Finite Group Databasebeta

← C2×#11182 #357935

Subgroups — C2×#11182 #357935

Order 512.

2466 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#419C211yesmaximal, characteristic
2C22×#419C211yesmaximal, characteristic
3C23×#101C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic
6C2×#1738C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11182C218yesmaximal, direct product factor
9C24×Q8C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C2×#419—22no—
17C2×#419—24no—
18C2×#419—24no—
19C2×#419—22no—
20C2×#419—24no—
21C2×#419C418yescomplemented
22C2×#419C2214yes—
23C2×#419C2214yes—
24C22×#103—22no—
25C22×#103—22no—
26C22×#101—22no—
27C22×#101—22no—
28C22×#101—24no—
29C22×#101—24no—
30C22×#101C2214yes—
31C2×#344—24no—
32C2×#344—24no—
33C2×#344C2214yes—
34C2×#344C2214yes—
35#1738—22no—
36#1738C2214yes—
37C2×#341—22no—
38C2×H(3,ℤ/4)—24no—
39C2×H(3,ℤ/4)C2214yes—
40C23×Q8—22no—
41C23×Q8—22no—
42C23×Q8—21no—
43C23×Q8—21no—
44C23×Q8—21no—
45C23×Q8—21no—
46C23×Q8—22no—
47C23×Q8—21no—
48C23×Q8—22no—
49C23×Q8—21no—
50C23×Q8—21no—
51C23×Q8—21no—
52C23×Q8—22no—
53C23×Q8—21no—
54C23×Q8—21no—
55C23×Q8—21no—
56C23×Q8—22no—
57C23×Q8C2×C414yes—
58C23×Q8D412yes—
59C23×Q8D412yes—
60C23×Q8D414yes—
61C23×Q8C2312yes—
62C24×C4—21no—
63C24×C4C2311yescharacteristic
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—21no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
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—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—22no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—22no—
92C22×M16—21no—
93C22×M16—21no—
94C22×M16—22no—
95C22×M16—22no—
96C22×M16C2×C414yes—
97C22×M16D414yes—
98C22×M16D414yes—
99C22×M16D412yes—
100C22×M16C2312yes—
101C22×M16C2312yes—
102C22×M16C2312yes—
103C22×M16C2312yes—
104C23×C8—21no—
105C23×C8—21no—
106C23×C8—21no—
107C23×C8D412yes—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—22no—
113C2×#117—22no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—22no—
117C2×#117—22no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117C2×C414yes—
121C2×#117D414yes—
122C2×#117C2312yes—
123C2×#117C2312yes—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C42—21no—
129C22×C42—21no—
130#419—216no—
131#419—216no—
132#419—28no—
133#419—28no—
134#419—28no—
135#419C2×C4116yescomplemented
136C2×#103—216no—
137C2×#103—216no—
138C2×#103—28no—
139C2×#103—28no—
140C2×#101—216no—
141C2×#101—216no—
142C2×#101—28no—
143C2×#101—28no—
144C2×#101—28no—
145#344—28no—
146#344—28no—
147#341—28no—
148H(3,ℤ/4)—28no—
149C25#4111yescharacteristic
150C22×Q8—24no—
151C22×Q8—24no—
152C22×Q8—24no—
153C22×Q8—24no—
154C22×Q8—24no—
155C22×Q8—24no—
156C22×Q8—24no—
157C22×Q8—24no—
158C22×Q8—22no—
159C22×Q8—22no—
160C22×Q8—22no—
161C22×Q8—22no—
162C22×Q8—22no—
163C22×Q8—24no—
164C22×Q8—24no—
165C22×Q8—24no—
166C22×Q8—24no—
167C22×Q8—24no—
168C22×Q8—24no—
169C22×Q8—24no—
170C22×Q8—24no—
171C22×Q8—24no—
172C22×Q8—24no—
173C22×Q8—22no—
174C22×Q8—24no—
175C22×Q8—22no—
176C22×Q8—22no—
177C22×Q8—24no—
178C22×Q8—22no—
179C22×Q8—24no—
180C22×Q8—24no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—24no—
184C22×Q8—22no—
185C22×Q8—24no—
186C22×Q8—24no—
187C22×Q8—24no—
188C22×Q8—24no—
189C22×Q8—24no—
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—22no—
193C22×Q8—22no—
194C22×Q8—22no—
195C22×Q8—22no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—42no—
