Finite Group Databasebeta

← #10574301

Subgroups — #10574301

Order 512.

7688 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62811C211yesmaximal, characteristic
2#60241C218yesmaximal, complemented
3#60240C218yesmaximal, complemented
4#60240C218yesmaximal, complemented
5#60239C218yesmaximal, complemented
6#60235C218yesmaximal, complemented
7#60234C214yesmaximal, complemented
8#60233C214yesmaximal, complemented
9#60142C212yesmaximal, complemented
10#60141C212yesmaximal, complemented
11#60140C212yesmaximal, complemented
12C2×#2933C212yesmaximal, complemented
13#60126C212yesmaximal, complemented
14#60065C212yesmaximal, complemented
15C2×#2880C211yesmaximal, characteristic, complemented
16C2×#2879C211yesmaximal, characteristic, complemented
17C2×#585C2211yescharacteristic
18C23×#41C2211yescharacteristic
19C2×#568C2212yescomplemented
20C22×#131C2212yescomplemented
21C22×#131C2212yescomplemented
22C23×M16C2212yescomplemented
23#3489C414yes—
24#3489C414yes—
25#3488C414yes—
26#3488C414yes—
27#3487C412yes—
28#3486C412yes—
29#3485C414yes—
30#3485C412yes—
31#3484C414yes—
32#3484C412yes—
33D4×#41C2218yes—
34D4×#41C2218yes—
35#3449C2214yes—
36#3449C2212yes—
37C2×#525C2214yes—
38C2×#525C2212yes—
39#3428C2211yescharacteristic
40#2981C22116yescomplemented
41#2981C22116yescomplemented
42#2980C22116yescomplemented
43#2979C22116yescomplemented
44#2978C2218yescomplemented
45#2978C2218yescomplemented
46#2978C22116yescomplemented
47#2977C2218yescomplemented
48#2977C2218yescomplemented
49#2977C22116yescomplemented
50#2976C22116yescomplemented
51#2976C22116yescomplemented
52#2976C22116yescomplemented
53#2976C22116yescomplemented
54#2975C2218yescomplemented
55#2974C22116yescomplemented
56#2974C22116yescomplemented
57#2973C2218yescomplemented
58#2973C2218yescomplemented
59#2972C2218yescomplemented
60#2935C2218yescomplemented
61#2935C2218yescomplemented
62D4×M16C2218yescomplemented
63D4×M16C2218yescomplemented
64#2933C2214yescomplemented
65#2933C2218yescomplemented
66#2933C2214yescomplemented
67#2933C2214yescomplemented
68#2933C2214yescomplemented
69#2933C2218yescomplemented
70#2933C2214yescomplemented
71#2933C2214yescomplemented
72#2933C2214yescomplemented
73#2933C2214yescomplemented
74#2933C2218yescomplemented
75#2933C2218yescomplemented
76#2932C2218yescomplemented
77#2931C2218yescomplemented
78#2930C2218yescomplemented
79#2930C2218yescomplemented
80#2930C2218yescomplemented
81#2930C2218yescomplemented
82#2929C2218yescomplemented
83#2929C2218yescomplemented
84#2929C2218yescomplemented
85#2929C2218yescomplemented
86C2×#436C2214yescomplemented
87C2×#435C2214yescomplemented
88C2×#435C2214yescomplemented
89C2×C8×D4C2214yescomplemented
90#2925C2218yescomplemented
91#2925C2218yescomplemented
92#2924C2218yescomplemented
93#2924C2218yescomplemented
94#2923C2218yescomplemented
95#2922C2218yescomplemented
96#2905C2212yescomplemented
97C2×#424C2212yescomplemented
98#2880C2214yescomplemented
99#2880C2214yescomplemented
100#2880C2214yescomplemented
101#2880C2214yescomplemented
102#2880C2218yescomplemented
103#2880C2218yescomplemented
104#2880C2218yescomplemented
105#2880C2218yescomplemented
106#2879C2212yes—
107#2879C2214yescomplemented
108#2879C2218yescomplemented
109#2879C2211yescharacteristic, complemented
110#2879C2211yescharacteristic, complemented
111#2879C2212yescomplemented
