Finite Group Databasebeta

← #10574599

Subgroups — #10574599

Order 512.

6277 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#412C211yesmaximal, characteristic
2#60342C218yesmaximal, complemented
3#60337C214yesmaximal, complemented
4#60324C218yesmaximal, complemented
5#60320C212yesmaximal, complemented
6#60317C212yesmaximal, complemented
7#60314C218yesmaximal, complemented
8#60281C214yesmaximal, complemented
9#60280C211yesmaximal, characteristic, complemented
10#60279C214yesmaximal, complemented
11#60278C212yesmaximal, complemented
12#60277C214yesmaximal, complemented
13M16×#41C214yesmaximal, complemented
14#60210C214yesmaximal, complemented
15#60205C214yesmaximal, complemented
16#60204C211yesmaximal, characteristic, complemented
17C2×#2965C212yesmaximal, complemented
18#3483C2211yescharacteristic
19#3482C2212yes—
20#3482C2214yes—
21#3481C2214yes—
22#3481C2211yescharacteristic
23#3481C2214yes—
24#3480C412yes—
25#3480C414yes—
26Q8×#41C412yes—
27#3475C414yes—
28#3475C412yes—
29#3475C418yes—
30#3475C414yes—
31D4×#41C412yes—
32D4×#41C414yes—
33#3444C2211yescharacteristic
34#3444C2214yes—
35#3444C2214yes—
36C2×C4×#41C2212yes—
37C2×C4×#41C2214yes—
38#2995C22116yescomplemented
39#2995C22116yescomplemented
40#2994C2218yescomplemented
41#2993C2218yescomplemented
42#2993C2218yescomplemented
43#2992C22116yescomplemented
44#2991C2214yescomplemented
45#2990C2214yescomplemented
46#2990C2218yescomplemented
47#2989C22116yescomplemented
48#2989C2218yescomplemented
49#2989C2218yescomplemented
50#2987C2218yescomplemented
51#2986C2212yescomplemented
52#2985C2218yescomplemented
53#2984C2214yescomplemented
54#2983C2218yescomplemented
55#2981C2218yescomplemented
56#2980C2218yescomplemented
57#2979C2212yescomplemented
58#2978C2218yescomplemented
59#2978C2218yescomplemented
60#2977C2214yescomplemented
61#2976C22116yescomplemented
62#2975C2218yescomplemented
63#2974C2218yescomplemented
64#2974C2214yescomplemented
65#2973C22116yescomplemented
66#2971C2218yescomplemented
67#2970C22116yescomplemented
68#2970C2218yescomplemented
69#2969C2218yescomplemented
70#2969C2218yescomplemented
71#2968C22116yescomplemented
72#2967C22116yescomplemented
73#2967C22116yescomplemented
74#2966C2218yescomplemented
75#2965C2212yes—
76#2965C2212yes—
77#2965C2214yes—
78#2965C2214yescomplemented
79#2965C2212yescomplemented
80#2965C2212yescomplemented
81#2965C2214yescomplemented
82#2965C2214yescomplemented
83#2965C2214yescomplemented
84#2965C2218yescomplemented
85#2965C2214yescomplemented
86#2965C2218yescomplemented
87#2965C2218yescomplemented
88#2965C2218yescomplemented
89#2965C2214yescomplemented
90#2965C2218yescomplemented
91#2965C2218yescomplemented
92C8×#41C2214yescomplemented
93C8×#41C2214yescomplemented
94C8×#41C2214yescomplemented
95Q8×M16C2218yescomplemented
96#2962C2218yescomplemented
97#2961C2218yescomplemented
98#2960C2212yescomplemented
99C2×#446C2214yescomplemented
100#2935C2218yescomplemented
101D4×M16C22116yescomplemented
102D4×M16C2218yescomplemented
103#2933C22116yescomplemented
