Finite Group Databasebeta

← #357754

Subgroups — #357754

Order 512.

2670 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C22×#421C211yesmaximal, characteristic
4C2×#2879C211yesmaximal, characteristic
5C2×#1738C211yesmaximal, characteristic, complemented
6C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
7#20335C211yesmaximal, characteristic, complemented
8#11084C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2905—24no—
17#2905—24no—
18C2×#424—22no—
19C2×#424C2214yescomplemented
20C2×#423—22no—
21C2×#421—24no—
22C2×#421—24no—
23C2×#421—24no—
24C2×#421—22no—
25C2×#421—22no—
26C2×#421C418yescomplemented
27C2×#421C2214yes—
28C2×#421C2214yes—
29C22×#104—22no—
30C22×#104—22no—
31#2879—24no—
32#2879—24no—
33C2×#408—22no—
34C2×#408C2214yes—
35C2×#407—22no—
36#1738—22no—
37#1738C2214yescomplemented
38C2×#341—22no—
39C2×H(3,ℤ/4)—24no—
40C2×H(3,ℤ/4)C2214yescomplemented
41#1729—22no—
42#1729C2214yescomplemented
43#1728—22no—
44C22×#41—21no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—21no—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41C2×C414yes—
61C22×#41D414yes—
62C22×#41Q812yes—
63C22×#41C2312yes—
64C23×Q8Q811yescharacteristic
65C23×D4—21no—
66C23×D4Q811yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—22no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—22no—
93C22×M16—22no—
94C22×M16—21no—
95C22×M16—21no—
96C22×M16—21no—
97C22×M16—21no—
98C22×M16—21no—
99C22×M16—21no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16C2×C414yes—
103C22×M16D414yes—
104C22×M16D412yes—
105C22×M16D414yes—
106C22×M16C2312yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C23×C8—21no—
110C23×C8—21no—
111C23×C8D412yes—
112C23×C8C2312yes—
113C2×#117—22no—
114C2×#117—22no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—22no—
120C2×#117—22no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117C2×C414yes—
124C2×#117D414yes—
125C2×#117D412yes—
126C2×#117D412yes—
127C2×#117C2312yes—
128C2×#117C2312yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C42D412yes—
134C22×C42D412yes—
135#424—216no—
136#424—28no—
137#424—28no—
138#423—216no—
139C2×C4⋊C8—28no—
140#421—216no—
141#421—28no—
142#421—28no—
143#421—216no—
144#421—28no—
145#421C2×C4116yescomplemented
146C2×#104—216no—
147C2×#104—216no—
148C2×#104—28no—
149C2×#104—28no—
150#408—216no—
151#408—28no—
152#408—28no—
153#407—216no—
154C2×C22⋊C8—28no—
155#341—28no—
156H(3,ℤ/4)—28no—
157#336—28no—
158C25—21no—
159C25#4111yescharacteristic
160C2×#41—24no—
161C2×#41—24no—
162C2×#41—24no—
163C2×#41—24no—
164C2×#41—24no—
165C2×#41—22no—
166C2×#41—22no—
167C2×#41—24no—
168C2×#41—24no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41—24no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—24no—
175C2×#41—24no—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—24no—
179C2×#41—24no—
180C2×#41—24no—
181C2×#41—24no—
182C2×#41—24no—
183C2×#41—22no—
184C2×#41—22no—
185C2×#41—22no—
186C2×#41—22no—
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—22no—
190C2×#41—22no—
191C2×#41—22no—
192C2×#41—22no—
193C2×#41—22no—
194C2×#41—22no—
195C2×#41—22no—
196C2×#41—22no—
197C2×#41—42no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41—42no—
202C2×#41—42no—
203C2×#41—42no—
204C2×#41—42no—
205C2×#41—42no—
206C2×#41—42no—
207C2×#41—42no—
208C2×#41—41no—
209C2×#41—41no—
210C2×#41—41no—
211C2×#41—41no—
212C2×#41—41no—
213C2×#41—41no—
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—41no—
224C2×#41—41no—
225C2×#41C4⋊C418yes—
226C2×#41C22×C414yes—
227C2×#41C2×D414yes—
228C22×Q8—21no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8C4⋊C414yes—
