Finite Group Databasebeta

← #6393365

Subgroups — #6393365

Order 512.

3446 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2C2×D4×M16C211yesmaximal, characteristic, complemented
3#34057C211yesmaximal, characteristic, complemented
4#22506C218yesmaximal, complemented
5#22434C218yesmaximal, complemented
6#21857C212yesmaximal, complemented
7#21774C212yesmaximal, complemented
8#21773C212yesmaximal, complemented
9#21383C212yesmaximal, complemented
10#20902C212yesmaximal, complemented
11C2×#1871C212yesmaximal, complemented
12C23×M16C2211yescharacteristic, complemented
13C23×M16C2211yescharacteristic, complemented
14#3520C414yescomplemented
15#3519C414yescomplemented
16#3513—24no—
17#3506C412yescomplemented
18#3505C412yescomplemented
19#3505C412yescomplemented
20#3501C411yescharacteristic, complemented
21#3496C411yescharacteristic, complemented
22#3492—21no—
23#3490—21no—
24#3490—21no—
25#3484—21no—
26#3481—24no—
27#3475C2214yes—
28D4×#41C2214yes—
29#3460—21no—
30#3459—21no—
31#3459—21no—
32#3444C2212yes—
33C2×#525C2212yes—
34C2×#525C2212yes—
35C4×H(5,𝔽2)—21no—
36C22×C4×D4C2211yescharacteristic
37D4×M16—24no—
38D4×M16C2218yescomplemented
39C2×#436—21no—
40C2×#435—21no—
41C2×#435—21no—
42C2×C8×D4—21no—
43C2×#423C2211yescharacteristic, complemented
44C2×#421C2214yescomplemented
45C22×#104C2214yescomplemented
46C2×#407C2211yescharacteristic, complemented
47C2×#407C2211yescharacteristic, complemented
48C2×C4×M16C2211yescharacteristic, complemented
49#2318—24no—
50#2315—21no—
51#2313—21no—
52#2312—21no—
53#2308—21no—
54#2290C2218yescomplemented
55#2283C2212yescomplemented
56#2280C2212yescomplemented
57C2×C4×C22⋊C4C2212yescomplemented
58#1995C2214yescomplemented
59#1986C2214yescomplemented
60#1980C2214yescomplemented
61#1963C2214yescomplemented
62#1897C2218yescomplemented
63#1896C2218yescomplemented
64#1871C2214yescomplemented
65#1871C2214yescomplemented
66#1871C2214yescomplemented
67#1871C2214yescomplemented
68#1871C2218yescomplemented
69#1871C2218yescomplemented
70#1826C2214yescomplemented
71#1826C2214yescomplemented
72#1806C2218yescomplemented
73#1789C2214yescomplemented
74#1789C2214yescomplemented
75#1759C2218yescomplemented
76#1733C2214yescomplemented
77C2×#339C2214yescomplemented
78C2×H(5,𝔽2)—21no—
79C22×#41C2312yes—
80C22×#41C2312yes—
81C23×D4D411yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—44no—
89C22×M16—44no—
90C22×M16C2311yescharacteristic
91C22×M16C2314yes—
92C22×M16C2314yes—
93C22×M16C2311yescharacteristic
94C22×M16C2311yescharacteristic
95C22×M16C2311yescharacteristic
96C23×C8—21no—
97C23×C8—21no—
98#559—24no—
99#556C2×C414yescomplemented
100#555C2×C414yescomplemented
101#554—24no—
102#554—24no—
103#554C2×C414yescomplemented
104#553—24no—
105#553—24no—
106#553—24no—
107#553—24no—
108#553C2×C414yescomplemented
109#553C2×C414yescomplemented
110#552—24no—
111#552C2×C414yescomplemented
