Finite Group Databasebeta

← #10575743

Subgroups — #10575743

Order 512.

6014 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic
2C2×#3458C211yesmaximal, characteristic, complemented
3#60876C2116yesmaximal, complemented
4#60874C218yesmaximal, complemented
5#60872C218yesmaximal, complemented
6#60870C214yesmaximal, complemented
7#60869C214yesmaximal, complemented
8#60866C214yesmaximal, complemented
9#60865C214yesmaximal, complemented
10#60664C212yesmaximal, complemented
11#60620C212yesmaximal, complemented
12#60511C212yesmaximal
13C2×#3095C212yesmaximal, complemented
14#60492C212yesmaximal, complemented
15#60491C212yesmaximal, complemented
16#60124C211yesmaximal, characteristic, complemented
17#3495—24no—
18#3495—24no—
19#3495C2218yes—
20#3495C2218yes—
21C2×#556—21no—
22C2×#554—21no—
23C2×#552—22no—
24C2×#552—21no—
25C2×#552—21no—
26C2×#551—22no—
27#3458—22no—
28#3458—21no—
29#3458—21no—
30#3458—24no—
31#3458C2212yes—
32#3458C2214yes—
33#3458C2212yes—
34#3458C2218yescomplemented
35C2×#544—21no—
36C2×#544—21no—
37C2×#544C2211yescharacteristic
38C2×#544C2214yescomplemented
39C2×#544C2214yescomplemented
40C2×#543—22no—
41C2×#542C2212yes—
42C2×#541C2212yes—
43C2×#536C2211yescharacteristic
44C2×#533—24no—
45C2×#533C2212yes—
46C2×#533C2214yes—
47C2×#529C2212yes—
48C2×#525C2211yescharacteristic
49C22×C22⋊Q8C2211yescharacteristic
50C2×#520C2211yescharacteristic
51C2×#519C2211yescharacteristic
52C22×#117C2212yes—
53C22×#117C2211yescharacteristic
54#3244C22132yescomplemented
55#3243C22132yescomplemented
56#3242C22132yescomplemented
57#3242C22132yescomplemented
58#3240C22116yescomplemented
59#3239C2218yescomplemented
60#3238C2218yescomplemented
61#3237C22116yescomplemented
62#3236C22116yescomplemented
63#3233C22116yescomplemented
64#3232C22116yescomplemented
65#3231C22116yescomplemented
66#3230C2218yescomplemented
67#3229C2218yescomplemented
68#3166C2218yescomplemented
69#3165C2218yescomplemented
70#3164C22116yescomplemented
71#3163C22116yescomplemented
72#3140C2218yescomplemented
73#3139C2218yescomplemented
74#3137C22116yescomplemented
75#3137C22116yescomplemented
76#3095C2218yes—
77#3095C2218yes—
78#3095C2214yes—
79#3095C2214yes—
80#3095C2218yescomplemented
81#3095C2218yescomplemented
82#3094C2214yes—
83#3094C2214yes—
84#3093C2218yes—
85#3092C2214yes—
86#3092C2214yes—
87#3091C2218yes—
88#3091C2218yes—
89C2×#484C2214yescomplemented
90C2×#485C2218yescomplemented
91C2×#483C2214yescomplemented
92#3084C22116yescomplemented
93#3083C22116yescomplemented
94#3082C22116yescomplemented
95#3082C22116yescomplemented
96#3078C2218yescomplemented
97#3078C2218yescomplemented
98#3078C2218yescomplemented
99#3077C2218yescomplemented
100#2924C2218yescomplemented
101#2924C2218yescomplemented
102#2921C2214yes—
103#2920C2214yes—
104#2911C2214yes—
105C2×#428C2214yes—
106#2905C2212yes—
107#2896C2214yes—
108C2×#419C2214yes—
109C2×#407C2212yes—
110#2873C2212yes—
111C22×#41C2311yescharacteristic
112C23×Q8C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C22×M16C2314yes—
115#556—28no—
