Finite Group Databasebeta

← #357707

Subgroups — #357707

Order 512.

2658 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
1C2×#2905C211yesmaximal, characteristic, complemented
2C2×#2896C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C22×#413C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic, complemented
6C2×#1733C211yesmaximal, characteristic, complemented
7C22×#338C211yesmaximal, characteristic, complemented
8#11059C214yesmaximal, complemented
9#11058C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C22×#117C2211yescharacteristic
17#2905—22no—
18#2905—22no—
19#2905—22no—
20#2905C2214yes—
21C2×#424—22no—
22C2×#424—22no—
23C2×#423—22no—
24#2896—24no—
25#2896—24no—
26#2896—22no—
27#2896—22no—
28#2896—22no—
29#2896—22no—
30C2×#417—22no—
31C2×#417C414yescomplemented
32C2×#419C2212yes—
33C2×#419C2212yes—
34C2×#418C2212yes—
35C2×#418C2212yes—
36C2×#416—22no—
37C2×#416C414yescomplemented
38C2×#413—24no—
39C2×#413—22no—
40C2×#413—22no—
41C2×#413—24no—
42C22×#101C2212yes—
43C22×#100C2212yes—
44C2×#344—24no—
45C2×#344C2214yes—
46#1733—22no—
47#1733C2214yes—
48C2×#339—22no—
49C2×#338—24no—
50C2×#338C2214yes—
51C22×#41—21no—
52C22×#41—21no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—21no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41—21no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41—21no—
64C22×#41—21no—
65C22×#41—22no—
66C22×#41—22no—
67C22×#41C2×C412yes—
68C22×#41C2×C412yes—
69C22×#41D414yes—
70C22×#41Q814yes—
71C23×Q8C2311yescharacteristic
72C23×D4—21no—
73C23×D4C2311yescharacteristic
74C24×C4—21no—
75C24×C4C2311yescharacteristic
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—22no—
93C22×M16—22no—
94C22×M16—22no—
95C22×M16—22no—
96C22×M16—21no—
97C22×M16—22no—
98C22×M16—21no—
99C22×M16—21no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16—21no—
103C22×M16—21no—
104C22×M16—22no—
105C22×M16—22no—
106C22×M16—22no—
107C22×M16C2×C412yes—
108C22×M16D412yes—
109C22×M16D412yes—
110C22×M16D414yes—
111C22×M16D412yes—
112C22×M16C2312yes—
113C22×M16C2312yes—
114C22×M16C2312yes—
115C22×M16C2312yes—
116C23×C8—21no—
117C23×C8—21no—
118C23×C8C2×C412yes—
119C23×C8D412yes—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117—22no—
132C2×#117C2×C412yes—
133C2×#117D414yes—
134C2×#117D412yes—
135C2×#117D412yes—
136C2×#117D412yes—
137C2×#117D412yes—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2×C412yes—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42—21no—
146#424—28no—
147#424—28no—
148#424—28no—
149#424—28no—
150#423—28no—
151#423—28no—
152C2×C4⋊C8—28no—
153#419—24no—
154#419—24no—
155#419—24no—
156#419—24no—
157#418—24no—
158#418—24no—
159#418—24no—
160#418—24no—
161#417—216no—
162#417—28no—
163#417—28no—
164#416—216no—
165#416—28no—
166#416—28no—
167C2×#103—24no—
168C2×#103C2×C418yescomplemented
169C2×#102—24no—
170C2×#102C2×C418yescomplemented
171#413—216no—
172#413—216no—
173C2×#101—24no—
174C2×#101—24no—
175C2×#101—24no—
176C2×#100—24no—
177C2×#100—24no—
178C2×#100—24no—
179#344—28no—
180#339—28no—
181#338—28no—
