Finite Group Databasebeta

← #6343513

Subgroups — #6343513

Order 512.

3268 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3C2×#2353C211yesmaximal, characteristic, complemented
4#17629C214yesmaximal, complemented
5#17623C214yesmaximal, complemented
6#17621C212yesmaximal, complemented
7#17620C212yesmaximal, complemented
8#17615C214yesmaximal, complemented
9#17593C212yesmaximal, complemented
10#17592C212yesmaximal, complemented
11#17587C212yesmaximal, complemented
12#17542C212yesmaximal, complemented
13#17541C212yesmaximal, complemented
14C2×#1504C212yesmaximal, complemented
15#3520C414yescomplemented
16#3519C414yescomplemented
17#3513—24no—
18#3506C2212yes—
19#3505C2212yes—
20#3505C2212yes—
21#3501C2211yescharacteristic
22#3496C2211yescharacteristic
23#3492—21no—
24#3490—21no—
25#3490—21no—
26#3484—21no—
27#3481—24no—
28#3475C414yescomplemented
29D4×#41C414yescomplemented
30#3460—21no—
31#3459—21no—
32#3459—21no—
33#3444C2212yes—
34C2×#525C2212yes—
35C2×#525C2212yes—
36C4×H(5,𝔽2)—21no—
37C22×C4×D4C2211yescharacteristic
38#2975C2212yescomplemented
39#2974—24no—
40#2973C2212yes—
41#2973C2212yescomplemented
42#2972C2212yescomplemented
43D4×M16—24no—
44#2920C2212yescomplemented
45C2×#407C2212yescomplemented
46C2×#407C2212yescomplemented
47#2353—21no—
48#2353—21no—
49#2353—21no—
50#2353—21no—
51#2353C2212yes—
52#2353C2212yescomplemented
53#2353C2212yescomplemented
54#2353C2212yescomplemented
55C2×#388—21no—
56C2×#387—21no—
57C2×#386—21no—
58C2×#383C2211yescharacteristic, complemented
59C2×#381C2211yescharacteristic, complemented
60C2×#380C2211yescharacteristic, complemented
61C2×C4×C22⋊C4—21no—
62C2×C4×C22⋊C4C2211yescharacteristic, complemented
63C2×#376C2211yescharacteristic, complemented
64C22×#95C2211yescharacteristic, complemented
65#1521C2218yescomplemented
66#1520C2214yescomplemented
67#1519C2214yescomplemented
68#1516C2218yescomplemented
69#1515C2214yescomplemented
70#1514C2214yescomplemented
71#1513C2218yescomplemented
72#1511C2214yescomplemented
73#1510C2214yescomplemented
74#1508C2214yescomplemented
75#1507C2214yescomplemented
76#1506C2214yescomplemented
77#1505C2214yescomplemented
78#1504C2214yescomplemented
79#1504C2214yescomplemented
80#1504C2218yescomplemented
81#1504C2214yescomplemented
82#1504C2214yescomplemented
83#1501C2218yescomplemented
84#1500C2218yescomplemented
85C2×#328C2214yescomplemented
86C2×#327C2214yescomplemented
87C2×H(5,𝔽2)—21no—
88C22×#41C2×C412yes—
89C22×#41C2×C412yescomplemented
90C23×D4D411yescharacteristic
91C24×C4—21no—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C22×M16—22no—
95C22×M16—22no—
96#559—24no—
97#556C2×C414yescomplemented
98#555C2×C414yescomplemented
99#554—24no—
100#554—24no—
101#554C2×C414yescomplemented
102#553—24no—
103#553—24no—
104#553—24no—
105#553—24no—
106#553C2×C414yescomplemented
107#553C2×C414yescomplemented
108#552—24no—
109#552C2×C414yescomplemented
110#552C2×C414yescomplemented
111#551—24no—
112#551—24no—
113#551—24no—
114#551—24no—
115#551—24no—
116#551—24no—
117#550C2×C414yescomplemented
118D4×Q8C2×C414yescomplemented
119#548C2×C414yescomplemented
120#548C2×C414yescomplemented
121#547—24no—
122#547C2×C414yescomplemented
123#547C2×C414yescomplemented
124#546—24no—
125#546—24no—
126#546—24no—
