Finite Group Databasebeta

← C2×#60433 #10574955

Subgroups — C2×#60433 #10574955

Order 512.

10398 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#578C211yesmaximal, characteristic, complemented
2C22×#577C211yesmaximal, characteristic, complemented
3C2×#3500C211yesmaximal, characteristic, complemented
4C2×C4×2−1+4C211yesmaximal, characteristic, complemented
5#60433C2132yesmaximal, direct product factor
6C2×#3046C213yesmaximal, complemented
7C2×#3045C213yesmaximal, complemented
8C2×#3044C213yesmaximal, complemented
9C2×#3043C213yesmaximal, complemented
10C2×#3040C213yesmaximal, complemented
11C2×#3037C213yesmaximal, complemented
12C2×#3035C213yesmaximal, complemented
13C22×#464C213yesmaximal, complemented
14C2×#2906C211yesmaximal, characteristic, complemented
15C2×#2898C211yesmaximal, characteristic, complemented
16C2×#2897C211yesmaximal, characteristic, complemented
17C22×2−1+4C2211yescharacteristic
18C22×2−1+4C2211yescharacteristic
19C22×H(5,𝔽2)C2211yescharacteristic
20C2×#578—216no—
21C2×#578C22116yescomplemented
22C2×#577—216no—
23C2×#577C22116yescomplemented
24C22×#137C2213yes—
25C22×#137C2213yescomplemented
26C22×#137C2213yescomplemented
27C22×AGL(1,ℤ/8)C2213yes—
28C22×#135C2213yes—
29C22×#135C2213yescomplemented
30C23×Q16C2213yescomplemented
31C23×SD16C2213yes—
32C22×#131C2211yescharacteristic
33C22×#131C2211yescharacteristic
34#3500—28no—
35#3500C22116yescomplemented
36C2×#548—21no—
37C2×#548—21no—
38C2×#546—23no—
39C2×#546—23no—
40C2×#536C2213yes—
41C2×#535C2213yes—
42C2×#532C2213yes—
43C22×#124C2213yes—
44C4×2−1+4—28no—
45C4×2−1+4C22116yescomplemented
46C2×#520—23no—
47C2×#520C2211yescharacteristic
48C2×#520C2213yescomplemented
49C2×#519—21no—
50C2×#519C2213yescomplemented
51C2×C4×#41—23no—
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2213yescomplemented
54C22×C4×Q8—21no—
55C22×C4×Q8C2213yescomplemented
56#3046C22148yescomplemented
57#3045C22148yescomplemented
58#3044C22148yescomplemented
59#3043C22148yescomplemented
60#3040C22148yescomplemented
61#3037C22148yescomplemented
62#3035C22148yescomplemented
63C2×#464C2216yescomplemented
64C2×#464C2216yescomplemented
65C2×#464C2216yescomplemented
66C2×#464C2213yescomplemented
67C2×#464C2216yescomplemented
68C2×#464C2213yescomplemented
69C2×#464C22148yescomplemented
70C2×#462C2213yescomplemented
71C2×#462C2216yescomplemented
72C2×#460C2213yescomplemented
73C2×#460C2216yescomplemented
74C2×#463C2216yescomplemented
75C2×#463C2211yescharacteristic, complemented
76C2×#463C2213yescomplemented
77C2×#461C2213yescomplemented
78C2×#459C2213yescomplemented
79#2906C22116yescomplemented
80C2×#424C2213yescomplemented
81C2×#424C2213yescomplemented