104#2932C2218yescomplemented
105#2931C2212yescomplemented
106#2930C2218yescomplemented
107#2930C2218yescomplemented
108#2929C2214yescomplemented
109C2×#436C2214yescomplemented
110C2×#435C2218yescomplemented
111#2922C2212yescomplemented
112#2922C2214yescomplemented
113#2922C2214yescomplemented
114#2922C2218yescomplemented
115#2920C2211yescharacteristic, complemented
116#2920C2214yescomplemented
117#2920C2218yescomplemented
118#2920C2214yescomplemented
119C2×#431C2214yescomplemented
120C2×#431C2212yescomplemented
121C2×#431C2214yescomplemented
122C4×#131C2212yescomplemented
123C4×#131C2214yescomplemented
124C2×C4×M16C2214yescomplemented
125C2×C4×M16C2214yescomplemented
126C22×C4×C8C2211yescharacteristic, complemented
127C22×#41C2×C412yes—
128C22×#41C2×C414yes—
129C2×#131C2314yes—
130C2×#131C2318yes—
131C22×M16C2318yes—
132C22×M16C2318yes—
133C23×C8C2312yes—
134#559C2×C414yes—
135#559C2×C411yescharacteristic
136#559C2×C414yes—
137Q82C2×C411yescharacteristic
138#557C2×C412yes—
139#557C2×C414yes—
140#556C2×C414yes—
141#556C2×C412yes—
142#556C2×C418yes—
143#556C2×C414yes—
144#555C2×C414yes—
145#555C2×C411yescharacteristic
146#555C2×C414yes—
147#554C2×C418yes—
148#554C2×C412yes—
149#554C2×C414yes—
150#554C2×C414yes—
151#553C2×C418yes—
152#553C2×C418yes—
153#553C2×C414yes—
154#553C2×C414yes—
155#553C2×C414yes—
156#553C2×C418yes—
157#552C2×C414yes—
158#552C2×C418yes—
159#552C2×C414yes—
160#552C2×C418yes—
161#552C2×C414yes—
162#552C2×C418yes—
163#551C2×C414yes—
164#551C2×C418yes—
165#551C2×C414yes—
166#551C2×C414yes—
167#551C2×C418yes—
168#551C2×C418yes—
169#550C2×C412yes—
170#550C2×C414yes—
171D4×Q8C2×C412yes—
172D4×Q8C2×C414yes—
173#548C2×C414yes—
174#548C2×C414yes—
175#548C2×C414yes—
176#547C2×C412yes—
177#547C2×C414yes—
178#547C2×C414yes—
179#547C2×C418yes—
180#546C2×C418yes—
181#546C2×C418yes—
182#546C2×C414yes—
183#546C2×C418yes—
184#546C2×C414yes—
185#546C2×C414yes—
186D42C2×C414yes—
187D42C2×C411yescharacteristic
188D42C2×C414yes—
189#533C2×C412yes—
190#533C2×C418yes—
191#533C2×C414yes—
192#533C2×C414yes—
193#533C2311yescharacteristic
194#533C2314yes—
195#533C2314yes—
196#532C2×C412yes—
197#532C2×C414yes—
198#532C2×C418yes—
199#532C2×C414yes—
200#532C2311yescharacteristic
201#532C2314yes—
202#532C2314yes—
203#529C2×C414yes—
204#529C2×C418yes—
205#529C2×C418yes—
206#529C2×C418yes—
207#529C2×C418yes—
208#529C2×C414yes—
209#529C2×C418yes—
210#529C2×C418yes—
211#529C2×C414yes—
212#529C2×C414yes—
213#529C2×C418yes—
214#529C2314yes—
215#529C2318yes—
216#529C2318yes—
217#529C2318yes—
218#529C2314yes—
219#529C2314yes—
220#525C2×C414yes—
221#525C2×C414yes—
222#525C2×C414yes—
223#525C2×C418yes—
224#525C2×C418yes—
225#525C2×C418yes—
226#525C2312yes—
227#525C2314yes—
228#525C2314yes—
229#525C2318yes—
230C4×#41C2×C412yes—
231C4×#41C2×C414yes—
232C4×#41C2×C414yes—
233C4×#41C2×C412yes—
234C4×#41C2×C418yes—
235C4×#41C2×C414yes—
236C4×#41C2×C412yes—
237C4×#41C2×C414yes—
238C4×#41C2×C414yes—
239C4×#41C2×C418yes—
240C4×#41C2×C412yes—
241C4×#41C2×C414yes—
242C4×#41C2312yes—