200C22×Q8—42no—
201C22×Q8—42no—
202C22×Q8—42no—
203C22×Q8—42no—
204C22×Q8—42no—
205C22×Q8—42no—
206C22×Q8—42no—
207C22×Q8—42no—
208C22×Q8—42no—
209C22×Q8—42no—
210C22×Q8—42no—
211C22×Q8—41no—
212C22×Q8—42no—
213C22×Q8—41no—
214C22×Q8—41no—
215C22×Q8—41no—
216C22×Q8—41no—
217C22×Q8—41no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8—42no—
221C22×Q8—42no—
222C22×Q8—42no—
223C22×Q8—42no—
224C22×Q8—41no—
225C22×Q8—41no—
226C22×Q8—42no—
227C22×Q8—41no—
228C22×Q8—41no—
229C22×Q8—41no—
230C22×Q8—42no—
231C22×Q8—42no—
232C22×Q8—41no—
233C22×Q8C22⋊C418yes—
234C22×Q8C22⋊C418yes—
235C22×Q8C22×C414yes—
236C22×Q8C2×D414yes—
237C22×Q8C2×D414yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—42no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—41no—
247C23×C4—42no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4C22×C412yes—
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D412yes—
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4#4111yescharacteristic
261C23×C4#4112yes—
262C23×C4#4111yescharacteristic
263C23×C4#4111yescharacteristic
264C23×C4#4111yescharacteristic
265C23×C4#4112yes—
266C23×C4#4111yescharacteristic
267C23×C4#4111yescharacteristic
268C23×C4#4111yescharacteristic
269C23×C4#4112yes—
270C23×C4#4111yescharacteristic
271C23×C4#4111yescharacteristic
272C23×C4C2411yescharacteristic
273C2×M16—24no—
274C2×M16—24no—
275C2×M16—24no—
276C2×M16—24no—
277C2×M16—24no—
278C2×M16—22no—
279C2×M16—22no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16—22no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—22no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16—24no—
292C2×M16—24no—
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—22no—
302C2×M16—22no—
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—42no—
314C2×M16—42no—
315C2×M16—41no—
316C2×M16—41no—
317C2×M16—42no—
318C2×M16—41no—
319C2×M16—41no—
320C2×M16—42no—
321C2×M16—42no—
322C2×M16—42no—
323C2×M16—42no—
324C2×M16—42no—
325C2×M16—42no—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—41no—
331C2×M16—41no—
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×M16C22×C414yes—
343C2×M16C2×D414yes—
344C2×M16C2×D414yes—
345C22×C8—24no—
346C22×C8—24no—
347C22×C8—24no—
348C22×C8—24no—
349C22×C8—24no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—41no—
356C22×C8—42no—
357C22×C8—41no—
358C22×C8—41no—
359C22×C8—41no—
360C22×C8—41no—
361C22×C8—41no—
362C22×C8—42no—
363C22×C8—42no—
364C22×C8C2×D414yes—
365#117—24no—
366#117—24no—
367#117—22no—
368#117—22no—
369#117—24no—
370#117—24no—
371#117—22no—
372#117—22no—
373#117—24no—
374#117—24no—
375#117—22no—
376#117—22no—
377#117—42no—
378#117—42no—
379#117—42no—
380#117—42no—
381#117—42no—
382#117—42no—
383#117C22×C414yes—
384#117C2×D414yes—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—41no—
408C2×C42—41no—
409#103—232no—
410#103—232no—
411#101—232no—
412C24—44no—
413C24C4×D412yes—
414C24#12112yes—
415C24#12311yescharacteristic
416C24#12311yescharacteristic
417C24#12312yes—
418C24#12411yescharacteristic
419C24#12411yescharacteristic
420C24#12611yescharacteristic
421C24#12611yescharacteristic
422C24#12612yes—
423C24C2×#4111yescharacteristic
424C2×Q8—24no—
425C2×Q8—24no—
426C2×Q8—24no—
427C2×Q8—28no—
428C2×Q8—28no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—24no—
432C2×Q8—24no—