82C2×#423C2213yescomplemented
83C22×C4⋊C8C2213yescomplemented
84#2898C22116yescomplemented
85#2897C22116yescomplemented
86C2×#417C2213yes—
87C2×#417C2213yescomplemented
88C2×#419C2213yescomplemented
89C2×#418C2213yes—
90C2×#416C2213yes—
91C2×#416C2213yescomplemented
92C22×#103C2213yescomplemented
93C22×#102C2213yes—
94C2×2−1+4—24no—
95C2×2−1+4—24no—
96C2×2−1+4—28no—
97C2×2−1+4—28no—
98C2×2−1+4—28no—
99C2×2−1+4D4116yescomplemented
100C2×2−1+4C2318yes—
101C2×2−1+4C2318yes—
102C2×H(5,𝔽2)—24no—
103C2×H(5,𝔽2)—28no—
104C2×H(5,𝔽2)—28no—
105C2×H(5,𝔽2)C2318yes—
106C22×#41—21no—
107C22×#41—23no—
108C22×#41—23no—
109C22×#41C2313yes—
110C22×#41C2313yes—
111C22×#41C2313yes—
112C22×#41C2311yescharacteristic
113C23×Q8—21no—
114C23×Q8—21no—
115C23×Q8C2313yes—
116C23×Q8C2313yes—
117C23×D4—23no—
118C23×D4C2313yes—
119#578—2128no—
120#577—2128no—
121C2×#137—224no—
122C2×#137—224no—
123C2×#137—224no—
124C2×#137C23124yes—
125C2×#137C23124yescomplemented
126C2×#137C23124yescomplemented
127C2×AGL(1,ℤ/8)—224no—
128C2×AGL(1,ℤ/8)C23124yes—
129C2×#135—224no—
130C2×#135—224no—
131C2×#135C23124yes—
132C2×#135C23124yescomplemented
133C22×Q16—224no—
134C22×Q16C2313yes—
135C22×Q16C2313yes—
136C22×Q16C2316yes—
137C22×Q16C23124yescomplemented
138C22×SD16—224no—
139C22×SD16C2311yescharacteristic
140C22×SD16C2313yes—
141C22×SD16C2313yes—
142C22×SD16C2313yes—
143C22×SD16C2316yes—
144C22×SD16C23124yes—
145C22×D8C2311yescharacteristic
146C22×D8C2313yes—
147C2×#131—28no—
148C2×#131—28no—
149C2×#131C2318yes—
150C2×#131C2318yes—
151C22×M16C2313yes—
152C22×M16C2313yes—
153C23×C8C2313yes—
154C23×C8C2313yes—
155#548—216no—
156#548—216no—
157#546—248no—
158#546—248no—
159#536—212no—
160#536C23124yes—
161#535—212no—
162#535C23124yes—
163#532—212no—
164#532C23124yes—
165C2×C4⋊Q8C2313yes—
166C2×#127C2313yes—
167C2×#124—23no—
168C2×#124—23no—
169C2×#124—212no—
170C2×#124C2313yes—
171C2×#124C2316yes—
172C2×#124C23124yes—
173C2×#124C2311yescharacteristic
174C2×#123—26no—
175C2×C22⋊Q8—23no—
176C2×C22⋊Q8—23no—
177C2×#121—23no—
178C2×#121—23no—
179C2×#121—23no—
180C2×#121—23no—
181C2×#120—26no—
182#520—24no—
183#520—248no—
184#520—212no—
185#520C2318yes—
186#520C23124yescomplemented
187#519—216no—
188#519—212no—
189#519C23124yescomplemented
190C4×#41—248no—
191C4×#41—212no—
192C4×#41D418yes—
193C4×#41C2318yes—
194C4×#41C23124yescomplemented
195C2×C4×Q8—21no—
196C2×C4×Q8—216no—
197C2×C4×Q8—23no—
198C2×C4×Q8—23no—
199C2×C4×Q8—23no—
200C2×C4×Q8—23no—
201C2×C4×Q8—212no—
202C2×C4×Q8D411yescharacteristic
203C2×C4×Q8D411yescharacteristic
204C2×C4×Q8C2313yes—
205C2×C4×Q8C2316yes—
206C2×C4×Q8C2313yes—
207C2×C4×Q8C23124yescomplemented
208C2×C4×D4—23no—