112#552C2×C414yescomplemented
113#551—24no—
114#551—24no—
115#551—24no—
116#551—24no—
117#551—24no—
118#551—24no—
119#550C2×C414yescomplemented
120D4×Q8C2×C414yescomplemented
121#548C2×C414yescomplemented
122#548C2×C414yescomplemented
123#547—24no—
124#547C2×C414yescomplemented
125#547C2×C414yescomplemented
126#546—24no—
127#546—24no—
128#546—24no—
129#546—24no—
130#546—24no—
131#546—24no—
132#546—24no—
133#546C2×C414yescomplemented
134#546C2×C414yescomplemented
135D42—24no—
136D42—24no—
137D42C2×C414yescomplemented
138#544—21no—
139#543—21no—
140#543—21no—
141#542—24no—
142#540—24no—
143#539—24no—
144#539—24no—
145#539—22no—
146#539—22no—
147#538—24no—
148#538—24no—
149#538—22no—
150#538—22no—
151#538—22no—
152#538—22no—
153#537—21no—
154#535—22no—
155#534—22no—
156#534—22no—
157#534—21no—
158#534—21no—
159#533C2×C412yescomplemented
160#533C2×C412yescomplemented
161#533C2312yes—
162#532—24no—
163#532C2×C412yescomplemented
164#532C2×C412yescomplemented
165#532C2312yes—
166#529—24no—
167#529—24no—
168#529—24no—
169#529—22no—
170#529—22no—
171#529—22no—
172#529—22no—
173#529C2×C414yescomplemented
174#529C2×C414yescomplemented
175#525—22no—
176#525—22no—
177#525—22no—
178#525—22no—
179#525—22no—
180#525—22no—
181#525—22no—
182#525—22no—
183#525—22no—
184#525—22no—
185#525—24no—
186#525—24no—
187#525C2×C414yes—
188#525C2×C414yes—
189#525C2×C414yescomplemented
190#525C2×C414yescomplemented
191#525C2314yes—
192#525C2314yes—
193#525C2314yes—
194C2×#123—22no—
195C2×#123—22no—
196C2×C22⋊Q8C2×C412yes—
197C2×C22⋊Q8C2×C412yes—
198C2×C22⋊Q8C2×C412yescomplemented
199C2×C22⋊Q8C2×C412yescomplemented
200C2×#121C2×C412yes—
201C2×#121C2×C412yes—
202C2×#121C2×C412yescomplemented
203C2×#121C2×C412yescomplemented
204C2×#120—22no—
205C2×#120—22no—
206#520—24no—
207#520—22no—
208#518—21no—
209#518—24no—
210#518—22no—
211#518—22no—
212C4×#41—24no—
213C4×#41—22no—
214C4×#41—22no—
215C4×#41C2314yes—
216C2×C4×D4—22no—
217C2×C4×D4—22no—
218C2×C4×D4—22no—
219C2×C4×D4—22no—
220C2×C4×D4—24no—
221C2×C4×D4C2×C411yescharacteristic
222C2×C4×D4C2×C411yescharacteristic
223C2×C4×D4C2×C411yescharacteristic
224C2×C4×D4C2×C411yescharacteristic
225C2×C4×D4C2×C414yes—
226C2×C4×D4D411yescharacteristic
227C2×C4×D4D411yescharacteristic
228C2×C4×D4D411yescharacteristic
229C2×C4×D4D411yescharacteristic
230C2×C4×D4D414yes—
231C2×C4×D4D414yes—
232C2×C4×D4C2314yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2314yes—
236C22×C4⋊C4D411yescharacteristic
237C22×C22⋊C4—22no—
238C22×C22⋊C4D411yescharacteristic
239C22×C22⋊C4D411yescharacteristic
240C22×C42C2314yes—
241C22×C42C2311yescharacteristic
242#436—28no—
243#435—28no—
244#435—28no—
245C8×D4—28no—
246#423—22no—
247#423C2314yes—
248C2×C4⋊C8—21no—
249C2×C4⋊C8—21no—
250#421—48no—
251C2×#104—48no—
252C2×#104C2318yes—
253C2×#104C2318yes—
254C2×#104C2318yes—
255C2×#104C2318yes—
