Finite Group Databasebeta

← C2×#11183 #357937

Subgroups — C2×#11183 #357937

Order 512.

3146 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#418C211yesmaximal, characteristic
2C22×#418C211yesmaximal, characteristic
3C2×#2309C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1740C211yesmaximal, characteristic, complemented
6C2×#1733C211yesmaximal, characteristic, complemented
7C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8#11183C218yesmaximal, direct product factor
9C24×D4C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C2×#418—22no—
17C2×#418—22no—
18C2×#418—22no—
19C2×#418—22no—
20C2×#418—22no—
21C2×#418—24no—
22C2×#418—24no—
23C2×#418C414yescomplemented
24C2×#418C2214yes—
25C2×#418C2214yes—
26C22×#102—22no—
27C22×#102C414yescomplemented
28#2309—22no—
29#2309—22no—
30#2309—22no—
31#2309C2214yes—
32C2×#390—22no—
33C2×#390—22no—
34C2×#379—22no—
35C2×#344—24no—
36C2×#344C2214yescomplemented
37#1740—22no—
38#1740C2214yescomplemented
39C2×#342—22no—
40#1733—22no—
41#1733C2214yescomplemented
42C2×#339—22no—
43C2×H(3,ℤ/4)—24no—
44C2×H(3,ℤ/4)C2214yescomplemented
45C26—21no—
46C23×D4—22no—
47C23×D4—22no—
48C23×D4—21no—
49C23×D4—21no—
50C23×D4—21no—
51C23×D4—22no—
52C23×D4—22no—
53C23×D4—22no—
54C23×D4—22no—
55C23×D4—22no—
56C23×D4—22no—
57C23×D4—21no—
58C23×D4—21no—
59C23×D4—21no—
60C23×D4—21no—
61C23×D4C2×C412yes—
62C23×D4C2×C412yes—
63C23×D4D412yes—
64C23×D4D412yes—
65C23×D4D412yes—
66C23×D4D412yes—
67C23×D4C2312yes—
68C24×C4C2311yescharacteristic
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—22no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16C2×C412yes—
86C22×M16D414yes—
87C22×M16C2312yes—
88C22×M16C2312yes—
89C23×C8—21no—
90C23×C8C2×C412yes—
91C2×#117—21no—
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117—21no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117—22no—
108C2×#117—22no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—22no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117C2×C412yes—
120C2×#117D414yes—
121C2×#117D412yes—
122C2×#117D412yes—
123C2×#117C2312yes—
124C2×#117C2312yes—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2×C412yes—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—28no—
135C22×C22⋊C4D412yes—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42D412yes—
140#418—216no—
141#418—28no—
142#418—28no—
143#418—28no—
144#418—28no—
145#418—28no—
146#418—28no—
147C2×#102—216no—
148C2×#102—28no—
149C2×#102—28no—
150C2×#102—28no—
151C2×#102C2×C4116yescomplemented
152#390—28no—
153#390—28no—
154#390—28no—
155#390—28no—
156#379—28no—
157#379—28no—
158#344—28no—
159#342—28no—
160#339—28no—
161H(3,ℤ/4)—28no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—22no—
169C25—42no—
170C25—42no—
171C25—42no—
172C25—42no—
173C25—88no—
174C25C2×D411yescharacteristic
175C22×D4—24no—
176C22×D4—24no—
177C22×D4—24no—
178C22×D4—24no—
179C22×D4—24no—
180C22×D4—24no—
181C22×D4—24no—
182C22×D4—24no—
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—22no—
189C22×D4—24no—
190C22×D4—24no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—24no—
194C22×D4—24no—
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—42no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4C22⋊C414yes—
257C22×D4C22⋊C414yes—
258C22×D4C22⋊C414yes—
259C22×D4C22⋊C414yes—
260C22×D4C22×C414yes—
261C22×D4C2×D414yes—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—41no—
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4#4112yes—
