Finite Group Databasebeta

← C2×#23721 #6432357

Subgroups — C2×#23721 #6432357

Order 512.

2288 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#137C211yesmaximal, characteristic, complemented
2C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
3C22×#440C211yesmaximal, characteristic, complemented
4C2×#2923C211yesmaximal, characteristic, complemented
5#23721C2116yesmaximal, direct product factor
6C2×#2089C211yesmaximal, characteristic, complemented
7C2×#2078C211yesmaximal, characteristic, complemented
8C2×#2064C211yesmaximal, characteristic, complemented
9C2×#2063C211yesmaximal, characteristic, complemented
10C2×#2052C211yesmaximal, characteristic, complemented
11C2×#2051C211yesmaximal, characteristic
12C2×#2046C211yesmaximal, characteristic, complemented
13C2×#2019C211yesmaximal, characteristic
14C2×#1778C211yesmaximal, characteristic, complemented
15C2×C4×#101C211yesmaximal, characteristic, complemented
16C2×C4×#100C211yesmaximal, characteristic, complemented
17C22×#137C2211yescharacteristic
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C2×C4×#41C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C4×#137—24no—
24C4×#137C2218yescomplemented
25C4×AGL(1,ℤ/8)—24no—
26C4×AGL(1,ℤ/8)C2218yes—
27C2×#442—21no—
28C2×#441—21no—
29C2×#440—22no—
30C2×#440—22no—
31C2×#440—24no—
32C2×#440—21no—
33C2×#440—21no—
34C2×#440C2218yescomplemented
35C2×C4×Q16—21no—
36C2×C4×SD16—21no—
37C2×C4×SD16—21no—
38C2×C4×D8—21no—
39#2923—24no—
40#2923C2218yescomplemented
41C2×#433—22no—
42C2×#432—22no—
43C22×#108C2211yescharacteristic
44C22×#108C2211yescharacteristic
45C2×#428C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C22×#107C2211yescharacteristic
48C2×#424C2211yescharacteristic
49C2×#424C2211yescharacteristic
50C2×#417C2211yescharacteristic
51C2×#417C2211yescharacteristic
52C2×#419C2211yescharacteristic
53C2×#418C2211yescharacteristic
54C22×#103C2211yescharacteristic
55C22×#102C2211yescharacteristic
56C22×#101C2211yescharacteristic
57C22×#101C2211yescharacteristic
58C22×#100C2211yescharacteristic
59C22×#100C2211yescharacteristic
60C2×#408C2211yescharacteristic
61C2×#408C2211yescharacteristic
62C2×C4×M16C2211yescharacteristic
63C2×C4×M16C2211yescharacteristic
64C2×C4×M16C2211yescharacteristic
65C22×#97C2211yescharacteristic
66#2089C2218yescomplemented
67#2078C2218yescomplemented
68#2064C2218yescomplemented
69#2063C2218yescomplemented
70#2052C2218yescomplemented
71#2051C2218yes—
72#2046C2218yescomplemented
73#2019C2218yes—
74#1778C2218yescomplemented
75C4×#101C2218yescomplemented
76C4×#100C2218yescomplemented
77C2×#343C2211yescharacteristic
78C2×#343C2211yescharacteristic
79C2×#343C2211yescharacteristic
80C2×#343C2211yescharacteristic
81C2×#341C2211yescharacteristic
82C2×#341C2211yescharacteristic
83C22×#41C2311yescharacteristic
84C23×Q8C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C2×#137—22no—
88C2×#137—24no—
89C2×#137—24no—
90C2×#137C2314yes—
91C2×AGL(1,ℤ/8)—22no—
92C2×AGL(1,ℤ/8)—24no—
93C2×AGL(1,ℤ/8)—24no—
94C2×AGL(1,ℤ/8)C2314yes—
95C22×Q16—21no—
96C22×SD16—21no—
97C22×SD16—24no—
98C22×SD16—21no—
99C22×SD16—24no—
100C22×SD16—22no—
101C22×SD16—22no—
102C22×SD16C2314yes—
103C22×D8—21no—
