Finite Group Databasebeta

← C2×#11114 #357779

Subgroups — C2×#11114 #357779

Order 512.

2806 conjugacy classes of subgroups.

The subgroup lattice has 965 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic, complemented
2C22×#421C211yesmaximal, characteristic
3C23×#104C211yesmaximal, characteristic
4C2×#2879C211yesmaximal, characteristic
5C22×#344C211yesmaximal, characteristic, complemented
6C22×#339C211yesmaximal, characteristic, complemented
7C2×#1728C211yesmaximal, characteristic, complemented
8#11114C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#430—22no—
17C2×#430—24no—
18C2×#430—24no—
19C2×#430C2214yescomplemented
20C22×#108—22no—
21C2×#421—22no—
22C2×#421—24no—
23C2×#421—24no—
24C2×#421C2214yes—
25C22×#104—22no—
26C22×#104—24no—
27C22×#104—24no—
28C22×#104C414yescomplemented
29C22×#104C414yescomplemented
30C22×#104C2214yes—
31#2879—22no—
32#2879—22no—
33#2879—22no—
34#2879C2214yes—
35C2×#408—22no—
36C2×#408—22no—
37C2×#407—22no—
38C2×#344—24no—
39C2×#344C2214yescomplemented
40C2×#339—24no—
41C2×#339C2214yescomplemented
42#1728—22no—
43#1728C2214yescomplemented
44C2×#336—22no—
45C22×#41—21no—
46C22×#41—21no—
47C22×#41—21no—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41C2×C412yes—
60C22×#41C2×C412yes—
61C22×#41D412yes—
62C22×#41D412yes—
63C22×#41Q812yes—
64C22×#41C2312yes—
65C23×Q8Q811yescharacteristic
66C23×D4—21no—
67C23×D4Q811yescharacteristic
68C24×C4—21no—
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×M16—22no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—22no—
92C22×M16—21no—
93C22×M16—22no—
94C22×M16—21no—
95C22×M16—22no—
96C22×M16—22no—
97C22×M16—22no—
98C22×M16—22no—
99C22×M16C2×C412yes—
100C22×M16C2×C412yes—
101C22×M16D412yes—
102C22×M16D412yes—
103C22×M16D414yes—
104C22×M16D414yes—
105C22×M16D414yes—
106C22×M16D412yes—
107C22×M16C2312yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C22×M16C2312yes—
111C23×C8—21no—
112C23×C8—21no—
113C23×C8—21no—
114C23×C8D412yes—
115C2×#117—22no—
116C2×#117—21no—
117C2×#117—22no—
118C2×#117—21no—
119C2×#117—22no—
120C2×#117—21no—
121C2×#117D414yes—
122C2×#117C2312yes—
123C22×C4⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C42—22no—
126C22×C42—22no—
127C22×C42—21no—
128C22×C42—22no—
129C22×C42—22no—
130C22×C42—21no—
131C22×C42—21no—
132C22×C42—21no—
133C22×C42C2×C412yes—
134C22×C42C2×C412yes—
135C22×C42C2312yes—
136#430—216no—
137#430—28no—
138#430—28no—
139C2×#108—216no—
140C2×#108—28no—
141#421—216no—
142#421—28no—
143#421—28no—
144C2×#104—216no—
145C2×#104—28no—
146C2×#104—216no—
147C2×#104—216no—
148C2×#104—28no—
149C2×#104—28no—
150C2×#104C2×C4116yescomplemented
151#408—28no—
152#408—28no—
153#408—28no—
154#408—28no—
155#407—28no—
156#407—28no—
157C2×C22⋊C8—28no—
158#344—28no—
159#339—28no—
160#336—28no—
161C25—21no—
162C25#4111yescharacteristic
163C2×#41—22no—
164C2×#41—22no—
165C2×#41—22no—
166C2×#41—22no—
167C2×#41—22no—
168C2×#41—22no—
169C2×#41—22no—
170C2×#41—22no—
171C2×#41—22no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—22no—
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—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—22no—
196C2×#41—22no—
197C2×#41—22no—
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—22no—
201C2×#41—22no—
202C2×#41—22no—
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—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×#41C4⋊C414yes—
228C2×#41C4⋊C414yes—
229C2×#41C22×C414yes—
230C2×#41C2×D414yes—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8C4⋊C412yes—
239C22×Q8C4⋊C412yes—
