Finite Group Databasebeta

← #6343492

Subgroups — #6343492

Order 512.

3062 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62814C211yesmaximal, characteristic
2#60124C211yesmaximal, characteristic, complemented
3C2×#2343C211yesmaximal, characteristic, complemented
4#17609C218yesmaximal, complemented
5#17604C218yesmaximal, complemented
6#17593C212yesmaximal, complemented
7#17588C212yesmaximal, complemented
8#17587C212yesmaximal, complemented
9#17546C212yesmaximal, complemented
10#17541C212yesmaximal, complemented
11C2×#1504C212yesmaximal, complemented
12#3495C414yescomplemented
13#3495C2214yes—
14#3494C414yescomplemented
15#3494C2214yes—
16#3493—21no—
17#3493—21no—
18#3492—21no—
19#3492—21no—
20#3491—21no—
21#3491—21no—
22#3490—21no—
23#3490—21no—
24#3475—24no—
25#3475—24no—
26#3458C411yescharacteristic, complemented
27#3455C412yescomplemented
28#3455C412yescomplemented
29#3449C411yescharacteristic, complemented
30#3444C2212yes—
31#3444C2212yes—
32C2×#525C2212yes—
33#3428C412yescomplemented
34C22×#117C2211yescharacteristic
35#2924—24no—
36#2924C2218yescomplemented
37#2921—21no—
38#2921—21no—
39#2920C2212yescomplemented
40#2920C2212yescomplemented
41#2905—21no—
42C2×#407C2212yes—
43#2873—21no—
44#2343—24no—
45#2343C2218yescomplemented
46C2×#387—21no—
47C2×#387—21no—
48C2×#385—21no—
49C2×#383C2211yescharacteristic, complemented
50C2×#382C2211yescharacteristic, complemented
51C2×#381C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic, complemented
53C2×C4×C22⋊C4—21no—
54C2×#376C2211yescharacteristic, complemented
55C22×#95C2211yescharacteristic
56#1521C2218yescomplemented
57#1518C2214yescomplemented
58#1517C2214yescomplemented
59#1516C2218yes—
60#1515C2214yescomplemented
61#1514C2214yescomplemented
62#1512C2218yescomplemented
63#1511C2214yescomplemented
64#1510C2214yescomplemented
65#1509C2218yescomplemented
66#1506C2214yescomplemented
67#1505C2214yescomplemented
68#1504C2218yes—
69#1504C2214yescomplemented
70#1504C2214yescomplemented
71#1504C2214yescomplemented
72#1504C2214yescomplemented
73#1503C2214yescomplemented
74#1502C2214yescomplemented
75#1500C2218yescomplemented
76C2×#328C2214yescomplemented
77C2×#327C2214yescomplemented
78C22×#41C2×C412yes—
79C24×C4—21no—
80C24×C4C2311yescharacteristic
81C22×M16—22no—
82#556—24no—
83#556—24no—
84#555—24no—
85#555—24no—
86#554—24no—
87#554—24no—
88#553—24no—
89#553—24no—
90#553—24no—
91#553—24no—
92#552—24no—
93#552—24no—
94#552—24no—
95#552—24no—
96#552—24no—
97#552—24no—
98#552—24no—
99#552—24no—
100#551—24no—
101#551—24no—
102#551—24no—
103#551—24no—
104#551—24no—
105#551—24no—
106#551—24no—
107#551—24no—
108#547—24no—
109#547—24no—
110#546—24no—
111#546—24no—
112#546—24no—
113#546—24no—
114#544—21no—
115#544—21no—
116#544C2×C414yescomplemented
117#544C2×C414yescomplemented
118#543—21no—
119#543—21no—
120#542C2×C414yescomplemented
121#542C2×C414yescomplemented
122#542C2×C414yescomplemented
123#542C2×C414yescomplemented
124#541C2×C414yescomplemented
125#541C2×C414yescomplemented
126#540C2×C414yescomplemented
127#540C2×C414yescomplemented
128#539—22no—
129#539—22no—
130#539—22no—
131#539—22no—
132#538—22no—
133#538—22no—
134#538—22no—
135#538—22no—
136#537—21no—
137#537—21no—
138#536C2×C414yescomplemented