237C22×Q8C2×Q812yes—
238C22×D4—24no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—21no—
250C22×D4—42no—
251C22×D4—41no—
252C22×D4—41no—
253C22×D4—41no—
254C22×D4—41no—
255C22×D4—42no—
256C22×D4C4⋊C414yes—
257C22×D4C2×Q812yes—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—41no—
268C23×C4—41no—
269C23×C4—41no—
270C23×C4—41no—
271C23×C4C22×C412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D412yes—
282C23×C4C2×Q811yescharacteristic
283C23×C4C2×Q811yescharacteristic
284C23×C4#4112yes—
285C23×C4#4111yescharacteristic
286C23×C4#4111yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4#4111yescharacteristic
289C23×C4#4111yescharacteristic
290C23×C4#4112yes—
291C23×C4#4112yes—
292C23×C4C2411yescharacteristic
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—42no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16—42no—
338C2×M16—42no—
339C2×M16—42no—
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—41no—
354C2×M16—41no—
355C2×M16—41no—
356C2×M16—41no—
357C2×M16—41no—
358C2×M16—41no—
359C2×M16—41no—
360C2×M16—41no—
361C2×M16C22×C414yes—
362C2×M16C2×D414yes—
363C22×C8—24no—
364C22×C8—24no—
365C22×C8—24no—
366C22×C8—24no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—42no—
378C22×C8—42no—
379C22×C8—41no—
380C22×C8—41no—
381C22×C8—41no—
382C22×C8—41no—
383C22×C8C2×D414yes—
384C22×C8C2×D414yes—
385#117—24no—
386#117—24no—
387#117—24no—
388#117—24no—
389#117—24no—
390#117—22no—
391#117—22no—
392#117—24no—
393#117—24no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—42no—
399#117—42no—
400#117—42no—
401#117—42no—
402#117C22⋊C418yes—
403#117C22×C414yes—
404#117C2×D414yes—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42C22⋊C418yes—
427C2×C42C2×D414yes—
428C2×C42C2×D414yes—
429C4⋊C8—232no—
430#104—232no—
431#104—232no—
432C22⋊C8—232no—
433C24—22no—
434C24—24no—
435C24—42no—
436C24—41no—
437C24—41no—
438C24—82no—
439C24—84no—
440C24C4×D412yes—
441C24#12112yes—
442C24C22⋊Q811yescharacteristic
443C24C22⋊Q811yescharacteristic
444C24#12311yescharacteristic
445C24#12311yescharacteristic
446C24#12311yescharacteristic
447C24#12311yescharacteristic
448C24#12312yes—
449C24#12612yes—
450C24C2×#4111yescharacteristic
451#41—24no—
452#41—24no—
453#41—24no—
454#41—24no—
455#41—24no—
456#41—24no—
457#41—24no—
458#41—24no—
459#41—28no—
460#41—28no—
461#41—28no—
462#41—28no—
463#41—42no—
464#41—42no—
465#41—42no—
466#41—42no—
467#41—42no—
468#41—42no—
469#41—42no—
470#41—42no—
471#41—44no—
472#41—44no—
473#41—44no—
474#41—44no—
475#41—44no—
476#41—44no—
477#41—44no—
478#41—44no—
479#41—44no—
480#41—44no—
481#41—44no—
482#41—44no—
483#41—44no—
484#41—44no—
485#41—44no—
486#41—44no—
487#41—44no—
488#41—44no—
489#41—44no—
490#41—44no—
491C2×Q8—22no—
492C2×Q8—24no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C2×C4⋊C414yes—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—28no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4C2×C4⋊C414yes—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—28no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—28no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—44no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4C2×C22⋊C412yes—
575C22×C4C2×C22⋊C412yes—
576C22×C4C2×C4⋊C412yes—
577C22×C4C2×C4⋊C412yes—
578C22×C4#11712yes—
579C22×C4#11712yes—
580C22×C4C4×D412yes—
581C22×C4C4×D412yes—
582C22×C4C4×D412yes—
583C22×C4C4×D412yes—
584C22×C4C4×D412yes—
585C22×C4C4×D412yes—
586C22×C4C4×D412yes—
587C22×C4#12012yes—
588C22×C4#12012yes—
589C22×C4#12012yes—
590C22×C4#12012yes—
591C22×C4#12012yes—
592C22×C4#12012yes—
593C22×C4#12112yes—
