Finite Group Databasebeta

← #10574259

Subgroups — #10574259

Order 512.

6722 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60219C2116yesmaximal, complemented
3#60216C2116yesmaximal, complemented
4#60209C214yesmaximal, complemented
5#60207C214yesmaximal, complemented
6#60206C214yesmaximal, complemented
7#60205C214yesmaximal, complemented
8#60192C211yesmaximal, characteristic, complemented
9C2×#2961C211yesmaximal, characteristic, complemented
10#60144C211yesmaximal, characteristic, complemented
11#60142C212yesmaximal, complemented
12#60140C212yesmaximal, complemented
13C2×#2932C211yesmaximal, characteristic, complemented
14#60126C212yesmaximal, complemented
15#60125C211yesmaximal, characteristic, complemented
16#60058C212yesmaximal, complemented
17C2×#2875C211yesmaximal, characteristic, complemented
18C2×#568C2212yes—
19C22×#131C2211yescharacteristic
20C22×#131C2211yescharacteristic
21C22×#131C2212yes—
22#3512C414yes—
23#3511C414yes—
24#3510C414yes—
25#3509C412yes—
26#3508C412yes—
27#3507C414yes—
28#3506C414yes—
29#3505C418yes—
30#3480C2218yes—
31#3475C2218yes—
32#3455C2214yes—
33#3449C2212yes—
34#3444C2214yes—
35C2×#533C2211yescharacteristic
36C2×#532C2211yescharacteristic
37#3428C2212yes—
38C2×C4×#41C2211yescharacteristic
39#2970C22132yescomplemented
40#2969C22132yescomplemented
41#2968C22132yescomplemented
42#2968C22132yescomplemented
43#2967C22132yescomplemented
44#2967C22132yescomplemented
45#2966C22132yescomplemented
46#2965C22132yescomplemented
47Q8×M16C2218yescomplemented
48#2962C2218yescomplemented
49#2961C2212yescomplemented
50#2961C2212yescomplemented
51#2961C2212yescomplemented
52#2961C2212yescomplemented
53#2961C2218yescomplemented
54#2961C2214yescomplemented
55#2960C2214yescomplemented
56C2×#446C2218yescomplemented
57#2935C22116yescomplemented
58#2935C2218yescomplemented
59D4×M16C2218yescomplemented
60#2933C22116yes—
61#2932C2212yes—
62#2932C2214yes—
63#2932C2212yes—
64#2932C2212yes—
65#2932C2212yes—
66#2932C2218yescomplemented
67#2932C2218yescomplemented
68#2931C2214yes—
69#2931C2218yescomplemented
70#2930C2218yes—
71#2930C2218yescomplemented
72#2930C2218yescomplemented
73#2929C2218yes—
74#2929C2218yescomplemented
75#2929C2218yescomplemented
76C2×#435C2218yescomplemented
77#2925C2218yes—
78#2925C2218yescomplemented
79#2925C22116yescomplemented
80#2924C22116yescomplemented
81#2923C2218yescomplemented
82#2922C2218yescomplemented
83#2921C2214yescomplemented
84#2920C2214yescomplemented
85#2905C2212yes—
86C2×#424C2212yes—
87C2×#423C2211yescharacteristic
88C2×#423C2211yescharacteristic
89#2879C2212yes—
90#2879C2212yes—
91C2×#408C2212yes—
92#2875C2218yes—
93#2875C2218yescomplemented
94#2875C2218yescomplemented
95#2875C2218yescomplemented
96C4×#131C2218yescomplemented
97C4×#131C2218yescomplemented
98#2873C2212yes—
99#2873C2212yes—
100#2873C2218yescomplemented
101C2×#405C2212yes—
102C2×#405C2211yescharacteristic
103C2×#405C2211yescharacteristic
104C2×#405C2212yescomplemented
105C2×#405C2212yescomplemented
106C2×#405C2218yescomplemented