116#556—28no—
117#554—28no—
118#554—28no—
119#552—216no—
120#552—216no—
121#552—28no—
122#552—28no—
123#552—28no—
124#552—28no—
125#551—216no—
126#551—216no—
127#544—24no—
128#544—28no—
129#544—24no—
130#544—28no—
131#544—24no—
132#544—24no—
133#544—24no—
134#544—22no—
135#544—22no—
136#544—24no—
137#544—22no—
138#544—22no—
139#544—24no—
140#544—28no—
141#544—28no—
142#544C2318yes—
143#544C2318yes—
144#544C2318yes—
145#544C2318yes—
146#544C2318yes—
147#544C23116yes—
148#544C23116yes—
149#543—24no—
150#543—24no—
151#543—24no—
152#543—24no—
153#543—216no—
154#542—28no—
155#542C23116yes—
156#541—28no—
157#541C23116yes—
158#536—24no—
159#536C2318yes—
160#533—28no—
161#533—28no—
162#533—216no—
163#533—216no—
164#533—28no—
165#533—28no—
166#533—24no—
167#533—24no—
168#533—24no—
169#533—24no—
170#533—24no—
171#533—24no—
172#533C2318yes—
173#533C2318yes—
174#533C2318yes—
175#533C2318yes—
176#533C2318yes—
177#533C2318yes—
178C2×C4⋊Q8—24no—
179C2×C4⋊Q8—24no—
180C2×C4⋊Q8—21no—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2314yes—
185#529—24no—
186#529—24no—
187#529C2318yes—
188#529C2318yes—
189C2×#126—22no—
190C2×#126—22no—
191C2×#126—22no—
192C2×#126—22no—
193C2×#125—24no—
194C2×#125—24no—
195C2×#125—22no—
196C2×#125—22no—
197C2×#125—21no—
198C2×#125—22no—
199C2×#125C2312yes—
200C2×#125C2318yes—
201C2×#124—22no—
202C2×#124C2312yes—
203#525—22no—
204#525—22no—
205#525C2314yes—
206#525C2314yes—
207C2×#123—21no—
208C2×#123—22no—
209C2×#123—22no—
210C2×#123—22no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—22no—
214C2×C22⋊Q8—22no—
215C2×C22⋊Q8—24no—
216C2×C22⋊Q8—24no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8—28no—
222C2×C22⋊Q8—28no—
223C2×C22⋊Q8—22no—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233#520—24no—
234#520C2318yes—
235#519—24no—
236#519C2318yes—
237C2×C4×Q8—21no—
238C2×C4×Q8—21no—
239C2×C4×Q8—24no—
240C2×C4×Q8—24no—
241C2×C4×Q8—22no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—22no—
248C2×C4×D4—22no—
249C2×C4×D4C2312yes—
250C2×#117—22no—
251C2×#117—22no—
252C2×#117—22no—
253C2×#117—22no—
254C2×#117—22no—
255C2×#117—22no—
256C2×#117—22no—
257C2×#117—21no—
258C2×#117—22no—
259C2×#117—22no—
260C2×#117D414yes—
261C2×#117D411yescharacteristic
262C2×#117D412yes—
263C2×#117D411yescharacteristic
264C2×#117D414yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C22×C4⋊C4—21no—
278C22×C4⋊C4—21no—
279C22×C4⋊C4D411yescharacteristic
280C22×C4⋊C4D411yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4—22no—
285C22×C22⋊C4—21no—
286C22×C22⋊C4D412yes—
287C22×C42—22no—
288C22×C42C2312yes—
289#501C23116yescomplemented
290#501C23132yescomplemented
291#501C23116yescomplemented
292#500C23116yescomplemented
293#499C23132yescomplemented
294#498C23116yescomplemented
295#491C23132yescomplemented
296#489C23116yescomplemented
297#489C23116yescomplemented
298#488C23132yescomplemented
299#487C23116yescomplemented
300#487C23116yescomplemented
301#485C23132yes—
302#485C23132yes—
303#485C23116yes—
304#485C23116yes—
305#484C23116yes—
306#484C23116yes—