139#535C2×C414yescomplemented
140#534—21no—
141#534—21no—
142#533—24no—
143#533C2×C412yescomplemented
144#533C2×C412yescomplemented
145#533C2×C412yescomplemented
146#533C2×C412yescomplemented
147#533C2312yes—
148#533C2312yes—
149#532C2×C412yescomplemented
150#532C2×C412yescomplemented
151#532C2×C412yescomplemented
152#532C2×C412yescomplemented
153#532C2312yes—
154#532C2312yes—
155#529—24no—
156#529—24no—
157#529—24no—
158#529—24no—
159#529—22no—
160#529—22no—
161#529—22no—
162#529—22no—
163#529—22no—
164#529—22no—
165#529—22no—
166#529—22no—
167#529C2×C414yescomplemented
168#529C2×C414yescomplemented
169#529C2314yes—
170#529C2314yes—
171#525—22no—
172#525—22no—
173#525—22no—
174#525—22no—
175#525—22no—
176#525—22no—
177#525—22no—
178#525—22no—
179#525—24no—
180#525C2×C414yes—
181#525C2×C414yes—
182#525C2314yes—
183#525C2314yes—
184C2×#123—22no—
185C2×C22⋊Q8C2×C412yes—
186C2×C22⋊Q8C2312yes—
187C2×#121C2×C412yes—
188C2×#121C2312yes—
189C2×#120—22no—
190#520—22no—
191#520—22no—
192#520C2×C414yescomplemented
193#520C2×C414yescomplemented
194#519C2×C414yescomplemented
195#518—22no—
196#518—22no—
197#518C2×C414yescomplemented
198C4×#41—24no—
199C4×#41—22no—
200C4×#41—22no—
201C4×#41—22no—
202C4×#41—22no—
203C4×#41C2×C414yescomplemented
204C4×#41C2×C414yescomplemented
205C2×C4×D4—22no—
206C2×C4×D4—22no—
207C2×#117—24no—
208C2×#117C2×C412yes—
209C2×#117C2×C411yescharacteristic
210C2×#117C2×C411yescharacteristic
211C2×#117C2×C411yescharacteristic
212C2×#117C2×C411yescharacteristic
213C2×#117C2×C414yes—
214C2×#117D411yescharacteristic
215C2×#117D411yescharacteristic
216C2×#117D411yescharacteristic
217C2×#117D411yescharacteristic
218C2×#117D414yes—
219C2×#117D414yes—
220C2×#117C2314yes—
221C22×C4⋊C4—21no—
222C22×C4⋊C4—21no—
223C22×C4⋊C4D411yescharacteristic
224C22×C4⋊C4D411yescharacteristic
225C22×C22⋊C4—21no—
226C22×C22⋊C4D411yescharacteristic
227C22×C22⋊C4D411yescharacteristic
228C22×C42—21no—
229C22×C42—21no—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#433—28no—
233#433—28no—
234#432—22no—
235#432—22no—
236#432C2314yes—
237#432C2314yes—
238#431—22no—
239#431—22no—
240#431C2314yes—
241#431C2314yes—
242#424—28no—
243#423—22no—
244#423—22no—
245#407—22no—
246#407—22no—
247#407C2314yes—
248#407C2314yes—
249C2×C22⋊C8—22no—
250C2×C22⋊C8C2314yes—
251#405—28no—
252C4×M16—22no—
253C4×M16—22no—
254#387—28no—
255#387—28no—
256#385—28no—
257#383—22no—
258#383C2314yes—
259#382—22no—
260#382C2314yes—
261#381—22no—
262#381C2314yes—
263C4×C4⋊C4—22no—
264C4×C4⋊C4C2314yes—
265C4×C22⋊C4—28no—
266#376—22no—
267#376C2314yes—
268C2×#95—22no—
269C2×#95—21no—
270C2×#95—21no—
271C2×#95—21no—
272C2×#95—21no—
273C2×#95—21no—
274C2×#95—21no—
275C2×#95C2314yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280#328C2318yes—
281#328C2318yes—
282#328C2318yes—
283#328C2318yes—
284#327C2318yes—
285#327C2318yes—
286#327C2318yes—
287#327C2318yes—
288C25C2×D411yescharacteristic
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—48no—
296C2×#41C22×C414yes—
297C2×#41C22×C414yes—
298C22×Q8C22×C412yes—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4C22×C412yes—
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—24no—
309C23×C4—44no—
310C23×C4—44no—
311C23×C4—44no—