243C4×#41C2312yes—
244C4×#41C2314yes—
245C4×#41C2314yes—
246C4×#41C2318yes—
247C4×#41C2314yes—
248C4×#41C2312yes—
249C4×#41C2312yes—
250C4×#41C2318yes—
251C4×#41C2314yes—
252C4×#41C2314yes—
253C4×#41C2312yes—
254C4×#41C2314yes—
255C2×C4×Q8C2×C412yes—
256C2×C4×Q8C2×C414yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2×C412yes—
260C2×C4×D4C2×C414yes—
261C2×C4×D4C2×C414yes—
262C2×C4×D4C2×C418yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×#117C2×C412yes—
268C2×#117C2×C414yes—
269C2×#117C2×C414yes—
270C2×#117C2×C418yes—
271C22×C42C2311yescharacteristic
272C22×C42C2314yes—
273C22×C42C2314yes—
274#446C2318yes—
275#446C2314yes—
276#446C2314yes—
277#446C2314yes—
278#446C2314yes—
279#446C2318yes—
280#446C2318yes—
281#446C23116yes—
282#446C23116yes—
283#446C23116yes—
284#446C23116yes—
285#446C2318yes—
286#446C2318yes—
287#446C23116yes—
288C8×Q8C2318yes—
289C8×Q8C2318yes—
290C8×Q8C2318yes—
291#436C2318yes—
292#436C2314yes—
293#436C2314yes—
294#436C2314yes—
295#436C2318yes—
296#436C2314yes—
297#436C23116yes—
298#436C23116yes—
299#436C23116yes—
300#436C2318yes—
301#436C23116yes—
302#436C2318yes—
303#436C23116yes—
304#436C2318yes—
305#435C2318yes—
306#435C2318yes—
307#435C2318yes—
308#435C2318yes—
309#435C2318yes—
310#435C2318yes—
311#435C2318yes—
312#435C2318yes—
313#435C23116yes—
314#435C23116yes—
315#435C23116yes—
316#435C23116yes—
317#435C23116yes—
318#435C23116yes—
319#435C23116yes—
320#435C23116yes—
321#435C23116yes—
322#435C23116yes—
323#435C23116yes—
324#435C23116yes—
325#435C23116yes—
326C8×D4C23116yes—
327C8×D4C2318yes—
328C8×D4C23116yes—
329C8×D4C23116yes—
330C8×D4C2318yes—
331C8×D4C2318yes—
332#433C2318yes—
333#433C23116yes—
334#433C2318yes—
335#433C2318yes—
336#433C23116yes—
337#433C23116yes—
338#432C2314yes—
339#432C23116yes—
340#432C2318yes—
341#432C23116yes—
342#432C23116yes—
343#432C2318yes—
344#431C2312yes—
345#431C2312yes—
346#431C2314yes—
347#431C2314yes—
348#431C2314yes—
349#431C2318yes—
350#431C2314yes—
351#431C2314yes—
352#431C2314yes—
353#431C2314yes—
354#431C2318yes—
355#431C2314yes—
356#431C2318yes—
357#431C2318yes—
358#431C2318yes—
359#431C2318yes—
360#431C2318yes—
361#431C2318yes—
362#424C2314yes—
363#424C2318yes—
364#424C2318yes—
365#424C23116yes—
366#423C2312yes—
367#423C2318yes—
368#423C23116yes—
369#423C2318yes—
370C2×C4⋊C8C2318yes—
371C2×C4⋊C8C2314yes—
372C2×C4⋊C8C2318yes—
373#408C2314yes—
374#408C2318yes—
375#408C2318yes—
376#408C23116yes—
377#407C2312yes—
378#407C2318yes—
379#407C23116yes—
380#407C2318yes—
381C2×C22⋊C8C2314yes—
382C2×C22⋊C8C2318yes—
383C2×C22⋊C8C2318yes—
384#405C2314yes—
385#405C2318yes—
386#405C2318yes—
387#405C23116yes—
388C4×M16C2314yes—
389C4×M16C2314yes—
390C4×M16C2314yes—
391C4×M16C2318yes—
392C4×M16C2314yes—
393C4×M16C2318yes—
394C4×M16C23116yes—
395C4×M16C2318yes—
396C4×M16C2312yes—
397C4×M16C2314yes—
398C4×M16C2314yes—
399C2×#97C2318yes—
400C2×#97C2318yes—
401C2×C4×C8C2312yes—
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2312yes—
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2314yes—