182C25—21no—
183C25#4111yescharacteristic
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—22no—
197C2×#41—22no—
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—24no—
204C2×#41—24no—
205C2×#41—24no—
206C2×#41—24no—
207C2×#41—24no—
208C2×#41—24no—
209C2×#41—24no—
210C2×#41—24no—
211C2×#41—24no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—24no—
215C2×#41—24no—
216C2×#41—24no—
217C2×#41—24no—
218C2×#41—41no—
219C2×#41—41no—
220C2×#41—41no—
221C2×#41—41no—
222C2×#41—41no—
223C2×#41—41no—
224C2×#41—41no—
225C2×#41—41no—
226C2×#41—42no—
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×#41—42no—
241C2×#41—42no—
242C2×#41—42no—
243C2×#41—42no—
244C2×#41—42no—
245C2×#41—42no—
246C2×#41C4⋊C418yes—
247C2×#41C4⋊C418yes—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—21no—
258C22×Q8—21no—
259C22×Q8C22×C412yes—
260C22×Q8C2×D412yes—
261C22×Q8C2×Q812yes—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—41no—
278C22×D4—41no—
279C22×D4—41no—
280C22×D4—41no—
281C22×D4—42no—
282C22×D4—42no—
283C22×D4C22×C412yes—
284C22×D4C2×D412yes—
285C22×D4C2×Q812yes—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4—41no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—41no—
299C23×C4C22×C411yescharacteristic
300C23×C4C22×C411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D412yes—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D412yes—
309C23×C4C2×D412yes—
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×Q812yes—
313C23×C4#4112yes—
314C23×C4#4112yes—
315C23×C4#4111yescharacteristic
316C23×C4#4111yescharacteristic
317C23×C4#4111yescharacteristic
318C23×C4#4112yes—
319C23×C4#4112yes—
320C23×C4C2411yescharacteristic
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—24no—
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—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—24no—
347C2×M16—24no—
348C2×M16—24no—
349C2×M16—24no—
350C2×M16—24no—
351C2×M16—24no—
352C2×M16—24no—
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16—42no—
367C2×M16—41no—
368C2×M16—41no—
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×M16—42no—
380C2×M16—42no—
381C2×M16—42no—
382C2×M16—42no—
383C2×M16—42no—
384C2×M16—42no—
385C2×M16—42no—
386C2×M16—42no—
387C2×M16—42no—
388C2×M16—42no—
389C2×M16—42no—
390C2×M16—42no—
391C2×M16C2×D414yes—
392C2×M16C2×D414yes—
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—24no—
396C22×C8—24no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—24no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—24no—
403C22×C8—24no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—42no—
407C22×C8—41no—
408C22×C8—41no—
409C22×C8—42no—
410C22×C8—42no—
411C22×C8C22×C414yes—
412C22×C8C2×D414yes—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117—22no—
423#117—22no—
424#117—22no—
425#117—24no—
426#117—22no—
427#117—24no—
428#117—22no—
429#117—24no—
430#117—22no—
431#117—42no—
432#117—42no—
433#117—42no—
434#117C22⋊C414yes—
435#117C22⋊C414yes—
436#117C2×D414yes—
437#117C2×D414yes—
438#117C2×D414yes—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4C22⋊C414yes—
