Finite Group Databasebeta

← #6594196

Subgroups — #6594196

Order 512.

1870 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36189C211yesmaximal, characteristic, complemented
2#36179C211yesmaximal, characteristic
3#33297C211yesmaximal, characteristic, complemented
4#33048C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29218C211yesmaximal, characteristic, complemented
7#29143C211yesmaximal, characteristic, complemented
8#27974C211yesmaximal, characteristic, complemented
9#27973C211yesmaximal, characteristic, complemented
10#27961C211yesmaximal, characteristic, complemented
11#27960C211yesmaximal, characteristic, complemented
12#27744C214yesmaximal, complemented
13#27717C214yesmaximal, complemented
14#27709C214yesmaximal, complemented
15#22495C214yesmaximal, complemented
16#21646C211yesmaximal, characteristic, complemented
17#20764C211yesmaximal, characteristic, complemented
18C2×#1834C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#547—21no—
21C2×#547—21no—
22C2×#547C2212yes—
23C2×#486C2211yescharacteristic
24C2×#435C2212yes—
25C2×C4×M16C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2868C2211yescharacteristic
28#2859C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2856C2211yescharacteristic
32#2856C2211yescharacteristic
33#2570C2212yes—
34#2542—21no—
35#2542—21no—
36#2542C2212yes—
37#2511—21no—
38#2507—21no—
39#2501—21no—
40#2501—21no—
41#2501—21no—
42#2501—21no—
43#2501C2212yes—
44#2501C2212yes—
45#2497—21no—
46#2487—21no—
47#2442C2212yes—
48#2441C2212yes—
49#2423—21no—
50#2417—21no—
51#2360—21no—
52#2352C2212yes—
53#2345—21no—
54C4×C4⋊Q8C2211yescharacteristic
55C4×#127C2211yescharacteristic
56#2285C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C42×D4C2211yescharacteristic
61#2100C2214yes—
62#2100C2214yes—
63#2099C2214yes—
64#2073C2214yes—
65#2071C2214yes—
66#2025C2214yes—
67#1993C2214yes—
68#1992C2214yes—
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1987C2214yes—
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1936C2214yes—
77#1936C2214yes—
78#1934C2214yes—
79#1895C2214yes—
80#1893C2214yes—
81#1875C2214yes—
82#1874C2214yes—
83#1836C2214yes—
84#1834C2211yescharacteristic
85#1834C2211yescharacteristic
86#1834C2211yescharacteristic
87#1834C2211yescharacteristic
88#1834C2211yescharacteristic
89#1834C2211yescharacteristic
90#1834C2211yescharacteristic
91#1834C2214yes—
92#1834C2211yescharacteristic
93#1834C2211yescharacteristic
94#1824C2214yes—
95#1823C2214yes—
96#1804C2214yes—
97#1771C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99#1762C2214yes—
100#1753C2212yes—
101#1752C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1736C2214yes—
105C2×#340C2214yes—
106C4×#97C2211yescharacteristic
107C22×#41—22no—
108C22×M16C2312yes—
109C23×C8C2312yes—
110#547—216no—
111#547—48no—
112#547—48no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2312yes—
117C2×#127C2311yescharacteristic
118C2×#125C2312yes—
119C2×#123—22no—
120C2×#123—22no—
121C2×#123—22no—
122C2×#123—22no—
123C2×#123—22no—
124C2×#123—22no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—22no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×#121—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121C2312yes—
135C2×#121C2312yes—
136C2×C4×Q8—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4D411yescharacteristic
140C2×C4×D4D411yescharacteristic
141C2×C4×D4C2312yes—
142C2×C4×D4C2311yescharacteristic
143C2×#117C2312yes—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#486—24no—
156#435—28no—
157C2×C4⋊C8C2312yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×C22⋊C8C2312yes—
163C2×C22⋊C8C2312yes—
164C4×M16—24no—
165C2×#97C2312yes—
166C2×#97C2312yes—
167C2×#97C2312yes—
168C2×C4×C8—24no—
169C2×C4×C8C2312yes—
170C2×C4×C8C2311yescharacteristic
171C2×C4×C8C2311yescharacteristic
172C2×C4×C8C2311yescharacteristic
173C2×C4×C8C2311yescharacteristic
174#400—22no—
175#400—22no—
176#399—22no—
177#399—22no—
178#399—22no—
179#399—22no—
180#399—22no—
181#399—22no—
182#399—22no—
183#398—22no—
184#398—22no—
185#396—22no—
186#391—21no—
187#391—21no—
188#391—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—22no—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#388—22no—
210#387—22no—
211#387—22no—
212#387—22no—
213#387—22no—
214#386—22no—
215#385—22no—
216#384—21no—
217#384—21no—
218#384—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384—21no—
223#384—21no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#384C2312yes—
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2312yes—
232#384C2312yes—
233#384C2312yes—
234#382C2312yes—
235#382C2312yes—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—22no—
241#380C2312yes—
242#380C2312yes—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4D411yescharacteristic
247C4×C4⋊C4D411yescharacteristic
248C4×C4⋊C4C2312yes—
249C4×C4⋊C4C2311yescharacteristic
250C4×C22⋊C4—22no—
251C4×C22⋊C4D411yescharacteristic
252C4×C22⋊C4D411yescharacteristic
253C4×C22⋊C4D411yescharacteristic
254C4×C22⋊C4D411yescharacteristic