433C2×Q8—24no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8C2×C22⋊C418yes—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4C2×C22⋊C412yes—
530C22×C4C2×C22⋊C412yes—
531C22×C4#11712yes—
532C22×C4#11712yes—
533C22×C4#11712yes—
534C22×C4#11712yes—
535C22×C4C4×D412yes—
536C22×C4C4×D412yes—
537C22×C4C4×D412yes—
538C22×C4C4×D412yes—
539C22×C4C4×D412yes—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4#12012yes—
543C22×C4#12012yes—
544C22×C4#12012yes—
545C22×C4#12012yes—
546C22×C4#12111yescharacteristic
547C22×C4#12111yescharacteristic
548C22×C4#12112yes—
549C22×C4#12111yescharacteristic
550C22×C4#12112yes—
551C22×C4#12111yescharacteristic
552C22×C4#12112yes—
553C22×C4#12112yes—
554C22×C4#12112yes—
555C22×C4#12112yes—
556C22×C4#12112yes—
557C22×C4#12112yes—
558C22×C4#12112yes—
559C22×C4#12112yes—
560C22×C4#12112yes—
561C22×C4#12112yes—
562C22×C4#12112yes—
563C22×C4#12311yescharacteristic
564C22×C4#12311yescharacteristic
565C22×C4#12311yescharacteristic
566C22×C4#12312yes—
567C22×C4#12312yes—
568C22×C4#12312yes—
569C22×C4#12312yes—
570C22×C4#12311yescharacteristic
571C22×C4#12312yes—
572C22×C4#12312yes—
573C22×C4#12312yes—
574C22×C4#12312yes—
575C22×C4#12311yescharacteristic
576C22×C4#12312yes—
577C22×C4#12311yescharacteristic
578C22×C4#12311yescharacteristic
579C22×C4#12312yes—
580C22×C4#12311yescharacteristic
581C22×C4#12312yes—
582C22×C4#12312yes—
583C22×C4#12311yescharacteristic
584C22×C4#12311yescharacteristic
585C22×C4#12312yes—
586C22×C4#12412yes—
587C22×C4#12412yes—
588C22×C4#12412yes—
589C22×C4#12412yes—
590C22×C4#12412yes—
591C22×C4#12412yes—
592C22×C4#12411yescharacteristic
593C22×C4#12411yescharacteristic
594C22×C4#12611yescharacteristic
595C22×C4#12611yescharacteristic
596C22×C4#12611yescharacteristic
597C22×C4#12612yes—
598C22×C4#12612yes—
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12612yes—
603C22×C4C23×C411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614C22×C4C2×#4111yescharacteristic
615C22×C4C2×#4111yescharacteristic
616C22×C4C2×#4111yescharacteristic
617M16—24no—
618M16—24no—
619M16—24no—
620M16—24no—
621M16—24no—
622M16—24no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—44no—
634M16—44no—
635M16—44no—
636M16—44no—
637M16—44no—
638M16—44no—
639M16—44no—
640M16—44no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—24no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—44no—
654C2×C8—44no—
655C2×C8—44no—
656C2×C8—44no—
657C2×C8—44no—
658C2×C8—44no—
659C2×C8—44no—
660C2×C8—44no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C42—24no—
674C42—24no—
675C42—42no—
676C42—42no—
677C42—44no—
678C42—44no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23#38612yes—
691C23#38612yes—
692C23#38812yes—
693C23#38812yes—
694C23#38812yes—
695C23#38812yes—
696C23#39412yes—
697C23#39412yes—
698C23#39711yescharacteristic
699C23#39711yescharacteristic
700C23#39711yescharacteristic
701C23#39712yes—
702C23#39712yes—
703C23#39712yes—
704C23#39712yes—
705C23#39711yescharacteristic
706C23C2×C4×D411yescharacteristic
707C23C2×#12111yescharacteristic
708C23C2×#12311yescharacteristic
709C23C2×#12311yescharacteristic
710C23C2×#12411yescharacteristic
711C23C2×#12611yescharacteristic
712C23C2×#12611yescharacteristic
713Q8—28no—
714Q8—28no—
715Q8—44no—
716Q8—44no—
717Q8—44no—
718Q8—44no—
719Q8—48no—
720Q8—48no—
721Q8—48no—
722Q8—48no—
723Q8—44no—
724Q8—44no—