406C2×C4×C8C2312yes—
407C2×C4×C8C2314yes—
408C2×C4×C8C2314yes—
409C2×C4×C8C2314yes—
410C2×C4×C8C2318yes—
411C2×#41—48no—
412C2×#41—416no—
413C2×#41C22×C412yes—
414C2×#41C22×C412yes—
415C2×#41C22×C414yes—
416C2×#41C22×C414yes—
417C2×#41C22×C418yes—
418C2×#41C22×C414yes—
419C2×#41C22×C418yes—
420C2×#41C22×C412yes—
421C2×#41C22×C414yes—
422C2×#41C22×C412yes—
423C2×#41C22×C414yes—
424C2×#41C2412yes—
425C2×#41C2414yes—
426C22×Q8C22×C412yes—
427C22×Q8C22×C414yes—
428C22×D4C22×C412yes—
429C22×D4C22×C414yes—
430C22×D4C22×C414yes—
431C22×D4C22×C418yes—
432C23×C4C22×C412yes—
433C23×C4C22×C414yes—
434C23×C4C22×C414yes—
435C23×C4C22×C418yes—
436C23×C4C2411yescharacteristic
437C23×C4C2414yes—
438C23×C4C2414yes—
439#131—48no—
440#131—416no—
441C2×M16—416no—
442C2×M16—416no—
443C2×M16C2418yes—
444C2×M16C2418yes—
445C2×M16C2418yes—
446C2×M16C24116yes—
447C2×M16C2418yes—
448C2×M16C2414yes—
449C2×M16C2418yes—
450C2×M16C2418yes—
451C22×C8—44no—
452C22×C8C2414yes—
453C22×C8C2412yes—
454C22×C8C2418yes—
455C22×C8C2414yes—
456C22×C8C2412yes—
457C22×C8C2418yes—
458C22×C8C2418yes—
459C22×C8C24116yes—
460C4⋊Q8C22×C412yes—
461C4⋊Q8C22×C414yes—
462C4⋊Q8C22×C418yes—
463C4⋊Q8C22×C414yes—
464C4⋊Q8C22×C411yescharacteristic
465C4⋊Q8C22×C414yes—
466C4⋊Q8C22×C414yes—
467#127C22×C411yescharacteristic
468#127C22×C414yes—
469#127C22×C414yes—
470#126C22×C418yes—
471#126C22×C418yes—
472#126C22×C418yes—
473#126C22×C418yes—
474#126C22×C418yes—
475#126C22×C418yes—
476#126C22×C418yes—
477#126C22×C418yes—
478#126C22×C418yes—
479#125C22×C412yes—
480#125C22×C418yes—
481#125C22×C418yes—
482#125C22×C414yes—
483#125C22×C418yes—
484#125C22×C418yes—
485#125C22×C418yes—
486#125C22×C414yes—
487#125C22×C414yes—
488#124C22×C412yes—
489#124C22×C414yes—
490#124C22×C414yes—
491#124C22×C418yes—
492#124C22×C414yes—
493#124C22×C414yes—
494#124C22×C414yes—
495#124C22×C418yes—
496#124C22×C418yes—
497#124C22×C418yes—
498#123C22×C418yes—
499#123C22×C418yes—
500#123C22×C418yes—
501#123C22×C418yes—
502#123C22×C418yes—
503#123C22×C418yes—
504#123C22×C418yes—
505#123C22×C418yes—
506#123C22×C418yes—
507#123C22×C414yes—
508#123C22×C414yes—
509#123C22×C414yes—
510#123C22×C418yes—
511#123C22×C418yes—
512#123C22×C418yes—
513C22⋊Q8C22×C414yes—
514C22⋊Q8C22×C414yes—
515C22⋊Q8C22×C414yes—
516C22⋊Q8C22×C418yes—
517C22⋊Q8C22×C418yes—
518C22⋊Q8C22×C418yes—
519C22⋊Q8C22×C414yes—
520C22⋊Q8C22×C414yes—
521C22⋊Q8C22×C414yes—
522C22⋊Q8C22×C418yes—
523C22⋊Q8C22×C418yes—
524C22⋊Q8C22×C418yes—
525C22⋊Q8C22×C414yes—
526C22⋊Q8C22×C418yes—
527C22⋊Q8C22×C418yes—
528C22⋊Q8C22×C418yes—
529C22⋊Q8C22×C418yes—
530#121C22×C414yes—
531#121C22×C414yes—
532#121C22×C414yes—
533#121C22×C418yes—
534#121C22×C418yes—
535#121C22×C418yes—
536#121C22×C414yes—
537#121C22×C414yes—
538#121C22×C414yes—
539#121C22×C418yes—
540#121C22×C418yes—
541#121C22×C418yes—
542#121C22×C414yes—
543#121C22×C418yes—
544#121C22×C418yes—
545#121C22×C418yes—
546#121C22×C418yes—
547#120C22×C414yes—
548#120C22×C418yes—
549#120C22×C418yes—
550#120C22×C414yes—
551#120C22×C414yes—
552#120C22×C418yes—
