Finite Group Databasebeta

← #357941

Subgroups — #357941

Order 512.

2506 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C2×#2896C211yesmaximal, characteristic
3C2×#2879C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1742C211yesmaximal, characteristic, complemented
6#20347C211yesmaximal, characteristic, complemented
7C22×#338C211yesmaximal, characteristic, complemented
8#11185C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C2×#421—22no—
17C2×#421—24no—
18C2×#421—24no—
19C2×#421C2214yes—
20C22×#104—22no—
21#2896—22no—
22#2896—22no—
23#2896—22no—
24#2896—22no—
25C2×#417C2214yes—
26C2×#419C412yescomplemented
27C2×#418C412yescomplemented
28C2×#416C414yescomplemented
29#2879—22no—
30#2879—22no—
31#2879—22no—
32#2879C2214yes—
33C2×#408—22no—
34C2×#408—22no—
35C2×#407—22no—
36C2×#344—24no—
37C2×#344C2214yescomplemented
38#1742—22no—
39#1742—22no—
40C2×#343C2214yescomplemented
41#1736—22no—
42#1736C2214yescomplemented
43#1735—22no—
44C2×#338—24no—
45C2×#338C2214yescomplemented
46C22×#41—21no—
47C22×#41—21no—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—21no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41C2×C412yes—
61C22×#41D412yes—
62C22×#41D412yes—
63C22×#41D412yes—
64C22×#41D412yes—
65C22×#41C2312yes—
66C23×Q8C2×C411yescharacteristic
67C23×D4—21no—
68C23×D4C2×C411yescharacteristic
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—21no—
92C22×M16—21no—
93C22×M16—21no—
94C22×M16—22no—
95C22×M16—21no—
96C22×M16—21no—
97C22×M16—22no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16C2×C412yes—
103C22×M16D412yes—
104C22×M16D412yes—
105C22×M16D414yes—
106C22×M16D412yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C22×M16C2312yes—
111C23×C8—21no—
112C23×C8—21no—
113C23×C8C2×C412yes—
114C23×C8D412yes—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—22no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—22no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—22no—
131C2×#117C2×C412yes—
132C2×#117C2×C412yes—
133C2×#117D414yes—
134C2×#117C2312yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—21no—
140C22×C42—21no—
141#421—216no—
142#421—28no—
143#421—28no—
144C2×#104—216no—
145C2×#104—28no—
146#419—24no—
147#419—24no—
148#418—24no—
149#418—24no—
150#417—28no—
151#417—28no—
152#416—28no—
153#416—28no—
154C2×#103C2×C418yescomplemented
155C2×#102C2×C418yescomplemented
156#408—28no—
157#408—28no—
158#408—28no—
159#408—28no—
160#407—28no—
161#407—28no—
162C2×C22⋊C8—28no—
163#344—28no—
164#343—28no—
165#340—28no—
166#338—28no—
167C25—21no—
168C25#4111yescharacteristic
169C2×#41—22no—
170C2×#41—22no—
171C2×#41—22no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—22no—
175C2×#41—22no—
176C2×#41—22no—
177C2×#41—22no—
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—24no—
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—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—22no—
202C2×#41—22no—
203C2×#41—22no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—22no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41—42no—
212C2×#41—42no—
213C2×#41—42no—
214C2×#41—42no—
215C2×#41—42no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41—42no—
220C2×#41—42no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—42no—
226C2×#41—42no—
227C2×#41—42no—
228C2×#41—42no—
229C2×#41—42no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41C22⋊C414yes—
234C2×#41C22⋊C414yes—
235C2×#41C2×D414yes—
236C2×#41C2×D414yes—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8C22⋊C412yes—
245C22×Q8C22⋊C412yes—
246C22×Q8C22×C412yes—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4C22⋊C412yes—
265C22×D4C22⋊C412yes—