112#2879C2218yescomplemented
113C2×#408C2212yes—
114C2×#408C2214yescomplemented
115C2×#408C2218yescomplemented
116C2×#408C2212yescomplemented
117C2×#408C2218yescomplemented
118C2×#407C2214yescomplemented
119C2×#407C2212yescomplemented
120C2×#407C2211yescharacteristic, complemented
121C22×C22⋊C8C2212yescomplemented
122C22×C22⋊C8C2211yescharacteristic, complemented
123#2873C2212yescomplemented
124C2×#405C2212yescomplemented
125#585—48no—
126C2×2−1+4C2×C412yes—
127C2×2−1+4C2×C414yes—
128C2×H(5,𝔽2)C2×C414yes—
129C2×H(5,𝔽2)C2×C412yes—
130C2×H(5,𝔽2)C2×C414yes—
131C22×#41—48no—
132C22×#41C2×C412yes—
133C22×#41C2×C411yescharacteristic
134C22×#41C2×C411yescharacteristic
135C22×#41C2×C414yes—
136C22×#41C2×C414yes—
137C22×#41C2311yescharacteristic
138C22×#41C2311yescharacteristic
139C22×#41C2312yes—
140C22×#41C2312yes—
141C22×#41C2314yes—
142C22×#41C2314yes—
143C22×#41C2318yes—
144C22×#41C2314yes—
145C23×Q8C2×C411yescharacteristic
146C23×D4C2×C411yescharacteristic
147C23×D4C2×C412yes—
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150#568—48no—
151C2×#131—48no—
152C2×#131—48no—
153C2×#131C2314yes—
154C2×#131C2314yes—
155C2×#131C2318yes—
156C2×#131C2314yes—
157C2×#131C2314yes—
158C2×#131C2314yes—
159C2×#131C2314yes—
160C2×#131C2318yescomplemented
161C2×#131C2314yescomplemented
162C2×#131C2314yescomplemented
163C22×M16—48no—
164C22×M16C2312yes—
165C22×M16C2312yes—
166C22×M16C2312yes—
167C22×M16C2314yes—
168C22×M16C2314yes—
169C22×M16C2314yes—
170C22×M16C2314yes—
171C22×M16C2314yes—
172C22×M16C2314yes—
173C22×M16C2318yescomplemented
174C22×M16C2314yescomplemented
175C23×C8C2312yes—
176C23×C8C2314yes—
177C23×C8C2314yes—
178C23×C8C2314yescomplemented
179#550C2×C418yes—
180#550C2×C418yes—
181D4×Q8C2×C418yes—
182D4×Q8C2×C418yes—
183#548C2×C418yes—
184#548C2×C418yes—
185#548C2×C418yes—
186#548C2×C418yes—
187#547C2×C4116yes—
188#547C2×C418yes—
189#547C2×C4116yes—
190#547C2×C418yes—
191#546C2×C4116yes—
192#546C2×C418yes—
193#546C2×C4116yes—
194#546C2×C418yes—
195#546C2×C4116yes—
196#546C2×C418yes—
197#546C2×C4116yes—
198#546C2×C418yes—
199D42C2×C418yes—
200D42C2×C4116yes—
201D42C2×C418yes—
202D42C2×C4116yes—
203#537C2×C414yes—
204#537C2×C414yes—
205#537C2×C418yes—
206#537C2×C418yes—
207#536C2×C414yes—
208#536C2×C418yes—
209#536C2×C414yes—
210#536C2×C418yes—
211#535C2×C414yes—
212#535C2×C418yes—
213#535C2×C414yes—
214#535C2×C418yes—
215#534C2×C418yes—
216#534C2×C418yes—
217#534C2×C418yes—
218#532C2318yes—
219#532C23116yes—
220#525C2×C414yes—
221#525C2×C418yes—
222#525C2×C414yes—
223#525C2×C418yes—
224#525C2×C414yes—
225#525C2×C414yes—
226#525C2×C418yes—
227#525C2×C418yes—
228#525C2314yes—
229#525C2318yes—
230#525C2314yes—
231#525C2314yes—
232#525C2314yes—
233#525C2318yes—
234#525C2318yes—
235#525C2318yes—
236#525C23116yes—
237C2×#123C2×C414yes—
238C2×#123C2×C418yes—
239C2×C22⋊Q8C2×C412yes—
240C2×C22⋊Q8C2×C412yes—
241C2×C22⋊Q8C2×C414yes—
242C2×C22⋊Q8C2×C414yes—
243C2×#121C2×C412yes—
244C2×#121C2×C412yes—
245C2×#121C2×C414yes—
246C2×#121C2×C414yes—
247C2×#120C2×C414yes—
248C2×#120C2×C418yes—
249#520C2×C414yes—
250#520C2×C414yes—
251#519C2×C412yes—
252#518C2×C412yes—
253#518C2×C414yes—
254C4×#41C2318yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2318yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261#436C2318yes—
262#436C2318yes—
263#436C23116yes—
264#436C2318yescomplemented