307#484C2318yes—
308#484C2318yes—
309#483C23116yes—
310#483C23116yes—
311#483C2318yes—
312#483C2318yes—
313#482C23116yes—
314#482C23116yes—
315#481C2318yes—
316#481C2318yes—
317#480C2318yes—
318#480C2318yes—
319#479C23132yescomplemented
320#479C23132yescomplemented
321#479C23132yescomplemented
322#478C23132yescomplemented
323#477C23116yescomplemented
324#477C23116yescomplemented
325#477C23116yescomplemented
326#476C23116yescomplemented
327#475C23116yescomplemented
328#475C23116yescomplemented
329#475C23116yescomplemented
330#474C23116yescomplemented
331#433C23132yes—
332#432C2318yes—
333#432C2318yes—
334#431C2318yes—
335#431C2318yes—
336#428C23116yes—
337#428C2318yes—
338#428C2318yes—
339#428C2318yes—
340#428C2318yes—
341#428C23116yes—
342#427C23116yes—
343C2×#107C2318yes—
344C2×#106C2318yes—
345#424C23116yes—
346#423C2318yes—
347#419C2318yes—
348#419C23116yes—
349#419C23116yes—
350#418C2318yes—
351#417C2318yes—
352#417C2318yes—
353#416C23116yes—
354C2×#103C2318yes—
355C2×#103C2318yes—
356#407C2314yes—
357#407C2314yes—
358#407C2314yes—
359#407C2314yes—
360C2×C22⋊C8C2314yes—
361C2×C22⋊C8C2314yes—
362#405C23116yes—
363C4×M16C2318yes—
364C25C2×D411yescharacteristic
365C2×#41—22no—
366C2×#41—28no—
367C2×#41C2414yes—
368C22×Q8—21no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—24no—
372C22×Q8—24no—
373C22×Q8—28no—
374C22×Q8C2412yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2414yes—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4C2411yescharacteristic
381C23×C4—28no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4C2×D411yescharacteristic
389C23×C4C2×D411yescharacteristic
390C23×C4C2×D411yescharacteristic
391C23×C4C2×D412yes—
392C23×C4C2×D412yes—
393C23×C4C2×D412yes—
394C23×C4C2×D412yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C2×M16—216no—
401C2×M16C2418yes—
402C2×M16C2418yes—
403C22×C8C2418yes—
404C4⋊Q8—28no—
405C4⋊Q8—28no—
406C4⋊Q8—28no—
407C4⋊Q8—216no—
408C4⋊Q8—28no—
409C4⋊Q8—216no—
410C4⋊Q8—28no—
411C4⋊Q8—24no—
412C4⋊Q8—24no—
413C4⋊Q8—24no—
414C4⋊Q8—24no—
415C4⋊Q8—24no—
416C4⋊Q8—24no—
417C4⋊Q8C2418yes—
418C4⋊Q8C2418yes—
419C4⋊Q8C2418yes—
420C4⋊Q8C2418yes—
421C4⋊Q8C2418yes—
422C4⋊Q8C2418yes—
423#126—216no—
424#126—216no—
425#126—216no—
426#126—28no—
427#126—28no—
428#125—28no—
429#125—28no—
430#125—28no—
431#125—216no—
432#125—28no—
433#125—216no—
434#125—216no—
435#125—216no—
436#125—28no—
437#125—28no—
438#125—28no—
439#125—24no—
440#125—28no—
441#125—28no—
442#125C2418yes—
443#125C24116yes—
444#125C24116yes—
445#124—216no—
446#124—24no—
447#124C2418yes—
448#123—24no—
449#123—24no—
450#123—28no—
451#123—28no—
452#123—216no—
453#123—216no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—24no—
457C22⋊Q8—24no—
458C22⋊Q8—24no—
459C22⋊Q8—24no—
460C22⋊Q8—24no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—28no—
464C22⋊Q8—28no—
465C22⋊Q8—28no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—28no—
469C22⋊Q8—28no—
470C22⋊Q8—28no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—216no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479C22⋊Q8—216no—