266C22×D4C22×C412yes—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—41no—
280C23×C4C22×C411yescharacteristic
281C23×C4C22×C411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4#4112yes—
293C23×C4#4112yes—
294C23×C4#4112yes—
295C23×C4#4112yes—
296C23×C4#4111yescharacteristic
297C23×C4#4112yes—
298C23×C4#4112yes—
299C23×C4#4111yescharacteristic
300C23×C4#4111yescharacteristic
301C23×C4C2411yescharacteristic
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
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—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
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—42no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—41no—
347C2×M16—41no—
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×M16—42no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16—42no—
367C2×M16—42no—
368C2×M16—42no—
369C2×M16—42no—
370C2×M16—42no—
371C2×M16—42no—
372C2×M16C2×D414yes—
373C2×M16C2×D414yes—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—24no—
377C22×C8—24no—
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—24no—
383C22×C8—24no—
384C22×C8—24no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—42no—
388C22×C8—41no—
389C22×C8—41no—
390C22×C8—42no—
391C22×C8—42no—
392C22×C8C22×C414yes—
393C22×C8C2×D414yes—
394#117—24no—
395#117—22no—
396#117—24no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—24no—
407#117—22no—
408#117—41no—
409#117—41no—
410#117—41no—
411#117—41no—
412#117—41no—
413#117—41no—
414#117—41no—
415#117—41no—
416#117—42no—
417#117—42no—
418#117—42no—
419#117C2×D414yes—
420C2×C4⋊C4—24no—
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—42no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4C22×C414yes—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—41no—
435C2×C22⋊C4—41no—
436C2×C22⋊C4—41no—
437C2×C22⋊C4—41no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—42no—
440C2×C42—24no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42—41no—
447C2×C42—42no—
448C2×C42—41no—
449C2×C42—41no—
450#104—232no—
451#103—216no—
452#102—216no—
453C22⋊C8—232no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—42no—
458C24—42no—
459C24—82no—
460C24—84no—
461C24C4×D411yescharacteristic
462C24C4×D411yescharacteristic
463C24#12111yescharacteristic
464C24#12111yescharacteristic
465C24#12311yescharacteristic
466C24#12311yescharacteristic
467C24#12312yes—
468C24#12412yes—
469C24#12612yes—
470C24#12612yes—
471C24C2×#4111yescharacteristic
472#41—24no—
473#41—24no—
474#41—24no—
475#41—24no—
476#41—24no—
477#41—24no—
478#41—24no—
479#41—24no—
480#41—28no—
481#41—28no—
482#41—28no—
483#41—28no—
484#41—42no—
485#41—42no—
486#41—42no—
487#41—42no—
488#41—42no—
489#41—42no—
490#41—42no—
491#41—42no—
492#41—44no—
493#41—44no—
494#41—44no—
495#41—44no—
496#41—44no—
497#41—44no—
498#41—44no—
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—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—24no—
520C2×Q8—24no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8C2×C22⋊C414yes—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4C2×C22⋊C414yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4C2×C22⋊C411yescharacteristic
597C22×C4C2×C22⋊C411yescharacteristic
598C22×C4C2×C22⋊C411yescharacteristic
599C22×C4C2×C22⋊C411yescharacteristic
600C22×C4#11712yes—
601C22×C4#11712yes—
602C22×C4#11712yes—
603C22×C4#11712yes—
604C22×C4C4×D412yes—
605C22×C4C4×D412yes—
606C22×C4C4×D412yes—
607C22×C4C4×D412yes—
608C22×C4C4×D411yescharacteristic
609C22×C4C4×D411yescharacteristic
610C22×C4C4×D411yescharacteristic
611C22×C4C4×D411yescharacteristic
612C22×C4C4×D411yescharacteristic