209C2×C4×D4—23no—
210C2×C4×D4—23no—
211C2×C4×D4—26no—
212C2×C4×D4—23no—
213C2×C4×D4—23no—
214C2×C4×D4D413yes—
215C2×C4×D4D413yes—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2313yes—
218C2×#117—23no—
219C2×#117—26no—
220C2×#117—23no—
221C2×#117C2313yes—
222C2×#117C2313yes—
223C22×C4⋊C4—23no—
224C22×C4⋊C4—23no—
225C22×C4⋊C4C2313yes—
226C22×C22⋊C4—23no—
227C22×C22⋊C4—23no—
228C22×C42—23no—
229C22×C42—23no—
230C22×C42C2313yes—
231#464C23124yescomplemented
232#464C23148yescomplemented
233#464C23148yescomplemented
234#464C23148yescomplemented
235#464C23124yescomplemented
236#464C23148yescomplemented
237#463C2318yescomplemented
238#463C23124yescomplemented
239#463C23148yescomplemented
240#462C23124yescomplemented
241#462C23148yescomplemented
242#461C23124yescomplemented
243#460C23124yescomplemented
244#460C23148yescomplemented
245#459C23124yescomplemented
246#424C23124yescomplemented
247#424C23124yescomplemented
248#423C23124yescomplemented
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2313yes—
251C2×C4⋊C8C2313yes—
252C2×C4⋊C8C2313yes—
253C2×C4⋊C8C2316yes—
254C2×C4⋊C8C23124yescomplemented
255#419C23124yescomplemented
256#418C23124yes—
257#417C23124yes—
258#417C23124yescomplemented
259#416C23124yes—
260#416C23124yescomplemented
261C2×#103C2313yes—
262C2×#103C2316yes—
263C2×#103C2311yescharacteristic
264C2×#103C2313yes—
265C2×#103C2313yes—
266C2×#103C23124yescomplemented
267C2×#102C2313yes—
268C2×#102C2316yes—
269C2×#102C23124yes—
270C2×#102C2313yes—
271C2×#102C2311yescharacteristic
272C2×#102C2313yes—
273C25—23no—
2742−1+4—264no—
2752−1+4—232no—
2762−1+4—232no—
2772−1+4—232no—
2782−1+4—432no—
2792−1+4C2×D4164yescomplemented
280H(5,𝔽2)—232no—
281H(5,𝔽2)—232no—
282H(5,𝔽2)—432no—
283C2×#41—28no—
284C2×#41—248no—
285C2×#41—224no—
286C2×#41—224no—
287C2×#41—26no—
288C2×#41—26no—
289C2×#41—26no—
290C2×#41—212no—
291C2×#41—212no—
292C2×#41—212no—
293C2×#41—212no—
294C2×#41—212no—
295C2×#41—48no—
296C2×#41—424no—
297C2×#41C2×D4124yes—
298C2×#41C2×D418yes—
299C2×#41C2×D414yes—
300C2×#41#4118yes—
301C2×#41C24112yes—
302C2×#41C24112yes—
303C2×#41C24112yes—
304C2×#41C2414yes—
305C22×Q8—216no—
306C22×Q8—28no—
307C22×Q8—28no—
308C22×Q8—23no—
309C22×Q8—26no—
310C22×Q8—23no—
311C22×Q8—26no—
312C22×Q8—212no—
313C22×Q8—212no—
314C22×Q8—212no—
315C22×Q8—48no—
316C22×Q8C2×D4124yes—
317C22×Q8C2×D411yescharacteristic
318C22×Q8C2413yes—
319C22×Q8C24112yes—
320C22×Q8C2411yescharacteristic
321C22×Q8C2413yes—
322C22×Q8C24112yes—
323C22×D4—23no—
324C22×D4—23no—
325C22×D4—23no—
326C22×D4—224no—
327C22×D4—212no—
328C22×D4—23no—
329C22×D4—26no—
330C22×D4—23no—
331C22×D4—23no—
332C22×D4—212no—
333C22×D4—424no—
334C22×D4C2×D413yes—
