Finite Group Databasebeta

← #6804375

Subgroups — #6804375

Order 512.

1846 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36595C211yesmaximal, characteristic, complemented
2#36559C211yesmaximal, characteristic, complemented
3#33277C211yesmaximal, characteristic, complemented
4#32596C214yesmaximal, complemented
5#31148C214yesmaximal, complemented
6#30218C211yesmaximal, characteristic, complemented
7#30203C211yesmaximal, characteristic, complemented
8#29192C211yesmaximal, characteristic, complemented
9#29178C211yesmaximal, characteristic, complemented
10#28615C211yesmaximal, characteristic, complemented
11#28615C211yesmaximal, characteristic, complemented
12#28508C211yesmaximal, characteristic, complemented
13#28437C211yesmaximal, characteristic
14#26889C214yesmaximal, complemented
15#26158C214yesmaximal, complemented
16#22269C211yesmaximal, characteristic, complemented
17#22220C211yesmaximal, characteristic, complemented
18C4×#493C211yesmaximal, characteristic, complemented
19#21339C211yesmaximal, characteristic, complemented
20C2×#559—21no—
21C2×#554—21no—
22C2×#493C2211yescharacteristic
23C2×#493C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#474C2214yes—
26C2×#459C2214yes—
27C2×C4×D8C2214yes—
28#2868C2211yescharacteristic
29#2867C2211yescharacteristic
30#2859C2211yescharacteristic
31#2859C2211yescharacteristic
32#2858C2211yescharacteristic
33#2858C2211yescharacteristic
34#2566—21no—
35#2566—21no—
36#2563—21no—
37#2548—21no—
38#2548—21no—
39#2548C2212yes—
40#2544—21no—
41#2544—21no—
42#2538—21no—
43#2538C2212yes—
44#2452—21no—
45#2452—21no—
46#2452C2212yes—
47#2452C2212yes—
48#2445—21no—
49#2445—21no—
50#2445C2212yes—
51#2445C2212yes—
52#2366—21no—
53#2366C2212yes—
54D4×C4⋊C4—21no—
55D4×C4⋊C4C2212yes—
56C4×C4⋊Q8C2211yescharacteristic
57C4×#127C2211yescharacteristic
58C4×#127C2211yescharacteristic
59C4×#127C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C4×#127C2211yescharacteristic
62C42×Q8C2211yescharacteristic
63#2093C2214yes—
64#2086C2214yes—
65#2071C2214yes—
66#2067C2214yes—
67#2054C2214yes—
68#2054C2214yes—
69#2041C2214yes—
70#2041C2214yes—
71#2023C2214yes—
72#2011C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1984C2212yes—
77#1970C2214yes—
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1957C2211yescharacteristic
85#1939C2212yes—
86#1934C2214yes—
87#1934C2214yes—
88#1925C2214yes—
89#1918C2214yes—
90#1916C2212yes—
91#1916C2212yes—
92#1879C2214yes—
93#1879C2214yes—
94#1879C2214yes—
95#1879C2214yes—
96#1862C2214yes—
97#1862C2214yes—
98#1845C2211yescharacteristic
99#1845C2211yescharacteristic
100#1834C2211yescharacteristic
101C4×C4⋊C8C2211yescharacteristic
102C4×C4⋊C8C2211yescharacteristic
103C4×C4⋊C8C2211yescharacteristic
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C22×D8C2314yes—
108C22×D8C2314yes—
109#559—48no—
110#554—48no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2311yescharacteristic
114C2×C4⋊Q8C2312yes—
115C2×#127—21no—
116C2×#127—21no—
117C2×#127—21no—
118C2×#127—21no—
119C2×#127C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#127C2312yes—
123C2×#127C2312yes—
124C2×#125—21no—
125C2×#125—21no—
126C2×#124—22no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124—21no—
131C2×#123—22no—
132C2×#123—22no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—22no—
136C2×C4×Q8—21no—
137C2×C4×Q8D411yescharacteristic
138C2×C4×Q8D411yescharacteristic
139C2×C4×Q8C2311yescharacteristic
140C2×C4×D4—22no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C22×C4⋊C4—22no—
157#493—24no—
158#493—24no—
159#486—24no—
160#474—48no—
161#459—48no—
162C4×D8—48no—
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182#396—22no—
183#396—22no—
184#396—22no—
185#396—22no—
186#394—22no—
187#394—22no—
188#394—22no—
189#394—22no—
190#394—22no—
191#394—22no—
192#393—22no—
193#393—22no—
194#391—21no—
195#390—22no—
196#390—22no—
197#390—21no—
198#390—21no—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#385—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#384—21no—
239#384—21no—
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#384C2312yes—
245#382—21no—
246#382—21no—
247#380—22no—
248#380—22no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4D411yescharacteristic
252C4×C4⋊C4D411yescharacteristic
253C4×C4⋊C4D411yescharacteristic
254C4×C4⋊C4D411yescharacteristic
255C4×C4⋊C4D411yescharacteristic
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2311yescharacteristic
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
260C43C2311yescharacteristic
261C43C2311yescharacteristic
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#336C2312yes—
268#336C2312yes—
269#336C2312yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274C22×Q8—21no—
275C22×Q8—22no—
276C22×Q8C2×D411yescharacteristic
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4C2412yes—
288C22×D4C2412yes—
289C22×D4C2412yes—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C2×D8—28no—
296C2×D8—28no—
297C2×D8—28no—
298C2×D8—44no—