447C2×C4⋊C4C22⋊C414yes—
448C2×C4⋊C4C22×C414yes—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—41no—
458C2×C22⋊C4—42no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—24no—
466C2×C42—22no—
467C2×C42—42no—
468C2×C42—41no—
469C4⋊C8—232no—
470#103—216no—
471#103—216no—
472#102—216no—
473#102—216no—
474#101—216no—
475#100—216no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—41no—
480C24—41no—
481C24—41no—
482C24—41no—
483C24—82no—
484C24—84no—
485C24C4×D411yescharacteristic
486C24C4×D411yescharacteristic
487C24#12111yescharacteristic
488C24#12111yescharacteristic
489C24C22⋊Q812yes—
490C24#12311yescharacteristic
491C24#12311yescharacteristic
492C24#12312yes—
493C24#12312yes—
494C24#12612yes—
495C24C2×#4111yescharacteristic
496#41—28no—
497#41—28no—
498#41—28no—
499#41—28no—
500#41—28no—
501#41—28no—
502#41—28no—
503#41—28no—
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—
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8C2×C4⋊C414yes—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4C2×C4⋊C414yes—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—42no—
627C22×C4—44no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4C2×C22⋊C411yescharacteristic
631C22×C4C2×C22⋊C411yescharacteristic
632C22×C4C2×C22⋊C411yescharacteristic
633C22×C4C2×C22⋊C411yescharacteristic
634C22×C4C2×C4⋊C412yes—
635C22×C4C2×C4⋊C412yes—
636C22×C4#11712yes—
637C22×C4#11712yes—
638C22×C4C4×D411yescharacteristic
639C22×C4C4×D411yescharacteristic
640C22×C4C4×D411yescharacteristic
641C22×C4C4×D411yescharacteristic
642C22×C4C4×D412yes—
643C22×C4C4×D412yes—
644C22×C4C4×D412yes—
645C22×C4C4×D412yes—
646C22×C4C4×D411yescharacteristic
647C22×C4C4×D411yescharacteristic
648C22×C4#12012yes—
649C22×C4#12012yes—
650C22×C4#12012yes—
651C22×C4#12012yes—
652C22×C4#12011yescharacteristic
653C22×C4#12011yescharacteristic
654C22×C4#12011yescharacteristic
655C22×C4#12011yescharacteristic
656C22×C4#12112yes—
657C22×C4#12112yes—
658C22×C4#12112yes—
659C22×C4#12112yes—
660C22×C4#12111yescharacteristic
661C22×C4#12111yescharacteristic
662C22×C4#12111yescharacteristic
663C22×C4#12111yescharacteristic
664C22×C4#12112yes—
665C22×C4#12112yes—
666C22×C4#12112yes—
667C22×C4#12112yes—
668C22×C4#12112yes—
669C22×C4#12112yes—
670C22×C4#12112yes—
671C22×C4#12112yes—
672C22×C4#12111yescharacteristic
673C22×C4#12111yescharacteristic
674C22×C4C22⋊Q812yes—
675C22×C4C22⋊Q812yes—
676C22×C4C22⋊Q812yes—
677C22×C4C22⋊Q812yes—
678C22×C4C22⋊Q812yes—
679C22×C4C22⋊Q812yes—
680C22×C4C22⋊Q812yes—
681C22×C4C22⋊Q812yes—
682C22×C4C22⋊Q812yes—
683C22×C4C22⋊Q812yes—
684C22×C4C22⋊Q812yes—
685C22×C4#12312yes—
686C22×C4#12312yes—
687C22×C4#12312yes—
688C22×C4#12312yes—
689C22×C4#12312yes—
690C22×C4#12311yescharacteristic
691C22×C4#12311yescharacteristic
692C22×C4#12312yes—
693C22×C4#12412yes—
694C22×C4#12412yes—
695C22×C4#12412yes—
696C22×C4#12412yes—
697C22×C4#12412yes—
698C22×C4#12412yes—
699C22×C4#12612yes—
700C22×C4#12612yes—
701C22×C4#12612yes—
702C22×C4#12712yes—
703C22×C4#12712yes—