613C22×C4C4×D411yescharacteristic
614C22×C4#12012yes—
615C22×C4#12012yes—
616C22×C4#12011yescharacteristic
617C22×C4#12011yescharacteristic
618C22×C4#12011yescharacteristic
619C22×C4#12011yescharacteristic
620C22×C4#12112yes—
621C22×C4#12112yes—
622C22×C4#12112yes—
623C22×C4#12112yes—
624C22×C4#12111yescharacteristic
625C22×C4#12111yescharacteristic
626C22×C4#12111yescharacteristic
627C22×C4#12111yescharacteristic
628C22×C4#12112yes—
629C22×C4#12112yes—
630C22×C4#12112yes—
631C22×C4#12112yes—
632C22×C4#12112yes—
633C22×C4#12112yes—
634C22×C4#12112yes—
635C22×C4#12112yes—
636C22×C4#12111yescharacteristic
637C22×C4#12111yescharacteristic
638C22×C4#12312yes—
639C22×C4#12312yes—
640C22×C4#12312yes—
641C22×C4#12312yes—
642C22×C4#12312yes—
643C22×C4#12312yes—
644C22×C4#12312yes—
645C22×C4#12312yes—
646C22×C4#12312yes—
647C22×C4#12312yes—
648C22×C4#12312yes—
649C22×C4#12312yes—
650C22×C4#12312yes—
651C22×C4#12312yes—
652C22×C4#12312yes—
653C22×C4#12312yes—
654C22×C4#12311yescharacteristic
655C22×C4#12311yescharacteristic
656C22×C4#12312yes—
657C22×C4#12412yes—
658C22×C4#12412yes—
659C22×C4#12412yes—
660C22×C4#12412yes—
661C22×C4#12412yes—
662C22×C4#12412yes—
663C22×C4#12412yes—
664C22×C4#12612yes—
665C22×C4#12612yes—
666C22×C4#12612yes—
667C22×C4#12612yes—
668C22×C4#12612yes—
669C22×C4#12612yes—
670C22×C4C23×C411yescharacteristic
671C22×C4C22×D411yescharacteristic
672C22×C4C22×D411yescharacteristic
673C22×C4C22×D411yescharacteristic
674C22×C4C22×D411yescharacteristic
675C22×C4C22×D411yescharacteristic
676C22×C4C22×D411yescharacteristic
677C22×C4C2×#4111yescharacteristic
678C22×C4C2×#4111yescharacteristic
679C22×C4C2×#4111yescharacteristic
680C22×C4C2×#4111yescharacteristic
681C22×C4C2×#4111yescharacteristic
682C22×C4C2×#4111yescharacteristic
683C22×C4C2×#4111yescharacteristic
684M16—24no—
685M16—24no—
686M16—24no—
687M16—24no—
688M16—42no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16—42no—
694M16—42no—
695M16—42no—
696M16—42no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16—44no—
701M16—44no—
702M16—44no—
703M16—44no—
704M16—44no—
705M16—44no—
706M16—44no—
707M16—44no—
708C2×C8—24no—
709C2×C8—24no—
710C2×C8—24no—
711C2×C8—24no—
712C2×C8—24no—
713C2×C8—24no—
714C2×C8—24no—
715C2×C8—24no—
716C2×C8—42no—
717C2×C8—42no—
718C2×C8—42no—
719C2×C8—42no—
720C2×C8—44no—
721C2×C8—44no—
722C2×C8—44no—
723C2×C8—44no—
724C2×C8—44no—
725C2×C8—44no—
726C2×C8—44no—
727C2×C8—44no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—44no—
735C22⋊C4—24no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—44no—
742C42—24no—
743C42—42no—
744C42—42no—
745C42—42no—
746C42—42no—
747C42—42no—
748C42—44no—
749C23—24no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—48no—
758C23—44no—
759C23—44no—
760C23—42no—
761C23—42no—
762C23—84no—
763C23—84no—
764C23—82no—
765C23—82no—
766C23—82no—
767C23—82no—
768C23—88no—
769C23—88no—
770C23#38611yescharacteristic
771C23#38611yescharacteristic
772C23#38611yescharacteristic
773C23#38611yescharacteristic
774C23#38812yes—
775C23#38812yes—
776C23#38812yes—
777C23#38812yes—
778C23#39412yes—
779C23#39412yes—
780C23#39712yes—
781C23#39712yes—
782C23#39712yes—
783C23#39712yes—
784C23#39712yes—
785C23#39712yes—
786C23C2×C4×D411yescharacteristic
787C23C2×#12111yescharacteristic
788C23C2×#12311yescharacteristic
789C23C2×#12311yescharacteristic
790C23C2×#12411yescharacteristic
791C23C2×#12611yescharacteristic
792C23C2×#12611yescharacteristic
793Q8—24no—
794Q8—24no—
795Q8—44no—
796Q8—44no—
797Q8—42no—
798Q8—42no—
799D4—24no—
800D4—24no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—44no—
805D4—48no—
806D4—48no—
807D4—44no—
808D4—44no—
809D4—42no—