594C22×C4#12112yes—
595C22×C4#12112yes—
596C22×C4#12112yes—
597C22×C4#12112yes—
598C22×C4#12112yes—
599C22×C4#12112yes—
600C22×C4#12112yes—
601C22×C4#12112yes—
602C22×C4#12112yes—
603C22×C4#12112yes—
604C22×C4#12112yes—
605C22×C4#12112yes—
606C22×C4#12112yes—
607C22×C4#12112yes—
608C22×C4C22⋊Q811yescharacteristic
609C22×C4C22⋊Q811yescharacteristic
610C22×C4C22⋊Q811yescharacteristic
611C22×C4C22⋊Q811yescharacteristic
612C22×C4C22⋊Q812yes—
613C22×C4C22⋊Q812yes—
614C22×C4C22⋊Q812yes—
615C22×C4C22⋊Q812yes—
616C22×C4C22⋊Q811yescharacteristic
617C22×C4C22⋊Q811yescharacteristic
618C22×C4C22⋊Q811yescharacteristic
619C22×C4C22⋊Q811yescharacteristic
620C22×C4C22⋊Q812yes—
621C22×C4C22⋊Q812yes—
622C22×C4C22⋊Q811yescharacteristic
623C22×C4C22⋊Q811yescharacteristic
624C22×C4#12312yes—
625C22×C4#12312yes—
626C22×C4#12311yescharacteristic
627C22×C4#12311yescharacteristic
628C22×C4#12311yescharacteristic
629C22×C4#12311yescharacteristic
630C22×C4#12312yes—
631C22×C4#12311yescharacteristic
632C22×C4#12311yescharacteristic
633C22×C4#12311yescharacteristic
634C22×C4#12311yescharacteristic
635C22×C4#12412yes—
636C22×C4#12412yes—
637C22×C4#12412yes—
638C22×C4#12412yes—
639C22×C4#12412yes—
640C22×C4#12412yes—
641C22×C4#12612yes—
642C22×C4#12612yes—
643C22×C4#12612yes—
644C22×C4#12711yescharacteristic
645C22×C4#12711yescharacteristic
646C22×C4#12711yescharacteristic
647C22×C4#12711yescharacteristic
648C22×C4C23×C411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×Q811yescharacteristic
657C22×C4C2×#4111yescharacteristic
658C22×C4C2×#4111yescharacteristic
659C22×C4C2×#4111yescharacteristic
660C22×C4C2×#4111yescharacteristic
661C22×C4C2×#4111yescharacteristic
662M16—24no—
663M16—24no—
664M16—24no—
665M16—24no—
666M16—42no—
667M16—42no—
668M16—42no—
669M16—42no—
670M16—42no—
671M16—42no—
672M16—42no—
673M16—42no—
674M16—44no—
675M16—44no—
676M16—44no—
677M16—44no—
678M16—44no—
679M16—44no—
680M16—44no—
681M16—44no—
682M16—44no—
683M16—44no—
684C2×C8—24no—
685C2×C8—24no—
686C2×C8—24no—
687C2×C8—24no—
688C2×C8—24no—
689C2×C8—24no—
690C2×C8—24no—
691C2×C8—24no—
692C2×C8—42no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—42no—
697C2×C8—42no—
698C2×C8—42no—
699C2×C8—42no—
700C2×C8—44no—
701C2×C8—44no—
702C2×C8—44no—
703C2×C8—44no—
704C2×C8—44no—
705C2×C8—44no—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—28no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—44no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—28no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—44no—
718C42—24no—
719C42—28no—
720C42—24no—
721C42—24no—
722C42—44no—
723C42C2×C22⋊C418yes—
724C23—24no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—48no—
733C23—42no—
734C23—42no—
735C23—44no—
736C23—44no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23—88no—
744C23—88no—
745C23#38512yes—
746C23#38512yes—
747C23#38612yes—
748C23#38612yes—
749C23#38812yes—
750C23#38812yes—
751C23#39412yes—
752C23#39412yes—
753C23#39612yes—
754C23#39612yes—
755C23#39712yes—
756C23#39712yes—
757C23#39911yescharacteristic
758C23#39911yescharacteristic
759C23#39911yescharacteristic
760C23#39911yescharacteristic
761C23C2×C4×D411yescharacteristic
762C23C2×#12111yescharacteristic
763C23C2×C22⋊Q811yescharacteristic
764C23C2×#12311yescharacteristic
765C23C2×#12311yescharacteristic
766C23C2×#12311yescharacteristic
767C23C2×#12611yescharacteristic
768Q8—24no—
769Q8—24no—
770Q8—42no—
771Q8—42no—
772Q8—44no—
773Q8—44no—
774D4—24no—
775D4—24no—
776D4—44no—
777D4—44no—
778D4—48no—
779D4—48no—
780D4—44no—
781D4—44no—
782D4—42no—
783D4—42no—
784D4—44no—