256#407—22no—
257#407—22no—
258#407C2314yes—
259#407C2314yes—
260C2×C22⋊C8—21no—
261C2×C22⋊C8—21no—
262C2×C22⋊C8—21no—
263C2×C22⋊C8—21no—
264C4×M16—22no—
265C4×M16C2314yes—
266C2×#97—21no—
267C2×C4×C8—21no—
268#388—28no—
269#387—28no—
270#386—28no—
271#385—28no—
272#383—22no—
273#382—22no—
274#381—22no—
275#381—22no—
276#380—22no—
277#380—22no—
278#380—22no—
279#379—22no—
280C4×C4⋊C4C2314yes—
281C4×C22⋊C4—22no—
282C4×C22⋊C4—22no—
283C4×C22⋊C4C2314yes—
284C4×C22⋊C4C2314yes—
285C4×C22⋊C4C2314yes—
286#376C2314yes—
287C2×#95—22no—
288#339C2318yes—
289#339C2318yes—
290#339C2318yes—
291#339C2318yes—
292C25C2×D411yescharacteristic
293C25C2×D411yescharacteristic
294H(5,𝔽2)—48no—
295C2×#41—24no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—44no—
303C2×#41—44no—
304C2×#41—44no—
305C2×#41—44no—
306C2×#41C22×C414yes—
307C2×#41C22×C414yes—
308C2×#41C2414yes—
309C22×Q8C22×C412yes—
310C22×Q8C22×C412yes—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—44no—
319C22×D4C22⋊C411yescharacteristic
320C22×D4C22⋊C411yescharacteristic
321C22×D4C22⋊C411yescharacteristic
322C22×D4C22⋊C411yescharacteristic
323C22×D4C22⋊C414yes—
324C22×D4C22×C412yes—
325C22×D4C22×C412yes—
326C22×D4C2×D414yes—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—24no—
330C23×C4—42no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4C22×C411yescharacteristic
335C23×C4C22×C412yes—
336C23×C4C22×C411yescharacteristic
337C23×C4C22×C412yes—
338C23×C4C22×C411yescharacteristic
339C23×C4C22×C411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D412yes—
344C23×C4C2×D412yes—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D412yes—
348C23×C4C2×D412yes—
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C2×M16—21no—
356C2×M16—24no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—24no—
360C2×M16—24no—
361C2×M16—21no—
362C2×M16—28no—
363C2×M16—28no—
364C2×M16—44no—
365C2×M16—44no—
366C2×M16—44no—
367C2×M16—44no—
368C2×M16—42no—
369C2×M16—42no—
370C2×M16—42no—
371C2×M16—48no—
372C2×M16—48no—
373C2×M16C2412yes—
374C2×M16C2412yes—
375C2×M16C2412yes—
376C2×M16C2412yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—24no—
381C22×C8—24no—
382C22×C8—21no—
383C22×C8—44no—
384C22×C8—44no—
385C4⋊Q8—24no—
386C4⋊Q8C22×C412yes—
387C4⋊Q8C22×C412yes—
388C4⋊Q8C22×C412yes—
389#127—24no—
390#127C22×C412yes—
391#126—24no—
392#126—24no—
393#126—24no—
394#126—24no—
395#126—24no—
396#126—24no—
397#126—24no—
398#126—24no—
399#125—24no—
400#125—24no—
401#125—24no—
402#125—22no—
403#125—22no—
404#125C22×C414yes—
405#124—24no—
406#124—24no—
407#124—24no—
408#124—24no—
409#124—24no—
410#124—22no—
411#124—22no—
412#124C22×C414yes—
413#123—24no—
414#123—24no—
415#123—24no—
416#123—24no—
417#123—24no—
418#123—24no—
419#123—24no—
420#123—24no—
421#123—24no—
422#123—24no—
423#123—24no—
424#123—24no—
425#123—24no—
426#123—24no—
427#123—24no—
428#123—24no—
