yes—
99C22×M16D412yes—
100C22×M16C2312yes—
101C22×M16C2312yes—
102C22×M16C2312yes—
103C23×C8—21no—
104C23×C8—22no—
105C23×C8—21no—
106C23×C8—21no—
107C23×C8—21no—
108C23×C8—21no—
109C23×C8—21no—
110C23×C8—22no—
111C23×C8—21no—
112C23×C8—21no—
113C23×C8—22no—
114C23×C8D412yes—
115C23×C8D414yes—
116C23×C8C2312yes—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—22no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—22no—
127C2×#117—21no—
128C2×#117—22no—
129C2×#117C2×C412yes—
130C2×#117C2×C412yes—
131C2×#117D414yes—
132C2×#117D412yes—
133C2×#117D412yes—
134C2×#117D412yes—
135C2×#117C2312yes—
136C2×#117C2312yes—
137C22×C4⋊C4—21no—
138C22×C4⋊C4D412yes—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C42—21no—
142C22×C42—21no—
143#424—28no—
144#424—28no—
145#424—28no—
146#424—28no—
147#423—28no—
148#423—28no—
149C2×C4⋊C8—28no—
150#421—216no—
151#421—28no—
152#421—28no—
153C2×#104—216no—
154C2×#104—28no—
155#419—24no—
156#419C2×C418yescomplemented
157#418—24no—
158#418C2×C418yescomplemented
159#417—28no—
160#417—28no—
161#416—28no—
162#416—28no—
163C2×#103—24no—
164C2×#102—24no—
165#408—216no—
166#408—28no—
167#408—28no—
168C2×C22⋊C8—216no—
169C2×C22⋊C8—28no—
170#344—28no—
171#341—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—22no—
183C2×#41—22no—
184C2×#41—24no—
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—24no—
190C2×#41—24no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
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—41no—
213C2×#41—41no—
214C2×#41—41no—
215C2×#41—41no—
216C2×#41—42no—
217C2×#41—41no—
218C2×#41—41no—
219C2×#41—42no—
220C2×#41—42no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—41no—
226C2×#41—41no—
227C2×#41—42no—
228C2×#41—42no—
229C2×#41—42no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41—42no—
234C2×#41—42no—
235C2×#41—42no—
236C2×#41—42no—
237C2×#41—42no—
238C2×#41—42no—
239C2×#41—42no—
240C2×#41C4⋊C418yes—
241C2×#41C2×D414yes—
242C2×#41C2×Q814yes—
243C22×Q8—21no—
244C22×Q8—22no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—22no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—22no—
251C22×Q8C4⋊C414yes—
252C22×Q8C22×C412yes—
253C22×D4—22no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—22no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—22no—
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×D4C22×C412yes—
273C23×C4—21no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—41no—
280C23×C4—41no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—41no—
286C23×C4C22×C411yescharacteristic
287C23×C4C22×C411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D412yes—
296C23×C4C2×D412yes—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×Q812yes—
300C23×C4#4112yes—
301C23×C4#4112yes—
302C23×C4#4111yescharacteristic
303C23×C4#4111yescharacteristic
304C23×C4#4111yescharacteristic
305C23×C4#4112yes—
306C23×C4#4112yes—
307C23×C4C2411yescharacteristic
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—24no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—24no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—42no—
341C2×M16—42no—
342C2×M16—42no—
343C2×M16—42no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16—42no—
349C2×M16—42no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C2×M16—42no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16C22×C414yes—
361C2×M16C2×D414yes—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—24no—
365C22×C8—24no—
366C22×C8—22no—