312C23×C4—82no—
313C23×C4C22×C411yescharacteristic
314C23×C4C22×C412yes—
315C23×C4C22×C411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D412yes—
323C23×C4C2×D412yes—
324C23×C4C2×D411yescharacteristic
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C2×M16—24no—
328C2×M16—24no—
329C2×M16—48no—
330C22×C8—24no—
331C4⋊Q8—24no—
332C4⋊Q8—24no—
333C4⋊Q8C22×C412yescomplemented
334C4⋊Q8C22×C412yescomplemented
335C4⋊Q8C22×C412yescomplemented
336C4⋊Q8C22×C412yescomplemented
337C4⋊Q8C22×C412yescomplemented
338C4⋊Q8C22×C412yescomplemented
339#127C22×C412yescomplemented
340#127C22×C412yescomplemented
341#126—24no—
342#126—24no—
343#126—24no—
344#126—24no—
345#126—24no—
346#126—24no—
347#126—24no—
348#126—24no—
349#126—24no—
350#126—24no—
351#126—24no—
352#126—24no—
353#125—24no—
354#125—24no—
355#125—24no—
356#125—24no—
357#125—24no—
358#125—24no—
359#125—22no—
360#125—22no—
361#125—22no—
362#125—22no—
363#125C22×C414yescomplemented
364#125C22×C414yescomplemented
365#124—24no—
366#124—24no—
367#124—24no—
368#124—24no—
369#124—22no—
370#124—22no—
371#124—22no—
372#124—22no—
373#124C22×C414yescomplemented
374#124C22×C414yescomplemented
375#123—24no—
376#123—24no—
377#123—24no—
378#123—24no—
379#123—24no—
380#123—24no—
381#123—24no—
382#123—24no—
383#123—24no—
384#123—24no—
385#123—24no—
386#123—24no—
387#123—24no—
388#123—24no—
389#123—24no—
390#123—24no—
391#123—24no—
392#123—24no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8—24no—
411C22⋊Q8—24no—
412C22⋊Q8—24no—
413C22⋊Q8—24no—
414C22⋊Q8—24no—
415C22⋊Q8C22×C414yes—
416C22⋊Q8C22×C414yes—
417C22⋊Q8C22×C414yes—
418C22⋊Q8C2414yes—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—22no—
428#121—22no—
429#121—22no—
430#121—22no—
431#121—24no—
432#121—24no—
433#121—24no—
434#121—24no—
435#121—24no—
436#121—24no—
437#121C22×C414yes—
438#121C22×C414yes—
439#121C22×C414yes—
440#121C2414yes—
441#120—24no—
442#120—24no—
443#120—24no—
444#120—24no—
445#120—24no—
446#120—24no—
447C4×Q8—24no—
448C4×Q8—24no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8C22×C414yescomplemented
458C4×Q8C22×C414yescomplemented
459C4×Q8C22×C414yescomplemented
460C4×Q8C22×C414yescomplemented
461C4×D4—24no—
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4—24no—
467C4×D4—24no—
468C4×D4—24no—
469C4×D4—24no—
470C4×D4—24no—
471C4×D4—24no—
472C4×D4—24no—
473C4×D4—24no—
474C4×D4—24no—
475C4×D4—24no—
476C4×D4—24no—
477C4×D4—24no—
478C4×D4—24no—
479C4×D4—24no—
480C4×D4—24no—
481C4×D4—24no—
482C4×D4—24no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4C22×C414yescomplemented
492C4×D4C22×C414yescomplemented
493C4×D4C22×C414yescomplemented
494C4×D4C22×C414yescomplemented
495#117—22no—
496#117—22no—
497#117—22no—
498#117—22no—
499#117—22no—
500#117—22no—
501#117—24no—
502#117—24no—
503#117—24no—
504#117—24no—
505#117—24no—
506#117—24no—
507#117—24no—
508#117—24no—
509#117—24no—
510#117—24no—
511#117C22⋊C414yes—
512#117C22⋊C414yes—
513#117C22⋊C414yes—
514#117C22⋊C414yes—
515#117C22⋊C414yes—
516#117C22⋊C414yes—
517#117C22⋊C414yes—
518#117C22⋊C414yes—
519#117C22×C414yes—
520#117C22×C414yes—
521#117C22×C414yes—
522#117C22×C414yes—
523#117C22×C414yes—
524#117C22×C414yes—
525#117C2×D414yes—
526#117C2×D414yes—
527#117C2×D414yes—