429#123—24no—
430#123—24no—
431#123—24no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—24no—
445C22⋊Q8—24no—
446C22⋊Q8—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—24no—
451C22⋊Q8C22×C414yes—
452C22⋊Q8C22×C414yes—
453C22⋊Q8C22×C414yes—
454C22⋊Q8C22×C414yes—
455C22⋊Q8C22×C414yes—
456C22⋊Q8C22×C414yes—
457#121—24no—
458#121—24no—
459#121—24no—
460#121—24no—
461#121—24no—
462#121—24no—
463#121—22no—
464#121—22no—
465#121—22no—
466#121—22no—
467#121—22no—
468#121—22no—
469#121—22no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—24no—
476#121—24no—
477#121—24no—
478#121—24no—
479#121—24no—
480#121C22×C414yes—
481#121C22×C414yes—
482#121C22×C414yes—
483#121C22×C414yes—
484#121C22×C414yes—
485#121C22×C414yes—
486#120—24no—
487#120—24no—
488#120—24no—
489#120—24no—
490#120—24no—
491#120—24no—
492#120—24no—
493#120—24no—
494#120—24no—
495#120—24no—
496#120—24no—
497C4×Q8—24no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8C22×C414yes—
503C4×Q8C22×C414yes—
504C4×D4—24no—
505C4×D4—24no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—24no—
510C4×D4—24no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—24no—
514C4×D4—24no—
515C4×D4—24no—
516C4×D4—24no—
517C4×D4—24no—
518C4×D4—24no—
519C4×D4—24no—
520C4×D4—24no—
521C4×D4—24no—
522C4×D4—24no—
523C4×D4—24no—
524C4×D4—24no—
525C4×D4—24no—
526C4×D4—24no—
527C4×D4—24no—
528C4×D4—24no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4C22⋊C414yes—
534C4×D4C22⋊C414yes—
535C4×D4C22⋊C414yes—
536C4×D4C22⋊C414yes—
537C4×D4C22⋊C414yes—
538C4×D4C22⋊C414yes—
539C4×D4C22⋊C414yes—
540C4×D4C22⋊C414yes—
541C4×D4C22×C414yes—
542C4×D4C22×C414yes—
543C4×D4C22×C414yes—
544C4×D4C22×C414yes—
545C4×D4C22×C414yes—
546C4×D4C22×C414yes—
547C4×D4C2×D414yes—
548C4×D4C2×D414yes—
549C4×D4C2×D414yes—
550C4×D4C2×D414yes—
551#117—22no—
552#117—22no—
553#117—22no—
554#117—22no—
555#117—22no—
556#117—22no—
557#117—24no—
558#117—24no—
559#117—24no—
560#117—24no—
561#117—24no—
562#117—24no—
563#117—44no—
564#117—44no—
565#117C22×C414yes—
566#117C22×C414yes—
567#117C2414yes—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4C22⋊C411yescharacteristic
576C2×C4⋊C4C22⋊C411yescharacteristic
577C2×C4⋊C4C22⋊C411yescharacteristic
578C2×C4⋊C4C22⋊C411yescharacteristic
579C2×C4⋊C4C22⋊C414yes—
580C2×C4⋊C4C22×C412yes—
581C2×C4⋊C4C22×C412yes—
582C2×C4⋊C4C22×C412yes—
583C2×C4⋊C4C22×C412yes—
584C2×C4⋊C4C2×D414yes—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—48no—
602C2×C22⋊C4C22⋊C411yescharacteristic
603C2×C22⋊C4C22⋊C411yescharacteristic
604C2×C22⋊C4C22⋊C411yescharacteristic
605C2×C22⋊C4C22⋊C411yescharacteristic
606C2×C22⋊C4C22⋊C411yescharacteristic
607C2×C22⋊C4C22⋊C411yescharacteristic
608C2×C22⋊C4C22⋊C411yescharacteristic
609C2×C22⋊C4C22⋊C411yescharacteristic
610C2×C22⋊C4C22⋊C414yes—
611C2×C22⋊C4C22⋊C414yes—
612C2×C22⋊C4C2×D414yes—