265#436C2318yescomplemented
266#436C23116yescomplemented
267#436C23116yescomplemented
268#436C23116yescomplemented
269#436C23116yescomplemented
270#436C23116yescomplemented
271#435C2318yes—
272#435C2318yes—
273#435C2318yes—
274#435C2318yes—
275#435C23116yes—
276#435C23116yes—
277#435C2318yescomplemented
278#435C2318yescomplemented
279#435C2318yescomplemented
280#435C2318yescomplemented
281#435C23116yescomplemented
282#435C23116yescomplemented
283#435C23116yescomplemented
284#435C23116yescomplemented
285#435C23116yescomplemented
286#435C23116yescomplemented
287#435C23116yescomplemented
288#435C23116yescomplemented
289#435C23116yescomplemented
290#435C23116yescomplemented
291C8×D4C2318yes—
292C8×D4C2318yes—
293C8×D4C23116yes—
294C8×D4C2318yescomplemented
295C8×D4C2318yescomplemented
296C8×D4C23116yescomplemented
297C8×D4C23116yescomplemented
298C8×D4C23116yescomplemented
299C8×D4C23116yescomplemented
300C8×D4C23116yescomplemented
301#433C23116yescomplemented
302#433C23116yescomplemented
303#433C23116yescomplemented
304#433C23116yescomplemented
305#432C23116yescomplemented
306#432C23116yescomplemented
307#431C23116yescomplemented
308#431C23116yescomplemented
309#424C2314yes—
310#424C2314yes—
311#424C2318yes—
312#424C2314yescomplemented
313#424C2314yescomplemented
314#424C2318yescomplemented
315#423C2318yescomplemented
316C2×C4⋊C8C2314yescomplemented
317C2×C4⋊C8C2314yescomplemented
318#408C2314yes—
319#408C2314yes—
320#408C2314yes—
321#408C2314yes—
322#408C2318yes—
323#408C2318yes—
324#408C2318yes—
325#408C2318yes—
326#408C23116yes—
327#408C23116yes—
328#408C2314yes—
329#408C2314yes—
330#408C2318yes—
331#408C2318yes—
332#408C2318yes—
333#408C2318yes—
334#408C2318yes—
335#408C2314yescomplemented
336#408C2318yescomplemented
337#408C2314yescomplemented
338#408C23116yescomplemented
339#408C23116yescomplemented
340#408C23116yescomplemented
341#408C23116yescomplemented
342#407C2318yes—
343#407C2314yes—
344#407C2314yes—
345#407C2318yes—
346#407C2318yes—
347#407C2314yes—
348#407C2314yes—
349#407C2314yes—
350#407C2318yes—
351#407C2314yes—
352#407C2318yescomplemented
353#407C23116yescomplemented
354#407C23116yescomplemented
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2312yes—
358C2×C22⋊C8C2314yes—
359C2×C22⋊C8C2312yes—
360C2×C22⋊C8C2312yes—
361C2×C22⋊C8C2312yes—
362C2×C22⋊C8C2312yes—
363C2×C22⋊C8C2312yes—
364C2×C22⋊C8C2314yes—
365C2×C22⋊C8C2314yes—
366C2×C22⋊C8C2318yes—
367C2×C22⋊C8C2314yes—
368C2×C22⋊C8C2312yes—
369C2×C22⋊C8C2318yes—
370C2×C22⋊C8C2318yes—
371C2×C22⋊C8C2314yescomplemented
372C2×C22⋊C8C2314yescomplemented
373C2×C22⋊C8C23116yescomplemented
374C2×C22⋊C8C23116yescomplemented
375#405C2314yes—
376#405C2314yes—
377#405C2318yes—
378#405C2314yescomplemented
379#405C2314yescomplemented
380#405C2318yescomplemented
381C4×M16C2318yescomplemented
382C2×#97C2314yescomplemented
383C2×C4×C8C2314yescomplemented
384C25C22×C411yescharacteristic
385C25C22×C412yes—
3862−1+4—48no—
3872−1+4—416no—
388H(5,𝔽2)—416no—
389H(5,𝔽2)—48no—
390H(5,𝔽2)—416no—
391C2×#41—28no—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—28no—
395C2×#41—48no—
396C2×#41—48no—
397C2×#41—44no—
398C2×#41—44no—
399C2×#41—416no—
400C2×#41—416no—
401C2×#41—48no—
402C2×#41—48no—
403C2×#41—48no—
404C2×#41—48no—
405C2×#41—416no—
406C2×#41—416no—
407C2×#41—416no—
408C2×#41C22×C414yes—
409C2×#41C22×C414yes—
