Finite Group Databasebeta

← C2×#11086 #357757

Subgroups — C2×#11086 #357757

Order 512.

2702 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#424C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C22×#416C211yesmaximal, characteristic
4C22×#413C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic, complemented
6C22×#341C211yesmaximal, characteristic, complemented
7C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8#11086C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C2×#424—24no—
17C2×#424—24no—
18C2×#424—22no—
19C2×#424C2214yescomplemented
20C22×C4⋊C8—22no—
21C2×#421—24no—
22C2×#421—22no—
23C2×#421C418yescomplemented
24C2×#421C2214yes—
25C22×#104—22no—
26C2×#416—22no—
27C2×#416—24no—
28C2×#416—24no—
29C2×#416C2214yes—
30C22×#103—21no—
31C22×#102—21no—
32C2×#413—22no—
33C2×#413—24no—
34C2×#413—24no—
35C2×#413C2214yes—
36C22×#101—21no—
37C22×#100—21no—
38C2×#344—24no—
39C2×#344C2214yescomplemented
40C2×#341—24no—
41C2×#341C2214yescomplemented
42C2×H(3,ℤ/4)—24no—
43C2×H(3,ℤ/4)C2214yescomplemented
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—21no—
47C22×#41—21no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—21no—
51C22×#41—22no—
52C22×#41—21no—
53C22×#41—22no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—21no—
57C22×#41—21no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41C2×C414yes—
61C22×#41D412yes—
62C22×#41Q814yes—
63C22×#41C2312yes—
64C23×Q8D411yescharacteristic
65C23×D4—21no—
66C23×D4D411yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—21no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—21no—
82C22×M16—22no—
83C22×M16—21no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—22no—
92C22×M16—21no—
93C22×M16C2×C414yes—
94C22×M16D414yes—
95C22×M16D414yes—
96C22×M16C2312yes—
97C22×M16C2312yes—
98C22×M16C2312yes—
99C23×C8—21no—
100C23×C8—22no—
101C23×C8—21no—
102C23×C8—21no—
103C23×C8—21no—
104C23×C8—22no—
105C23×C8—21no—
106C23×C8—22no—
107C23×C8—21no—
108C23×C8—21no—
109C23×C8—21no—
110C23×C8—21no—
111C23×C8D414yes—
112C23×C8C2312yes—
113C2×#117—22no—
114C2×#117—22no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—22no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—22no—
121C2×#117—21no—
122C2×#117—22no—
123C2×#117C2×C414yes—
124C2×#117D414yes—
125C2×#117D414yes—
126C2×#117D412yes—
127C2×#117C2312yes—
128C2×#117C2312yes—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C42—21no—
134C22×C42D412yes—
135#424—216no—
136#424—28no—
137#424—28no—
138C2×C4⋊C8—216no—
139C2×C4⋊C8—28no—
140#421—216no—
141#421—28no—
142#421C2×C4116yescomplemented
143C2×#104—216no—
144C2×#104—28no—
145#416—216no—
146#416—28no—
147#416—28no—
148C2×#103—28no—
149C2×#103—24no—
150C2×#102—28no—
151C2×#102—24no—
152#413—216no—
153#413—28no—
154#413—28no—
155C2×#101—28no—
156C2×#101—24no—
157C2×#100—28no—
158C2×#100—24no—
159#344—28no—
160#341—28no—
161H(3,ℤ/4)—28no—
162C25—21no—
163C25#4111yescharacteristic
164C2×#41—24no—
165C2×#41—24no—
166C2×#41—24no—
167C2×#41—24no—
168C2×#41—24no—
169C2×#41—22no—
170C2×#41—22no—
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—22no—
182C2×#41—22no—
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—22no—
192C2×#41—22no—
193C2×#41—22no—
194C2×#41—22no—
195C2×#41—22no—
196C2×#41—22no—
197C2×#41—22no—
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—22no—
201C2×#41—42no—
202C2×#41—42no—
203C2×#41—42no—
204C2×#41—42no—
205C2×#41—42no—
206C2×#41—42no—
207C2×#41—42no—
208C2×#41—42no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41—42no—
212C2×#41—42no—
213C2×#41—42no—
214C2×#41—42no—
215C2×#41—42no—
216C2×#41—41no—
217C2×#41—41no—
218C2×#41—42no—
219C2×#41—41no—
220C2×#41—41no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—41no—