480C22⋊Q8—216no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483C22⋊Q8—216no—
484C22⋊Q8—216no—
485C22⋊Q8—216no—
486C22⋊Q8C2414yes—
487C22⋊Q8C2414yes—
488C22⋊Q8C2418yes—
489C22⋊Q8C2412yes—
490C22⋊Q8C2412yes—
491C22⋊Q8C2414yes—
492#121—21no—
493#121—21no—
494#121—22no—
495#121C2412yes—
496#121C2412yes—
497#121C2414yes—
498#120—24no—
499#120—24no—
500C4×Q8—28no—
501C4×Q8—28no—
502C4×Q8—28no—
503C4×Q8—28no—
504C4×Q8—28no—
505C4×Q8—28no—
506C4×Q8—28no—
507C4×Q8—28no—
508C4×Q8—28no—
509C4×Q8—28no—
510C4×Q8—28no—
511C4×Q8—28no—
512C4×Q8—24no—
513C4×Q8—24no—
514C4×Q8—24no—
515C4×Q8C2418yes—
516C4×Q8C2418yes—
517C4×Q8C2418yes—
518C4×D4—24no—
519C4×D4—24no—
520C4×D4—24no—
521C4×D4—24no—
522C4×D4—28no—
523C4×D4—28no—
524C4×D4—216no—
525C4×D4—24no—
526C4×D4C2418yes—
527#117—24no—
528#117—24no—
529#117—24no—
530#117—24no—
531#117—24no—
532#117—24no—
533#117—24no—
534#117—24no—
535#117—24no—
536#117—24no—
537#117—24no—
538#117—24no—
539#117—28no—
540#117—28no—
541#117—22no—
542#117—28no—
543#117—216no—
544#117—28no—
545#117—28no—
546#117C2×D414yes—
547#117C2×D414yes—
548#117C2×D418yes—
549#117C2×D414yes—
550#117C2×D418yes—
551#117C2×D414yes—
552#117C2×D414yes—
553#117C2×D418yes—
554#117C2×D414yes—
555#117C2418yes—
556#117C2418yes—
557#117C2418yes—
558#117C2418yes—
559#117C2414yes—
560#117C2414yes—
561#117C2414yes—
562#117C2418yes—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D412yes—
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D412yes—
596C2×C4⋊C4C2×D414yes—
597C2×C4⋊C4C2×D414yes—
598C2×C4⋊C4C2×D414yes—
599C2×C4⋊C4C2×D414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C22⋊C4—24no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4C2×D412yes—
629C2×C22⋊C4C2×D418yes—
630C2×C22⋊C4C2×D412yes—
631C2×C22⋊C4C2×D412yes—
632C2×C22⋊C4C2×D412yes—
633C2×C22⋊C4C2×D418yes—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—24no—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—24no—
641C2×C42—24no—
642C2×C42—24no—
643C2×C42—21no—
644C2×C42C2×D412yes—
645C2×C42C2×D414yes—
646C2×C42C2×D412yes—
647C2×C42C2×D414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652#107C24132yes—
653#107C24116yes—
654#107C24116yes—
655#106C24132yes—
656#106C24116yes—
657#106C24116yes—
658C4⋊C8C24116yes—
659C4⋊C8C24116yes—
660#103C24132yes—
661#103C24132yes—
662#103C24116yes—
663#103C24116yes—
664#102C24116yes—
665#102C24116yes—
666C22⋊C8C2418yes—
667C22⋊C8C2418yes—
668C22⋊C8C2418yes—
669C22⋊C8C2418yes—
670#97C24116yes—
671C4×C8C24116yes—
672C24—24no—
673C24—21no—
674C24—42no—
675C24—81no—
676C24C22×D411yescharacteristic
677C24C22×D412yes—
678C24C22×D411yescharacteristic
679C24C22×D412yes—
680C24C22×D411yescharacteristic
681#41—216no—
682#41—48no—
683C2×Q8—24no—
684C2×Q8—22no—
685C2×Q8—21no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—28no—
689C2×Q8—28no—
690C2×Q8—28no—
691C2×Q8—216no—
692C2×Q8—28no—
693C2×Q8—24no—
694C2×Q8—44no—
695C2×Q8—48no—
696C2×Q8—88no—
697C2×Q8—84no—
698C2×Q8—88no—
699C2×Q8C2514yes—
