Finite Group Databasebeta

← #6763606

Subgroups — #6763606

Order 512.

1693 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36194C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33048C211yesmaximal, characteristic, complemented
4#31769C214yesmaximal, complemented
5#31479C214yesmaximal, complemented
6#30203C211yesmaximal, characteristic, complemented
7#29878C211yesmaximal, characteristic, complemented
8#29218C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#27974C211yesmaximal, characteristic, complemented
11#27962C211yesmaximal, characteristic, complemented
12#26426C214yesmaximal, complemented
13#26225C214yesmaximal, complemented
14#25813C211yesmaximal, characteristic, complemented
15#25673C211yesmaximal, characteristic, complemented
16#22247C211yesmaximal, characteristic, complemented
17#21863C211yesmaximal, characteristic, complemented
18#21324C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#500C2211yescharacteristic
24C2×#500C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28#2868C2211yescharacteristic
29#2858C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2571C2212yes—
35#2563—21no—
36#2545—21no—
37#2538—21no—
38#2497—21no—
39#2497—21no—
40#2492—21no—
41#2492—21no—
42#2491—21no—
43#2491C2212yes—
44#2452—21no—
45#2452C2212yes—
46#2439C2212yes—
47#2439C2212yes—
48#2436—21no—
49#2432—21no—
50#2416—21no—
51#2416C2212yes—
52#2369—21no—
53#2361—21no—
54#2361C2212yes—
55#2355—21no—
56#2354C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2101C2214yes—
63#2100C2214yes—
64#2087C2214yes—
65#2076C2214yes—
66#2073C2214yes—
67#2071C2214yes—
68#2067C2214yes—
69#2057C2214yes—
70#2033C2214yes—
71#2023C2214yes—
72#1993C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1990C2211yescharacteristic
80#1987C2214yes—
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1936C2214yes—
85#1925C2214yes—
86#1924C2212yes—
87#1918C2214yes—
88#1918C2214yes—
89#1917C2212yes—
90#1895C2214yes—
91#1875C2214yes—
92#1875C2214yes—
93#1870C2212yes—
94#1862C2214yes—
95#1852C2214yes—
96#1851C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1825C2214yes—
101#1804C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1744C2211yescharacteristic
106#1736C2214yes—
107C22×#41—21no—
108C23×Q8—21no—
109C22×M16C2312yes—
110#548—48no—
111#532—24no—
112#532—42no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×#127C2311yescharacteristic
125C2×#124—22no—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—22no—
133C2×#121—22no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×D4—22no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117C2312yes—
148C2×#117C2312yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#500—24no—
154#500—42no—
155#486—42no—
156#431—42no—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C4×M16—42no—
169C2×#97C2312yes—
170C2×C4×C8C2311yescharacteristic
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174#400—22no—
175#400—22no—
176#396—22no—
177#396—22no—
178#396—22no—
179#396—22no—
180#394—22no—
181#394—22no—
182#393—22no—
183#393—22no—
184#393—22no—
185#393—22no—
186#391—21no—
187#391—21no—
188#391—21no—
189#391—21no—
190#391—21no—
191#391—22no—
192#391—22no—
193#390—22no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#389—22no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#389C2312yes—
211#389C2312yes—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#387—22no—
217#387—22no—
218#386—22no—
219#386—22no—
220#385—22no—
221#385—22no—
222#384—21no—
223#384—21no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#384C2312yes—
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#382—22no—
230#382C2312yes—
231#382C2312yes—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380C2312yes—
240#380C2312yes—
241#380C2312yes—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4D411yescharacteristic
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2311yescharacteristic
254C4×C22⋊C4D411yescharacteristic
255C4×C22⋊C4D411yescharacteristic
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4C2311yescharacteristic
259C4×C22⋊C4C2311yescharacteristic
260C43C2311yescharacteristic
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C2×#41—44no—
277C2×#41—44no—
278C2×#41—82no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—44no—
285C22×Q8—44no—
286C22×Q8—82no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×D411yescharacteristic