127#546—24no—
128#546—24no—
129#546—24no—
130#546—24no—
131#546C2×C414yescomplemented
132#546C2×C414yescomplemented
133D42—24no—
134D42—24no—
135D42C2×C414yescomplemented
136#544—21no—
137#543—21no—
138#543—21no—
139#542—24no—
140#540—24no—
141#539—24no—
142#539—24no—
143#539—22no—
144#539—22no—
145#538—24no—
146#538—24no—
147#538—22no—
148#538—22no—
149#538—22no—
150#538—22no—
151#537—21no—
152#535—22no—
153#534—22no—
154#534—22no—
155#534—21no—
156#534—21no—
157#533C2×C412yescomplemented
158#533C2×C412yescomplemented
159#533C2312yes—
160#532—24no—
161#532C2×C412yescomplemented
162#532C2×C412yescomplemented
163#532C2312yes—
164#529—24no—
165#529—24no—
166#529—24no—
167#529—22no—
168#529—22no—
169#529—22no—
170#529—22no—
171#529C2×C414yescomplemented
172#529C2314yes—
173#525—22no—
174#525—22no—
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—24no—
184#525—24no—
185#525C2×C414yes—
186#525C2×C414yes—
187#525C2×C414yescomplemented
188#525C2×C414yescomplemented
189#525C2314yes—
190#525C2314yes—
191#525C2314yes—
192C2×#123—22no—
193C2×#123—22no—
194C2×C22⋊Q8C2×C412yes—
195C2×C22⋊Q8C2×C412yescomplemented
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×#121C2×C412yes—
199C2×#121C2×C412yescomplemented
200C2×#121C2312yes—
201C2×#121C2312yes—
202C2×#120—22no—
203C2×#120—22no—
204#520—24no—
205#520—22no—
206#518—21no—
207#518—24no—
208#518—22no—
209#518—22no—
210C4×#41—24no—
211C4×#41—22no—
212C4×#41—22no—
213C4×#41C2×C414yescomplemented
214C2×C4×D4—22no—
215C2×C4×D4—22no—
216C2×C4×D4—22no—
217C2×C4×D4—22no—
218C2×C4×D4—24no—
219C2×C4×D4C2×C414yes—
220C2×C4×D4C2×C414yes—
221C2×C4×D4D414yes—
222C2×C4×D4D414yes—
223C2×C4×D4D411yescharacteristic
224C2×C4×D4D411yescharacteristic
225C2×C4×D4D411yescharacteristic
226C2×C4×D4D411yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2×C412yes—
232C2×#117C2×C412yescomplemented
233C22×C4⋊C4—21no—
234C22×C4⋊C4D411yescharacteristic
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4D411yescharacteristic
239C22×C22⋊C4D411yescharacteristic
240C22×C42—21no—
241C22×C42—21no—
242C22×C42C2311yescharacteristic
243#436—28no—
244#435—28no—
245#435—28no—
246C8×D4—28no—
247#432—22no—
248#432C2314yes—
249#431—22no—
250#431C2314yes—
251#423—22no—
252#407—22no—
253#407—22no—
254#407—22no—
255#407—22no—
256#407C2314yes—
257#407C2314yes—
258#407C2314yes—
259C2×C22⋊C8—22no—
260C2×C22⋊C8—22no—
261C2×C22⋊C8C2314yes—
262C2×C22⋊C8C2314yes—
263C4×M16—22no—
264#388—22no—
265#388—22no—
266#388—22no—
267#388—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#386—22no—
273#386—22no—
274#386—22no—
275#386—22no—
276#383—21no—
277#383—21no—
278#383C2312yes—
279#383C2312yes—
280#381—21no—
281#381—21no—
282#381C2312yes—
283#381C2312yes—
284#380—21no—
285#380—21no—
286#380C2312yes—
287#380C2312yes—
288C4×C22⋊C4—21no—
289C4×C22⋊C4—21no—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4C2312yes—
295C4×C22⋊C4C2312yes—
296#376—21no—
297#376—21no—
298#376C2312yes—
299#376C2312yes—
300C2×#95—21no—
301C2×#95—21no—
302C2×#95—21no—
303C2×#95—21no—
304C2×#95—21no—
305C2×#95—21no—
306C2×#95—21no—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313#328C2318yes—
314#328C2318yes—
315#328C2318yes—
316#328C2318yes—
317#327C2318yes—
318#327C2318yes—