528#117C2×D414yes—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4—82no—
537C2×C4⋊C4C22⋊C411yescharacteristic
538C2×C4⋊C4C22⋊C411yescharacteristic
539C2×C4⋊C4C22⋊C411yescharacteristic
540C2×C4⋊C4C22⋊C411yescharacteristic
541C2×C4⋊C4C22⋊C411yescharacteristic
542C2×C4⋊C4C22⋊C411yescharacteristic
543C2×C4⋊C4C22⋊C411yescharacteristic
544C2×C4⋊C4C22⋊C411yescharacteristic
545C2×C4⋊C4C22⋊C414yes—
546C2×C4⋊C4C22⋊C414yes—
547C2×C4⋊C4C22×C412yes—
548C2×C4⋊C4C22×C412yes—
549C2×C4⋊C4C2×D414yes—
550C2×C4⋊C4C2×D414yes—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—44no—
560C2×C22⋊C4C22⋊C411yescharacteristic
561C2×C22⋊C4C22⋊C411yescharacteristic
562C2×C22⋊C4C22⋊C411yescharacteristic
563C2×C22⋊C4C22⋊C411yescharacteristic
564C2×C22⋊C4C22⋊C411yescharacteristic
565C2×C22⋊C4C22⋊C411yescharacteristic
566C2×C22⋊C4C22⋊C411yescharacteristic
567C2×C22⋊C4C22⋊C411yescharacteristic
568C2×C22⋊C4C22⋊C414yes—
569C2×C22⋊C4C22⋊C414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C42—22no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—44no—
578C2×C42—82no—
579C2×C42C22×C411yescharacteristic
580C2×C42C22×C411yescharacteristic
581C2×C42C22×C412yes—
582C2×C42C22×C412yes—
583C2×C42C22×C411yescharacteristic
584C2×C42C22×C411yescharacteristic
585C2×C42C2×D412yes—
586C2×C42C2×D412yes—
587C2×C42C2×D412yes—
588C2×C42C2×D412yes—
589C2×C42C2×D411yescharacteristic
590C2×C42C2×D411yescharacteristic
591C2×C42C2×D411yescharacteristic
592C2×C42C2×D411yescharacteristic
593C2×C42C2412yes—
594C2×C42C2412yes—
595C4⋊C8—24no—
596C4⋊C8—24no—
597C4⋊C8—24no—
598C4⋊C8—24no—
599C22⋊C8—24no—
600C22⋊C8—24no—
601C22⋊C8—24no—
602C22⋊C8C2418yes—
603#97—24no—
604#97—24no—
605C4×C8—24no—
606C4×C8—24no—
607#95—21no—
608#95—21no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—21no—
616#95—21no—
617#95C2412yes—
618#95C2412yes—
619#95C2412yes—
620#95C2412yes—
621C24—24no—
622C24—22no—
623C24—42no—
624C24—41no—
625C24—41no—
626C24C2×C22⋊C412yes—
627C24C2×C22⋊C411yescharacteristic
628C24C2×C22⋊C411yescharacteristic
629C24C22×D411yescharacteristic
630C24C22×D412yes—
631#41—48no—
632#41—48no—
633#41—48no—
634#41—48no—
635#41—82no—
636#41—82no—
637#41—82no—
638#41—82no—
639#41—84no—
640#41—84no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—44no—
647C2×Q8C23×C414yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—44no—
660C2×D4—48no—
661C2×D4—82no—
662C2×D4—82no—
663C2×D4—84no—
664C2×D4C23×C414yes—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—42no—
682C22×C4—41no—
683C22×C4—42no—
684C22×C4—41no—
685C22×C4—44no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—44no—
692C22×C4—42no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—48no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—84no—
710C22×C4—816no—
711C22×C4C2×C22⋊C412yes—
712C22×C4C2×C22⋊C412yes—
713C22×C4C2×C22⋊C412yes—
714C22×C4C2×C22⋊C412yes—
715C22×C4C2×C22⋊C411yescharacteristic
716C22×C4C2×C22⋊C411yescharacteristic
717C22×C4C2×C22⋊C411yescharacteristic
718C22×C4C2×C22⋊C411yescharacteristic
719C22×C4C2×C22⋊C411yescharacteristic
720C22×C4C2×C22⋊C411yescharacteristic
721C22×C4C2×C22⋊C412yes—
722C22×C4C2×C22⋊C412yes—
723C22×C4C2×C22⋊C411yescharacteristic
724C22×C4C2×C22⋊C411yescharacteristic