279C23×C4#4112yes—
280C23×C4#4112yes—
281C23×C4#4112yes—
282C23×C4#4112yes—
283C23×C4#4112yes—
284C23×C4#4111yescharacteristic
285C23×C4#4111yescharacteristic
286C23×C4#4111yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4C2411yescharacteristic
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—24no—
292C2×M16—24no—
293C2×M16—24no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—42no—
310C2×M16—42no—
311C2×M16—41no—
312C2×M16—41no—
313C2×M16—42no—
314C2×M16—42no—
315C2×M16—42no—
316C2×M16—42no—
317C2×M16—42no—
318C2×M16—42no—
319C2×M16—42no—
320C2×M16—42no—
321C2×M16—42no—
322C2×M16—42no—
323C2×M16—42no—
324C2×M16C2×D414yes—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—24no—
328C22×C8—24no—
329C22×C8—24no—
330C22×C8—22no—
331C22×C8—41no—
332C22×C8—41no—
333C22×C8—42no—
334C22×C8C22×C414yes—
335#117—24no—
336#117—24no—
337#117—24no—
338#117—22no—
339#117—22no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—24no—
344#117—24no—
345#117—24no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—24no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—42no—
366#117—41no—
367#117—41no—
368#117—42no—
369#117—42no—
370#117—42no—
371#117—42no—
372#117—41no—
373#117—41no—
374#117—42no—
375#117—42no—
376#117—42no—
377#117—42no—
378#117—42no—
379#117—42no—
380#117C2×D414yes—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4C22×C414yes—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—232no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—816no—
418C2×C22⋊C4C2×D414yes—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—41no—
429C2×C42—41no—
430C2×C42—42no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42C2×D414yes—
437#102—232no—
438#102—232no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—44no—
447C24—416no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—88no—
465C24—88no—
466C24—88no—
467C24—88no—
468C24—88no—
469C24—88no—
470C24—816no—
471C24—816no—
472C24—816no—
473C24—816no—
474C24C4×D411yescharacteristic
475C24C4×D411yescharacteristic
476C24#12011yescharacteristic
477C24#12011yescharacteristic
478C24#12111yescharacteristic
479C24#12111yescharacteristic
480C24#12112yes—
481C24#12112yes—
482C24#12312yes—
483C24#12412yes—
484C24C22×D411yescharacteristic
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—44no—
525C2×D4—44no—
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—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
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—44no—
560C2×D4C2×C22⋊C418yes—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4C2×C22⋊C411yescharacteristic
575C22×C4C2×C22⋊C411yescharacteristic
576C22×C4C2×C22⋊C411yescharacteristic
577C22×C4C2×C22⋊C411yescharacteristic
578C22×C4#11712yes—
579C22×C4#11712yes—
580C22×C4#11712yes—
581C22×C4#11712yes—
582C22×C4C4×D412yes—
583C22×C4C4×D412yes—
584C22×C4C4×D412yes—
585C22×C4C4×D412yes—
586C22×C4C4×D411yescharacteristic
587C22×C4C4×D411yescharacteristic
588C22×C4C4×D411yescharacteristic
589C22×C4C4×D411yescharacteristic
590C22×C4C4×D411yescharacteristic
591C22×C4C4×D411yescharacteristic
592C22×C4#12012yes—
593C22×C4#12012yes—
594C22×C4#12011yescharacteristic
595C22×C4#12011yescharacteristic
596C22×C4#12112yes—
597C22×C4#12112yes—
598C22×C4#12112yes—
599C22×C4#12112yes—
600C22×C4#12111yescharacteristic
601C22×C4#12111yescharacteristic
602C22×C4#12111yescharacteristic
603C22×C4#12111yescharacteristic
604C22×C4#12112yes—