319#327C2318yes—
320#327C2318yes—
321C25C2×D411yescharacteristic
322C25C2×D411yescharacteristic
323H(5,𝔽2)—44no—
324H(5,𝔽2)—44no—
325C2×#41—24no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—84no—
333C2×#41—84no—
334C2×#41C22×C414yes—
335C2×#41C22×C414yes—
336C2×#41C22×C414yescomplemented
337C22×Q8C22×C412yes—
338C22×Q8C22×C412yescomplemented
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4C22⋊C414yes—
349C22×D4C22⋊C414yes—
350C22×D4C22×C412yes—
351C22×D4C22×C412yescomplemented
352C22×D4C2×D411yescharacteristic
353C22×D4C2×D411yescharacteristic
354C22×D4C2×D411yescharacteristic
355C22×D4C2×D411yescharacteristic
356C23×C4—21no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—44no—
365C23×C4—44no—
366C23×C4—82no—
367C23×C4—82no—
368C23×C4—82no—
369C23×C4C22×C412yes—
370C23×C4C22×C412yes—
371C23×C4C22×C412yes—
372C23×C4C22×C412yes—
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2×D412yes—
378C23×C4C2×D412yes—
379C23×C4C2×D411yescharacteristic
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2×D411yescharacteristic
383C23×C4C2×D412yes—
384C23×C4C2×D412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C2×M16—24no—
391C2×M16—24no—
392C2×M16—24no—
393C2×M16—84no—
394C2×M16—84no—
395C22×C8—24no—
396C22×C8—24no—
397C4⋊Q8—24no—
398C4⋊Q8C22×C412yescomplemented
399C4⋊Q8C22×C412yescomplemented
400C4⋊Q8C22×C412yescomplemented
401#127—24no—
402#127C22×C412yescomplemented
403#126—24no—
404#126—24no—
405#126—24no—
406#126—24no—
407#126—24no—
408#126—24no—
409#126—24no—
410#126—24no—
411#125—24no—
412#125—24no—
413#125—24no—
414#125—22no—
415#125—22no—
416#125C22×C414yescomplemented
417#124—24no—
418#124—24no—
419#124—24no—
420#124—24no—
421#124—24no—
422#124—22no—
423#124—22no—
424#124C22×C414yescomplemented
425#123—24no—
426#123—24no—
427#123—24no—
428#123—24no—
429#123—24no—
430#123—24no—
431#123—24no—
432#123—24no—
433#123—24no—
434#123—24no—
435#123—24no—
436#123—24no—
437#123—24no—
438#123—24no—
439#123—24no—
440#123—24no—
441#123—24no—
442#123—24no—
443#123—24no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—24no—
457C22⋊Q8—24no—
458C22⋊Q8—24no—
459C22⋊Q8—24no—
460C22⋊Q8—24no—
461C22⋊Q8—24no—
462C22⋊Q8—24no—
463C22⋊Q8C22×C414yes—
464C22⋊Q8C22×C414yes—
465C22⋊Q8C22×C414yes—
466C22⋊Q8C22×C414yescomplemented
467C22⋊Q8C22×C414yescomplemented
468C22⋊Q8C2414yes—
469#121—24no—
470#121—24no—
471#121—24no—
472#121—24no—
473#121—24no—
474#121—24no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—24no—
488#121—24no—
489#121—24no—
490#121—24no—
491#121—24no—
492#121C22×C414yes—
493#121C22×C414yes—
494#121C22×C414yes—
495#121C22×C414yescomplemented
496#121C22×C414yescomplemented
497#121C2414yes—
498#120—24no—
499#120—24no—
500#120—24no—
501#120—24no—
502#120—24no—
503#120—24no—
504#120—24no—
505#120—24no—
506#120—24no—
507#120—24no—
508#120—24no—
509C4×Q8—24no—
510C4×Q8—22no—
511C4×Q8—22no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8C22×C414yescomplemented
515C4×Q8C22×C414yescomplemented
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—24no—
530C4×D4—24no—
531C4×D4—24no—
532C4×D4—24no—
533C4×D4—24no—
534C4×D4—24no—
535C4×D4—24no—
536C4×D4—24no—
537C4×D4—24no—
538C4×D4—24no—
539C4×D4—24no—
540C4×D4—24no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4C22⋊C414yes—