335C22×D4C2413yes—
336C22×D4C24112yes—
337C22×D4C2411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—23no—
340C23×C4—23no—
341C23×C4—23no—
342C23×C4—23no—
343C23×C4—21no—
344C23×C4—23no—
345C23×C4—23no—
346C23×C4—23no—
347C23×C4C2×D413yes—
348C23×C4C2×D413yes—
349C23×C4C2413yes—
350#137—296no—
351#137—296no—
352#137—296no—
353AGL(1,ℤ/8)—296no—
354#135—296no—
355#135—296no—
356C2×Q16—212no—
357C2×Q16—224no—
358C2×Q16—296no—
359C2×Q16—212no—
360C2×Q16C24112yes—
361C2×Q16C24124yes—
362C2×Q16C24112yes—
363C2×SD16—212no—
364C2×SD16—224no—
365C2×SD16—296no—
366C2×SD16—212no—
367C2×SD16—24no—
368C2×SD16—212no—
369C2×SD16C24112yes—
370C2×SD16C24124yes—
371C2×SD16C2414yes—
372C2×SD16C24112yes—
373C2×SD16C24112yes—
374C2×D8—24no—
375C2×D8—212no—
376C2×D8C24112yes—
377C2×D8C2414yes—
378#131—232no—
379#131—232no—
380C2×M16—212no—
381C2×M16—212no—
382C2×M16C24112yes—
383C2×M16C24112yes—
384C22×C8—212no—
385C22×C8—212no—
386C22×C8C2411yescharacteristic
387C22×C8C2411yescharacteristic
388C22×C8C2413yes—
389C22×C8C2413yes—
390C22×C8C24112yes—
391C22×C8C24112yes—
392C4⋊Q8—26no—
393C4⋊Q8C24112yes—
394#127—26no—
395#127C24112yes—
396#124—26no—
397#124—212no—
398#124—224no—
399#124—224no—
400#124—22no—
401#124C24112yes—
402#124C24124yes—
403#124C2414yes—
404#123—248no—
405C22⋊Q8—224no—
406C22⋊Q8—224no—
407#121—224no—
408#121—224no—
409#121—224no—
410#121—224no—
411#120—248no—
412C4×Q8—28no—
413C4×Q8—224no—
414C4×Q8—224no—
415C4×Q8—26no—
416C4×Q8—224no—
417C4×Q8—212no—
418C4×Q8—224no—
419C4×Q8—26no—
420C4×Q8C2×D418yes—
421C4×Q8C2×D418yes—
422C4×Q8C24112yes—
423C4×Q8C24124yes—
424C4×Q8C24112yes—
425C4×D4—224no—
426C4×D4—224no—
427C4×D4—224no—
428C4×D4—248no—
429C4×D4—224no—
430C4×D4—224no—
431C4×D4—22no—
432C4×D4—26no—
433C4×D4C2×D4124yes—
434C4×D4C2×D4124yes—
435C4×D4C2414yes—
436C4×D4C24112yes—
437#117—26no—
438#117—224no—
439#117—248no—
440#117—224no—
441#117C2×D4112yes—
442#117C24112yes—
443#117C24112yes—
444C2×C4⋊C4—26no—
445C2×C4⋊C4—23no—
446C2×C4⋊C4—23no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—26no—
449C2×C4⋊C4—23no—
450C2×C4⋊C4—23no—
451C2×C4⋊C4—23no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4C2×D413yes—
454C2×C4⋊C4C2×D413yes—
455C2×C4⋊C4C2413yes—
456C2×C4⋊C4C24112yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C22⋊C4—23no—
459C2×C22⋊C4—23no—
460C2×C22⋊C4—23no—
461C2×C22⋊C4—26no—
462C2×C22⋊C4—26no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—23no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4C2×D416yes—
470C2×C42—23no—
471C2×C42—26no—
472C2×C42—23no—
473C2×C42—23no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42C2×D413yes—
477C2×C42C2×D413yes—