224C2×#41—41no—
225C2×#41—41no—
226C2×#41—41no—
227C2×#41—42no—
228C2×#41—42no—
229C2×#41C4⋊C418yes—
230C2×#41C22×C414yes—
231C2×#41C2×Q814yes—
232C22×Q8—22no—
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8C4⋊C414yes—
241C22×Q8C2×D412yes—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—41no—
260C22×D4C4⋊C414yes—
261C22×D4C2×D412yes—
262C23×C4—22no—
263C23×C4—21no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—41no—
271C23×C4—41no—
272C23×C4—41no—
273C23×C4—41no—
274C23×C4—41no—
275C23×C4C22×C412yes—
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D412yes—
285C23×C4C2×Q812yes—
286C23×C4#4111yescharacteristic
287C23×C4#4111yescharacteristic
288C23×C4#4112yes—
289C23×C4#4111yescharacteristic
290C23×C4#4111yescharacteristic
291C23×C4#4111yescharacteristic
292C23×C4#4111yescharacteristic
293C23×C4#4111yescharacteristic
294C23×C4#4111yescharacteristic
295C23×C4#4111yescharacteristic
296C23×C4C2411yescharacteristic
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—24no—
310C2×M16—24no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
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—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—41no—
341C2×M16—41no—
342C2×M16—41no—
343C2×M16—41no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16C22×C414yes—
349C2×M16C2×D414yes—
350C2×M16C2×D414yes—
351C22×C8—24no—
352C22×C8—24no—
353C22×C8—24no—
354C22×C8—24no—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—24no—
358C22×C8—24no—
359C22×C8—24no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—42no—
370C22×C8—42no—
371C22×C8—41no—
372C22×C8—41no—
373C22×C8—41no—
374C22×C8—41no—
375C22×C8—42no—
376C22×C8—42no—
377C22×C8—42no—
378C22×C8—41no—
379C22×C8—41no—
380C22×C8—41no—
381C22×C8—41no—
382C22×C8—41no—
383C22×C8—42no—
384C22×C8—41no—
385C22×C8—42no—
386C22×C8—42no—
387C22×C8—42no—
388C22×C8C2×D414yes—
389#117—24no—
390#117—24no—
391#117—24no—
392#117—24no—
393#117—24no—
394#117—22no—
395#117—22no—
396#117—24no—
397#117—22no—
398#117—24no—
399#117—22no—
400#117—24no—
401#117—22no—
402#117—42no—
403#117—42no—
404#117—42no—
405#117C22⋊C418yes—
406#117C22×C414yes—
407#117C2×D414yes—
408#117C2×D414yes—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—41no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—41no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—41no—
430C2×C42—42no—
431C2×C42C22⋊C418yes—
432C2×C42C2×D414yes—
433C4⋊C8—232no—
434#104—232no—
435#103—216no—
436#102—216no—
437#101—216no—
438#100—216no—
439C24—22no—
440C24—24no—
441C24—44no—
442C24—42no—
443C24—41no—
444C24—41no—
445C24—84no—
446C24C4×D412yes—
447C24#12112yes—
448C24C22⋊Q812yes—
449C24#12311yescharacteristic
450C24#12311yescharacteristic
451C24#12311yescharacteristic
452C24#12311yescharacteristic
453C24#12312yes—
454C24#12611yescharacteristic
455C24#12611yescharacteristic
456C24C2×#4111yescharacteristic
457#41—24no—
458#41—24no—
459#41—24no—
460#41—24no—
461#41—24no—
462#41—24no—
463#41—24no—
464#41—24no—
465#41—28no—
466#41—28no—
467#41—28no—
468#41—28no—
469#41—42no—
470#41—42no—
471#41—42no—
472#41—42no—
473#41—42no—
474#41—42no—
475#41—42no—
476#41—42no—
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—
491#41—44no—
492#41—44no—
493#41—44no—
494#41—44no—
495#41—44no—
496#41—44no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×Q8C2×C4⋊C414yes—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—28no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4C2×C4⋊C414yes—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—28no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—48no—
559C22×C4—42no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—84no—
580C22×C4C2×C22⋊C412yes—
581C22×C4C2×C22⋊C412yes—
582C22×C4C2×C4⋊C412yes—