546C4×D4C22⋊C414yes—
547C4×D4C22⋊C414yes—
548C4×D4C22⋊C414yes—
549C4×D4C22⋊C414yes—
550C4×D4C22⋊C414yes—
551C4×D4C22⋊C414yes—
552C4×D4C22⋊C414yes—
553C4×D4C22×C414yes—
554C4×D4C22×C414yes—
555C4×D4C22×C414yes—
556C4×D4C22×C414yes—
557C4×D4C22×C414yescomplemented
558C4×D4C22×C414yescomplemented
559C4×D4C2×D414yes—
560C4×D4C2×D414yes—
561C4×D4C2×D414yes—
562C4×D4C2×D414yes—
563#117—22no—
564#117—22no—
565#117—22no—
566#117—22no—
567#117—22no—
568#117—22no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117C22×C414yes—
576#117C22×C414yes—
577#117C22×C414yescomplemented
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—82no—
586C2×C4⋊C4C22⋊C414yes—
587C2×C4⋊C4C22⋊C414yes—
588C2×C4⋊C4C22×C412yes—
589C2×C4⋊C4C22×C412yes—
590C2×C4⋊C4C22×C412yescomplemented
591C2×C4⋊C4C22×C412yescomplemented
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—44no—
615C2×C22⋊C4—44no—
616C2×C22⋊C4—82no—
617C2×C22⋊C4C22⋊C414yes—
618C2×C22⋊C4C22⋊C414yes—
619C2×C22⋊C4C22⋊C414yes—
620C2×C22⋊C4C22⋊C414yes—
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—24no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—44no—
637C2×C42—82no—
638C2×C42C22×C412yes—
639C2×C42C22×C412yes—
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D412yes—
643C2×C42C2×D412yes—
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C4⋊C8—24no—
647C4⋊C8—24no—
648C22⋊C8—24no—
649C22⋊C8—24no—
650C22⋊C8—24no—
651C22⋊C8—24no—
652C22⋊C8—24no—
653C22⋊C8C2418yes—
654#97—24no—
655C4×C8—24no—
656#95—21no—
657#95—21no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—21no—
669#95—21no—
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—42no—
682C24—41no—
683C24—41no—
684C24C2×C22⋊C412yes—
685C24C2×C22⋊C412yes—
686C24C2×C22⋊C412yes—
687C24C2×C22⋊C412yes—
688C24C22×D411yescharacteristic
689C24C22×D411yescharacteristic
690C24C22×D411yescharacteristic
691C24C22×D411yescharacteristic
692C24C22×D411yescharacteristic
693#41—44no—
694#41—44no—
695#41—48no—
696#41—416no—
697#41—84no—
698#41—84no—
699#41—84no—
700#41—84no—
701#41—84no—
702#41—84no—
703#41—84no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—22no—
708C2×Q8—82no—
709C2×Q8—82no—
710C2×Q8C23×C414yes—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—41no—
729C2×D4—41no—
730C2×D4—41no—
731C2×D4—41no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—416no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—82no—
740C2×D4—82no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4C2×C22⋊C414yes—
746C2×D4C2×C22⋊C414yes—
747C2×D4C2×C22⋊C414yes—
748C2×D4C2×C22⋊C414yes—
749C2×D4C23×C414yes—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—42no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—82no—
792C22×C4—82no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4—81no—
797C22×C4—82no—
798C22×C4—82no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—84no—
804C22×C4—84no—
805C22×C4—82no—
806C22×C4—82no—
807C22×C4—816no—
808C22×C4C2×C22⋊C412yes—
809C22×C4C2×C22⋊C412yes—
810C22×C4C2×C22⋊C412yes—
811C22×C4C2×C22⋊C412yes—
812C22×C4C2×C22⋊C412yes—
813C22×C4C2×C22⋊C412yes—
814C22×C4C2×C22⋊C412yes—
815C22×C4C2×C22⋊C412yes—
816C22×C4C2×C22⋊C412yes—
817C22×C4C2×C22⋊C412yes—
818C22×C4C2×C22⋊C412yes—
819C22×C4C2×C22⋊C412yes—