104C22×M16C2311yescharacteristic
105C22×M16C2311yescharacteristic
106C22×M16C2311yescharacteristic
107C22×M16C2311yescharacteristic
108C22×M16C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C4×#41—22no—
113C4×#41—22no—
114C4×#41D414yes—
115C4×#41C2314yes—
116C2×C4×Q8—22no—
117C2×C4×Q8—21no—
118C2×C4×Q8—21no—
119C2×C4×Q8—22no—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—22no—
123C2×C4×Q8D411yescharacteristic
124C2×C4×Q8D411yescharacteristic
125C2×C4×Q8C2314yes—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4D411yescharacteristic
136C2×C4×D4D411yescharacteristic
137C2×C4×D4C2314yes—
138C2×#117—21no—
139C2×#117C2311yescharacteristic
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42—21no—
146C22×C42C2311yescharacteristic
147#442—28no—
148#441—28no—
149#440—28no—
150#440—28no—
151#440—216no—
152#440—216no—
153C4×Q16—28no—
154C4×SD16—28no—
155C4×SD16—28no—
156C4×D8—28no—
157#433—216no—
158#432—216no—
159C2×#108—24no—
160C2×#108—24no—
161C2×#108C2314yes—
162C2×#108C2314yes—
163#428—22no—
164#428—22no—
165#428C2314yes—
166#428C2314yes—
167C2×#107—22no—
168C2×#107—22no—
169C2×#107—21no—
170C2×#107—21no—
171C2×#107C2314yes—
172C2×#106—21no—
173C2×#106—21no—
174#424—22no—
175#424—22no—
176#424C2314yes—
177#424C2314yes—
178C2×C4⋊C8—22no—
179C2×C4⋊C8—22no—
180#419—22no—
181#419C2314yes—
182#418—22no—
183#418C2314yes—
184#417—22no—
185#417—22no—
186#417C2314yes—
187#417C2314yes—
188C2×#103—21no—
189C2×#103—21no—
190C2×#103—22no—
191C2×#103—22no—
192C2×#103—21no—
193C2×#103—21no—
194C2×#103C2314yes—
195C2×#102—21no—
196C2×#102—21no—
197C2×#102—22no—
198C2×#102—22no—
199C2×#102—21no—
200C2×#102—21no—
201C2×#102C2314yes—
202C2×#101—24no—
203C2×#101—24no—
204C2×#101C2314yes—
205C2×#101C2314yes—
206C2×#100—24no—
207C2×#100—24no—
208C2×#100C2314yes—
209C2×#100C2314yes—
210#408—22no—
211#408—22no—
212#408C2314yes—
213#408C2314yes—
214C2×C22⋊C8—22no—
215C2×C22⋊C8—22no—
216C4×M16—22no—
217C4×M16—22no—
218C4×M16—22no—
219C4×M16C2314yes—
220C4×M16C2314yes—
221C4×M16C2314yes—
222C2×#97—21no—
223C2×#97—21no—
224C2×#97—21no—
225C2×#97D412yes—
226C2×#97D412yes—
227C2×#97D414yes—
228C2×#97C2314yes—
229C2×C4×C8—21no—
230C2×C4×C8—21no—
231C2×C4×C8—21no—
232#343C2314yes—
233#343C2314yes—
234#343C2314yes—
235#343C2314yes—
236#341C2314yes—
237#341C2314yes—
238C25—21no—
239C2×#41—21no—
240C2×#41—21no—
241C2×#41—22no—
242C2×#41—22no—
243C2×#41—22no—
244C2×#41—22no—
245C2×#41C2×D412yes—
246C2×#41C2412yes—
247C22×Q8—21no—
248C22×Q8—22no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8C2×D411yescharacteristic
256C22×Q8#4114yes—
257C22×Q8C2412yes—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—21no—
266C22×D4—22no—
267C22×D4C2×D411yescharacteristic
268C22×D4#4114yes—
269C22×D4C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—41no—
279C23×C4—41no—
280C23×C4—84no—
281C23×C4#4111yescharacteristic
282C23×C4#4111yescharacteristic
283C23×C4C2411yescharacteristic
284#137—216no—
285#137—28no—
286#137—28no—
287AGL(1,ℤ/8)—216no—
288AGL(1,ℤ/8)—28no—
289AGL(1,ℤ/8)—28no—
290C2×Q16—28no—
291C2×Q16—24no—
292C2×SD16—216no—
293C2×SD16—216no—
294C2×SD16—28no—
295C2×SD16—28no—
296C2×SD16—24no—
297C2×SD16—28no—