240C22×Q8C2×Q812yes—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4C4⋊C412yes—
259C22×D4C4⋊C412yes—
260C22×D4C2×Q812yes—
261C23×C4—22no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—48no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—41no—
279C23×C4C22×C411yescharacteristic
280C23×C4C22×C411yescharacteristic
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D412yes—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×Q811yescharacteristic
292C23×C4C2×Q811yescharacteristic
293C23×C4#4112yes—
294C23×C4#4112yes—
295C23×C4#4112yes—
296C23×C4#4111yescharacteristic
297C23×C4#4111yescharacteristic
298C23×C4#4111yescharacteristic
299C23×C4#4112yes—
300C23×C4C2411yescharacteristic
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—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
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—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
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×M16C22⋊C418yes—
367C2×M16C22⋊C418yes—
368C2×M16C22×C414yes—
369C2×M16C2×D414yes—
370C2×M16C2×D414yes—
371C2×M16C2×D414yes—
372C2×M16C2×D414yes—
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—24no—
376C22×C8—24no—
377C22×C8—22no—
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×C8C2×D414yes—
393#117—24no—
394#117—22no—
395#117—24no—
396#117—22no—
397#117—24no—
398#117—22no—
399#117—42no—
400#117—42no—
401#117—42no—
402#117C2×D414yes—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—41no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—42no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—41no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42C22×C414yes—
433#108—232no—
434#104—232no—
435#104—232no—
436C22⋊C8—232no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—44no—
441C24—42no—
442C24—42no—
443C24—84no—
444C24C4×D411yescharacteristic
445C24C4×D411yescharacteristic
446C24#12112yes—
447C24C22⋊Q811yescharacteristic
448C24C22⋊Q811yescharacteristic
449C24#12311yescharacteristic
450C24#12311yescharacteristic
451C24#12412yes—
452C24#12412yes—
453C24#12612yes—
454C24C2×#4111yescharacteristic
455#41—24no—
456#41—24no—
457#41—24no—
458#41—24no—
459#41—24no—
460#41—24no—
461#41—24no—
462#41—24no—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—28no—
467#41—42no—
468#41—42no—
469#41—42no—
470#41—42no—
471#41—42no—
472#41—42no—
473#41—42no—
474#41—42no—
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—
491#41—44no—
492#41—44no—
493#41—44no—
494#41—44no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—24no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8C2×C4⋊C414yes—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—22no—
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—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4C2×C4⋊C414yes—
549C22×C4—28no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—44no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—84no—
586C22×C4C2×C22⋊C412yes—
587C22×C4C2×C22⋊C412yes—
588C22×C4C2×C4⋊C411yescharacteristic
589C22×C4C2×C4⋊C411yescharacteristic
590C22×C4C2×C4⋊C411yescharacteristic
591C22×C4C2×C4⋊C411yescharacteristic
592C22×C4#11712yes—
593C22×C4#11712yes—
594C22×C4C4×D412yes—
595C22×C4C4×D412yes—
596C22×C4C4×D412yes—
597C22×C4C4×D412yes—
598C22×C4C4×D411yescharacteristic
599C22×C4C4×D411yescharacteristic
600C22×C4C4×D411yescharacteristic
601C22×C4C4×D411yescharacteristic
602C22×C4C4×D411yescharacteristic
603C22×C4C4×D411yescharacteristic
604C22×C4#12012yes—
605C22×C4#12012yes—