292C22×D4C2412yes—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C2×M16—24no—
302C2×M16—42no—
303C2×M16—42no—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C4⋊Q8—24no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—42no—
315C4⋊Q8—44no—
316C4⋊Q8—44no—
317C4⋊Q8—44no—
318C4⋊Q8—44no—
319C4⋊Q8—82no—
320C4⋊Q8#4114yes—
321#127—22no—
322#127—22no—
323#124—44no—
324#124—48no—
325#124—44no—
326#124—82no—
327C22⋊Q8—48no—
328C22⋊Q8—44no—
329C22⋊Q8—82no—
330C22⋊Q8—82no—
331#121—28no—
332#121—24no—
333#121—42no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—48no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—42no—
344C4×D4—44no—
345C4×D4—42no—
346C4×D4—48no—
347#117—44no—
348#117—44no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4C2×D411yescharacteristic
398C2×C22⋊C4C2×D411yescharacteristic
399C2×C22⋊C4C2×D411yescharacteristic
400C2×C22⋊C4C2×D411yescharacteristic
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107—28no—
425#107—44no—
426C4⋊C8—42no—
427C4⋊C8—42no—
428#102—44no—
429#102—44no—
430#102—44no—
431#102—44no—
432C22⋊C8—24no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435#97—42no—
436C4×C8—22no—
437C4×C8—22no—
438C4×C8—22no—
439C4×C8—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95C2×D411yescharacteristic
455#95C2×D411yescharacteristic
456#95C2×D411yescharacteristic
457#95C2×D411yescharacteristic
458#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460C24—22no—
461C24C22×D411yescharacteristic
462C24C22×D411yescharacteristic
463#41—816no—
464C2×Q8—24no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—82no—
477C2×Q8—82no—
478C2×Q8—82no—
479C2×Q8—816no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—41no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—82no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—82no—
530C22×C4—82no—
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C42−1+414yes—
544C22×C4C2511yescharacteristic
545M16—48no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C4⋊C4—22no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—41no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4C2×#4114yes—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—22no—
624C42—22no—
625C42—44no—
626C42—44no—
627C42—82no—
628C42—82no—
629C42AGL(1,ℤ/8)14yes—
630C42C2×#4112yes—
631C42H(5,𝔽2)12yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#53612yes—
653C23C23×D411yescharacteristic
654Q8—48no—
655Q8—88no—
656Q8—84no—
657Q8—84no—
658Q8—164no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—88no—
663D4—88no—
664D4—84no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—24no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—88no—
723C2×C4—88no—
724C2×C4#53612yes—
725C2×C4#54612yes—
726C2×C4#54612yes—
727C2×C4C2×AGL(1,ℤ/8)12yes—
728C2×C4C2×AGL(1,ℤ/8)12yes—
729C2×C4C2×AGL(1,ℤ/8)12yes—
730C2×C4#57512yes—
731C2×C4#57612yes—
732C2×C4#57812yes—
733C2×C4C22×#4111yescharacteristic
734C2×C4C2×H(5,𝔽2)11yescharacteristic
735C2×C4C2×2−1+412yes—
736C2×C4#58512yes—
737C8—42no—
738C8—42no—
739C8—42no—
740C8—42no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22C2×#53611yescharacteristic
763C22C2×#54611yescharacteristic
764C22#350011yescharacteristic
765C22C22×AGL(1,ℤ/8)11yescharacteristic
766C22C2×#57511yescharacteristic
767C22C2×#57611yescharacteristic
768C22C2×#57811yescharacteristic
769C4—22no—
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—44no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4#331314yes—
787C4#332514yes—
788C4#351612yes—
789C4#354112yes—
790C2—42no—
791C2—81no—
792C2—162no—
793C2#3808311yescharacteristic
794C2#6086411yescharacteristic
795C2#6088011yescharacteristic
796C2C2×#331311yescharacteristic
797C2C2×#332511yescharacteristic
798C2#6253811yescharacteristic
799C2#6254611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36194C2semidirect
3. #33048C2semidirect
4. #31769C2semidirect
5. #31479C2semidirect
6. #30203C2semidirect
7. #29878C2semidirect
8. #29218C2semidirect
9. #28655C2semidirect
10. #27974C2semidirect
11. #27962C2semidirect
12. #26426C2semidirect
13. #26225C2semidirect
14. #25813C2semidirect
15. #25673C2semidirect
16. #22247C2semidirect
17. #21863C2semidirect
18. #21324C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361942
#361222
#330482
#317692
#314792
#302032
#298782
#292182
#286552
#279742
#279622
#264262
#262252
#258132
#256732
#222472
#218632
#213242
#211022