553C4×Q8C22×C412yes—
554C4×Q8C22×C412yes—
555C4×Q8C22×C414yes—
556C4×Q8C22×C414yes—
557C4×Q8C22×C418yes—
558C4×Q8C22×C412yes—
559C4×Q8C22×C414yes—
560C4×Q8C22×C412yes—
561C4×Q8C22×C414yes—
562C4×Q8C22×C414yes—
563C4×Q8C22×C418yes—
564C4×Q8C22×C412yes—
565C4×Q8C22×C414yes—
566C4×Q8C22×C412yes—
567C4×Q8C22×C414yes—
568C4×Q8C22×C414yes—
569C4×Q8C22×C418yes—
570C4×Q8C22×C414yes—
571C4×Q8C22×C418yes—
572C4×Q8C2412yes—
573C4×Q8C2412yes—
574C4×Q8C2414yes—
575C4×Q8C2414yes—
576C4×Q8C2418yes—
577C4×D4C22×C414yes—
578C4×D4C22×C412yes—
579C4×D4C22×C414yes—
580C4×D4C22×C418yes—
581C4×D4C22×C414yes—
582C4×D4C22×C414yes—
583C4×D4C22×C418yes—
584C4×D4C22×C418yes—
585C4×D4C22×C412yes—
586C4×D4C22×C414yes—
587C4×D4C22×C414yes—
588C4×D4C22×C418yes—
589C4×D4C22×C414yes—
590C4×D4C22×C412yes—
591C4×D4C22×C418yes—
592C4×D4C22×C414yes—
593C4×D4C22×C414yes—
594C4×D4C22×C414yes—
595C4×D4C22×C414yes—
596C4×D4C22×C418yes—
597C4×D4C22×C418yes—
598C4×D4C22×C418yes—
599C4×D4C22×C412yes—
600C4×D4C22×C414yes—
601C4×D4C22×C414yes—
602C4×D4C22×C418yes—
603C4×D4C22×C414yes—
604C4×D4C22×C412yes—
605C4×D4C22×C418yes—
606C4×D4C22×C414yes—
607C4×D4C22×C414yes—
608C4×D4C22×C418yes—
609C4×D4C22×C414yes—
610C4×D4C22×C414yes—
611C4×D4C22×C418yes—
612C4×D4C22×C418yes—
613C4×D4C22×C412yes—
614C4×D4C22×C414yes—
615C4×D4C22×C414yes—
616C4×D4C22×C418yes—
617C4×D4C22×C418yes—
618C4×D4C22×C418yes—
619C4×D4C22×C418yes—
620C4×D4C22×C414yes—
621C4×D4C22×C418yes—
622C4×D4C2414yes—
623C4×D4C2412yes—
624C4×D4C2414yes—
625C4×D4C2418yes—
626C4×D4C2414yes—
627C4×D4C2414yes—
628C4×D4C2418yes—
629C4×D4C2418yes—
630C4×D4C2412yes—
631C4×D4C2414yes—
632C4×D4C2414yes—
633C4×D4C2418yes—
634#117C22×C414yes—
635#117C22×C412yes—
636#117C22×C414yes—
637#117C22×C418yes—
638#117C22×C412yes—
639#117C22×C414yes—
640#117C22×C414yes—
641#117C22×C418yes—
642#117C22×C414yes—
643#117C22×C418yes—
644#117C22×C414yes—
645#117C22×C418yes—
646#117C22×C414yes—
647#117C22×C418yes—
648#117C22×C414yes—
649#117C22×C414yes—
650#117C22×C418yes—
651#117C22×C418yes—
652#117C22×C412yes—
653#117C22×C414yes—
654#117C22×C414yes—
655#117C22×C418yes—
656#117C22×C412yes—
657#117C22×C414yes—
658#117C22×C414yes—
659#117C22×C418yes—
660#117C2412yes—
661#117C2414yes—
662#117C2414yes—
663#117C2418yes—
664C2×C4⋊C4C22×C412yes—
665C2×C4⋊C4C22×C414yes—
666C2×C4⋊C4C22×C414yes—
667C2×C4⋊C4C22×C418yes—
668C2×C4⋊C4C22×C412yes—
669C2×C4⋊C4C22×C414yes—
670C2×C4⋊C4C22×C414yes—
671C2×C4⋊C4C22×C418yes—
672C2×C22⋊C4C22×C414yes—
673C2×C22⋊C4C22×C414yes—
674C2×C22⋊C4C22×C414yes—
675C2×C22⋊C4C22×C418yes—
676C2×C22⋊C4C22×C418yes—
677C2×C22⋊C4C22×C418yes—
678C2×C42C22×C412yes—
679C2×C42C22×C414yes—
680C2×C42C22×C414yes—
681C2×C42C22×C418yes—
682C2×C42C22×C414yes—
683C2×C42C22×C418yes—
684C2×C42C22×C412yes—
685C2×C42C22×C414yes—
686C2×C42C22×C412yes—
687C2×C42C22×C414yes—
688C2×C42C22×C414yes—
689C2×C42C22×C418yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2411yescharacteristic
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2414yes—
702C4⋊C8C2414yes—
703C4⋊C8C2414yes—