478C2×C42C2×D4112yes—
479C2×C42C2413yes—
480C2×C42C2411yescharacteristic
481C2×C42C24112yes—
482C4⋊C8C2414yes—
483C4⋊C8C24112yes—
484C4⋊C8C24112yes—
485C4⋊C8C24112yes—
486C4⋊C8C24124yes—
487#103C24112yes—
488#103C24124yes—
489#103C2414yes—
490#103C24112yes—
491#103C24112yes—
492#102C24112yes—
493#102C24124yes—
494#102C24112yes—
495#102C2414yes—
496#102C24112yes—
497C24—21no—
498C24—23no—
499C24—21no—
500C24—212no—
501C24—412no—
502C24—86no—
503C24—86no—
504C24C22×D413yes—
505#41—2192no—
506#41—248no—
507#41—224no—
508#41—224no—
509#41—224no—
510#41—224no—
511#41—224no—
512#41—432no—
513#41—496no—
514#41—424no—
515#41—424no—
516#41#121132yes—
517#41C22×D4148yes—
518#41C22×D4116yes—
519#41C2×#41116yes—
520C2×Q8—264no—
521C2×Q8—224no—
522C2×Q8—248no—
523C2×Q8—212no—
524C2×Q8—23no—
525C2×Q8—212no—
526C2×Q8—23no—
527C2×Q8—21no—
528C2×Q8—26no—
529C2×Q8—224no—
530C2×Q8—26no—
531C2×Q8—22no—
532C2×Q8—224no—
533C2×Q8—26no—
534C2×Q8—224no—
535C2×Q8—22no—
536C2×Q8—432no—
537C2×Q8—412no—
538C2×Q8—424no—
539C2×Q8#12118yes—
540C2×Q8C22×D4112yes—
541C2×Q8C22×D4148yes—
542C2×Q8C22×D414yes—
543C2×Q8C2516yes—
544C2×Q8C2512yes—
545C2×Q8C2516yes—
546C2×D4—224no—
547C2×D4—212no—
548C2×D4—212no—
549C2×D4—212no—
550C2×D4—21no—
551C2×D4—26no—
552C2×D4—22no—
553C2×D4—224no—
554C2×D4—212no—
555C2×D4—23no—
556C2×D4—21no—
557C2×D4—212no—
558C2×D4—212no—
559C2×D4—22no—
560C2×D4—26no—
561C2×D4—224no—
562C2×D4—22no—
563C2×D4—412no—
564C2×D4—412no—
565C2×D4—496no—
566C2×D4—412no—
567C2×D4—424no—
568C2×D4—86no—
569C2×D4—86no—
570C2×D4#121124yes—
571C2×D4C22×D414yes—
572C2×D4C22×D4112yes—
573C2×D4C2516yes—
574C2×D4C2512yes—
575C2×D4C2512yes—
576C22×C4—224no—
577C22×C4—212no—
578C22×C4—23no—
579C22×C4—224no—
580C22×C4—212no—
581C22×C4—212no—
582C22×C4—21no—
583C22×C4—23no—
584C22×C4—23no—
585C22×C4—21no—
586C22×C4—212no—
587C22×C4—24no—
588C22×C4—212no—
589C22×C4—212no—
590C22×C4—212no—
591C22×C4—46no—
592C22×C4—46no—
593C22×C4—44no—
594C22×C4—412no—
595C22×C4—412no—
596C22×C4—412no—
597C22×C4—86no—
598C22×C4—86no—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D413yes—
601C22×C4C22×D413yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D4112yes—
604C22×C4C22×D4112yes—
605C22×C4C22×D416yes—
606C22×C4C22×D413yes—
607C22×C4C22×D4112yes—
608C22×C4C2×#41112yes—
609C22×C4C2516yes—
610C22×C4C2511yescharacteristic
611Q16—224no—
612Q16—248no—
613Q16—224no—
614SD16—224no—
615SD16—248no—
616SD16—224no—
617SD16—28no—
618SD16—224no—
619D8—28no—
620D8—224no—
621M16—224no—
622M16—224no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—26no—
626C2×C8—26no—
627C2×C8—224no—
628C2×C8—224no—
629C2×C8C2512yes—
630C2×C8C2516yes—
631C2×C8C2512yes—