107C2×C4×M16C2211yescharacteristic
108C2×C4×M16C2212yescomplemented
109C22×#97C2211yescharacteristic
110C22×#97C2212yescomplemented
111C22×#41C2312yes—
112C22×#41C2311yescharacteristic
113#568—216no—
114C2×#131—28no—
115C2×#131—28no—
116C2×#131—216no—
117C2×#131C2314yes—
118C2×#131C2314yes—
119C2×#131C2318yes—
120C2×#131C2318yes—
121C2×#131C2314yes—
122C2×#131C2314yes—
123C2×#131C2314yes—
124C2×#131C2314yes—
125C2×#131C2314yes—
126C2×#131C2314yes—
127C22×M16C2311yescharacteristic
128C22×M16C2312yes—
129C22×M16C2312yes—
130C22×M16C2312yes—
131C22×M16C2318yes—
132C22×M16C2312yes—
133C22×M16C2314yes—
134C22×M16C2311yescharacteristic
135C23×C8C2311yescharacteristic
136C23×C8C2312yes—
137C23×C8C2312yes—
138C23×C8C2314yes—
139C23×C8C2311yescharacteristic
140#559C2×C4116yes—
141#559C2×C418yes—
142#557C2×C418yes—
143#556C2×C418yes—
144#556C2×C418yes—
145#556C2×C4116yes—
146#555C2×C418yes—
147#554C2×C418yes—
148#553C2×C4116yes—
149#553C2×C4116yes—
150#553C2×C4132yes—
151#552C2×C4116yes—
152#552C2×C4116yes—
153#551C2×C4132yes—
154#550C2×C418yes—
155#548C2×C4116yes—
156#547C2×C418yes—
157#546C2×C4116yes—
158#542C2×C4116yes—
159#541C2×C418yes—
160#540C2×C418yes—
161#539C2×C4116yes—
162#538C2×C4116yes—
163#537C2×C418yes—
164#536C2×C414yes—
165#536C2×C414yes—
166#535C2×C414yes—
167#535C2×C414yes—
168#534C2×C418yes—
169#533C2×C414yes—
170#533C2×C412yes—
171#533C2×C412yes—
172#533C2×C418yes—
173#533C2312yes—
174#533C2312yes—
175#533C2314yes—
176#532C2×C414yes—
177#532C2×C412yes—
178#532C2×C412yes—
179#532C2×C418yes—
180#532C2312yes—
181#532C2312yes—
182#532C2314yes—
183#532C2318yes—
184C2×C4⋊Q8C2×C411yescharacteristic
185C2×C4⋊Q8C2×C412yes—
186C2×#127C2×C411yescharacteristic
187#529C2×C4116yes—
188#529C2×C4116yes—
189#529C23116yes—
190#529C23132yes—
191C2×#125C2×C412yes—
192C2×#124C2×C412yes—
193#525C2×C4116yes—
194#525C2318yes—
195#525C2318yes—
196C2×C22⋊Q8C2×C414yes—
197C2×#121C2×C414yes—
198#520C2×C418yes—
199#520C2×C418yes—
200#519C2×C414yes—
201#518C2×C418yes—
202#518C2×C414yes—
203C4×#41C2×C412yes—
204C4×#41C2×C412yes—
205C4×#41C2×C412yes—
206C4×#41C2×C412yes—
207C4×#41C23116yes—
208C4×#41C2318yes—
209C4×#41C2318yes—
210C4×#41C2314yes—
211C4×#41C2314yes—
212C2×C4×Q8C2×C412yes—
213C2×C4×Q8C2314yes—
214C2×C4×D4C2×C414yes—
215C2×C4×D4C2×C412yes—
216C2×C4×D4C2314yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2318yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223#446C23116yes—
224#446C23116yes—
225#446C23116yes—
226#446C23116yes—
227#446C23116yes—
228#446C23132yes—
229C8×Q8C23116yes—
230#436C23132yes—
231#436C23132yes—
232#436C23116yes—
233#435C23116yes—
234#435C23116yes—
235#435C23116yes—
236#435C23116yes—
237#435C23132yes—
238#435C23132yes—
239#435C23132yes—
240#435C23132yes—
241#435C23132yes—
242C8×D4C23132yes—
243C8×D4C23132yes—
244C8×D4C23116yes—
245#433C23132yes—
246#433C23132yes—
247#433C23132yes—
248#432C23116yes—
249#432C23132yes—
250#431C23116yes—
251#431C23132yes—
252#424C2314yes—
253#424C2314yes—
254#424C2318yes—
255#424C2318yes—
256#424C2318yes—
257#423C2312yes—