704C4⋊C8C2418yes—
705C4⋊C8C2418yes—
706C4⋊C8C2418yes—
707C4⋊C8C24116yes—
708C4⋊C8C2418yes—
709C4⋊C8C2418yes—
710C4⋊C8C2418yes—
711C4⋊C8C24116yes—
712C4⋊C8C24116yes—
713C4⋊C8C24116yes—
714C22⋊C8C2414yes—
715C22⋊C8C2414yes—
716C22⋊C8C2418yes—
717C22⋊C8C2418yes—
718C22⋊C8C2418yes—
719C22⋊C8C24116yes—
720C22⋊C8C2418yes—
721C22⋊C8C2418yes—
722C22⋊C8C2418yes—
723C22⋊C8C24116yes—
724C22⋊C8C24116yes—
725C22⋊C8C24116yes—
726#97C2418yes—
727#97C2418yes—
728#97C2418yes—
729#97C24116yes—
730#97C2418yes—
731#97C2418yes—
732#97C2414yes—
733#97C2418yes—
734C4×C8C2414yes—
735C4×C8C2412yes—
736C4×C8C2414yes—
737C4×C8C2412yes—
738C4×C8C2418yes—
739C4×C8C2418yes—
740C4×C8C2418yes—
741C4×C8C24116yes—
742C4×C8C2411yescharacteristic
743C4×C8C2412yes—
744C4×C8C2411yescharacteristic
745C4×C8C2414yes—
746C4×C8C2414yes—
747C4×C8C2414yes—
748C24C23×C411yescharacteristic
749C24C23×C414yes—
750C24C23×C414yes—
751#41—28no—
752#41—28no—
753#41—216no—
754#41—44no—
755#41—48no—
756#41—48no—
757#41—416no—
758#41—48no—
759#41—416no—
760#41—44no—
761#41—48no—
762#41—44no—
763#41—48no—
764C2×Q8—44no—
765C2×Q8—48no—
766C2×Q8C23×C412yes—
767C2×Q8C23×C412yes—
768C2×Q8C23×C414yes—
769C2×Q8C23×C414yes—
770C2×Q8C23×C418yes—
771C2×Q8C23×C412yes—
772C2×Q8C23×C414yes—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—416no—
777C2×D4C23×C414yes—
778C2×D4C23×C412yes—
779C2×D4C23×C414yes—
780C2×D4C23×C418yes—
781C2×D4C23×C412yes—
782C2×D4C23×C414yes—
783C2×D4C23×C414yes—
784C2×D4C23×C418yes—
785C2×D4C23×C414yes—
786C2×D4C23×C418yes—
787C2×D4C23×C414yes—
788C2×D4C23×C418yes—
789C2×D4C23×C414yes—
790C2×D4C23×C414yes—
791C2×D4C23×C418yes—
792C2×D4C23×C412yes—
793C22×C4—28no—
794C22×C4—216no—
795C22×C4—42no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—416no—
800C22×C4C23×C414yes—
801C22×C4C23×C414yes—
802C22×C4C23×C412yes—
803C22×C4C23×C412yes—
804C22×C4C23×C414yes—
805C22×C4C23×C414yes—
806C22×C4C23×C412yes—
807C22×C4C23×C412yes—
808C22×C4C23×C414yes—
809C22×C4C23×C414yes—
810C22×C4C23×C418yes—
811C22×C4C23×C412yes—
812C22×C4C23×C414yes—
813C22×C4C23×C414yes—
814C22×C4C23×C418yes—
815C22×C4C23×C412yes—
816C22×C4C23×C414yes—
817C22×C4C23×C411yescharacteristic
818C22×C4C23×C414yes—
819C22×C4C23×C414yes—
820C22×C4C23×C414yes—
821C22×C4C23×C418yes—
822C22×C4C23×C418yes—
823C22×C4C23×C414yes—
824C22×C4C23×C418yes—
825C22×C4C23×C414yes—
826C22×C4C23×C412yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2511yescharacteristic
830C22×C4C2514yes—
831C22×C4C2514yes—
832M16—216no—
833M16—216no—
834M16—48no—
835M16—48no—
836M16—416no—
837M16—48no—
838M16—44no—
839M16—48no—
840C2×C8—28no—
841C2×C8—24no—
842C2×C8—216no—
843C2×C8—44no—
844C2×C8—42no—
845C2×C8—48no—
846C2×C8—48no—
847C2×C8—416no—
848C2×C8C2514yes—
849C2×C8C2512yes—
850C2×C8C2518yes—
851C2×C8C2518yes—
852C2×C8C2518yes—
853C2×C8C2512yes—
854C4⋊C4C23×C414yes—
855C4⋊C4C23×C412yes—
856C4⋊C4C23×C414yes—
857C4⋊C4C23×C412yes—
858C4⋊C4C23×C414yes—
859C4⋊C4C23×C418yes—
860C4⋊C4C23×C412yes—
861C4⋊C4C23×C414yes—
862C4⋊C4C23×C414yes—
863C4⋊C4C23×C418yes—