632C2×C8C2516yes—
633C4⋊C4—224no—
634C4⋊C4—212no—
635C4⋊C4—212no—
636C4⋊C4—23no—
637C4⋊C4—212no—
638C4⋊C4—212no—
639C4⋊C4—212no—
640C4⋊C4—21no—
641C4⋊C4C22×D4112yes—
642C4⋊C4C22×D4112yes—
643C4⋊C4C2516yes—
644C4⋊C4C2512yes—
645C22⋊C4—212no—
646C22⋊C4—212no—
647C22⋊C4—212no—
648C22⋊C4—224no—
649C22⋊C4—224no—
650C22⋊C4—24no—
651C22⋊C4—212no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4C22×D4124yes—
655C42—212no—
656C42—212no—
657C42—224no—
658C42—212no—
659C42C22×D4112yes—
660C42C22×D412yes—
661C42C22×D4112yes—
662C42C22×D416yes—
663C42C2512yes—
664C42C2516yes—
665C23—26no—
666C23—26no—
667C23—22no—
668C23—24no—
669C23—26no—
670C23—22no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—46no—
675C23—42no—
676C23—46no—
677C23—42no—
678C23—46no—
679C23—424no—
680C23—812no—
681C23—812no—
682C23—1624no—
683C23C2×#121112yes—
684C23C23×D416yes—
685C23C23×D411yescharacteristic
686Q8—26no—
687Q8—248no—
688Q8—212no—
689Q8—26no—
690Q8—22no—
691Q8—26no—
692Q8—22no—
693Q8—424no—
694Q8—46no—
695Q8—42no—
696Q8C2×#121116yes—
697Q8C23×D4112yes—
698D4—248no—
699D4—26no—
700D4—22no—
701D4—22no—
702D4—26no—
703D4—22no—
704D4—24no—
705D4—424no—
706D4—424no—
707D4—424no—
708D4—46no—
709D4—42no—
710D4—812no—
711D4—812no—
712D4C2×#121148yes—
713D4C23×D414yes—
714C2×C4—22no—
715C2×C4—26no—
716C2×C4—22no—
717C2×C4—26no—
718C2×C4—26no—
719C2×C4—212no—
720C2×C4—248no—
721C2×C4—248no—
722C2×C4—22no—
723C2×C4—26no—
724C2×C4—26no—
725C2×C4—22no—
726C2×C4—412no—
727C2×C4—412no—
728C2×C4—48no—
729C2×C4—46no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—46no—
733C2×C4—424no—
734C2×C4—424no—
735C2×C4—424no—
736C2×C4—812no—
737C2×C4—812no—
738C2×C4C2×#121112yes—
739C2×C4C2×#121124yes—
740C2×C4C23×D412yes—
741C2×C4C23×D416yes—
742C2×C4C23×D416yes—
743C2×C4C23×D412yes—
744C2×C4C23×D412yes—
745C2×C4C23×D4112yes—
746C2×C4C23×D416yes—
747C2×C4C23×D411yescharacteristic
748C2×C4C22×#4112yes—
749C2×C4C22×#41112yes—
750C2×C4C2611yescharacteristic
751C8—22no—
752C8—22no—
753C8—26no—
754C8—26no—
755C22—224no—
756C22—26no—
757C22—26no—
758C22—24no—
759C22—48no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—46no—
764C22—42no—
765C22—46no—
766C22—42no—
767C22—46no—
768C22—84no—
769C22—812no—
770C22—1624no—
771C22C22×#121112yes—
772C22C22×#12112yes—
773C22#358412yes—
774C22#358612yes—
775C22C24×D411yescharacteristic
776C4—22no—
777C4—26no—
778C4—22no—
779C4—26no—
780C4—212no—
781C4—46no—
782C4—42no—
783C4—42no—
784C4—46no—
785C4C22×#121112yes—
786C4C22×#12112yes—
787C4C24×D411yescharacteristic
788C4C23×#4111yescharacteristic
789C2—212no—
790C2—44no—
791C2—82no—
792C2—86no—
793C2#6043314yesdirect product factor
794C2C23×#12111yescharacteristic