258#423C2312yes—
259#423C2312yes—
260#423C2312yes—
261#423C2314yes—
262#423C2314yes—
263#423C2318yes—
264C2×C4⋊C8C2314yes—
265C2×C4⋊C8C2314yes—
266C2×C4⋊C8C2318yes—
267#408C2314yes—
268#408C2314yes—
269#408C2318yes—
270#408C2318yes—
271#408C2318yes—
272#408C2318yes—
273#408C2318yes—
274#407C2318yes—
275#407C2318yes—
276C2×C22⋊C8C2318yes—
277#405C2314yes—
278#405C2314yes—
279#405C2314yes—
280#405C2314yes—
281#405C2314yes—
282#405C2314yes—
283#405C2314yes—
284#405C2314yes—
285#405C2318yes—
286#405C2318yes—
287#405C23116yes—
288#405C23116yes—
289#405C23116yes—
290#405C23116yes—
291#405C2318yes—
292#405C2318yes—
293#405C23116yes—
294#405C23116yes—
295C4×M16C2314yes—
296C4×M16C2314yes—
297C4×M16C23116yes—
298C4×M16C2318yes—
299C4×M16C2318yes—
300C4×M16C23116yes—
301C4×M16C23116yes—
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2314yes—
307C2×#97C2314yes—
308C2×#97C2312yes—
309C2×#97C2312yes—
310C2×#97C2312yes—
311C2×#97C23116yes—
312C2×#97C2314yes—
313C2×#97C23116yes—
314C2×C4×C8C2312yes—
315C2×C4×C8C2312yes—
316C2×C4×C8C2312yes—
317C2×C4×C8C2314yes—
318C2×C4×C8C23116yes—
319C2×#41—24no—
320C2×#41—28no—
321C2×#41—24no—
322C2×#41—28no—
323C2×#41C22×C412yes—
324C2×#41C22×C412yes—
325C2×#41C22×C414yes—
326C2×#41C22×C414yes—
327C2×#41C22×C4116yes—
328C2×#41C2412yes—
329C2×#41C2414yes—
330C2×#41C2414yes—
331C2×#41C2412yes—
332C22×Q8C22×C411yescharacteristic
333C22×Q8C22×C412yes—
334C22×Q8C22×C414yes—
335C22×D4C22×C412yes—
336C22×D4C22×C411yescharacteristic
337C22×D4C22×C414yes—
338C22×D4C22×C412yes—
339C22×D4C22×C414yes—
340C23×C4C22×C412yes—
341C23×C4C22×C414yes—
342C23×C4C2414yes—
343C23×C4C2412yes—
344C23×C4C2411yescharacteristic
345#131—216no—
346#131—216no—
347#131—232no—
348#131—216no—
349#131—216no—
350#131—216no—
351#131—216no—
352#131—216no—
353#131—216no—
354#131—232no—
355C2×M16—24no—
356C2×M16—28no—
357C2×M16—28no—
358C2×M16—232no—
359C2×M16—216no—
360C2×M16—28no—
361C2×M16—28no—
362C2×M16#4118yescomplemented
363C2×M16C2414yes—
364C2×M16C2412yes—
365C2×M16C2414yes—
366C2×M16C2414yes—
367C2×M16C2412yes—
368C2×M16C2414yes—
369C2×M16C2418yes—
370C2×M16C2418yes—
371C2×M16C2418yes—
372C2×M16C24116yes—
373C2×M16C2418yes—
374C2×M16C2412yes—
375C2×M16C2412yes—
376C22×C8—24no—
377C22×C8—28no—
378C22×C8—216no—
379C22×C8—28no—
380C22×C8#4118yescomplemented
381C22×C8C2411yescharacteristic
382C22×C8C2411yescharacteristic
383C22×C8C2412yes—
384C22×C8C2414yes—
385C22×C8C2418yes—
386C22×C8C2412yes—
387C22×C8C2412yes—
388C22×C8C2418yes—
389C22×C8C2418yes—
390C22×C8C2418yes—
391C22×C8C2414yes—
392C22×C8C24116yes—
393C22×C8C2412yes—
394C22×C8C2411yescharacteristic
395C22×C8C2412yes—
396C22×C8C2411yescharacteristic
397C22×C8C2412yes—
398C4⋊Q8C22×C414yes—
399C4⋊Q8C22×C412yes—
400C4⋊Q8C22×C412yes—
401C4⋊Q8C22×C414yes—
402C4⋊Q8C22×C414yes—
403C4⋊Q8C22×C414yes—
404C4⋊Q8C22×C414yes—
405C4⋊Q8C22×C418yes—
406#127C22×C412yes—
407#127C22×C412yes—
408#127C22×C414yes—
409#127C22×C418yes—
410#126C22×C4132yes—
411#126C22×C4132yes—
412#126C22×C4132yes—
413#125C22×C414yes—
414#125C22×C414yes—