583C22×C4C2×C4⋊C412yes—
584C22×C4#11712yes—
585C22×C4#11712yes—
586C22×C4C4×D412yes—
587C22×C4C4×D412yes—
588C22×C4C4×D412yes—
589C22×C4C4×D412yes—
590C22×C4C4×D412yes—
591C22×C4C4×D412yes—
592C22×C4C4×D412yes—
593C22×C4#12012yes—
594C22×C4#12012yes—
595C22×C4#12012yes—
596C22×C4#12012yes—
597C22×C4#12012yes—
598C22×C4#12012yes—
599C22×C4#12111yescharacteristic
600C22×C4#12111yescharacteristic
601C22×C4#12111yescharacteristic
602C22×C4#12111yescharacteristic
603C22×C4#12112yes—
604C22×C4#12112yes—
605C22×C4#12112yes—
606C22×C4#12112yes—
607C22×C4#12112yes—
608C22×C4#12112yes—
609C22×C4#12112yes—
610C22×C4#12112yes—
611C22×C4#12112yes—
612C22×C4#12112yes—
613C22×C4#12112yes—
614C22×C4#12112yes—
615C22×C4#12112yes—
616C22×C4C22⋊Q812yes—
617C22×C4C22⋊Q812yes—
618C22×C4C22⋊Q812yes—
619C22×C4C22⋊Q812yes—
620C22×C4C22⋊Q812yes—
621C22×C4C22⋊Q812yes—
622C22×C4C22⋊Q812yes—
623C22×C4C22⋊Q812yes—
624C22×C4C22⋊Q812yes—
625C22×C4C22⋊Q812yes—
626C22×C4C22⋊Q812yes—
627C22×C4#12311yescharacteristic
628C22×C4#12311yescharacteristic
629C22×C4#12311yescharacteristic
630C22×C4#12311yescharacteristic
631C22×C4#12312yes—
632C22×C4#12312yes—
633C22×C4#12311yescharacteristic
634C22×C4#12311yescharacteristic
635C22×C4#12311yescharacteristic
636C22×C4#12311yescharacteristic
637C22×C4#12312yes—
638C22×C4#12412yes—
639C22×C4#12412yes—
640C22×C4#12412yes—
641C22×C4#12412yes—
642C22×C4#12411yescharacteristic
643C22×C4#12411yescharacteristic
644C22×C4#12411yescharacteristic
645C22×C4#12411yescharacteristic
646C22×C4#12611yescharacteristic
647C22×C4#12611yescharacteristic
648C22×C4#12611yescharacteristic
649C22×C4#12611yescharacteristic
650C22×C4#12611yescharacteristic
651C22×C4#12611yescharacteristic
652C22×C4#12712yes—
653C22×C4#12712yes—
654C22×C4C23×C411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×Q811yescharacteristic
663C22×C4C2×#4111yescharacteristic
664C22×C4C2×#4111yescharacteristic
665C22×C4C2×#4111yescharacteristic
666C22×C4C2×#4111yescharacteristic
667C22×C4C2×#4111yescharacteristic
668M16—24no—
669M16—24no—
670M16—24no—
671M16—24no—
672M16—24no—
673M16—24no—
674M16—42no—
675M16—42no—
676M16—42no—
677M16—42no—
678M16—42no—
679M16—42no—
680M16—44no—
681M16—44no—
682M16—44no—
683M16—44no—
684M16—44no—
685M16—44no—
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—42no—
701C2×C8—42no—
702C2×C8—44no—
703C2×C8—44no—
704C2×C8—44no—
705C2×C8—44no—
706C2×C8—44no—
707C2×C8—44no—
708C2×C8—44no—
709C2×C8—44no—
710C2×C8—44no—
711C2×C8—44no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—28no—
715C4⋊C4—24no—
716C4⋊C4—42no—
717C4⋊C4—44no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—28no—
721C22⋊C4—24no—
722C22⋊C4—42no—
723C22⋊C4—44no—
724C42—24no—
725C42—28no—
726C42—24no—
727C42—42no—
728C42—44no—
729C42C2×C22⋊C418yes—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—44no—
745C23—44no—
746C23—88no—
747C23—84no—
748C23—88no—
749C23—84no—
750C23—84no—
751C23#38512yes—
752C23#38512yes—
753C23#38612yes—
754C23#38612yes—
755C23#38812yes—
756C23#38812yes—
757C23#39412yes—
758C23#39412yes—
759C23#39612yes—
760C23#39612yes—
761C23#39711yescharacteristic
762C23#39711yescharacteristic
763C23#39711yescharacteristic
764C23#39711yescharacteristic
765C23#39912yes—
766C23#39912yes—
767C23C2×C4×D411yescharacteristic
768C23C2×#12111yescharacteristic
769C23C2×C22⋊Q811yescharacteristic
770C23C2×#12311yescharacteristic
771C23C2×#12311yescharacteristic
772C23C2×#12311yescharacteristic
773C23C2×#12611yescharacteristic
774Q8—24no—
775Q8—24no—
776Q8—42no—
777Q8—42no—
778Q8—44no—
779Q8—44no—
780D4—24no—
781D4—24no—
782D4—44no—
783D4—44no—
784D4—48no—
785D4—48no—
786D4—44no—
787D4—44no—
788D4—42no—
789D4—42no—
790D4—44no—