795C2C2×#358411yescharacteristic
796C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#578C2semidirect
2. C22×#577C2semidirect
3. C2×#3500C2semidirect
4. C2×C4×2−1+4C2semidirect
5. #60433C2direct (N × H)
6. C2×#3046C2semidirect
7. C2×#3045C2semidirect
8. C2×#3044C2semidirect
9. C2×#3043C2semidirect
10. C2×#3040C2semidirect
11. C2×#3037C2semidirect
12. C2×#3035C2semidirect
13. C22×#464C2semidirect
14. C2×#2906C2semidirect
15. C2×#2898C2semidirect
16. C2×#2897C2semidirect
21. C2×#578C22semidirect
23. C2×#577C22semidirect
25. C22×#137C22semidirect
26. C22×#137C22semidirect
29. C22×#135C22semidirect
30. C23×Q16C22semidirect
35. #3500C22semidirect
45. C4×2−1+4C22semidirect
48. C2×#520C22semidirect
50. C2×#519C22semidirect
53. C2×C4×#41C22semidirect
55. C22×C4×Q8C22semidirect
56. #3046C22semidirect
57. #3045C22semidirect
58. #3044C22semidirect
59. #3043C22semidirect
60. #3040C22semidirect
61. #3037C22semidirect
62. #3035C22semidirect
63. C2×#464C22semidirect
64. C2×#464C22semidirect
65. C2×#464C22semidirect
66. C2×#464C22semidirect
67. C2×#464C22semidirect
68. C2×#464C22semidirect
69. C2×#464C22semidirect
70. C2×#462C22semidirect
71. C2×#462C22semidirect
72. C2×#460C22semidirect
73. C2×#460C22semidirect
74. C2×#463C22semidirect
75. C2×#463C22semidirect
76. C2×#463C22semidirect
77. C2×#461C22semidirect
78. C2×#459C22semidirect
79. #2906C22semidirect
80. C2×#424C22semidirect
81. C2×#424C22semidirect
82. C2×#423C22semidirect
83. C22×C4⋊C8C22semidirect
84. #2898C22semidirect
85. #2897C22semidirect
87. C2×#417C22semidirect
88. C2×#419C22semidirect
91. C2×#416C22semidirect
92. C22×#103C22semidirect
99. C2×2−1+4D4semidirect
125. C2×#137C23semidirect
126. C2×#137C23semidirect
132. C2×#135C23semidirect
137. C22×Q16C23semidirect
186. #520C23semidirect
189. #519C23semidirect
194. C4×#41C23semidirect
207. C2×C4×Q8C23semidirect
231. #464C23semidirect
232. #464C23semidirect
233. #464C23semidirect
234. #464C23semidirect
235. #464C23semidirect
236. #464C23semidirect
237. #463C23semidirect
238. #463C23semidirect
239. #463C23semidirect
240. #462C23semidirect
241. #462C23semidirect
242. #461C23semidirect
243. #460C23semidirect
244. #460C23semidirect
245. #459C23semidirect
246. #424C23semidirect
247. #424C23semidirect
248. #423C23semidirect
254. C2×C4⋊C8C23semidirect
255. #419C23semidirect
258. #417C23semidirect
260. #416C23semidirect
266. C2×#103C23semidirect
279. 2−1+4C2×D4semidirect
793. C2#60433direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5782
C22×#5772
C2×#35002
C2×C4×2−1+42
#604332
C2×#30462
C2×#30452
C2×#30442
C2×#30432
C2×#30402
C2×#30372
C2×#30352
C22×#4642
C2×#29062
C2×#28982
C2×#28972