410C2×#41C22×C414yes—
411C2×#41C22×C414yes—
412C2×#41C22×C418yes—
413C2×#41C22×C418yes—
414C2×#41C22×C418yes—
415C2×#41C22×C418yes—
416C2×#41C22×C418yes—
417C2×#41C22×C414yes—
418C2×#41C22×C414yes—
419C2×#41C22×C4116yes—
420C2×#41C22×C418yes—
421C2×#41C22×C414yes—
422C2×#41C22×C414yes—
423C2×#41C22×C418yes—
424C2×#41C2414yes—
425C2×#41C2414yes—
426C2×#41C2414yes—
427C2×#41C2414yes—
428C2×#41C2418yes—
429C2×#41C2418yes—
430C22×Q8—44no—
431C22×Q8C22×C411yescharacteristic
432C22×Q8C22×C412yes—
433C22×Q8C22×C411yescharacteristic
434C22×Q8C22×C414yes—
435C22×Q8C22×C412yes—
436C22×Q8C22×C414yes—
437C22×Q8C22×C414yes—
438C22×Q8C22×C418yes—
439C22×D4—44no—
440C22×D4—48no—
441C22×D4C22×C412yes—
442C22×D4C22×C411yescharacteristic
443C22×D4C22×C414yes—
444C22×D4C22×C412yes—
445C22×D4C22×C412yes—
446C22×D4C22×C411yescharacteristic
447C22×D4C22×C414yes—
448C22×D4C22×C418yes—
449C22×D4C22×C418yes—
450C22×D4C22×C414yes—
451C22×D4C22×C412yes—
452C22×D4C22×C412yes—
453C22×D4C22×C412yes—
454C22×D4C22×C414yes—
455C22×D4C22×C414yes—
456C22×D4C22×C418yes—
457C22×D4C22×C418yes—
458C22×D4C22×C418yes—
459C22×D4C22×C4116yes—
460C22×D4C22×C414yes—
461C22×D4C22×C418yes—
462C23×C4—28no—
463C23×C4—48no—
464C23×C4C22×C412yes—
465C23×C4C22×C412yes—
466C23×C4C22×C411yescharacteristic
467C23×C4C22×C411yescharacteristic
468C23×C4C22×C411yescharacteristic
469C23×C4C22×C414yes—
470C23×C4C22×C414yes—
471C23×C4C22×C412yes—
472C23×C4C22×C412yes—
473C23×C4C22×C412yes—
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2418yes—
484C23×C4C2411yescharacteristic
485#131—48no—
486#131—48no—
487#131—48no—
488#131—48no—
489#131—48no—
490#131—48no—
491#131—48no—
492#131—48no—
493#131—416no—
494#131—416no—
495C2×M16—28no—
496C2×M16—28no—
497C2×M16—28no—
498C2×M16—48no—
499C2×M16—48no—
500C2×M16—48no—
501C2×M16—48no—
502C2×M16—48no—
503C2×M16—48no—
504C2×M16—48no—
505C2×M16—416no—
506C2×M16C2414yes—
507C2×M16C2414yes—
508C2×M16C2414yes—
509C2×M16C2414yes—
510C2×M16C2414yes—
511C2×M16C2414yes—
512C2×M16C2418yes—
513C2×M16C2418yes—
514C2×M16C2418yes—
515C2×M16C2418yes—
516C2×M16C2418yes—
517C2×M16C24116yes—
518C2×M16C2418yes—
519C22×C8—28no—
520C22×C8—48no—
521C22×C8—48no—
522C22×C8—48no—
523C22×C8C2412yes—
524C22×C8C2412yes—
525C22×C8C2414yes—
526C22×C8C2412yes—
527C22×C8C2414yes—
528C22×C8C2414yes—
529C22×C8C2412yes—
530C22×C8C2412yes—
531C22×C8C2412yes—
532C22×C8C2418yes—
533C22×C8C2418yes—
534C22×C8C2418yes—
535C22×C8C2418yes—
536C22×C8C2418yes—
537C22×C8C2418yes—
538C22×C8C24116yes—
539C4⋊Q8C22×C418yes—
540C4⋊Q8C22×C4116yes—
541#127C22×C418yes—
542#127C22×C4116yes—
543#124C22×C418yes—
544#124C22×C418yes—
545#124C22×C4116yes—
546#124C22×C4116yes—
547#123C22×C418yes—
548#123C22×C4116yes—
549#123C22×C418yes—
550#123C22×C418yes—
551#123C22×C418yes—
552#123C22×C4116yes—
553#123C22×C4116yes—
554#123C22×C4116yes—
555#123C22×C4116yes—
556#123C22×C4116yes—
557C22⋊Q8C22×C414yes—
558C22⋊Q8C22×C414yes—
559C22⋊Q8C22×C418yes—
560C22⋊Q8C22×C418yes—
561C22⋊Q8C22×C414yes—
562C22⋊Q8C22×C414yes—
563C22⋊Q8C22×C414yes—
564C22⋊Q8C22×C414yes—
565C22⋊Q8C22×C418yes—
566C22⋊Q8C22×C418yes—
567C22⋊Q8C22×C414yes—
568C22⋊Q8C22×C414yes—
569C22⋊Q8C22×C418yes—
570C22⋊Q8C22×C418yes—
571C22⋊Q8C22×C418yes—
572C22⋊Q8C22×C418yes—
573C22⋊Q8C22×C4116yes—
574C22⋊Q8C22×C4116yes—
575#121C22×C414yes—
576#121C22×C414yes—
577#121C22×C418yes—