299C2×D8—44no—
300C2×D8—44no—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—44no—
308C4⋊Q8—44no—
309C4⋊Q8—82no—
310#127—22no—
311#127—22no—
312#127—22no—
313#127—22no—
314#127—22no—
315#127—44no—
316#127—44no—
317#127—44no—
318#127—44no—
319#127—82no—
320#127—82no—
321#127#4114yes—
322#125—44no—
323#125—44no—
324#124—48no—
325#124—44no—
326#124—44no—
327#124—82no—
328#124—82no—
329#123—48no—
330#123—48no—
331C22⋊Q8—48no—
332C22⋊Q8—48no—
333C22⋊Q8—48no—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8—44no—
337C4×Q8D818yescomplemented
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—48no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—82no—
351C4×D4—82no—
352C4×D4—82no—
353C4×D4—82no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—48no—
372C2×C4⋊C4C2×D411yescharacteristic
373C2×C4⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D411yescharacteristic
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⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—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×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—28no—
430#107—44no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433C4⋊C8—42no—
434#102—28no—
435#102—28no—
436#102—44no—
437#102—44no—
438#102—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442C4×C8—24no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—42no—
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—
461C24—22no—
462C24—22no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—42no—
469C2×Q8—82no—
470C2×Q8—82no—
471C2×Q8C2×D814yes—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—44no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4—82no—
511C2×D4—82no—
512C2×D4—82no—
513C2×D4C2×#4114yes—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—82no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
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×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C2511yescharacteristic
549D8—416no—
550D8—88no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8H(5,𝔽2)14yes—
563C4⋊C4—22no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—42no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4C2×D814yes—
593C4⋊C4C2×D814yes—
594C4⋊C4C2×D814yes—
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—44no—
605C22⋊C4—44no—
606C22⋊C4—82no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—82no—
610C22⋊C4—82no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—44no—
634C42C2×D814yes—
635C42C2×D814yes—
636C42C2×D814yes—
637C42C2×#4112yes—
638C422−1+412yes—
639C23—24no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23C23×D411yescharacteristic
661Q8—44no—
662Q8—84no—
663Q8—164no—
664D4—28no—
665D4—48no—
666D4—48no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—44no—
672D4—88no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—164no—
678D4—164no—
679D4—164no—
680C2×C4—21no—
681C2×C4—21no—
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—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
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—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—88no—
726C2×C4—164no—
727C2×C4—164no—
728C2×C4—164no—
729C2×C4—164no—
730C2×C4#54812yes—
731C2×C4#54812yes—
732C2×C4C22×D812yes—
733C2×C4C22×D812yes—
734C2×C4C22×D812yes—
735C2×C4C22×D812yes—
736C2×C4C22×D812yes—
737C2×C4C22×D812yes—
738C2×C4C22×D812yes—
739C2×C4#57512yes—
740C2×C4#57612yes—
741C2×C4#57712yes—
742C2×C4C22×#4111yescharacteristic
743C2×C4C2×H(5,𝔽2)12yes—
744C2×C4C2×2−1+411yescharacteristic
745C2×C4#58512yes—
746C8—24no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#344911yescharacteristic
772C22C2×#54811yescharacteristic
773C22#349811yescharacteristic
774C22C23×D811yescharacteristic
775C22C2×#57511yescharacteristic
776C22C2×#57611yescharacteristic
777C22C2×#57711yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4#335814yes—
796C4#337014yes—
797C4#351312yes—
798C4#355412yes—
799C2—84no—
800C2—162no—
801C2—162no—
802C2#3916111yescharacteristic
803C2#6094011yescharacteristic
804C2#6100611yescharacteristic
805C2C2×#335811yescharacteristic
806C2C2×#337011yescharacteristic
807C2#6241511yescharacteristic
808C2#6242711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28437C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36595C2semidirect
2. #36559C2semidirect
3. #33277C2semidirect
4. #32596C2semidirect
5. #31148C2semidirect
6. #30218C2semidirect
7. #30203C2semidirect
8. #29192C2semidirect
9. #29178C2semidirect
10. #28615C2semidirect
11. #28615C2semidirect
12. #28508C2semidirect
14. #26889C2semidirect
15. #26158C2semidirect
16. #22269C2semidirect
17. #22220C2semidirect
18. C4×#493C2semidirect
19. #21339C2semidirect
337. C4×Q8D8semidirect

Maximal subgroups

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

subgroupindex
#365952
#365592
#332772
#325962
#311482
#302182
#302032
#291922
#291782
#286152
#285082
#284372
#268892
#261582
#222692
#222202
C4×#4932
#213392