791D4—44no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—416no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—88no—
808C2×C4—84no—
809C2×C4#38012yes—
810C2×C4#38012yes—
811C2×C4#38012yes—
812C2×C4#38012yes—
813C2×C4#38512yes—
814C2×C4#38512yes—
815C2×C4#38512yes—
816C2×C4#38512yes—
817C2×C4#38512yes—
818C2×C4#38512yes—
819C2×C4#38612yes—
820C2×C4#38612yes—
821C2×C4#38812yes—
822C2×C4#38812yes—
823C2×C4#38812yes—
824C2×C4#38812yes—
825C2×C4#38812yes—
826C2×C4#38812yes—
827C2×C4#39012yes—
828C2×C4#39012yes—
829C2×C4#39012yes—
830C2×C4#39012yes—
831C2×C4#39212yes—
832C2×C4#39212yes—
833C2×C4#39212yes—
834C2×C4#39212yes—
835C2×C4#39312yes—
836C2×C4#39312yes—
837C2×C4#39312yes—
838C2×C4#39312yes—
839C2×C4#39412yes—
840C2×C4#39412yes—
841C2×C4#39412yes—
842C2×C4#39412yes—
843C2×C4#39412yes—
844C2×C4#39412yes—
845C2×C4#39612yes—
846C2×C4#39612yes—
847C2×C4#39612yes—
848C2×C4#39612yes—
849C2×C4#39612yes—
850C2×C4#39612yes—
851C2×C4#39711yescharacteristic
852C2×C4#39711yescharacteristic
853C2×C4#39711yescharacteristic
854C2×C4#39711yescharacteristic
855C2×C4#39912yes—
856C2×C4#39912yes—
857C2×C4C22×C22⋊C411yescharacteristic
858C2×C4C22×C4⋊C411yescharacteristic
859C2×C4C2×#11711yescharacteristic
860C2×C4C2×C4×D411yescharacteristic
861C2×C4C2×C4×D411yescharacteristic
862C2×C4C2×C4×D411yescharacteristic
863C2×C4C2×#12011yescharacteristic
864C2×C4C2×#12011yescharacteristic
865C2×C4C2×#12011yescharacteristic
866C2×C4C2×#12111yescharacteristic
867C2×C4C2×#12111yescharacteristic
868C2×C4C2×#12111yescharacteristic
869C2×C4C2×#12111yescharacteristic
870C2×C4C2×#12111yescharacteristic
871C2×C4C2×#12111yescharacteristic
872C2×C4C2×#12111yescharacteristic
873C2×C4C2×C22⋊Q811yescharacteristic
874C2×C4C2×C22⋊Q811yescharacteristic
875C2×C4C2×C22⋊Q811yescharacteristic
876C2×C4C2×C22⋊Q811yescharacteristic
877C2×C4C2×C22⋊Q811yescharacteristic
878C2×C4C2×#12311yescharacteristic
879C2×C4C2×#12311yescharacteristic
880C2×C4C2×#12411yescharacteristic
881C2×C4C2×#12411yescharacteristic
882C2×C4C2×#12411yescharacteristic
883C2×C4C2×#12611yescharacteristic
884C2×C4C2×#12711yescharacteristic
885C8—44no—
886C8—44no—
887C8—44no—
888C8—44no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—44no—
912C22—84no—
913C22—84no—
914C22—88no—
915C22—88no—
916C22—84no—
917C22#143912yes—
918C22#143912yes—
919C22#143912yes—
920C22#143912yes—
921C22#208014yes—
922C22C2×#38511yescharacteristic
923C22C2×#38611yescharacteristic
924C22C2×#38811yescharacteristic
925C22C2×#39411yescharacteristic
926C22C2×#39611yescharacteristic
927C22C2×#39711yescharacteristic
928C22C2×#39911yescharacteristic
929C4—48no—
930C4—44no—
931C4—84no—
932C4#143912yes—
933C4#143912yes—
934C4#143912yes—
935C4#143912yes—
936C4C2×#38011yescharacteristic
937C4C2×#38511yescharacteristic
938C4C2×#38811yescharacteristic
939C4C2×#39011yescharacteristic
940C4C2×#39211yescharacteristic
941C4C2×#39311yescharacteristic
942C4C2×#39411yescharacteristic
943C4C2×#39611yescharacteristic
944C2—21no—
945C2—21no—
946C2—22no—
947C2—21no—
948C2—21no—
949C2—21no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—84no—
954C2#1108614yesdirect product factor
955C2C2×#143911yescharacteristic
956C2C2×#208012yes—
subgroupG/H
centerC22×C4#124
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#397
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#424C2semidirect
5. C22×#344C2semidirect
6. C22×#341C2semidirect
7. C22×H(3,ℤ/4)C2semidirect
8. #11086C2direct (N × H)
19. C2×#424C22semidirect
23. C2×#421C4semidirect
39. C2×#344C22semidirect
41. C2×#341C22semidirect
43. C2×H(3,ℤ/4)C22semidirect
142. #421C2×C4semidirect
954. C2#11086direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4242
C22×#4212
C22×#4162
C22×#4132
C22×#3442
C22×#3412
C22×H(3,ℤ/4)2
#110862