578#121C22×C418yes—
579#121C22×C414yes—
580#121C22×C414yes—
581#121C22×C414yes—
582#121C22×C414yes—
583#121C22×C418yes—
584#121C22×C418yes—
585#121C22×C414yes—
586#121C22×C414yes—
587#121C22×C418yes—
588#121C22×C418yes—
589#121C22×C418yes—
590#121C22×C418yes—
591#121C22×C4116yes—
592#121C22×C4116yes—
593#121C22×C4116yes—
594#121C22×C4116yes—
595#121C22×C4116yes—
596#121C22×C4116yes—
597#121C22×C4116yes—
598#121C22×C4116yes—
599#120C22×C418yes—
600#120C22×C4116yes—
601#120C22×C418yes—
602#120C22×C418yes—
603#120C22×C4116yes—
604#120C22×C418yes—
605#120C22×C4116yes—
606#120C22×C4116yes—
607#120C22×C4116yes—
608#120C22×C4116yes—
609C4×Q8C22×C418yes—
610C4×Q8C22×C418yes—
611C4×D4C22×C418yes—
612C4×D4C22×C418yes—
613C4×D4C22×C4116yes—
614C4×D4C22×C4116yes—
615C4×D4C22×C418yes—
616C4×D4C22×C418yes—
617C4×D4C22×C4116yes—
618C4×D4C22×C4116yes—
619C4×D4C22×C4116yes—
620C4×D4C22×C4116yes—
621C4×D4C22×C418yes—
622C4×D4C22×C418yes—
623C4×D4C2418yes—
624C4×D4C2418yes—
625C4×D4C2418yes—
626C4×D4C2418yes—
627C4×D4C24116yes—
628C4×D4C24116yes—
629#117C22×C418yes—
630#117C22×C414yes—
631#117C22×C418yes—
632#117C22×C414yes—
633#117C2414yes—
634#117C2414yes—
635#117C2418yes—
636C2×C4⋊C4C22×C414yes—
637C2×C4⋊C4C22×C414yes—
638C2×C4⋊C4C22×C412yes—
639C2×C4⋊C4C22×C412yes—
640C2×C4⋊C4C22×C414yes—
641C2×C4⋊C4C22×C414yes—
642C2×C4⋊C4C22×C418yes—
643C2×C4⋊C4C22×C418yes—
644C2×C22⋊C4C22×C418yes—
645C2×C22⋊C4C22×C414yes—
646C2×C22⋊C4C22×C414yes—
647C2×C22⋊C4C22×C414yes—
648C2×C22⋊C4C22×C418yes—
649C2×C22⋊C4C22×C418yes—
650C2×C22⋊C4C22×C414yes—
651C2×C22⋊C4C22×C414yes—
652C2×C22⋊C4C22×C418yes—
653C2×C22⋊C4C22×C418yes—
654C2×C42C2414yes—
655C2×C42C2418yes—
656C4⋊C8C2418yes—
657C4⋊C8C2418yes—
658C4⋊C8C2418yes—
659C4⋊C8C2418yes—
660C4⋊C8C24116yes—
661C4⋊C8C24116yes—
662C22⋊C8C2411yescharacteristic
663C22⋊C8C2411yescharacteristic
664C22⋊C8C2412yes—
665C22⋊C8C2418yes—
666C22⋊C8C2412yes—
667C22⋊C8C2414yes—
668C22⋊C8C2411yescharacteristic
669C22⋊C8C2414yes—
670C22⋊C8C2411yescharacteristic
671C22⋊C8C2418yes—
672C22⋊C8C2412yes—
673C22⋊C8C2412yes—
674C22⋊C8C2412yes—
675C22⋊C8C2412yes—
676C22⋊C8C2418yes—
677C22⋊C8C24116yes—
678C22⋊C8C24116yes—
679C22⋊C8C2418yes—
680C22⋊C8C2418yes—
681C22⋊C8C2418yes—
682C22⋊C8C2418yes—
683C22⋊C8C2418yes—
684C22⋊C8C2418yes—
685C22⋊C8C2418yes—
686C22⋊C8C2418yes—
687C22⋊C8C24116yes—
688C22⋊C8C2418yes—
689C22⋊C8C2418yes—
690C22⋊C8C24116yes—
691#97C2418yes—
692#97C2418yes—
693#97C24116yes—
694C4×C8C2418yes—
695C4×C8C2418yes—
696C4×C8C24116yes—
697C24—24no—
698C24—44no—
699C24—42no—
700C24—44no—
701C24—81no—
702C24—82no—
703C24C23×C412yes—
704C24C23×C411yescharacteristic
705C24C23×C412yes—
706C24C23×C412yes—
707C24C23×C414yes—
708C24C23×C414yes—
709C24C23×C412yes—
710C24C23×C411yescharacteristic
711C24C23×C414yes—
712C24C23×C418yes—
713C24C23×C411yescharacteristic
714#41—216no—
715#41—216no—
716#41—216no—
717#41—216no—
718#41—28no—
719#41—28no—
720#41—28no—
721#41—28no—
722#41—28no—
723#41—28no—
724#41—28no—
725#41—28no—
726#41—416no—
727#41—48no—
728#41—416no—
729#41—48no—
730#41—416no—
731#41—416no—
732#41—416no—
733#41—432no—
734#41—48no—
735#41—48no—
736#41—48no—
737#41—48no—
738#41—416no—
739#41—416no—
740#41—416no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—44no—
745C2×Q8—48no—
746C2×Q8—48no—
747C2×Q8—48no—
748C2×Q8—416no—
749C2×Q8C23×C414yes—
750C2×Q8C23×C414yes—