704C22×C4C23×C411yescharacteristic
705C22×C4C22×D411yescharacteristic
706C22×C4C22×D411yescharacteristic
707C22×C4C22×D411yescharacteristic
708C22×C4C22×D411yescharacteristic
709C22×C4C22×D411yescharacteristic
710C22×C4C22×D411yescharacteristic
711C22×C4C22×D411yescharacteristic
712C22×C4C22×Q811yescharacteristic
713C22×C4C2×#4111yescharacteristic
714C22×C4C2×#4111yescharacteristic
715C22×C4C2×#4111yescharacteristic
716C22×C4C2×#4111yescharacteristic
717C22×C4C2×#4111yescharacteristic
718M16—24no—
719M16—24no—
720M16—24no—
721M16—24no—
722M16—42no—
723M16—42no—
724M16—42no—
725M16—42no—
726M16—42no—
727M16—42no—
728M16—42no—
729M16—42no—
730M16—42no—
731M16—42no—
732M16—42no—
733M16—42no—
734M16—44no—
735M16—44no—
736M16—44no—
737M16—44no—
738M16—44no—
739M16—44no—
740M16—44no—
741M16—44no—
742C2×C8—24no—
743C2×C8—24no—
744C2×C8—24no—
745C2×C8—24no—
746C2×C8—24no—
747C2×C8—24no—
748C2×C8—24no—
749C2×C8—24no—
750C2×C8—42no—
751C2×C8—42no—
752C2×C8—42no—
753C2×C8—42no—
754C2×C8—44no—
755C2×C8—44no—
756C2×C8—44no—
757C2×C8—44no—
758C2×C8—44no—
759C2×C8—44no—
760C2×C8—44no—
761C2×C8—44no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—42no—
767C4⋊C4—44no—
768C4⋊C4C2×C22⋊C418yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—42no—
775C22⋊C4—44no—
776C42—24no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—24no—
781C42—42no—
782C42—44no—
783C23—24no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—82no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23#38512yes—
809C23#38512yes—
810C23#38611yescharacteristic
811C23#38611yescharacteristic
812C23#38611yescharacteristic
813C23#38611yescharacteristic
814C23#38812yes—
815C23#38812yes—
816C23#39412yes—
817C23#39412yes—
818C23#39612yes—
819C23#39612yes—
820C23#39712yes—
821C23#39712yes—
822C23#39912yes—
823C23#39912yes—
824C23C2×C4×D411yescharacteristic
825C23C2×#12111yescharacteristic
826C23C2×C22⋊Q811yescharacteristic
827C23C2×#12311yescharacteristic
828C23C2×#12311yescharacteristic
829C23C2×#12311yescharacteristic
830C23C2×#12611yescharacteristic
831Q8—24no—
832Q8—24no—
833Q8—42no—
834Q8—42no—
835Q8—42no—
836Q8—42no—
837Q8—42no—
838Q8—42no—
839D4—24no—
840D4—24no—
841D4—48no—
842D4—48no—
843D4—48no—
844D4—48no—
845D4—42no—
846D4—42no—
847D4—42no—
848D4—42no—
849D4—42no—
850D4—42no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—48no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—48no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—48no—
864C2×C4—44no—
865C2×C4—84no—
866C2×C4—84no—
867C2×C4—84no—
868C2×C4—88no—
869C2×C4#38012yes—
870C2×C4#38012yes—
871C2×C4#38012yes—
872C2×C4#38012yes—
873C2×C4#38512yes—
874C2×C4#38512yes—
875C2×C4#38512yes—
876C2×C4#38512yes—
877C2×C4#38512yes—
878C2×C4#38512yes—
879C2×C4#38611yescharacteristic
880C2×C4#38611yescharacteristic
881C2×C4#38611yescharacteristic
882C2×C4#38611yescharacteristic
883C2×C4#38812yes—
884C2×C4#38812yes—
885C2×C4#38812yes—
886C2×C4#38812yes—
887C2×C4#38812yes—
888C2×C4#38812yes—
889C2×C4#39012yes—
890C2×C4#39012yes—
891C2×C4#39012yes—
892C2×C4#39012yes—