255C4×C22⋊C4C2311yescharacteristic
256C4×C22⋊C4C2311yescharacteristic
257C43C2311yescharacteristic
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273C2×#41—48no—
274C2×#41—48no—
275C2×#41—48no—
276C22×Q8—21no—
277C22×Q8—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C2×D411yescharacteristic
283C22×D4C2412yes—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—42no—
297C22×C8—24no—
298C22×C8—24no—
299C22×C8—42no—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C4⋊Q8—28no—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—44no—
308C4⋊Q8—44no—
309#127—22no—
310#127—22no—
311#125—44no—
312#123—48no—
313#123—48no—
314#123—48no—
315#123—48no—
316#123—48no—
317#123—48no—
318C22⋊Q8—48no—
319C22⋊Q8—48no—
320C22⋊Q8—44no—
321C22⋊Q8—48no—
322C22⋊Q8—82no—
323#121—28no—
324#121—28no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329C4×Q8—82no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—28no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4#4118yes—
336#117—44no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—82no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
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⋊C4—22no—
398C2×C22⋊C4C2×D411yescharacteristic
399C2×C22⋊C4C2×D411yescharacteristic
400C2×C22⋊C4C2×D411yescharacteristic
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C4⋊C8—24no—
424#102—28no—
425#102—44no—
426#102—44no—
427#102—44no—
428C22⋊C8—24no—
429C22⋊C8—24no—
430#97—24no—
431#97—24no—
432#97—42no—
433C4×C8—24no—
434C4×C8—22no—
435C4×C8—22no—
436C4×C8—22no—
437C4×C8#4114yescomplemented
438#95—22no—
439#95—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#95C2×D411yescharacteristic
449#95C2×D411yescharacteristic
450#95C2×D411yescharacteristic
451#95C2×D411yescharacteristic
452#95C2×D411yescharacteristic
453#95C2×D411yescharacteristic
454C24—22no—
455C24C22×D411yescharacteristic
456C24C22×D411yescharacteristic
457#41—832no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—22no—
469C2×D4—24no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4#12414yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—82no—
517C22×C4—82no—
518C22×C4AGL(1,ℤ/8)14yes—
519C22×C4AGL(1,ℤ/8)14yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C2×#4114yes—
533C22×C4C2×#4114yes—
534C22×C4C2511yescharacteristic
535M16—48no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—48no—
548C2×C8C2×#4114yes—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—42no—
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4#12414yes—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C22⋊C4#12414yes—
607C22⋊C4#12414yes—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—22no—
621C42—82no—
622C42—82no—
623C42C2×#4114yes—
624C42C2×#4112yes—
625C422−1+412yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23C2×#12412yes—
644C23C2×#12412yes—
645C23C2×AGL(1,ℤ/8)12yes—
646C23C2×AGL(1,ℤ/8)12yes—
647C23C23×D411yescharacteristic
648Q8—88no—
649Q8—84no—
650D4—28no—
651D4—44no—
652D4—44no—
653D4—88no—
654D4—88no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—88no—
711C2×C4—88no—
712C2×C4—88no—
713C2×C4—164no—
714C2×C4C2×#12412yes—
715C2×C4C2×#12412yes—
716C2×C4C2×#12412yes—
717C2×C4C2×#12412yes—
718C2×C4#54712yes—
719C2×C4#54712yes—
720C2×C4C2×AGL(1,ℤ/8)12yes—
721C2×C4C2×AGL(1,ℤ/8)12yes—
722C2×C4C2×AGL(1,ℤ/8)12yes—
723C2×C4C2×AGL(1,ℤ/8)12yes—
724C2×C4#57712yes—
725C2×C4#57812yes—
726C2×C4C22×#4111yescharacteristic
727C2×C4C22×#4112yes—
728C2×C4C2×2−1+411yescharacteristic
729C2×C4#58512yes—
730C8—24no—
731C8—42no—
732C8—42no—
733C8—42no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22#313814yes—
755C22C22×#12411yescharacteristic
756C22C2×#54711yescharacteristic
757C22#350011yescharacteristic
758C22C22×AGL(1,ℤ/8)11yescharacteristic
759C22C22×AGL(1,ℤ/8)11yescharacteristic
760C22C2×#57711yescharacteristic
761C22C2×#57811yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4#334314yes—
780C4#334514yes—
781C4#347512yes—
782C4#351512yes—
783C2—24no—
784C2—42no—
785C2—162no—
786C2#3616411yescharacteristic
787C2C2×#313811yescharacteristic
788C2#6062311yescharacteristic
789C2C2×#334311yescharacteristic
790C2C2×#334511yescharacteristic
791C2#6253811yescharacteristic
792C2#6254111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36179C2
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. #36189C2semidirect
3. #33297C2semidirect
4. #33048C2semidirect
5. #33042C2semidirect
6. #29218C2semidirect
7. #29143C2semidirect
8. #27974C2semidirect
9. #27973C2semidirect
10. #27961C2semidirect
11. #27960C2semidirect
12. #27744C2semidirect
13. #27717C2semidirect
14. #27709C2semidirect
15. #22495C2semidirect
16. #21646C2semidirect
17. #20764C2semidirect
18. C2×#1834C2semidirect
19. C4×#435C2semidirect
437. C4×C8#41semidirect

Maximal subgroups

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

subgroupindex
#361892
#361792
#332972
#330482
#330422
#292182
#291432
#279742
#279732
#279612
#279602
#277442
#277172
#277092
#224952
#216462
#207642
C2×#18342
C4×#4352