613C2×C22⋊C4C2×D414yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—24no—
617C2×C42—24no—
618C2×C42—44no—
619C2×C42—44no—
620C2×C42C22×C411yescharacteristic
621C2×C42C22×C412yes—
622C2×C42C22×C411yescharacteristic
623C2×C42C2×D412yes—
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D412yes—
626C2×C42C2×D411yescharacteristic
627C2×C42C2418yes—
628C2×C42C2412yes—
629C4⋊C8—24no—
630C4⋊C8—24no—
631#104—216no—
632#104—48no—
633#104—48no—
634#104—48no—
635C22⋊C8—24no—
636C22⋊C8—24no—
637C22⋊C8—24no—
638C22⋊C8—24no—
639#97—24no—
640C4×C8—24no—
641#95—24no—
642#95—24no—
643#95—24no—
644#95—24no—
645#95—24no—
646#95—24no—
647C24—24no—
648C24—22no—
649C24—22no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24C2×C22⋊C411yescharacteristic
656C24C2×C22⋊C412yes—
657C24C2×C22⋊C411yescharacteristic
658C24C2×C22⋊C411yescharacteristic
659C24C2×C22⋊C412yes—
660C24C2×C22⋊C411yescharacteristic
661C24C22×D411yescharacteristic
662C24C22×D412yes—
663C24C22×D412yes—
664#41—28no—
665#41—28no—
666#41—48no—
667#41—48no—
668#41—48no—
669#41—416no—
670#41—82no—
671#41—82no—
672#41—82no—
673#41—82no—
674#41—84no—
675#41—84no—
676#41—84no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8C23×C414yes—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—416no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—84no—
709C2×D4—84no—
710C2×D4—84no—
711C2×D4—84no—
712C2×D4C2×C22⋊C414yes—
713C2×D4C2×C22⋊C414yes—
714C2×D4C2×C22⋊C414yes—
715C2×D4C2×C22⋊C414yes—
716C2×D4C23×C414yes—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—28no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—48no—
759C22×C4—82no—
760C22×C4—82no—
761C22×C4—82no—
762C22×C4—82no—
763C22×C4—81no—
764C22×C4—84no—
765C22×C4—84no—
766C22×C4C2×C22⋊C411yescharacteristic
767C22×C4C2×C22⋊C411yescharacteristic
768C22×C4C2×C22⋊C412yes—
769C22×C4C2×C22⋊C411yescharacteristic
770C22×C4C2×C22⋊C411yescharacteristic
771C22×C4C2×C22⋊C412yes—
772C22×C4C2×C22⋊C412yes—
773C22×C4C2×C22⋊C412yes—
774C22×C4C2×C22⋊C412yes—
775C22×C4C2×C22⋊C412yes—
776C22×C4C2×C22⋊C411yescharacteristic
777C22×C4C2×C22⋊C411yescharacteristic
778C22×C4C2×C22⋊C412yes—
779C22×C4C2×C22⋊C412yes—
780C22×C4C2×C22⋊C411yescharacteristic
781C22×C4C2×C22⋊C411yescharacteristic
782C22×C4C2×C22⋊C412yes—
783C22×C4C2×C22⋊C412yes—
784C22×C4C2×C22⋊C412yes—
785C22×C4C2×C22⋊C412yes—
786C22×C4C23×C411yescharacteristic
787C22×C4C23×C411yescharacteristic
788C22×C4C23×C412yes—
789C22×C4C23×C412yes—
790C22×C4C23×C412yes—
791C22×C4C23×C412yes—
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D412yes—
794C22×C4C22×D412yes—
795C22×C4C22×D412yes—
796C22×C4C22×D412yes—
797C22×C4C22×D412yes—
798C22×C4C22×D412yes—
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D412yes—
802C22×C4C22×D412yes—
803C22×C4C2511yescharacteristic
804M16—24no—
805M16—22no—
806M16—24no—
807M16—24no—
808M16—24no—
809M16—48no—
810M16—48no—