785D4—44no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—44no—
801C2×C4—88no—
802C2×C4—88no—
803C2×C4#38012yes—
804C2×C4#38012yes—
805C2×C4#38012yes—
806C2×C4#38012yes—
807C2×C4#38512yes—
808C2×C4#38512yes—
809C2×C4#38512yes—
810C2×C4#38512yes—
811C2×C4#38512yes—
812C2×C4#38512yes—
813C2×C4#38612yes—
814C2×C4#38612yes—
815C2×C4#38812yes—
816C2×C4#38812yes—
817C2×C4#38812yes—
818C2×C4#38812yes—
819C2×C4#38812yes—
820C2×C4#38812yes—
821C2×C4#39012yes—
822C2×C4#39012yes—
823C2×C4#39012yes—
824C2×C4#39012yes—
825C2×C4#39212yes—
826C2×C4#39212yes—
827C2×C4#39212yes—
828C2×C4#39212yes—
829C2×C4#39312yes—
830C2×C4#39312yes—
831C2×C4#39312yes—
832C2×C4#39312yes—
833C2×C4#39412yes—
834C2×C4#39412yes—
835C2×C4#39412yes—
836C2×C4#39412yes—
837C2×C4#39412yes—
838C2×C4#39412yes—
839C2×C4#39612yes—
840C2×C4#39612yes—
841C2×C4#39612yes—
842C2×C4#39612yes—
843C2×C4#39612yes—
844C2×C4#39612yes—
845C2×C4#39712yes—
846C2×C4#39712yes—
847C2×C4#39911yescharacteristic
848C2×C4#39911yescharacteristic
849C2×C4#39911yescharacteristic
850C2×C4#39911yescharacteristic
851C2×C4C22×C22⋊C411yescharacteristic
852C2×C4C22×C4⋊C411yescharacteristic
853C2×C4C2×#11711yescharacteristic
854C2×C4C2×C4×D411yescharacteristic
855C2×C4C2×C4×D411yescharacteristic
856C2×C4C2×C4×D411yescharacteristic
857C2×C4C2×#12011yescharacteristic
858C2×C4C2×#12011yescharacteristic
859C2×C4C2×#12011yescharacteristic
860C2×C4C2×#12111yescharacteristic
861C2×C4C2×#12111yescharacteristic
862C2×C4C2×#12111yescharacteristic
863C2×C4C2×#12111yescharacteristic
864C2×C4C2×#12111yescharacteristic
865C2×C4C2×#12111yescharacteristic
866C2×C4C2×#12111yescharacteristic
867C2×C4C2×C22⋊Q811yescharacteristic
868C2×C4C2×C22⋊Q811yescharacteristic
869C2×C4C2×C22⋊Q811yescharacteristic
870C2×C4C2×C22⋊Q811yescharacteristic
871C2×C4C2×C22⋊Q811yescharacteristic
872C2×C4C2×#12311yescharacteristic
873C2×C4C2×#12311yescharacteristic
874C2×C4C2×#12411yescharacteristic
875C2×C4C2×#12411yescharacteristic
876C2×C4C2×#12411yescharacteristic
877C2×C4C2×#12611yescharacteristic
878C2×C4C2×#12711yescharacteristic
879C8—44no—
880C8—44no—
881C8—44no—
882C8—44no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—48no—
907C22—44no—
908C22—84no—
909C22—88no—
910C22—88no—
911C22—84no—
912C22#143912yes—
913C22#143912yes—
914C22#143912yes—
915C22#143912yes—
916C22C2×#38511yescharacteristic
917C22C2×#38611yescharacteristic
918C22C2×#38811yescharacteristic
919C22C2×#39411yescharacteristic
920C22C2×#39611yescharacteristic
921C22C2×#39711yescharacteristic
922C22C2×#39911yescharacteristic
923C4—48no—
924C4—44no—
925C4—84no—
926C4#143912yes—
927C4#143912yes—
928C4#143912yes—
929C4#143912yes—
930C4C2×#38011yescharacteristic
931C4C2×#38511yescharacteristic
932C4C2×#38811yescharacteristic
933C4C2×#39011yescharacteristic
934C4C2×#39211yescharacteristic
935C4C2×#39311yescharacteristic
936C4C2×#39411yescharacteristic
937C4C2×#39611yescharacteristic
938C2—21no—
939C2—21no—
940C2—21no—
941C2—21no—
942C2—22no—
943C2—22no—
944C2—21no—
945C2—22no—
946C2—22no—
947C2—21no—
948C2—84no—
949C2C2×#143911yescharacteristic
950C2#2374012yes—
subgroupG/H
centerC2×C4C2×#127
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22C2×#399
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. C2×#1738C2semidirect
6. C22×H(3,ℤ/4)C2semidirect
7. #20335C2semidirect
8. #11084C2semidirect
19. C2×#424C22semidirect
26. C2×#421C4semidirect
37. #1738C22semidirect
40. C2×H(3,ℤ/4)C22semidirect
42. #1729C22semidirect
145. #421C2×C4semidirect

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×#28792
C2×#17382
C22×H(3,ℤ/4)2
#203352
#110842