367C22×C8—24no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—24no—
372C22×C8—24no—
373C22×C8—24no—
374C22×C8—24no—
375C22×C8—24no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—22no—
384C22×C8—42no—
385C22×C8—42no—
386C22×C8—41no—
387C22×C8—41no—
388C22×C8—41no—
389C22×C8—41no—
390C22×C8—42no—
391C22×C8—42no—
392C22×C8—42no—
393C22×C8—42no—
394C22×C8—42no—
395C22×C8—42no—
396C22×C8—42no—
397C22×C8—42no—
398C22×C8C2×D414yes—
399C22×C8C2×D414yes—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—24no—
413#117—22no—
414#117—24no—
415#117—22no—
416#117—24no—
417#117—22no—
418#117—42no—
419#117—42no—
420#117—42no—
421#117C22⋊C414yes—
422#117C22⋊C414yes—
423#117C22×C414yes—
424#117C2×D414yes—
425#117C2×D414yes—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4C22⋊C414yes—
434C2×C4⋊C4C22⋊C414yes—
435C2×C4⋊C4C2×D414yes—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—42no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—24no—
453C2×C42—22no—
454C2×C42—41no—
455C2×C42—42no—
456C4⋊C8—232no—
457#104—232no—
458#103—216no—
459#102—216no—
460C22⋊C8—232no—
461C24—22no—
462C24—24no—
463C24—44no—
464C24—48no—
465C24—41no—
466C24—41no—
467C24—42no—
468C24C4×D411yescharacteristic
469C24C4×D411yescharacteristic
470C24#12111yescharacteristic
471C24#12111yescharacteristic
472C24C22⋊Q812yes—
473C24#12311yescharacteristic
474C24#12312yes—
475C24#12311yescharacteristic
476C24#12312yes—
477C24#12612yes—
478C24C2×#4111yescharacteristic
479#41—24no—
480#41—24no—
481#41—24no—
482#41—24no—
483#41—24no—
484#41—24no—
485#41—24no—
486#41—24no—
487#41—28no—
488#41—28no—
489#41—28no—
490#41—28no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—42no—
495#41—42no—
496#41—42no—
497#41—42no—
498#41—42no—
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
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—
519C2×Q8—22no—
520C2×Q8—24no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—24no—
526C2×Q8—24no—
527C2×Q8—24no—
528C2×Q8—24no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8C2×C4⋊C414yes—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—28no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4C2×C4⋊C414yes—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—28no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
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—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4C2×C22⋊C411yescharacteristic
604C22×C4C2×C22⋊C411yescharacteristic
605C22×C4C2×C22⋊C411yescharacteristic
606C22×C4C2×C22⋊C411yescharacteristic
607C22×C4C2×C4⋊C412yes—
608C22×C4C2×C4⋊C412yes—
609C22×C4#11712yes—
610C22×C4#11712yes—
611C22×C4C4×D411yescharacteristic
612C22×C4C4×D411yescharacteristic
613C22×C4C4×D411yescharacteristic
614C22×C4C4×D411yescharacteristic
615C22×C4C4×D412yes—
616C22×C4C4×D412yes—
617C22×C4C4×D412yes—
618C22×C4C4×D412yes—
619C22×C4C4×D411yescharacteristic
620C22×C4C4×D411yescharacteristic
621C22×C4#12012yes—
622C22×C4#12012yes—
623C22×C4#12012yes—
624C22×C4#12012yes—
625C22×C4#12011yescharacteristic
626C22×C4#12011yescharacteristic
627C22×C4#12011yescharacteristic
628C22×C4#12011yescharacteristic
629C22×C4#12112yes—
630C22×C4#12112yes—
631C22×C4#12112yes—
632C22×C4#12112yes—
633C22×C4#12111yescharacteristic
634C22×C4#12111yescharacteristic
635C22×C4#12111yescharacteristic
636C22×C4#12111yescharacteristic
637C22×C4#12112yes—
638C22×C4#12112yes—
639C22×C4#12112yes—
640C22×C4#12112yes—
641C22×C4#12112yes—
642C22×C4#12112yes—
643C22×C4#12112yes—
644C22×C4#12112yes—