811M16—42no—
812M16—42no—
813M16—42no—
814M16H(5,𝔽2)14yescomplemented
815C2×C8—24no—
816C2×C8—22no—
817C2×C8—22no—
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—48no—
821C2×C8—48no—
822C2×C8—42no—
823C2×C8—42no—
824C2×C8—42no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—84no—
844C4⋊C4—84no—
845C4⋊C4C2×C22⋊C414yes—
846C4⋊C4C2×C22⋊C414yes—
847C4⋊C4C2×C22⋊C414yes—
848C4⋊C4C2×C22⋊C414yes—
849C4⋊C4C23×C414yes—
850C4⋊C4C23×C414yes—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—84no—
873C22⋊C4—84no—
874C22⋊C4C2×C22⋊C414yes—
875C22⋊C4C2×C22⋊C414yes—
876C22⋊C4C2×C22⋊C414yes—
877C22⋊C4C2×C22⋊C414yes—
878C22⋊C4C2×C22⋊C414yes—
879C22⋊C4C2×C22⋊C414yes—
880C22⋊C4C2×C22⋊C414yes—
881C22⋊C4C2×C22⋊C414yes—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—28no—
889C42—84no—
890C42C2×C22⋊C412yes—
891C42C2×C22⋊C412yes—
892C42C2×C22⋊C412yes—
893C42C2×C22⋊C412yes—
894C42C23×C412yes—
895C42C23×C412yes—
896C42C22×D412yes—
897C42C22×D412yes—
898C23—22no—
899C23—24no—
900C23—22no—
901C23—22no—
902C23—24no—
903C23—22no—
904C23—24no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—41no—
916C23—41no—
917C23—42no—
918C23—42no—
919C23—42no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—41no—
924C23—41no—
925C23—44no—
926C23—44no—
927C23—82no—
928C23—82no—
929C23—82no—
930C23—82no—
931C23—88no—
932C23—88no—
933C23#42114yescomplemented
934C23C22×C22⋊C412yes—
935C23C22×C22⋊C412yes—
936C23C22×C22⋊C411yescharacteristic
937C23C22×C22⋊C412yes—
938C23C22×C22⋊C411yescharacteristic
939C23C22×C22⋊C412yes—
940C23C23×D411yescharacteristic
941Q8—28no—
942Q8—44no—
943Q8—82no—
944Q8—82no—
945Q8—82no—
946D4—28no—
947D4—28no—
948D4—28no—
949D4—44no—
950D4—44no—
951D4—44no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—82no—
958D4—82no—
959D4—82no—
960D4—84no—
961D4—84no—
962D4—84no—
963D4—84no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—48no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—84no—
1019C2×C4—84no—
1020C2×C4—84no—
1021C2×C4—82no—
1022C2×C4—82no—
1023C2×C4—82no—
1024C2×C4—82no—
1025C2×C4—816no—
1026C2×C4C22×C22⋊C412yes—
1027C2×C4C22×C22⋊C412yes—
1028C2×C4C22×C22⋊C412yes—
1029C2×C4C22×C22⋊C412yes—
1030C2×C4C22×C22⋊C411yescharacteristic
1031C2×C4C22×C22⋊C411yescharacteristic
1032C2×C4C22×C22⋊C412yes—
1033C2×C4C22×C22⋊C412yes—
1034C2×C4C22×C22⋊C412yes—
1035C2×C4C22×C22⋊C412yes—
1036C2×C4C24×C411yescharacteristic
1037C2×C4C23×D411yescharacteristic
1038C2×C4C2×H(5,𝔽2)12yes—
1039C2×C4#58512yes—
1040C8—24no—
1041C8—42no—
1042C8—42no—
1043C8—42no—
1044C22—21no—
1045C22—21no—
1046C22—21no—
1047C22—22no—
1048C22—21no—
1049C22—22no—
1050C22—22no—
1051C22—21no—
1052C22—22no—
1053C22—22no—
1054C22—21no—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—21no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—44no—
1063C22—48no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—84no—