700C2×Q8C2512yes—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—21no—
706C2×D4—24no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—82no—
710C2×D4C2512yes—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—28no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—82no—
739C22×C4—84no—
740C22×C4—84no—
741C22×C4—82no—
742C22×C4—84no—
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D412yes—
745C22×C4C22×D412yes—
746C22×C4C22×D412yes—
747C22×C4C22×D412yes—
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D414yes—
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D412yes—
753C22×C4C22×D412yes—
754C22×C4C22×D412yes—
755C22×C4C22×D412yes—
756C22×C4C22×D412yes—
757C22×C4C22×D412yes—
758C22×C4C22×D412yes—
759C22×C4C22×D414yes—
760C22×C4C22×D414yes—
761C22×C4C22×D414yes—
762C22×C4C22×D412yes—
763C22×C4C22×D411yescharacteristic
764C22×C42−1+418yes—
765C22×C4C2511yescharacteristic
766C22×C4C2511yescharacteristic
767C22×C4C2512yes—
768C22×C4C2511yescharacteristic
769C22×C4C2512yes—
770M16—216no—
771M16—216no—
772C2×C8—216no—
773C2×C8C25116yes—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—22no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—216no—
800C4⋊C4—216no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—28no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4C22×D414yes—
807C4⋊C4C22×D414yes—
808C4⋊C4C22×D418yes—
809C4⋊C4C22×D414yes—
810C4⋊C4C22×D414yes—
811C4⋊C4C22×D418yes—
812C4⋊C4C2518yes—
813C4⋊C4C2518yes—
814C4⋊C4C2514yes—
815C4⋊C4C2512yes—
816C4⋊C4C2512yes—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—28no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—22no—
827C22⋊C4—24no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—24no—
833C22⋊C4—28no—
834C22⋊C4C22×D418yes—
835C22⋊C4C22×D418yes—
836C22⋊C4C22×D418yes—
837C22⋊C4C22×D418yes—
838C42—28no—
839C42—28no—
840C42—28no—
841C42—28no—
842C42—28no—
843C42—28no—
844C42—28no—
845C42—24no—
846C42C22×D414yes—
847C42C22×D414yes—
848C42C22×D414yes—
849C42C22×D414yes—
850C42C22×D414yes—
851C42C22×D414yes—
852C42C2514yes—
853C42C2514yes—
854C23—22no—
855C23—24no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—24no—
860C23—22no—
861C23—41no—
862C23—42no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—88no—
873C23#53614yes—
874C23C23×D411yescharacteristic
875C23C23×D412yes—
876C23C23×D411yescharacteristic
877C23C23×D411yescharacteristic
878C23C23×D412yes—
879Q8—28no—
880Q8—24no—
881Q8—48no—
882Q8—44no—
883Q8—42no—
884Q8—88no—
885Q8—88no—
886Q8—88no—
887Q8—88no—
888Q8—88no—
889D4—24no—
890D4—44no—
891D4—44no—
892D4—48no—
893D4—42no—
894D4—84no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—44no—
920C2×C4—42no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—42no—
924C2×C4—44no—
925C2×C4—48no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—48no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—48no—
932C2×C4—48no—
933C2×C4—88no—
934C2×C4—84no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4#53614yes—
940C2×C4#53618yes—
941C2×C4C23×D411yescharacteristic
942C2×C4C23×D414yes—