298C2×SD16—24no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×D8—28no—
302C2×D8—24no—
303C2×M16—21no—
304C2×M16—21no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—21no—
308C2×M16—21no—
309C2×M16—21no—
310C2×M16—21no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16#4114yes—
320C2×M16#4114yes—
321C2×M16C2412yes—
322C2×M16C2412yes—
323C2×M16C2412yes—
324C2×M16C2412yes—
325C2×M16C2412yes—
326C2×M16C2412yes—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—21no—
334C22×C8—21no—
335C22×C8—21no—
336C22×C8—21no—
337C22×C8C2×D412yes—
338C22×C8C2×D412yes—
339C22×C8C2×D412yes—
340C22×C8C2×D412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8—24no—
349C4×Q8—42no—
350C4×Q8—42no—
351C4×Q8—42no—
352C4×Q8—42no—
353C4×Q8C2×D414yes—
354C4×Q8C2×D414yes—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—24no—
365C4×D4—42no—
366C4×D4—42no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4C2×D414yes—
370C4×D4C2×D414yes—
371#117—21no—
372#117—21no—
373#117—24no—
374#117—24no—
375#117C2×D412yes—
376#117C2412yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42—41no—
412C2×C42—41no—
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D412yes—
417C2×C42C2×D412yes—
418C2×C42C2×D411yescharacteristic
419C2×C42#4112yes—
420C2×C42C2412yes—
421#108—28no—
422#108—28no—
423#107—28no—
424#107—24no—
425#107—24no—
426#106—24no—
427#106—24no—
428C4⋊C8—28no—
429C4⋊C8—28no—
430#103—24no—
431#103—24no—
432#103—28no—
433#103—24no—
434#103—24no—
435#102—24no—
436#102—24no—
437#102—28no—
438#102—24no—
439#102—24no—
440#101—28no—
441#101—28no—
442#100—28no—
443#100—28no—
444C22⋊C8—28no—
445C22⋊C8—28no—
446#97—24no—
447#97—24no—
448#97—24no—
449#97C2×D418yes—
450#97C2×D418yes—
451C4×C8—24no—
452C4×C8—24no—
453C4×C8—24no—
454C24—21no—
455C24—24no—
456C24—22no—
457C24—41no—
458C24—41no—
459C24—42no—
460C24—82no—
461C24—82no—
462C24C2×#4111yescharacteristic
463#41—24no—
464#41—24no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—42no—
470#41—42no—
471#41—42no—
472#41—42no—
473C2×Q8—21no—
474C2×Q8—24no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8C22×D412yes—
494C2×Q8C2×#4114yes—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4C22×D412yes—
520C2×D4C2×#4114yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—88no—
550C22×C4—88no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4#12111yescharacteristic
554C22×C4#12111yescharacteristic
555C22×C4#12111yescharacteristic
556C22×C4#12111yescharacteristic
557C22×C4#12112yes—
558C22×C4#12112yes—
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2511yescharacteristic
571Q16—216no—
572SD16—232no—
573SD16—216no—
574SD16—216no—
575D8—216no—
576M16—24no—
577M16—24no—
578M16—22no—
579M16—22no—
580M16—22no—
581M16—22no—
582M16—22no—
583M16—22no—
584M16—22no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—42no—
589M16—42no—
590M16—42no—
591M16—42no—
592M16C2×#4114yes—
593M16C2×#4114yes—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—42no—
611C2×C8—42no—
612C2×C8—42no—
613C2×C8—42no—
614C2×C8C22×D414yes—
615C2×C8C22×D414yes—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4C22×D412yes—