751C2×Q8C23×C414yes—
752C2×Q8C23×C414yes—
753C2×Q8C23×C418yes—
754C2×Q8C23×C418yes—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—216no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—416no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—416no—
769C2×D4—416no—
770C2×D4—48no—
771C2×D4—416no—
772C2×D4—432no—
773C2×D4—416no—
774C2×D4—84no—
775C2×D4—88no—
776C2×D4C23×C418yes—
777C2×D4C23×C414yes—
778C2×D4C23×C418yes—
779C2×D4C23×C418yes—
780C2×D4C23×C418yes—
781C2×D4C23×C418yes—
782C2×D4C23×C414yes—
783C2×D4C23×C414yes—
784C2×D4C23×C414yes—
785C2×D4C23×C418yes—
786C2×D4C23×C418yes—
787C2×D4C23×C4116yes—
788C2×D4C23×C418yes—
789C2×D4C23×C4116yes—
790C2×D4C23×C4116yes—
791C2×D4C23×C418yes—
792C2×D4C23×C418yes—
793C2×D4C23×C418yes—
794C2×D4C23×C418yes—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—416no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4C23×C412yes—
819C22×C4C23×C412yes—
820C22×C4C23×C414yes—
821C22×C4C23×C414yes—
822C22×C4C23×C412yes—
823C22×C4C23×C412yes—
824C22×C4C23×C412yes—
825C22×C4C23×C412yes—
826C22×C4C23×C412yes—
827C22×C4C23×C418yes—
828C22×C4C23×C411yescharacteristic
829C22×C4C23×C411yescharacteristic
830C22×C4C23×C412yes—
831C22×C4C23×C414yes—
832C22×C4C23×C411yescharacteristic
833C22×C4C23×C411yescharacteristic
834C22×C4C23×C412yes—
835C22×C4C23×C418yes—
836C22×C4C23×C414yes—
837C22×C4C23×C418yes—
838C22×C4C23×C414yes—
839C22×C4C23×C414yes—
840C22×C4C23×C414yes—
841C22×C4C23×C418yes—
842C22×C4C23×C414yes—
843C22×C4C23×C414yes—
844C22×C4C23×C414yes—
845C22×C4C23×C414yes—
846C22×C4C23×C4116yes—
847C22×C4C23×C412yes—
848C22×C4C23×C411yescharacteristic
849C22×C4H(5,𝔽2)18yes—
850C22×C4C2514yes—
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2518yes—
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858M16—28no—
859M16—28no—
860M16—28no—
861M16—28no—
862M16—28no—
863M16—28no—
864M16—48no—
865M16—48no—
866M16—48no—
867M16—48no—
868M16—48no—
869M16—48no—
870M16—416no—
871C2×C8—24no—
872C2×C8—24no—
873C2×C8—24no—
874C2×C8—24no—
875C2×C8—24no—
876C2×C8—24no—
877C2×C8—28no—
878C2×C8—28no—
879C2×C8—28no—
880C2×C8—48no—
881C2×C8—48no—
882C2×C8—48no—
883C2×C8—48no—
884C2×C8—48no—
885C2×C8—48no—
886C2×C8—416no—
887C2×C8C2512yes—
888C2×C8C2512yes—
889C2×C8C2518yes—
890C2×C8C2518yes—
891C2×C8C2518yes—
892C2×C8C2512yes—
893C2×C8C2512yes—
894C4⋊C4C23×C414yes—
895C4⋊C4C23×C414yes—
896C4⋊C4C23×C418yes—
897C4⋊C4C23×C418yes—
898C4⋊C4C23×C418yes—
899C4⋊C4C23×C418yes—
900C4⋊C4C23×C414yes—
901C4⋊C4C23×C414yes—
902C4⋊C4C23×C418yes—
903C4⋊C4C23×C4116yes—
904C4⋊C4C23×C418yes—
905C4⋊C4C23×C4116yes—
906C22⋊C4C23×C418yes—
907C22⋊C4C23×C418yes—
908C22⋊C4C23×C418yes—
909C22⋊C4C23×C418yes—
910C22⋊C4C23×C418yes—
911C22⋊C4C23×C4116yes—
912C22⋊C4C23×C418yes—
913C22⋊C4C23×C418yes—
914C22⋊C4C23×C4116yes—
915C22⋊C4C23×C418yes—
916C22⋊C4C23×C4116yes—
917C22⋊C4C23×C418yes—
918C22⋊C4C23×C4116yes—
919C22⋊C4C23×C418yes—
920C22⋊C4C23×C4116yes—
921C42C23×C4116yes—
922C42C23×C418yes—
923C42C2518yes—
924C23—22no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—22no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23—28no—
933C23—28no—
934C23—41no—
935C23—42no—
936C23—41no—
937C23—41no—
938C23—42no—
939C23—42no—
940C23—44no—
941C23—44no—
942C23—44no—
943C23—42no—
944C23—44no—
945C23—44no—
946C23—42no—
947C23—42no—
948C23—41no—
949C23—44no—
950C23—42no—