820C22×C4C2×C22⋊C412yes—
821C22×C4C2×C22⋊C412yes—
822C22×C4C2×C22⋊C412yes—
823C22×C4C2×C22⋊C412yes—
824C22×C4C23×C411yescharacteristic
825C22×C4C23×C411yescharacteristic
826C22×C4C23×C412yes—
827C22×C4C23×C412yes—
828C22×C4C23×C412yes—
829C22×C4C23×C412yes—
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C2511yescharacteristic
846M16—48no—
847M16—84no—
848M16—84no—
849C2×C8—28no—
850C2×C8—84no—
851C2×C8—84no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—82no—
871C4⋊C4—82no—
872C4⋊C4C2×C22⋊C414yes—
873C4⋊C4C2×C22⋊C414yes—
874C4⋊C4C2×C22⋊C414yes—
875C4⋊C4C2×C22⋊C414yes—
876C4⋊C4C23×C414yes—
877C4⋊C4C23×C414yes—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—82no—
902C22⋊C4—82no—
903C22⋊C4C2×C22⋊C414yes—
904C22⋊C4C2×C22⋊C414yes—
905C22⋊C4C2×C22⋊C414yes—
906C22⋊C4C2×C22⋊C414yes—
907C22⋊C4C2×C22⋊C414yes—
908C22⋊C4C2×C22⋊C414yes—
909C22⋊C4C2×C22⋊C414yes—
910C22⋊C4C2×C22⋊C414yes—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—44no—
917C42—44no—
918C42—82no—
919C42—82no—
920C42C2×C22⋊C412yes—
921C42C2×C22⋊C412yes—
922C42C2×C22⋊C412yes—
923C42C2×C22⋊C412yes—
924C42C23×C412yes—
925C42C23×C412yes—
926C42C22×D412yes—
927C42C22×D412yes—
928C23—22no—
929C23—22no—
930C23—21no—
931C23—21no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—21no—
937C23—21no—
938C23—24no—
939C23—24no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—24no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—42no—
950C23—42no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—42no—
956C23—42no—
957C23—42no—
958C23—42no—
959C23—48no—
960C23—48no—
961C23—44no—
962C23—44no—
963C23—82no—
964C23—82no—
965C23—82no—
966C23—82no—
967C23—84no—
968C23—84no—
969C23C22×C22⋊C412yes—
970C23C22×C22⋊C412yes—
971C23C22×C22⋊C412yes—
972C23C22×C22⋊C411yescharacteristic
973C23C22×C22⋊C412yes—
974C23C22×C22⋊C411yescharacteristic
975C23#57512yes—
976C23#57512yes—
977C23C23×D411yescharacteristic
978Q8—44no—
979Q8—44no—
980Q8—82no—
981Q8—82no—
982Q8—82no—
983D4—28no—
984D4—28no—
985D4—44no—
986D4—44no—
987D4—44no—
988D4—44no—
989D4—48no—
990D4—48no—
991D4—48no—
992D4—48no—
993D4—44no—
994D4—44no—
995D4—82no—
996D4—82no—
997D4—82no—
998D4—84no—
999D4—84no—
1000D4—84no—
1001D4—84no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—42no—
1049C2×C4—48no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—82no—
1069C2×C4—88no—
1070C2×C4—88no—
1071C2×C4—84no—
1072C2×C4—84no—
1073C2×C4—84no—
1074C2×C4C22×C22⋊C411yescharacteristic
1075C2×C4C22×C22⋊C412yes—
1076C2×C4C22×C22⋊C412yes—
1077C2×C4C22×C22⋊C412yes—
1078C2×C4C22×C22⋊C412yes—
1079C2×C4C22×C22⋊C411yescharacteristic
1080C2×C4C22×C22⋊C412yes—
1081C2×C4C22×C22⋊C412yes—
1082C2×C4C22×C22⋊C412yes—
1083C2×C4C22×C22⋊C412yes—
1084C2×C4C24×C411yescharacteristic
1085C2×C4C23×D411yescharacteristic
1086C8—48no—
1087C22—24no—
1088C22—24no—
1089C22—21no—
1090C22—21no—
1091C22—22no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—21no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—42no—
1107C22—42no—
1108C22—48no—
1109C22—48no—
1110C22—42no—
1111C22—42no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—84no—
1120C22—84no—
1121C22—164no—
1122C22—164no—
1123C22#288312yes—
1124C22#289614yes—
1125C22#290112yes—
1126C22C23×C22⋊C411yescharacteristic