605C22×C4#12112yes—
606C22×C4#12112yes—
607C22×C4#12112yes—
608C22×C4#12111yescharacteristic
609C22×C4#12111yescharacteristic
610C22×C4#12112yes—
611C22×C4#12112yes—
612C22×C4#12312yes—
613C22×C4#12312yes—
614C22×C4#12312yes—
615C22×C4#12312yes—
616C22×C4#12312yes—
617C22×C4#12312yes—
618C22×C4#12312yes—
619C22×C4#12312yes—
620C22×C4#12312yes—
621C22×C4#12312yes—
622C22×C4#12311yescharacteristic
623C22×C4#12311yescharacteristic
624C22×C4#12311yescharacteristic
625C22×C4#12311yescharacteristic
626C22×C4#12312yes—
627C22×C4#12312yes—
628C22×C4#12312yes—
629C22×C4#12312yes—
630C22×C4#12312yes—
631C22×C4#12312yes—
632C22×C4#12312yes—
633C22×C4#12412yes—
634C22×C4#12412yes—
635C22×C4#12412yes—
636C22×C4#12412yes—
637C22×C4#12412yes—
638C22×C4#12412yes—
639C22×C4#12412yes—
640C22×C4#12612yes—
641C22×C4#12612yes—
642C22×C4#12612yes—
643C22×C4#12612yes—
644C22×C4#12612yes—
645C22×C4#12612yes—
646C22×C4#12612yes—
647C22×C4#12612yes—
648C22×C4C23×C411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654C22×C4C2×#4111yescharacteristic
655C22×C4C2×#4111yescharacteristic
656C22×C4C2×#4111yescharacteristic
657C22×C4C2×#4111yescharacteristic
658C22×C4C2×#4111yescharacteristic
659C22×C4C2×#4111yescharacteristic
660C22×C4C2×#4111yescharacteristic
661C22×C4C2×#4111yescharacteristic
662M16—24no—
663M16—24no—
664M16—42no—
665M16—42no—
666M16—42no—
667M16—42no—
668M16—42no—
669M16—42no—
670M16—44no—
671M16—44no—
672M16—44no—
673M16—44no—
674C2×C8—24no—
675C2×C8—24no—
676C2×C8—24no—
677C2×C8—24no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8—44no—
681C2×C8—44no—
682C2×C8—44no—
683C2×C8—44no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—832no—
711C42—24no—
712C42—24no—
713C42—24no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—42no—
720C42—42no—
721C42—44no—
722C42—44no—
723C42—44no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—28no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—416no—
737C23—416no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—416no—
743C23—48no—
744C23—48no—
745C23—48no—
746C23—48no—
747C23—44no—
748C23—44no—
749C23—88no—
750C23—88no—
751C23—88no—
752C23—88no—
753C23—816no—
754C23—816no—
755C23—816no—
756C23—816no—
757C23—816no—
758C23—816no—
759C23—88no—
760C23—88no—
761C23—88no—
762C23—88no—
763C23—816no—
764C23—816no—
765C23—816no—
766C23—816no—
767C23—816no—
768C23—816no—
769C23#38611yescharacteristic
770C23#38611yescharacteristic
771C23#38611yescharacteristic
772C23#38611yescharacteristic
773C23#38812yes—
774C23#38812yes—
775C23#38812yes—
776C23#38812yes—
777C23#39412yes—
778C23#39412yes—
779C23#39412yes—
780C23#39412yes—
781C23#39412yes—
782C23#39412yes—
783C23#39712yes—
784C23#39712yes—
785C23C2×C4×D411yescharacteristic
786C23C2×#12011yescharacteristic
787C23C2×#12111yescharacteristic
788C23C2×#12111yescharacteristic
789C23C2×#12111yescharacteristic
790C23C2×#12311yescharacteristic
791C23C2×#12411yescharacteristic
792D4—28no—
793D4—28no—
794D4—44no—
795D4—44no—
796D4—44no—
797D4—44no—
798D4—48no—
799D4—48no—
800D4—48no—
801D4—48no—
802D4—44no—
803D4—44no—
804C2×C4—48no—
805C2×C4—48no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—88no—
811C2×C4—88no—
812C2×C4—84no—
813C2×C4—88no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4#38112yes—
818C2×C4#38112yes—
819C2×C4#38112yes—
820C2×C4#38112yes—
821C2×C4#38611yescharacteristic
822C2×C4#38611yescharacteristic
823C2×C4#38611yescharacteristic
824C2×C4#38611yescharacteristic