1070C22—82no—
1071C22—82no—
1072C22—84no—
1073C22—84no—
1074C22—164no—
1075C22—164no—
1076C22C2×#42112yes—
1077C22C2×#42114yes—
1078C22C23×C22⋊C411yescharacteristic
1079C22#349612yes—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—21no—
1085C4—21no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—44no—
1091C4—44no—
1092C4—44no—
1093C4—88no—
1094C4C4×H(5,𝔽2)12yes—
1095C4#348411yescharacteristic
1096C4#348511yescharacteristic
1097C2—22no—
1098C2—22no—
1099C2—24no—
1100C2—42no—
1101C2—42no—
1102C2—41no—
1103C2—42no—
1104C2—84no—
1105C2#3425611yescharacteristic
1106C2C22×#42111yescharacteristic
1107C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62773C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×M16C2semidirect
3. #34057C2semidirect
4. #22506C2semidirect
5. #22434C2semidirect
6. #21857C2semidirect
7. #21774C2semidirect
8. #21773C2semidirect
9. #21383C2semidirect
10. #20902C2semidirect
11. C2×#1871C2semidirect
12. C23×M16C22semidirect
13. C23×M16C22semidirect
14. #3520C4semidirect
15. #3519C4semidirect
17. #3506C4semidirect
18. #3505C4semidirect
19. #3505C4semidirect
20. #3501C4semidirect
21. #3496C4semidirect
38. D4×M16C22semidirect
43. C2×#423C22semidirect
44. C2×#421C22semidirect
45. C22×#104C22semidirect
46. C2×#407C22semidirect
47. C2×#407C22semidirect
48. C2×C4×M16C22semidirect
54. #2290C22semidirect
55. #2283C22semidirect
56. #2280C22semidirect
57. C2×C4×C22⋊C4C22semidirect
58. #1995C22semidirect
59. #1986C22semidirect
60. #1980C22semidirect
61. #1963C22semidirect
62. #1897C22semidirect
63. #1896C22semidirect
64. #1871C22semidirect
65. #1871C22semidirect
66. #1871C22semidirect
67. #1871C22semidirect
68. #1871C22semidirect
69. #1871C22semidirect
70. #1826C22semidirect
71. #1826C22semidirect
72. #1806C22semidirect
73. #1789C22semidirect
74. #1789C22semidirect
75. #1759C22semidirect
76. #1733C22semidirect
77. C2×#339C22semidirect
99. #556C2×C4semidirect
100. #555C2×C4semidirect
103. #554C2×C4semidirect
108. #553C2×C4semidirect
109. #553C2×C4semidirect
111. #552C2×C4semidirect
112. #552C2×C4semidirect
119. #550C2×C4semidirect
120. D4×Q8C2×C4semidirect
121. #548C2×C4semidirect
122. #548C2×C4semidirect
124. #547C2×C4semidirect
125. #547C2×C4semidirect
133. #546C2×C4semidirect
134. #546C2×C4semidirect
137. D42C2×C4semidirect
159. #533C2×C4semidirect
160. #533C2×C4semidirect
163. #532C2×C4semidirect
164. #532C2×C4semidirect
173. #529C2×C4semidirect
174. #529C2×C4semidirect
189. #525C2×C4semidirect
190. #525C2×C4semidirect
198. C2×C22⋊Q8C2×C4semidirect
199. C2×C22⋊Q8C2×C4semidirect
202. C2×#121C2×C4semidirect
203. C2×#121C2×C4semidirect
814. M16H(5,𝔽2)semidirect
933. C23#421semidirect

Maximal subgroups

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

subgroupindex
#627732
C2×D4×M162
#340572
#225062
#224342
#218572
#217742
#217732
#213832
#209022
C2×#18712