1127C22C2×#57511yescharacteristic
1128C22C2×#57511yescharacteristic
1129C4—21no—
1130C4—21no—
1131C4—21no—
1132C4—21no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—82no—
1146C4—82no—
1147C4—82no—
1148C2—21no—
1149C2—21no—
1150C2—22no—
1151C2—22no—
1152C2—24no—
1153C2—42no—
1154C2—42no—
1155C2—42no—
1156C2—84no—
1157C2C2×#288311yescharacteristic
1158C2C2×#289611yescharacteristic
1159C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62773C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. C2×#2353C2semidirect
4. #17629C2semidirect
5. #17623C2semidirect
6. #17621C2semidirect
7. #17620C2semidirect
8. #17615C2semidirect
9. #17593C2semidirect
10. #17592C2semidirect
11. #17587C2semidirect
12. #17542C2semidirect
13. #17541C2semidirect
14. C2×#1504C2semidirect
15. #3520C4semidirect
16. #3519C4semidirect
28. #3475C4semidirect
29. D4×#41C4semidirect
38. #2975C22semidirect
41. #2973C22semidirect
42. #2972C22semidirect
44. #2920C22semidirect
45. C2×#407C22semidirect
46. C2×#407C22semidirect
52. #2353C22semidirect
53. #2353C22semidirect
54. #2353C22semidirect
58. C2×#383C22semidirect
59. C2×#381C22semidirect
60. C2×#380C22semidirect
62. C2×C4×C22⋊C4C22semidirect
63. C2×#376C22semidirect
64. C22×#95C22semidirect
65. #1521C22semidirect
66. #1520C22semidirect
67. #1519C22semidirect
68. #1516C22semidirect
69. #1515C22semidirect
70. #1514C22semidirect
71. #1513C22semidirect
72. #1511C22semidirect
73. #1510C22semidirect
74. #1508C22semidirect
75. #1507C22semidirect
76. #1506C22semidirect
77. #1505C22semidirect
78. #1504C22semidirect
79. #1504C22semidirect
80. #1504C22semidirect
81. #1504C22semidirect
82. #1504C22semidirect
83. #1501C22semidirect
84. #1500C22semidirect
85. C2×#328C22semidirect
86. C2×#327C22semidirect
89. C22×#41C2×C4semidirect
97. #556C2×C4semidirect
98. #555C2×C4semidirect
101. #554C2×C4semidirect
106. #553C2×C4semidirect
107. #553C2×C4semidirect
109. #552C2×C4semidirect
110. #552C2×C4semidirect
117. #550C2×C4semidirect
118. D4×Q8C2×C4semidirect
119. #548C2×C4semidirect
120. #548C2×C4semidirect
122. #547C2×C4semidirect
123. #547C2×C4semidirect
131. #546C2×C4semidirect
132. #546C2×C4semidirect
135. D42C2×C4semidirect
157. #533C2×C4semidirect
158. #533C2×C4semidirect
161. #532C2×C4semidirect
162. #532C2×C4semidirect
171. #529C2×C4semidirect
187. #525C2×C4semidirect
188. #525C2×C4semidirect
195. C2×C22⋊Q8C2×C4semidirect
199. C2×#121C2×C4semidirect
213. C4×#41C2×C4semidirect
232. C2×#117C2×C4semidirect
336. C2×#41C22×C4semidirect
338. C22×Q8C22×C4semidirect
351. C22×D4C22×C4semidirect
398. C4⋊Q8C22×C4semidirect
399. C4⋊Q8C22×C4semidirect
400. C4⋊Q8C22×C4semidirect
402. #127C22×C4semidirect
416. #125C22×C4semidirect
424. #124C22×C4semidirect
466. C22⋊Q8C22×C4semidirect
467. C22⋊Q8C22×C4semidirect
495. #121C22×C4semidirect
496. #121C22×C4semidirect
514. C4×Q8C22×C4semidirect
515. C4×Q8C22×C4semidirect
557. C4×D4C22×C4semidirect
558. C4×D4C22×C4semidirect
577. #117C22×C4semidirect
590. C2×C4⋊C4C22×C4semidirect
591. C2×C4⋊C4C22×C4semidirect

Maximal subgroups

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

subgroupindex
#627732
#602302
C2×#23532
#176292
#176232
#176212
#176202
#176152
#175932
#175922
#175872
#175422
#175412
C2×#15042