864C4⋊C4C23×C414yes—
865C4⋊C4C23×C414yes—
866C4⋊C4C23×C418yes—
867C4⋊C4C23×C418yes—
868C4⋊C4C23×C414yes—
869C4⋊C4C23×C418yes—
870C4⋊C4C23×C412yes—
871C4⋊C4C23×C414yes—
872C4⋊C4C23×C414yes—
873C4⋊C4C23×C418yes—
874C4⋊C4C23×C414yes—
875C4⋊C4C23×C418yes—
876C4⋊C4C23×C414yes—
877C4⋊C4C23×C418yes—
878C4⋊C4C23×C418yes—
879C4⋊C4C23×C418yes—
880C4⋊C4C23×C418yes—
881C4⋊C4C23×C414yes—
882C4⋊C4C23×C418yes—
883C22⋊C4C23×C414yes—
884C22⋊C4C23×C414yes—
885C22⋊C4C23×C414yes—
886C22⋊C4C23×C414yes—
887C22⋊C4C23×C414yes—
888C22⋊C4C23×C418yes—
889C22⋊C4C23×C418yes—
890C22⋊C4C23×C414yes—
891C22⋊C4C23×C418yes—
892C22⋊C4C23×C414yes—
893C22⋊C4C23×C418yes—
894C22⋊C4C23×C414yes—
895C22⋊C4C23×C414yes—
896C22⋊C4C23×C418yes—
897C22⋊C4C23×C418yes—
898C22⋊C4C23×C414yes—
899C22⋊C4C23×C418yes—
900C22⋊C4C23×C414yes—
901C22⋊C4C23×C414yes—
902C22⋊C4C23×C418yes—
903C22⋊C4C23×C418yes—
904C22⋊C4C23×C414yes—
905C22⋊C4C23×C418yes—
906C22⋊C4C23×C418yes—
907C22⋊C4C23×C414yes—
908C22⋊C4C23×C418yes—
909C22⋊C4C23×C414yes—
910C42C23×C412yes—
911C42C23×C414yes—
912C42C23×C414yes—
913C42C23×C412yes—
914C42C23×C411yescharacteristic
915C42C23×C414yes—
916C42C23×C414yes—
917C42C23×C412yes—
918C42C23×C414yes—
919C42C23×C414yes—
920C42C23×C418yes—
921C42C23×C412yes—
922C42C23×C414yes—
923C42C23×C414yes—
924C42C23×C418yes—
925C42C23×C414yes—
926C42C23×C418yes—
927C42C23×C412yes—
928C42C23×C414yes—
929C42C23×C414yes—
930C42C23×C414yes—
931C42C23×C411yescharacteristic
932C42C2512yes—
933C42C2511yescharacteristic
934C42C2514yes—
935C42C2514yes—
936C42C2514yes—
937C42C2511yescharacteristic
938C23—24no—
939C23—28no—
940C23—41no—
941C23—44no—
942C23—48no—
943C23—44no—
944C23—44no—
945C23C24×C411yescharacteristic
946C23C24×C414yes—
947C23C24×C414yes—
948C23C24×C414yes—
949C23C24×C412yes—
950Q8—24no—
951Q8—24no—
952Q8—28no—
953Q8—44no—
954Q8—48no—
955Q8—42no—
956Q8—44no—
957D4—28no—
958D4—28no—
959D4—216no—
960D4—24no—
961D4—24no—
962D4—28no—
963D4—44no—
964D4—48no—
965D4—44no—
966D4—48no—
967D4—44no—
968D4—48no—
969D4—44no—
970D4—42no—
971D4—44no—
972D4—48no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—216no—
991C2×C4—41no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—42no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—44no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4#56818yes—
1005C2×C4C24×C412yes—
1006C2×C4C24×C414yes—
1007C2×C4C24×C412yes—
1008C2×C4C24×C414yes—
1009C2×C4C24×C414yes—
1010C2×C4C24×C411yescharacteristic
1011C2×C4C24×C414yes—
1012C2×C4C24×C414yes—
1013C2×C4C24×C412yes—
1014C2×C4C24×C414yes—
1015C2×C4C24×C414yes—
1016C2×C4C24×C418yes—
1017C2×C4C24×C412yes—
1018C2×C4C24×C412yes—
1019C2×C4C2611yescharacteristic
1020C8—24no—
1021C8—22no—
1022C8—28no—
1023C8—28no—
1024C8—28no—
1025C8#58514yes—
1026C22—22no—
1027C22—22no—
1028C22—24no—
1029C22—22no—
1030C22—24no—
1031C22—24no—
1032C22—24no—
1033C22—28no—
1034C22—24no—
1035C22—21no—
1036C22—24no—
1037C22—24no—
1038C22—44no—
1039C22—88no—
1040C22—88no—
1041C22C2×#56814yes—
1042C22C25×C411yescharacteristic
1043C4—22no—
1044C4—24no—