943C2×C4C23×D412yes—
944C2×C4C23×D414yes—
945C2×C4C23×D411yescharacteristic
946C2×C4C23×D414yes—
947C2×C4C23×D414yes—
948C2×C4C23×D411yescharacteristic
949C2×C4C23×D412yes—
950C2×C4C2×2−1+418yes—
951C2×C4C2×2−1+414yes—
952C2×C4C2611yescharacteristic
953C8—216no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—22no—
959C22—21no—
960C22—21no—
961C22—22no—
962C22—21no—
963C22—22no—
964C22—21no—
965C22—22no—
966C22—44no—
967C22—44no—
968C22—48no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—82no—
973C22—84no—
974C22—84no—
975C22C2×#53612yes—
976C22C2×#53614yes—
977C22#358612yes—
978C22C24×D411yescharacteristic
979C4—24no—
980C4—24no—
981C4—24no—
982C4—24no—
983C4—21no—
984C4—22no—
985C4—21no—
986C4—48no—
987C4—42no—
988C4—44no—
989C4—48no—
990C4—42no—
991C4—42no—
992C4—44no—
993C4C2×#53614yes—
994C4C2×#53612yes—
995C4C22×2−1+412yes—
996C2—22no—
997C2—22no—
998C2—24no—
999C2—41no—
1000C2—42no—
1001C2—82no—
1002C2C22×#53611yescharacteristic
1003C2C2×#358611yescharacteristic
1004C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3458C2semidirect
3. #60876C2semidirect
4. #60874C2semidirect
5. #60872C2semidirect
6. #60870C2semidirect
7. #60869C2semidirect
8. #60866C2semidirect
9. #60865C2semidirect
10. #60664C2semidirect
11. #60620C2semidirect
13. C2×#3095C2semidirect
14. #60492C2semidirect
15. #60491C2semidirect
16. #60124C2semidirect
34. #3458C22semidirect
38. C2×#544C22semidirect
39. C2×#544C22semidirect
54. #3244C22semidirect
55. #3243C22semidirect
56. #3242C22semidirect
57. #3242C22semidirect
58. #3240C22semidirect
59. #3239C22semidirect
60. #3238C22semidirect
61. #3237C22semidirect
62. #3236C22semidirect
63. #3233C22semidirect
64. #3232C22semidirect
65. #3231C22semidirect
66. #3230C22semidirect
67. #3229C22semidirect
68. #3166C22semidirect
69. #3165C22semidirect
70. #3164C22semidirect
71. #3163C22semidirect
72. #3140C22semidirect
73. #3139C22semidirect
74. #3137C22semidirect
75. #3137C22semidirect
80. #3095C22semidirect
81. #3095C22semidirect
89. C2×#484C22semidirect
90. C2×#485C22semidirect
91. C2×#483C22semidirect
92. #3084C22semidirect
93. #3083C22semidirect
94. #3082C22semidirect
95. #3082C22semidirect
96. #3078C22semidirect
97. #3078C22semidirect
98. #3078C22semidirect
99. #3077C22semidirect
100. #2924C22semidirect
101. #2924C22semidirect
289. #501C23semidirect
290. #501C23semidirect
291. #501C23semidirect
292. #500C23semidirect
293. #499C23semidirect
294. #498C23semidirect
295. #491C23semidirect
296. #489C23semidirect
297. #489C23semidirect
298. #488C23semidirect
299. #487C23semidirect
300. #487C23semidirect
319. #479C23semidirect
320. #479C23semidirect
321. #479C23semidirect
322. #478C23semidirect
323. #477C23semidirect
324. #477C23semidirect
325. #477C23semidirect
326. #476C23semidirect
327. #475C23semidirect
328. #475C23semidirect
329. #475C23semidirect
330. #474C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
C2×#34582
#608762
#608742
#608722
#608702
#608692
#608662
#608652
#606642
#606202
#605112
C2×#30952
#604922
#604912
#601242