951C23—44no—
952C23—41no—
953C23—48no—
954C23—48no—
955C23—48no—
956C23—88no—
957C23—816no—
958C23#51814yes—
959C23C24×C411yescharacteristic
960C23C24×C418yes—
961C23C24×C412yes—
962C23C24×C414yes—
963C23C24×C414yes—
964C23C24×C411yescharacteristic
965C23C24×C412yes—
966C23C24×C411yescharacteristic
967Q8—28no—
968Q8—28no—
969Q8—28no—
970Q8—28no—
971Q8—48no—
972Q8—48no—
973D4—216no—
974D4—216no—
975D4—216no—
976D4—216no—
977D4—216no—
978D4—28no—
979D4—28no—
980D4—28no—
981D4—28no—
982D4—48no—
983D4—48no—
984D4—48no—
985D4—48no—
986D4—416no—
987D4—48no—
988D4—416no—
989D4—48no—
990D4—48no—
991D4—416no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—28no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—216no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—416no—
1024C2×C4—48no—
1025C2×C4—44no—
1026C2×C4—48no—
1027C2×C4—44no—
1028C2×C4—48no—
1029C2×C4#51814yes—
1030C2×C4#51818yes—
1031C2×C4C24×C414yes—
1032C2×C4C24×C418yes—
1033C2×C4C24×C418yes—
1034C2×C4C24×C411yescharacteristic
1035C2×C4C24×C411yescharacteristic
1036C2×C4C24×C412yes—
1037C2×C4C24×C418yes—
1038C2×C4C24×C414yes—
1039C2×C4C24×C412yes—
1040C2×C4C24×C411yescharacteristic
1041C2×C4C2×H(5,𝔽2)14yes—
1042C2×C4C2×H(5,𝔽2)14yes—
1043C2×C4C2×H(5,𝔽2)14yes—
1044C2×C4C2611yescharacteristic
1045C8—22no—
1046C8—22no—
1047C8—22no—
1048C8—22no—
1049C8—28no—
1050C8—28no—
1051C8—28no—
1052C22—22no—
1053C22—21no—
1054C22—22no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22—24no—
1059C22—28no—
1060C22—22no—
1061C22—24no—
1062C22—21no—
1063C22—24no—
1064C22—21no—
1065C22—22no—
1066C22—24no—
1067C22—28no—
1068C22—21no—
1069C22—22no—
1070C22—24no—
1071C22—24no—
1072C22—28no—
1073C22—44no—
1074C22—48no—
1075C22—44no—
1076C22—48no—
1077C22—88no—
1078C22—82no—
1079C22—84no—
1080C22—88no—
1081C22—84no—
1082C22—88no—
1083C22—168no—
1084C22C2×#51812yes—
1085C22C2×#51814yes—
1086C22#357312yes—
1087C22C25×C411yescharacteristic
1088C4—28no—
1089C4—28no—
1090C4—21no—
1091C4—21no—
1092C4—22no—
1093C4—24no—
1094C4—24no—
1095C4—28no—
1096C4C2×#51812yes—
1097C4C2×#51814yes—
1098C4C22×H(5,𝔽2)12yes—
1099C2—22no—
1100C2—22no—
1101C2—24no—
1102C2—42no—
1103C2—44no—
1104C2—41no—
1105C2—44no—
1106C2—48no—
1107C2C22×#51811yescharacteristic
1108C2C2×#357311yescharacteristic
1109C2#6307611yescharacteristic
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62811C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60241C2semidirect
3. #60240C2semidirect
4. #60240C2semidirect
5. #60239C2semidirect
6. #60235C2semidirect
7. #60234C2semidirect
8. #60233C2semidirect
9. #60142C2semidirect
10. #60141C2semidirect
11. #60140C2semidirect
12. C2×#2933C2semidirect
13. #60126C2semidirect
14. #60065C2semidirect
15. C2×#2880C2semidirect
16. C2×#2879C2semidirect
19. C2×#568C22semidirect
20. C22×#131C22semidirect
21. C22×#131C22semidirect
22. C23×M16C22semidirect
40. #2981C22semidirect
41. #2981C22semidirect
42. #2980C22semidirect
43. #2979C22semidirect
44. #2978C22semidirect
45. #2978C22semidirect
46. #2978C22semidirect
47. #2977C22semidirect
48. #2977C22semidirect
49. #2977C22semidirect
50. #2976C22semidirect
51. #2976C22semidirect
52. #2976C22semidirect
53. #2976C22semidirect
54. #2975C22semidirect
55. #2974C22semidirect
56. #2974C22semidirect
57. #2973C22semidirect
58. #2973C22semidirect
59. #2972C22semidirect
60. #2935C22semidirect