645C22×C4#12111yescharacteristic
646C22×C4#12111yescharacteristic
647C22×C4C22⋊Q812yes—
648C22×C4C22⋊Q812yes—
649C22×C4C22⋊Q812yes—
650C22×C4C22⋊Q812yes—
651C22×C4C22⋊Q812yes—
652C22×C4C22⋊Q812yes—
653C22×C4C22⋊Q812yes—
654C22×C4C22⋊Q812yes—
655C22×C4C22⋊Q812yes—
656C22×C4C22⋊Q812yes—
657C22×C4C22⋊Q812yes—
658C22×C4#12312yes—
659C22×C4#12312yes—
660C22×C4#12312yes—
661C22×C4#12312yes—
662C22×C4#12312yes—
663C22×C4#12311yescharacteristic
664C22×C4#12311yescharacteristic
665C22×C4#12312yes—
666C22×C4#12412yes—
667C22×C4#12412yes—
668C22×C4#12412yes—
669C22×C4#12412yes—
670C22×C4#12412yes—
671C22×C4#12412yes—
672C22×C4#12612yes—
673C22×C4#12612yes—
674C22×C4#12612yes—
675C22×C4#12712yes—
676C22×C4#12712yes—
677C22×C4C23×C411yescharacteristic
678C22×C4C22×D411yescharacteristic
679C22×C4C22×D411yescharacteristic
680C22×C4C22×D411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C22×D411yescharacteristic
684C22×C4C22×D411yescharacteristic
685C22×C4C22×Q811yescharacteristic
686C22×C4C2×#4111yescharacteristic
687C22×C4C2×#4111yescharacteristic
688C22×C4C2×#4111yescharacteristic
689C22×C4C2×#4111yescharacteristic
690C22×C4C2×#4111yescharacteristic
691M16—24no—
692M16—24no—
693M16—24no—
694M16—24no—
695M16—42no—
696M16—42no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16—42no—
701M16—42no—
702M16—42no—
703M16—44no—
704M16—44no—
705M16—44no—
706M16—44no—
707M16—44no—
708M16—44no—
709C2×C8—24no—
710C2×C8—24no—
711C2×C8—24no—
712C2×C8—24no—
713C2×C8—24no—
714C2×C8—24no—
715C2×C8—24no—
716C2×C8—24no—
717C2×C8—42no—
718C2×C8—42no—
719C2×C8—42no—
720C2×C8—42no—
721C2×C8—42no—
722C2×C8—42no—
723C2×C8—42no—
724C2×C8—42no—
725C2×C8—44no—
726C2×C8—44no—
727C2×C8—44no—
728C2×C8—44no—
729C2×C8—44no—
730C2×C8—44no—
731C2×C8—44no—
732C2×C8—44no—
733C2×C8—44no—
734C2×C8—44no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—42no—
740C4⋊C4—44no—
741C4⋊C4C2×C22⋊C418yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—42no—
748C22⋊C4—44no—
749C42—24no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—24no—
754C42—42no—
755C42—44no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—42no—
761C23—42no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—42no—
766C23—44no—
767C23—42no—
768C23—416no—
769C23—48no—
770C23—44no—
771C23—44no—
772C23—42no—
773C23—42no—
774C23—88no—
775C23—84no—
776C23—84no—
777C23#38512yes—
778C23#38512yes—
779C23#38611yescharacteristic
780C23#38611yescharacteristic
781C23#38611yescharacteristic
782C23#38611yescharacteristic
783C23#38812yes—
784C23#38812yes—
785C23#39412yes—
786C23#39412yes—
787C23#39612yes—
788C23#39612yes—
789C23#39712yes—
790C23#39712yes—
791C23#39912yes—
792C23#39912yes—
793C23C2×C4×D411yescharacteristic
794C23C2×#12111yescharacteristic
795C23C2×C22⋊Q811yescharacteristic
796C23C2×#12311yescharacteristic
797C23C2×#12311yescharacteristic
798C23C2×#12311yescharacteristic
799C23C2×#12611yescharacteristic
800Q8—24no—
801Q8—24no—
802Q8—44no—
803Q8—44no—
804Q8—42no—
805Q8—42no—
806D4—24no—
807D4—24no—
808D4—44no—
809D4—44no—
810D4—44no—
811D4—44no—
812D4—48no—
813D4—48no—
814D4—44no—
815D4—44no—
816D4—42no—
817D4—42no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—48no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—48no—
830C2×C4—48no—
831C2×C4—44no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—88no—
835C2×C4—84no—
836C2×C4#38012yes—
837C2×C4#38012yes—
838C2×C4#38012yes—
839C2×C4#38012yes—
840C2×C4#38512yes—
841C2×C4#38512yes—
842C2×C4#38512yes—
843C2×C4#38512yes—