810D4—42no—
811C2×C4—24no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—84no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—88no—
828C2×C4—84no—
829C2×C4#38112yes—
830C2×C4#38112yes—
831C2×C4#38112yes—
832C2×C4#38112yes—
833C2×C4#38611yescharacteristic
834C2×C4#38611yescharacteristic
835C2×C4#38611yescharacteristic
836C2×C4#38612yes—
837C2×C4#38612yes—
838C2×C4#38612yes—
839C2×C4#38612yes—
840C2×C4#38611yescharacteristic
841C2×C4#38812yes—
842C2×C4#38812yes—
843C2×C4#38812yes—
844C2×C4#38812yes—
845C2×C4#38812yes—
846C2×C4#38812yes—
847C2×C4#38812yes—
848C2×C4#38812yes—
849C2×C4#38812yes—
850C2×C4#38812yes—
851C2×C4#38812yes—
852C2×C4#38812yes—
853C2×C4#39412yes—
854C2×C4#39412yes—
855C2×C4#39412yes—
856C2×C4#39412yes—
857C2×C4#39412yes—
858C2×C4#39412yes—
859C2×C4#39412yes—
860C2×C4#39412yes—
861C2×C4#39412yes—
862C2×C4#39412yes—
863C2×C4#39412yes—
864C2×C4#39412yes—
865C2×C4#39412yes—
866C2×C4#39412yes—
867C2×C4#39712yes—
868C2×C4#39712yes—
869C2×C4#39712yes—
870C2×C4#39712yes—
871C2×C4#39712yes—
872C2×C4#39712yes—
873C2×C4#39712yes—
874C2×C4#39712yes—
875C2×C4#39712yes—
876C2×C4#39712yes—
877C2×C4C22×C22⋊C411yescharacteristic
878C2×C4C2×#11711yescharacteristic
879C2×C4C2×#11711yescharacteristic
880C2×C4C2×C4×D411yescharacteristic
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C2×C4×D411yescharacteristic
883C2×C4C2×#12011yescharacteristic
884C2×C4C2×#12011yescharacteristic
885C2×C4C2×#12111yescharacteristic
886C2×C4C2×#12111yescharacteristic
887C2×C4C2×#12111yescharacteristic
888C2×C4C2×#12111yescharacteristic
889C2×C4C2×#12111yescharacteristic
890C2×C4C2×#12111yescharacteristic
891C2×C4C2×#12111yescharacteristic
892C2×C4C2×#12311yescharacteristic
893C2×C4C2×#12311yescharacteristic
894C2×C4C2×#12311yescharacteristic
895C2×C4C2×#12311yescharacteristic
896C2×C4C2×#12311yescharacteristic
897C2×C4C2×#12311yescharacteristic
898C2×C4C2×#12311yescharacteristic
899C2×C4C2×#12311yescharacteristic
900C2×C4C2×#12411yescharacteristic
901C2×C4C2×#12411yescharacteristic
902C2×C4C2×#12411yescharacteristic
903C2×C4C2×#12611yescharacteristic
904C2×C4C2×#12611yescharacteristic
905C8—44no—
906C8—44no—
907C8—44no—
908C8—44no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—48no—
933C22—44no—
934C22—88no—
935C22—88no—
936C22—84no—
937C22—84no—
938C22#144012yes—
939C22#144012yes—
940C22#144012yes—
941C22#144012yes—
942C22C2×#38611yescharacteristic
943C22C2×#38811yescharacteristic
944C22C2×#38811yescharacteristic
945C22C2×#39411yescharacteristic
946C22C2×#39711yescharacteristic
947C22C2×#39711yescharacteristic
948C22C2×#39711yescharacteristic
949C4—44no—
950C4—84no—
951C4—84no—
952C4#144012yes—
953C4#144012yes—
954C4#144012yes—
955C4#144012yes—
956C4C2×#38111yescharacteristic
957C4C2×#38611yescharacteristic
958C4C2×#38811yescharacteristic
959C4C2×#38811yescharacteristic
960C4C2×#39411yescharacteristic
961C4C2×#39411yescharacteristic
962C4C2×#39411yescharacteristic
963C4C2×#39711yescharacteristic
964C2—21no—
965C2—22no—
966C2—22no—
967C2—21no—
968C2—21no—
969C2—21no—
970C2—21no—
971C2—21no—
972C2—22no—
973C2—22no—
974C2—84no—
975C2C2×#144011yescharacteristic
976C2#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
4. C22×#344C2semidirect
5. C2×#1742C2semidirect
6. #20347C2semidirect
7. C22×#338C2semidirect
8. #11185C2semidirect
26. C2×#419C4semidirect
27. C2×#418C4semidirect
28. C2×#416C4semidirect
37. C2×#344C22semidirect
40. C2×#343C22semidirect
42. #1736C22semidirect
45. C2×#338C22semidirect
154. C2×#103C2×C4semidirect
155. C2×#102C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4212
C2×#28962
C2×#28792
C22×#3442
C2×#17422
#203472
C22×#3382
#111852