61. #2935C22semidirect
62. D4×M16C22semidirect
63. D4×M16C22semidirect
64. #2933C22semidirect
65. #2933C22semidirect
66. #2933C22semidirect
67. #2933C22semidirect
68. #2933C22semidirect
69. #2933C22semidirect
70. #2933C22semidirect
71. #2933C22semidirect
72. #2933C22semidirect
73. #2933C22semidirect
74. #2933C22semidirect
75. #2933C22semidirect
76. #2932C22semidirect
77. #2931C22semidirect
78. #2930C22semidirect
79. #2930C22semidirect
80. #2930C22semidirect
81. #2930C22semidirect
82. #2929C22semidirect
83. #2929C22semidirect
84. #2929C22semidirect
85. #2929C22semidirect
86. C2×#436C22semidirect
87. C2×#435C22semidirect
88. C2×#435C22semidirect
89. C2×C8×D4C22semidirect
90. #2925C22semidirect
91. #2925C22semidirect
92. #2924C22semidirect
93. #2924C22semidirect
94. #2923C22semidirect
95. #2922C22semidirect
96. #2905C22semidirect
97. C2×#424C22semidirect
98. #2880C22semidirect
99. #2880C22semidirect
100. #2880C22semidirect
101. #2880C22semidirect
102. #2880C22semidirect
103. #2880C22semidirect
104. #2880C22semidirect
105. #2880C22semidirect
107. #2879C22semidirect
108. #2879C22semidirect
109. #2879C22semidirect
110. #2879C22semidirect
111. #2879C22semidirect
112. #2879C22semidirect
114. C2×#408C22semidirect
115. C2×#408C22semidirect
116. C2×#408C22semidirect
117. C2×#408C22semidirect
118. C2×#407C22semidirect
119. C2×#407C22semidirect
120. C2×#407C22semidirect
121. C22×C22⋊C8C22semidirect
122. C22×C22⋊C8C22semidirect
123. #2873C22semidirect
124. C2×#405C22semidirect
160. C2×#131C23semidirect
161. C2×#131C23semidirect
162. C2×#131C23semidirect
173. C22×M16C23semidirect
174. C22×M16C23semidirect
178. C23×C8C23semidirect
264. #436C23semidirect
265. #436C23semidirect
266. #436C23semidirect
267. #436C23semidirect
268. #436C23semidirect
269. #436C23semidirect
270. #436C23semidirect
277. #435C23semidirect
278. #435C23semidirect
279. #435C23semidirect
280. #435C23semidirect
281. #435C23semidirect
282. #435C23semidirect
283. #435C23semidirect
284. #435C23semidirect
285. #435C23semidirect
286. #435C23semidirect
287. #435C23semidirect
288. #435C23semidirect
289. #435C23semidirect
290. #435C23semidirect
294. C8×D4C23semidirect
295. C8×D4C23semidirect
296. C8×D4C23semidirect
297. C8×D4C23semidirect
298. C8×D4C23semidirect
299. C8×D4C23semidirect
300. C8×D4C23semidirect
301. #433C23semidirect
302. #433C23semidirect
303. #433C23semidirect
304. #433C23semidirect
305. #432C23semidirect
306. #432C23semidirect
307. #431C23semidirect
308. #431C23semidirect
312. #424C23semidirect
313. #424C23semidirect
314. #424C23semidirect
315. #423C23semidirect
316. C2×C4⋊C8C23semidirect
317. C2×C4⋊C8C23semidirect
335. #408C23semidirect
336. #408C23semidirect
337. #408C23semidirect
338. #408C23semidirect
339. #408C23semidirect
340. #408C23semidirect
341. #408C23semidirect
352. #407C23semidirect
353. #407C23semidirect
354. #407C23semidirect
371. C2×C22⋊C8C23semidirect
372. C2×C22⋊C8C23semidirect
373. C2×C22⋊C8C23semidirect
374. C2×C22⋊C8C23semidirect
378. #405C23semidirect
379. #405C23semidirect
380. #405C23semidirect
381. C4×M16C23semidirect
382. C2×#97C23semidirect
383. C2×C4×C8C23semidirect

Maximal subgroups

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

subgroupindex
#628112
#602412
#602402
#602392
#602352
#602342
#602332
#601422
#601412
#601402
C2×#29332
#601262
#600652
C2×#28802
C2×#28792