825C2×C4#38612yes—
826C2×C4#38612yes—
827C2×C4#38612yes—
828C2×C4#38612yes—
829C2×C4#38812yes—
830C2×C4#38812yes—
831C2×C4#38812yes—
832C2×C4#38812yes—
833C2×C4#38812yes—
834C2×C4#38812yes—
835C2×C4#38812yes—
836C2×C4#38812yes—
837C2×C4#38812yes—
838C2×C4#38812yes—
839C2×C4#38812yes—
840C2×C4#38812yes—
841C2×C4#39412yes—
842C2×C4#39412yes—
843C2×C4#39412yes—
844C2×C4#39412yes—
845C2×C4#39412yes—
846C2×C4#39412yes—
847C2×C4#39412yes—
848C2×C4#39412yes—
849C2×C4#39412yes—
850C2×C4#39412yes—
851C2×C4#39712yes—
852C2×C4#39712yes—
853C2×C4#39712yes—
854C2×C4#39712yes—
855C2×C4#39712yes—
856C2×C4#39712yes—
857C2×C4#39712yes—
858C2×C4#39712yes—
859C2×C4#39712yes—
860C2×C4#39712yes—
861C2×C4#39712yes—
862C2×C4#39712yes—
863C2×C4#39712yes—
864C2×C4#39712yes—
865C2×C4C22×C22⋊C411yescharacteristic
866C2×C4C2×#11711yescharacteristic
867C2×C4C2×#11711yescharacteristic
868C2×C4C2×C4×D411yescharacteristic
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C2×#12011yescharacteristic
872C2×C4C2×#12111yescharacteristic
873C2×C4C2×#12111yescharacteristic
874C2×C4C2×#12111yescharacteristic
875C2×C4C2×#12111yescharacteristic
876C2×C4C2×#12111yescharacteristic
877C2×C4C2×#12311yescharacteristic
878C2×C4C2×#12311yescharacteristic
879C2×C4C2×#12311yescharacteristic
880C2×C4C2×#12311yescharacteristic
881C2×C4C2×#12311yescharacteristic
882C2×C4C2×#12311yescharacteristic
883C2×C4C2×#12311yescharacteristic
884C2×C4C2×#12311yescharacteristic
885C2×C4C2×#12311yescharacteristic
886C2×C4C2×#12411yescharacteristic
887C2×C4C2×#12411yescharacteristic
888C2×C4C2×#12411yescharacteristic
889C2×C4C2×#12611yescharacteristic
890C2×C4C2×#12611yescharacteristic
891C2×C4C2×#12611yescharacteristic
892C2×C4C2×#12611yescharacteristic
893C8—44no—
894C8—44no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—416no—
918C22—48no—
919C22—88no—
920C22—88no—
921C22—816no—
922C22—88no—
923C22—88no—
924C22—816no—
925C22—816no—
926C22—88no—
927C22—88no—
928C22—816no—
929C22#144012yes—
930C22#144012yes—
931C22#144012yes—
932C22#144012yes—
933C22#190414yes—
934C22C2×#38611yescharacteristic
935C22C2×#38811yescharacteristic
936C22C2×#38811yescharacteristic
937C22C2×#39411yescharacteristic
938C22C2×#39411yescharacteristic
939C22C2×#39411yescharacteristic
940C22C2×#39711yescharacteristic
941C4—84no—
942C4—84no—
943C4—84no—
944C4—84no—
945C4#144012yes—
946C4#144012yes—
947C4#144012yes—
948C4#144012yes—
949C4C2×#38111yescharacteristic
950C4C2×#38611yescharacteristic
951C4C2×#38811yescharacteristic
952C4C2×#38811yescharacteristic
953C4C2×#39411yescharacteristic
954C4C2×#39711yescharacteristic
955C4C2×#39711yescharacteristic
956C4C2×#39711yescharacteristic
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—22no—
962C2—22no—
963C2—22no—
964C2—21no—
965C2—21no—
966C2—88no—
967C2#1118314yesdirect product factor
968C2C2×#144011yescharacteristic
969C2C2×#190412yes—
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC24×D4C22
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
4. C22×#344C2semidirect
5. C2×#1740C2semidirect
6. C2×#1733C2semidirect
7. C22×H(3,ℤ/4)C2semidirect
8. #11183C2direct (N × H)
23. C2×#418C4semidirect
27. C22×#102C4semidirect
36. C2×#344C22semidirect
38. #1740C22semidirect
41. #1733C22semidirect
44. C2×H(3,ℤ/4)C22semidirect
151. C2×#102C2×C4semidirect
967. C2#11183direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4182
C2×#23092
C22×#3442
C2×#17402
C2×#17332
C22×H(3,ℤ/4)2
#111832