1045C4—22no—
1046C4—24no—
1047C4—24no—
1048C4—24no—
1049C4—28no—
1050C4—22no—
1051C4—24no—
1052C4—21no—
1053C4—24no—
1054C4—24no—
1055C4C2×#56814yes—
1056C4C2×#56814yes—
1057C4C2×#58512yes—
1058C2—24no—
1059C2—41no—
1060C2—44no—
1061C2—44no—
1062C2—44no—
1063C2C4×#58511yescharacteristic
1064C2C22×#56812yes—
subgroupG/H
centerC42C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#412C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60342C2semidirect
3. #60337C2semidirect
4. #60324C2semidirect
5. #60320C2semidirect
6. #60317C2semidirect
7. #60314C2semidirect
8. #60281C2semidirect
9. #60280C2semidirect
10. #60279C2semidirect
11. #60278C2semidirect
12. #60277C2semidirect
13. M16×#41C2semidirect
14. #60210C2semidirect
15. #60205C2semidirect
16. #60204C2semidirect
17. C2×#2965C2semidirect
38. #2995C22semidirect
39. #2995C22semidirect
40. #2994C22semidirect
41. #2993C22semidirect
42. #2993C22semidirect
43. #2992C22semidirect
44. #2991C22semidirect
45. #2990C22semidirect
46. #2990C22semidirect
47. #2989C22semidirect
48. #2989C22semidirect
49. #2989C22semidirect
50. #2987C22semidirect
51. #2986C22semidirect
52. #2985C22semidirect
53. #2984C22semidirect
54. #2983C22semidirect
55. #2981C22semidirect
56. #2980C22semidirect
57. #2979C22semidirect
58. #2978C22semidirect
59. #2978C22semidirect
60. #2977C22semidirect
61. #2976C22semidirect
62. #2975C22semidirect
63. #2974C22semidirect
64. #2974C22semidirect
65. #2973C22semidirect
66. #2971C22semidirect
67. #2970C22semidirect
68. #2970C22semidirect
69. #2969C22semidirect
70. #2969C22semidirect
71. #2968C22semidirect
72. #2967C22semidirect
73. #2967C22semidirect
74. #2966C22semidirect
78. #2965C22semidirect
79. #2965C22semidirect
80. #2965C22semidirect
81. #2965C22semidirect
82. #2965C22semidirect
83. #2965C22semidirect
84. #2965C22semidirect
85. #2965C22semidirect
86. #2965C22semidirect
87. #2965C22semidirect
88. #2965C22semidirect
89. #2965C22semidirect
90. #2965C22semidirect
91. #2965C22semidirect
92. C8×#41C22semidirect
93. C8×#41C22semidirect
94. C8×#41C22semidirect
95. Q8×M16C22semidirect
96. #2962C22semidirect
97. #2961C22semidirect
98. #2960C22semidirect
99. C2×#446C22semidirect
100. #2935C22semidirect
101. D4×M16C22semidirect
102. D4×M16C22semidirect
103. #2933C22semidirect
104. #2932C22semidirect
105. #2931C22semidirect
106. #2930C22semidirect
107. #2930C22semidirect
108. #2929C22semidirect
109. C2×#436C22semidirect
110. C2×#435C22semidirect
111. #2922C22semidirect
112. #2922C22semidirect
113. #2922C22semidirect
114. #2922C22semidirect
115. #2920C22semidirect
116. #2920C22semidirect
117. #2920C22semidirect
118. #2920C22semidirect
119. C2×#431C22semidirect
120. C2×#431C22semidirect
121. C2×#431C22semidirect
122. C4×#131C22semidirect
123. C4×#131C22semidirect
124. C2×C4×M16C22semidirect
125. C2×C4×M16C22semidirect
126. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#4122
#603422
#603372
#603242
#603202
#603172
#603142
#602812
#602802
#602792
#602782
#602772
M16×#412
#602102
#602052
#602042
C2×#29652