631C4⋊C4C22×D412yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C42—22no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—44no—
643C42—44no—
644C42#12112yes—
645C42#12112yes—
646C42#12112yes—
647C42#12112yes—
648C42C22×D412yes—
649C42C22×D412yes—
650C42C22×D412yes—
651C42C22×D412yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—42no—
657C23—44no—
658C23—44no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—82no—
664C23—82no—
665C23—88no—
666C23—82no—
667C23—82no—
668C23—88no—
669C23—82no—
670C23—82no—
671C23C2×#12111yescharacteristic
672C23C2×#12111yescharacteristic
673C23#52912yes—
674C23#52912yes—
675C23C22×#4111yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—24no—
679Q8—22no—
680Q8—44no—
681Q8—44no—
682Q8—42no—
683Q8—42no—
684Q8—42no—
685D4—22no—
686D4—24no—
687D4—24no—
688D4—22no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—88no—
724C2×C4—88no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C2×#12112yes—
732C2×C4C2×#12112yes—
733C2×C4C2×#12112yes—
734C2×C4C2×#12112yes—
735C2×C4C2×#12111yescharacteristic
736C2×C4C2×#12111yescharacteristic
737C2×C4#52512yes—
738C2×C4#52512yes—
739C2×C4#52512yes—
740C2×C4#52512yes—
741C2×C4#52512yes—
742C2×C4#52512yes—
743C2×C4#52912yes—
744C2×C4#52912yes—
745C2×C4#53212yes—
746C2×C4#53212yes—
747C2×C4C23×D411yescharacteristic
748C2×C4C23×D411yescharacteristic
749C2×C4C22×#4111yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4C22×#4111yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C8—24no—
754C8—24no—
755C8—24no—
756C8—24no—
757C8—42no—
758C8—42no—
759C8—42no—
760C8—42no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—84no—
772C22—88no—
773C22—84no—
774C22—82no—
775C22—82no—
776C22—84no—
777C22—88no—
778C22#239212yes—
779C22#239212yes—
780C22#306812yes—
781C22#306912yes—
782C22C22×#12111yescharacteristic
783C22C2×#52911yescharacteristic
784C22C2×#52911yescharacteristic
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—82no—
794C4—82no—
795C4#239212yes—
796C4#239212yes—
797C4C2×#52511yescharacteristic
798C4C2×#52511yescharacteristic
799C4C2×#52511yescharacteristic
800C4C2×#53211yescharacteristic
801C2—22no—
802C2—21no—
803C2—21no—
804C2—82no—
805C2—84no—
806C2#2372114yesdirect product factor
807C2C2×#239211yescharacteristic
808C2C2×#306811yescharacteristic
809C2C2×#306911yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×C4×#137C2semidirect
3. C22×#440C2semidirect
4. C2×#2923C2semidirect
5. #23721C2direct (N × H)
6. C2×#2089C2semidirect
7. C2×#2078C2semidirect
8. C2×#2064C2semidirect
9. C2×#2063C2semidirect
10. C2×#2052C2semidirect
12. C2×#2046C2semidirect
14. C2×#1778C2semidirect
15. C2×C4×#101C2semidirect
16. C2×C4×#100C2semidirect
24. C4×#137C22semidirect
34. C2×#440C22semidirect
40. #2923C22semidirect
66. #2089C22semidirect
67. #2078C22semidirect
68. #2064C22semidirect
69. #2063C22semidirect
70. #2052C22semidirect
72. #2046C22semidirect
74. #1778C22semidirect
75. C4×#101C22semidirect
76. C4×#100C22semidirect
806. C2#23721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1372
C2×C4×AGL(1,ℤ/8)2
C22×#4402
C2×#29232
#237212
C2×#20892
C2×#20782
C2×#20642
C2×#20632
C2×#20522
C2×#20512
C2×#20462
C2×#20192
C2×#17782
C2×C4×#1012
C2×C4×#1002