725C2×C4—28no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—88no—
741C2×C4—88no—
742C2×C4#38112yes—
743C2×C4#38112yes—
744C2×C4#38112yes—
745C2×C4#38112yes—
746C2×C4#38612yes—
747C2×C4#38612yes—
748C2×C4#38612yes—
749C2×C4#38612yes—
750C2×C4#38612yes—
751C2×C4#38612yes—
752C2×C4#38812yes—
753C2×C4#38812yes—
754C2×C4#38812yes—
755C2×C4#38812yes—
756C2×C4#38812yes—
757C2×C4#38812yes—
758C2×C4#38812yes—
759C2×C4#38812yes—
760C2×C4#38812yes—
761C2×C4#38812yes—
762C2×C4#38812yes—
763C2×C4#38812yes—
764C2×C4#39412yes—
765C2×C4#39412yes—
766C2×C4#39412yes—
767C2×C4#39412yes—
768C2×C4#39412yes—
769C2×C4#39412yes—
770C2×C4#39412yes—
771C2×C4#39412yes—
772C2×C4#39412yes—
773C2×C4#39412yes—
774C2×C4#39412yes—
775C2×C4#39412yes—
776C2×C4#39412yes—
777C2×C4#39412yes—
778C2×C4#39712yes—
779C2×C4#39712yes—
780C2×C4#39712yes—
781C2×C4#39712yes—
782C2×C4#39712yes—
783C2×C4#39712yes—
784C2×C4#39712yes—
785C2×C4#39712yes—
786C2×C4#39711yescharacteristic
787C2×C4#39711yescharacteristic
788C2×C4#39711yescharacteristic
789C2×C4#39711yescharacteristic
790C2×C4C22×C22⋊C411yescharacteristic
791C2×C4C2×#11711yescharacteristic
792C2×C4C2×#11711yescharacteristic
793C2×C4C2×C4×D411yescharacteristic
794C2×C4C2×C4×D411yescharacteristic
795C2×C4C2×C4×D411yescharacteristic
796C2×C4C2×#12011yescharacteristic
797C2×C4C2×#12011yescharacteristic
798C2×C4C2×#12111yescharacteristic
799C2×C4C2×#12111yescharacteristic
800C2×C4C2×#12111yescharacteristic
801C2×C4C2×#12111yescharacteristic
802C2×C4C2×#12111yescharacteristic
803C2×C4C2×#12111yescharacteristic
804C2×C4C2×#12111yescharacteristic
805C2×C4C2×#12311yescharacteristic
806C2×C4C2×#12311yescharacteristic
807C2×C4C2×#12311yescharacteristic
808C2×C4C2×#12311yescharacteristic
809C2×C4C2×#12311yescharacteristic
810C2×C4C2×#12311yescharacteristic
811C2×C4C2×#12311yescharacteristic
812C2×C4C2×#12311yescharacteristic
813C2×C4C2×#12411yescharacteristic
814C2×C4C2×#12411yescharacteristic
815C2×C4C2×#12411yescharacteristic
816C2×C4C2×#12611yescharacteristic
817C2×C4C2×#12611yescharacteristic
818C8—44no—
819C8—44no—
820C8—44no—
821C8—44no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22#144012yes—
845C22#144012yes—
846C22#144012yes—
847C22#144012yes—
848C22#208214yes—
849C22C2×#38611yescharacteristic
850C22C2×#38811yescharacteristic
851C22C2×#38811yescharacteristic
852C22C2×#39411yescharacteristic
853C22C2×#39711yescharacteristic
854C22C2×#39711yescharacteristic
855C22C2×#39711yescharacteristic
856C4—48no—
857C4—84no—
858C4—84no—
859C4#144012yes—
860C4#144012yes—
861C4#144012yes—
862C4#144012yes—
863C4C2×#38111yescharacteristic
864C4C2×#38611yescharacteristic
865C4C2×#38811yescharacteristic
866C4C2×#38811yescharacteristic
867C4C2×#39411yescharacteristic
868C4C2×#39411yescharacteristic
869C4C2×#39411yescharacteristic
870C4C2×#39711yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—22no—
876C2—22no—
877C2—22no—
878C2—21no—
879C2—21no—
880C2#1118214yesdirect product factor
881C2C2×#144011yescharacteristic
882C2C2×#208212yes—
subgroupG/H
center, socleC23#397
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25#41
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
8. #11182C2direct (N × H)
21. C2×#419C4semidirect
135. #419C2×C4semidirect
880. C2#11182direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4192
C23×#1012
C22×#3442
C2×#17382
C22×H(3,ℤ/4)2
#111822