606C22×C4#12011yescharacteristic
607C22×C4#12011yescharacteristic
608C22×C4#12011yescharacteristic
609C22×C4#12012yes—
610C22×C4#12012yes—
611C22×C4#12011yescharacteristic
612C22×C4#12112yes—
613C22×C4#12112yes—
614C22×C4#12112yes—
615C22×C4#12112yes—
616C22×C4#12112yes—
617C22×C4#12112yes—
618C22×C4#12112yes—
619C22×C4#12112yes—
620C22×C4#12112yes—
621C22×C4#12112yes—
622C22×C4#12112yes—
623C22×C4#12112yes—
624C22×C4#12112yes—
625C22×C4#12112yes—
626C22×C4#12112yes—
627C22×C4C22⋊Q812yes—
628C22×C4C22⋊Q812yes—
629C22×C4C22⋊Q812yes—
630C22×C4C22⋊Q812yes—
631C22×C4C22⋊Q812yes—
632C22×C4C22⋊Q812yes—
633C22×C4C22⋊Q812yes—
634C22×C4C22⋊Q812yes—
635C22×C4C22⋊Q811yescharacteristic
636C22×C4C22⋊Q811yescharacteristic
637C22×C4C22⋊Q811yescharacteristic
638C22×C4C22⋊Q811yescharacteristic
639C22×C4C22⋊Q811yescharacteristic
640C22×C4C22⋊Q811yescharacteristic
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#12311yescharacteristic
650C22×C4#12311yescharacteristic
651C22×C4#12412yes—
652C22×C4#12412yes—
653C22×C4#12412yes—
654C22×C4#12412yes—
655C22×C4#12612yes—
656C22×C4#12612yes—
657C22×C4#12612yes—
658C22×C4#12712yes—
659C22×C4#12712yes—
660C22×C4C23×C411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×Q811yescharacteristic
669C22×C4C2×#4111yescharacteristic
670C22×C4C2×#4111yescharacteristic
671C22×C4C2×#4111yescharacteristic
672C22×C4C2×#4111yescharacteristic
673C22×C4C2×#4111yescharacteristic
674M16—24no—
675M16—24no—
676M16—24no—
677M16—28no—
678M16—28no—
679M16—24no—
680M16—24no—
681M16—24no—
682M16—24no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16—42no—
688M16—42no—
689M16—42no—
690M16—42no—
691M16—44no—
692M16—44no—
693M16—44no—
694M16—44no—
695M16—44no—
696M16—44no—
697M16C2×C22⋊C418yes—
698C2×C8—24no—
699C2×C8—24no—
700C2×C8—24no—
701C2×C8—28no—
702C2×C8—28no—
703C2×C8—24no—
704C2×C8—24no—
705C2×C8—24no—
706C2×C8—24no—
707C2×C8—24no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8—42no—
711C2×C8—42no—
712C2×C8—44no—
713C2×C8—44no—
714C2×C8—44no—
715C2×C8—44no—
716C2×C8—44no—
717C2×C8—44no—
718C4⋊C4—24no—
719C4⋊C4—42no—
720C4⋊C4—44no—
721C22⋊C4—24no—
722C22⋊C4—42no—
723C22⋊C4—44no—
724C42—24no—
725C42—24no—
726C42—24no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—44no—
731C42—44no—
732C42—44no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—42no—
738C23—44no—
739C23—44no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—44no—
744C23—44no—
745C23—48no—
746C23—42no—
747C23—42no—
748C23—44no—
749C23—44no—
750C23—84no—
751C23—84no—
752C23—88no—
753C23—88no—
754C23#38511yescharacteristic
755C23#38511yescharacteristic
756C23#38511yescharacteristic
757C23#38511yescharacteristic
758C23#38812yes—
759C23#38812yes—
760C23#39012yes—
761C23#39012yes—
762C23#39312yes—
763C23#39312yes—
764C23#39412yes—
765C23#39412yes—
766C23#39612yes—
767C23#39612yes—
768C23#39712yes—
769C23#39712yes—
770C23C2×C4×D411yescharacteristic
771C23C2×#12111yescharacteristic
772C23C2×C22⋊Q811yescharacteristic
773C23C2×#12311yescharacteristic
774C23C2×#12411yescharacteristic
775C23C2×#12411yescharacteristic
776C23C2×#12611yescharacteristic
777Q8—24no—
778Q8—24no—
779Q8—42no—
780Q8—42no—
781Q8—44no—
782Q8—44no—
783D4—24no—
784D4—24no—
785D4—44no—
786D4—44no—
787D4—48no—
788D4—48no—
789D4—44no—
790D4—44no—
791D4—42no—
792D4—42no—
793D4—44no—
794D4—44no—
795C2×C4—28no—
796C2×C4—24no—
797C2×C4—416no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—416no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4#38012yes—
817C2×C4#38012yes—
818C2×C4#38012yes—