844C2×C4#38512yes—
845C2×C4#38512yes—
846C2×C4#38611yescharacteristic
847C2×C4#38611yescharacteristic
848C2×C4#38611yescharacteristic
849C2×C4#38611yescharacteristic
850C2×C4#38812yes—
851C2×C4#38812yes—
852C2×C4#38812yes—
853C2×C4#38812yes—
854C2×C4#38812yes—
855C2×C4#38812yes—
856C2×C4#39012yes—
857C2×C4#39012yes—
858C2×C4#39012yes—
859C2×C4#39012yes—
860C2×C4#39212yes—
861C2×C4#39212yes—
862C2×C4#39212yes—
863C2×C4#39212yes—
864C2×C4#39312yes—
865C2×C4#39312yes—
866C2×C4#39312yes—
867C2×C4#39312yes—
868C2×C4#39412yes—
869C2×C4#39412yes—
870C2×C4#39412yes—
871C2×C4#39412yes—
872C2×C4#39412yes—
873C2×C4#39412yes—
874C2×C4#39612yes—
875C2×C4#39612yes—
876C2×C4#39612yes—
877C2×C4#39612yes—
878C2×C4#39612yes—
879C2×C4#39612yes—
880C2×C4#39712yes—
881C2×C4#39712yes—
882C2×C4#39912yes—
883C2×C4#39912yes—
884C2×C4C22×C22⋊C411yescharacteristic
885C2×C4C22×C4⋊C411yescharacteristic
886C2×C4C2×#11711yescharacteristic
887C2×C4C2×C4×D411yescharacteristic
888C2×C4C2×C4×D411yescharacteristic
889C2×C4C2×C4×D411yescharacteristic
890C2×C4C2×#12011yescharacteristic
891C2×C4C2×#12011yescharacteristic
892C2×C4C2×#12011yescharacteristic
893C2×C4C2×#12111yescharacteristic
894C2×C4C2×#12111yescharacteristic
895C2×C4C2×#12111yescharacteristic
896C2×C4C2×#12111yescharacteristic
897C2×C4C2×#12111yescharacteristic
898C2×C4C2×#12111yescharacteristic
899C2×C4C2×#12111yescharacteristic
900C2×C4C2×C22⋊Q811yescharacteristic
901C2×C4C2×C22⋊Q811yescharacteristic
902C2×C4C2×C22⋊Q811yescharacteristic
903C2×C4C2×C22⋊Q811yescharacteristic
904C2×C4C2×C22⋊Q811yescharacteristic
905C2×C4C2×#12311yescharacteristic
906C2×C4C2×#12311yescharacteristic
907C2×C4C2×#12411yescharacteristic
908C2×C4C2×#12411yescharacteristic
909C2×C4C2×#12411yescharacteristic
910C2×C4C2×#12611yescharacteristic
911C2×C4C2×#12711yescharacteristic
912C8—44no—
913C8—44no—
914C8—44no—
915C8—44no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—48no—
939C22—44no—
940C22—88no—
941C22—84no—
942C22—88no—
943C22—84no—
944C22#143912yes—
945C22#143912yes—
946C22#143912yes—
947C22#143912yes—
948C22#188114yes—
949C22C2×#38511yescharacteristic
950C22C2×#38611yescharacteristic
951C22C2×#38811yescharacteristic
952C22C2×#39411yescharacteristic
953C22C2×#39611yescharacteristic
954C22C2×#39711yescharacteristic
955C22C2×#39911yescharacteristic
956C4—44no—
957C4—48no—
958C4—84no—
959C4#143912yes—
960C4#143912yes—
961C4#143912yes—
962C4#143912yes—
963C4C2×#38011yescharacteristic
964C4C2×#38511yescharacteristic
965C4C2×#38811yescharacteristic
966C4C2×#39011yescharacteristic
967C4C2×#39211yescharacteristic
968C4C2×#39311yescharacteristic
969C4C2×#39411yescharacteristic
970C4C2×#39611yescharacteristic
971C2—21no—
972C2—21no—
973C2—22no—
974C2—21no—
975C2—21no—
976C2—21no—
977C2—21no—
978C2—22no—
979C2—22no—
980C2—84no—
981C2#1106514yesdirect product factor
982C2C2×#143911yescharacteristic
983C2C2×#188112yes—
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#386
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2905C2semidirect
5. C22×#344C2semidirect
6. C22×#341C2semidirect
7. C2×#1735C2semidirect
8. #11065C2direct (N × H)
19. #2905C22semidirect
30. #2896C4semidirect
33. C2×#419C4semidirect
34. C2×#418C4semidirect
42. C2×#344C22semidirect
44. C2×#341C22semidirect
46. #1735C22semidirect
156. #419C2×C4semidirect
158. #418C2×C4semidirect
981. C2#11065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29052
C22×#4212
C2×#28962
C22×#4082
C22×#3442
C22×#3412
C2×#17352
#110652