893C2×C4#39212yes—
894C2×C4#39212yes—
895C2×C4#39212yes—
896C2×C4#39212yes—
897C2×C4#39312yes—
898C2×C4#39312yes—
899C2×C4#39312yes—
900C2×C4#39312yes—
901C2×C4#39412yes—
902C2×C4#39412yes—
903C2×C4#39412yes—
904C2×C4#39412yes—
905C2×C4#39412yes—
906C2×C4#39412yes—
907C2×C4#39612yes—
908C2×C4#39612yes—
909C2×C4#39612yes—
910C2×C4#39612yes—
911C2×C4#39612yes—
912C2×C4#39612yes—
913C2×C4#39712yes—
914C2×C4#39712yes—
915C2×C4#39912yes—
916C2×C4#39912yes—
917C2×C4C22×C22⋊C411yescharacteristic
918C2×C4C22×C4⋊C411yescharacteristic
919C2×C4C2×#11711yescharacteristic
920C2×C4C2×C4×D411yescharacteristic
921C2×C4C2×C4×D411yescharacteristic
922C2×C4C2×C4×D411yescharacteristic
923C2×C4C2×#12011yescharacteristic
924C2×C4C2×#12011yescharacteristic
925C2×C4C2×#12011yescharacteristic
926C2×C4C2×#12111yescharacteristic
927C2×C4C2×#12111yescharacteristic
928C2×C4C2×#12111yescharacteristic
929C2×C4C2×#12111yescharacteristic
930C2×C4C2×#12111yescharacteristic
931C2×C4C2×#12111yescharacteristic
932C2×C4C2×#12111yescharacteristic
933C2×C4C2×C22⋊Q811yescharacteristic
934C2×C4C2×C22⋊Q811yescharacteristic
935C2×C4C2×C22⋊Q811yescharacteristic
936C2×C4C2×C22⋊Q811yescharacteristic
937C2×C4C2×C22⋊Q811yescharacteristic
938C2×C4C2×#12311yescharacteristic
939C2×C4C2×#12311yescharacteristic
940C2×C4C2×#12411yescharacteristic
941C2×C4C2×#12411yescharacteristic
942C2×C4C2×#12411yescharacteristic
943C2×C4C2×#12611yescharacteristic
944C2×C4C2×#12711yescharacteristic
945C8—44no—
946C8—44no—
947C8—44no—
948C8—44no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—44no—
973C22—84no—
974C22—84no—
975C22—84no—
976C22—84no—
977C22—84no—
978C22—84no—
979C22—84no—
980C22#143912yes—
981C22#143912yes—
982C22#143912yes—
983C22#143912yes—
984C22C2×#38511yescharacteristic
985C22C2×#38611yescharacteristic
986C22C2×#38811yescharacteristic
987C22C2×#39411yescharacteristic
988C22C2×#39611yescharacteristic
989C22C2×#39711yescharacteristic
990C22C2×#39911yescharacteristic
991C4—48no—
992C4—44no—
993C4—84no—
994C4#143912yes—
995C4#143912yes—
996C4#143912yes—
997C4#143912yes—
998C4C2×#38011yescharacteristic
999C4C2×#38511yescharacteristic
1000C4C2×#38811yescharacteristic
1001C4C2×#39011yescharacteristic
1002C4C2×#39211yescharacteristic
1003C4C2×#39311yescharacteristic
1004C4C2×#39411yescharacteristic
1005C4C2×#39611yescharacteristic
1006C2—21no—
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—21no—
1011C2—21no—
1012C2—22no—
1013C2—22no—
1014C2—22no—
1015C2—22no—
1016C2—84no—
1017C2C2×#143911yescharacteristic
1018C2#2099512yes—
subgroupG/H
centerC2×C4#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#386
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×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. C2×#1733C2semidirect
7. C22×#338C2semidirect
8. #11059C2semidirect
9. #11058C2semidirect
31. C2×#417C4semidirect
37. C2×#416C4semidirect
168. C2×#103C2×C4semidirect
170. C2×#102C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29052
C2×#28962
C22×#4132
C22×#3442
C2×#17332
C22×#3382
#110592
#110582