819C2×C4#38012yes—
820C2×C4#38511yescharacteristic
821C2×C4#38511yescharacteristic
822C2×C4#38511yescharacteristic
823C2×C4#38511yescharacteristic
824C2×C4#38512yes—
825C2×C4#38512yes—
826C2×C4#38512yes—
827C2×C4#38512yes—
828C2×C4#38612yes—
829C2×C4#38612yes—
830C2×C4#38612yes—
831C2×C4#38612yes—
832C2×C4#38812yes—
833C2×C4#38812yes—
834C2×C4#38812yes—
835C2×C4#38812yes—
836C2×C4#38812yes—
837C2×C4#38812yes—
838C2×C4#39012yes—
839C2×C4#39012yes—
840C2×C4#39212yes—
841C2×C4#39212yes—
842C2×C4#39212yes—
843C2×C4#39212yes—
844C2×C4#39312yes—
845C2×C4#39312yes—
846C2×C4#39412yes—
847C2×C4#39412yes—
848C2×C4#39412yes—
849C2×C4#39412yes—
850C2×C4#39412yes—
851C2×C4#39412yes—
852C2×C4#39612yes—
853C2×C4#39612yes—
854C2×C4#39612yes—
855C2×C4#39612yes—
856C2×C4#39612yes—
857C2×C4#39612yes—
858C2×C4#39712yes—
859C2×C4#39712yes—
860C2×C4#39912yes—
861C2×C4#39912yes—
862C2×C4#39912yes—
863C2×C4#39912yes—
864C2×C4C22×C22⋊C411yescharacteristic
865C2×C4C22×C4⋊C411yescharacteristic
866C2×C4C2×#11711yescharacteristic
867C2×C4C2×C4×D411yescharacteristic
868C2×C4C2×C4×D411yescharacteristic
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×#12011yescharacteristic
871C2×C4C2×#12011yescharacteristic
872C2×C4C2×#12011yescharacteristic
873C2×C4C2×#12111yescharacteristic
874C2×C4C2×#12111yescharacteristic
875C2×C4C2×#12111yescharacteristic
876C2×C4C2×#12111yescharacteristic
877C2×C4C2×#12111yescharacteristic
878C2×C4C2×#12111yescharacteristic
879C2×C4C2×#12111yescharacteristic
880C2×C4C2×C22⋊Q811yescharacteristic
881C2×C4C2×C22⋊Q811yescharacteristic
882C2×C4C2×C22⋊Q811yescharacteristic
883C2×C4C2×C22⋊Q811yescharacteristic
884C2×C4C2×C22⋊Q811yescharacteristic
885C2×C4C2×#12311yescharacteristic
886C2×C4C2×#12311yescharacteristic
887C2×C4C2×#12311yescharacteristic
888C2×C4C2×#12311yescharacteristic
889C2×C4C2×#12411yescharacteristic
890C2×C4C2×#12611yescharacteristic
891C2×C4C2×#12711yescharacteristic
892C8—28no—
893C8—44no—
894C8—44no—
895C8—44no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—48no—
920C22—84no—
921C22—84no—
922C22—88no—
923C22—88no—
924C22#143912yes—
925C22#143912yes—
926C22#143912yes—
927C22#143912yes—
928C22#186114yes—
929C22C2×#38511yescharacteristic
930C22C2×#38811yescharacteristic
931C22C2×#39011yescharacteristic
932C22C2×#39311yescharacteristic
933C22C2×#39411yescharacteristic
934C22C2×#39611yescharacteristic
935C22C2×#39711yescharacteristic
936C4—48no—
937C4—44no—
938C4—84no—
939C4#143912yes—
940C4#143912yes—
941C4#143912yes—
942C4#143912yes—
943C4C2×#38011yescharacteristic
944C4C2×#38511yescharacteristic
945C4C2×#38611yescharacteristic
946C4C2×#38811yescharacteristic
947C4C2×#39211yescharacteristic
948C4C2×#39411yescharacteristic
949C4C2×#39611yescharacteristic
950C4C2×#39911yescharacteristic
951C2—21no—
952C2—21no—
953C2—21no—
954C2—21no—
955C2—22no—
956C2—21no—
957C2—22no—
958C2—22no—
959C2—21no—
960C2—84no—
961C2#1111414yesdirect product factor
962C2C2×#143911yescharacteristic
963C2C2×#186112yes—
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#385
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×#430C2semidirect
5. C22×#344C2semidirect
6. C22×#339C2semidirect
7. C2×#1728C2semidirect
8. #11114C2direct (N × H)
19. C2×#430C22semidirect
28. C22×#104C4semidirect
29. C22×#104C4semidirect
39. C2×#344C22semidirect
41. C2×#339C22semidirect
43. #1728C22semidirect
150. C2×#104C2×C4semidirect
961. C2#11114direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4302
C22×#4212
C23×#1042
C2×#28792
C22×#3442
C22×#3392
C2×#17282
#111142