725C22×C4C2×C22⋊C411yescharacteristic
726C22×C4C2×C22⋊C411yescharacteristic
727C22×C4C2×C22⋊C412yes—
728C22×C4C2×C22⋊C412yes—
729C22×C4C2×C22⋊C412yes—
730C22×C4C23×C411yescharacteristic
731C22×C4C23×C412yes—
732C22×C4C23×C411yescharacteristic
733C22×C4C23×C412yes—
734C22×C4C22×D412yes—
735C22×C4C22×D412yes—
736C22×C4C22×D411yescharacteristic
737C22×C4C22×D412yes—
738C22×C4C22×D411yescharacteristic
739C22×C4C22×D412yes—
740C22×C4C22×D412yes—
741C22×C4C22×D412yes—
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D412yes—
744C22×C4C2511yescharacteristic
745M16—48no—
746M16—48no—
747C2×C8—28no—
748C2×C8—48no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—48no—
772C4⋊C4—84no—
773C4⋊C4C2×C22⋊C414yes—
774C4⋊C4C2×C22⋊C414yes—
775C4⋊C4C2×C22⋊C414yes—
776C4⋊C4C2×C22⋊C414yes—
777C4⋊C4C2×C22⋊C414yes—
778C4⋊C4C2×C22⋊C414yes—
779C4⋊C4C2×C22⋊C414yes—
780C4⋊C4C2×C22⋊C414yes—
781C4⋊C4C23×C414yes—
782C4⋊C4C23×C414yes—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—48no—
802C22⋊C4C2×C22⋊C414yes—
803C22⋊C4C2×C22⋊C414yes—
804C22⋊C4C2×C22⋊C414yes—
805C22⋊C4C2×C22⋊C414yes—
806C22⋊C4C2×C22⋊C414yes—
807C22⋊C4C2×C22⋊C414yes—
808C22⋊C4C2×C22⋊C414yes—
809C22⋊C4C2×C22⋊C414yes—
810C42—24no—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—24no—
816C42—48no—
817C42—84no—
818C42C2×C22⋊C412yes—
819C42C2×C22⋊C412yes—
820C42C2×C22⋊C412yes—
821C42C2×C22⋊C412yes—
822C42C2×C22⋊C412yes—
823C42C2×C22⋊C412yes—
824C42C2×C22⋊C412yes—
825C42C2×C22⋊C412yes—
826C42C23×C412yes—
827C42C23×C412yes—
828C42C23×C412yes—
829C42C23×C412yes—
830C42C22×D412yes—
831C42C22×D412yes—
832C42C22×D412yes—
833C42C22×D412yes—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—24no—
842C23—22no—
843C23—24no—
844C23—24no—
845C23—42no—
846C23—41no—
847C23—42no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—48no—
852C23—48no—
853C23—44no—
854C23—82no—
855C23—82no—
856C23#41014yes—
857C23C22×C22⋊C412yes—
858C23C22×C22⋊C411yescharacteristic
859C23C22×C22⋊C412yes—
860C23C22×C22⋊C411yescharacteristic
861C23C23×D411yescharacteristic
862Q8—44no—
863Q8—44no—
864Q8—82no—
865Q8—82no—
866Q8—82no—
867Q8—82no—
868D4—44no—
869D4—44no—
870D4—44no—
871D4—44no—
872D4—48no—
873D4—48no—
874D4—48no—
875D4—82no—
876D4—82no—
877D4—82no—
878D4—82no—
879D4—84no—
880D4—84no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—42no—
906C2×C4—41no—
907C2×C4—42no—
908C2×C4—41no—
909C2×C4—42no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—42no—
924C2×C4—48no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—84no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4—84no—
940C2×C4—82no—
941C2×C4—82no—
942C2×C4—816no—
943C2×C4—84no—
944C2×C4—84no—
945C2×C4—84no—
946C2×C4C22×C22⋊C411yescharacteristic
947C2×C4C22×C22⋊C412yes—
948C2×C4C22×C22⋊C412yes—
949C2×C4C22×C22⋊C412yes—
950C2×C4C22×C22⋊C412yes—
951C2×C4C22×C22⋊C412yes—
952C2×C4C22×C22⋊C411yescharacteristic
953C2×C4C22×C22⋊C412yes—
954C2×C4C22×C22⋊C412yes—
955C2×C4C22×C22⋊C412yes—
956C2×C4C22×C22⋊C412yes—
957C2×C4C22×C22⋊C412yes—
958C2×C4C24×C411yescharacteristic
959C2×C4C23×D411yescharacteristic
960C8—48no—
961C22—24no—
962C22—24no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—22no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—48no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—164no—
983C22C2×#41014yes—
984C22C2×#41012yes—
985C22#290112yes—
986C22C23×C22⋊C411yescharacteristic
987C22#358511yescharacteristic
988C22#358611yescharacteristic
989C4—21no—
990C4—21no—
991C4—22no—
992C4—22no—
993C4—21no—
994C4—21no—
995C4—22no—
996C4—22no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—22no—
1001C4—22no—
1002C4—22no—
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4—44no—
1007C4—82no—
1008C4—82no—
1009C4—82no—
1010C2—21no—
1011C2—21no—
1012C2—22no—
1013C2—22no—
1014C2—24no—
1015C2—42no—
1016C2—84no—
1017C2C22×#41011yescharacteristic
1018C2#6008911yescharacteristic
1019C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62814C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60124C2semidirect
3. C2×#2343C2semidirect
4. #17609C2semidirect
5. #17604C2semidirect
6. #17593C2semidirect
7. #17588C2semidirect
8. #17587C2semidirect
9. #17546C2semidirect
10. #17541C2semidirect
11. C2×#1504C2semidirect
12. #3495C4semidirect
14. #3494C4semidirect
26. #3458C4semidirect
27. #3455C4semidirect
28. #3455C4semidirect
29. #3449C4semidirect
33. #3428C4semidirect
36. #2924C22semidirect
39. #2920C22semidirect
40. #2920C22semidirect
45. #2343C22semidirect
49. C2×#383C22semidirect
50. C2×#382C22semidirect
52. C2×C4×C4⋊C4C22semidirect
54. C2×#376C22semidirect
56. #1521C22semidirect
57. #1518C22semidirect
58. #1517C22semidirect
60. #1515C22semidirect
61. #1514C22semidirect
62. #1512C22semidirect
63. #1511C22semidirect
64. #1510C22semidirect
65. #1509C22semidirect
66. #1506C22semidirect
67. #1505C22semidirect
69. #1504C22semidirect
70. #1504C22semidirect
71. #1504C22semidirect
72. #1504C22semidirect
73. #1503C22semidirect
74. #1502C22semidirect
75. #1500C22semidirect
76. C2×#328C22semidirect
77. C2×#327C22semidirect
116. #544C2×C4semidirect
117. #544C2×C4semidirect
120. #542C2×C4semidirect
121. #542C2×C4semidirect
122. #542C2×C4semidirect
123. #542C2×C4semidirect
124. #541C2×C4semidirect
125. #541C2×C4semidirect
126. #540C2×C4semidirect
127. #540C2×C4semidirect
138. #536C2×C4semidirect
139. #535C2×C4semidirect
143. #533C2×C4semidirect
144. #533C2×C4semidirect
145. #533C2×C4semidirect
146. #533C2×C4semidirect
149. #532C2×C4semidirect
150. #532C2×C4semidirect
151. #532C2×C4semidirect
152. #532C2×C4semidirect
167. #529C2×C4semidirect
168. #529C2×C4semidirect
192. #520C2×C4semidirect
193. #520C2×C4semidirect
194. #519C2×C4semidirect
197. #518C2×C4semidirect
203. C4×#41C2×C4semidirect
204. C4×#41C2×C4semidirect
333. C4⋊Q8C22×C4semidirect
334. C4⋊Q8C22×C4semidirect
335. C4⋊Q8C22×C4semidirect
336. C4⋊Q8C22×C4semidirect
337. C4⋊Q8C22×C4semidirect
338. C4⋊Q8C22×C4semidirect
339. #127C22×C4semidirect
340. #127C22×C4semidirect
363. #125C22×C4semidirect
364. #125C22×C4semidirect
373. #124C22×C4semidirect
374. #124C22×C4semidirect
457. C4×Q8C22×C4semidirect
458. C4×Q8C22×C4semidirect
459. C4×Q8C22×C4semidirect
460. C4×Q8C22×C4semidirect
491. C4×D4C22×C4semidirect
492. C4×D4C22×C4semidirect
493. C4×D4C22×C4semidirect
494. C4×D4C22×C4semidirect

Maximal subgroups

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

subgroupindex
#628142
#601242
C2×#23432
#176092
#176042
#175932
#175882
#175872
#175462
#175412
C2×#15042