415#125C22×C418yes—
416#125C22×C4116yes—
417#125C22×C4132yes—
418#124C22×C414yes—
419#124C22×C414yes—
420#124C22×C418yes—
421#124C22×C4116yes—
422#124C22×C4132yes—
423#124C22×C418yes—
424#124C22×C418yes—
425#123C22×C4132yes—
426#123C22×C4116yes—
427#123C22×C4116yes—
428#123C22×C4132yes—
429#123C22×C4132yes—
430C22⋊Q8C22×C418yes—
431C22⋊Q8C22×C418yes—
432C22⋊Q8C22×C418yes—
433C22⋊Q8C22×C418yes—
434C22⋊Q8C22×C4116yes—
435C22⋊Q8C22×C4116yes—
436C22⋊Q8C22×C4116yes—
437C22⋊Q8C22×C4132yes—
438#121C22×C418yes—
439#121C22×C418yes—
440#121C22×C418yes—
441#121C22×C418yes—
442#121C22×C4116yes—
443#121C22×C4116yes—
444#121C22×C4116yes—
445#121C22×C4132yes—
446#121C22×C4132yes—
447#120C22×C4116yes—
448#120C22×C4116yes—
449C4×Q8C22×C414yes—
450C4×Q8C22×C414yes—
451C4×Q8C22×C414yes—
452C4×Q8C22×C414yes—
453C4×Q8C22×C418yes—
454C4×Q8C22×C418yes—
455C4×Q8C22×C4116yes—
456C4×Q8C22×C4116yes—
457C4×Q8C22×C4116yes—
458C4×Q8C2418yes—
459C4×Q8C2418yes—
460C4×D4C22×C418yes—
461C4×D4C22×C414yes—
462C4×D4C22×C418yes—
463C4×D4C22×C414yes—
464C4×D4C22×C418yes—
465C4×D4C22×C418yes—
466C4×D4C22×C414yes—
467C4×D4C22×C414yes—
468C4×D4C22×C418yes—
469C4×D4C22×C418yes—
470C4×D4C22×C4132yes—
471C4×D4C22×C4116yes—
472C4×D4C22×C4132yes—
473C4×D4C22×C4116yes—
474C4×D4C22×C4132yes—
475C4×D4C22×C4116yes—
476C4×D4C2418yes—
477C4×D4C2418yes—
478C4×D4C24132yes—
479#117C22×C412yes—
480#117C22×C412yes—
481#117C22×C414yes—
482#117C22×C414yes—
483#117C22×C414yes—
484#117C22×C4116yes—
485#117C22×C414yes—
486#117C22×C4116yes—
487#117C22×C4116yes—
488#117C22×C4132yes—
489#117C2412yes—
490#117C2414yes—
491#117C2412yes—
492#117C2414yes—
493#117C2418yes—
494#117C24116yes—
495C2×C4⋊C4C22×C412yes—
496C2×C4⋊C4C22×C414yes—
497C2×C4⋊C4C22×C414yes—
498C2×C4⋊C4C22×C4116yes—
499C2×C4⋊C4C22×C414yes—
500C2×C4⋊C4C22×C418yes—
501C2×C4⋊C4C22×C414yes—
502C2×C22⋊C4C22×C412yes—
503C2×C22⋊C4C22×C414yes—
504C2×C22⋊C4C22×C414yes—
505C2×C22⋊C4C22×C4116yes—
506C2×C22⋊C4C22×C418yes—
507C2×C42C22×C414yes—
508C2×C42C22×C412yes—
509C2×C42C22×C411yescharacteristic
510C2×C42C22×C411yescharacteristic
511C2×C42C22×C414yes—
512C2×C42C22×C411yescharacteristic
513C2×C42C22×C411yescharacteristic
514C2×C42C22×C414yes—
515C2×C42C2412yes—
516C2×C42C2411yescharacteristic
517C2×C42C2414yes—
518C2×C42C24116yes—
519C2×C42C2412yes—
520C2×C42C2412yes—
521C2×C42C2418yes—
522C2×C42C2411yescharacteristic
523C4⋊C8C2418yes—
524C4⋊C8C2418yes—
525C4⋊C8C2418yes—
526C4⋊C8C2418yes—
527C4⋊C8C24116yes—
528C4⋊C8C24116yes—
529C4⋊C8C24132yes—
530C22⋊C8C24116yes—
531C22⋊C8C24116yes—
532C22⋊C8C24132yes—
533C22⋊C8C24132yes—
534#97C2414yes—
535#97C2418yes—
536#97C2414yes—
537#97C2418yes—
538#97C2418yes—
539#97C2414yes—
540#97C2418yes—
541#97C2414yes—
542#97C24116yes—
543#97C2418yes—
544#97C24116yes—
545C4×C8C2418yes—
546C4×C8C2418yes—
547C4×C8C2418yes—
548C4×C8C24116yes—
549C4×C8C2418yes—
550C4×C8C2418yes—
551C4×C8C24116yes—
552C24C23×C414yes—
553C24C23×C412yes—
554C24C23×C411yescharacteristic
555#41—28no—
556#41—216no—
557#41—28no—
558#41—216no—
559#41—24no—
560#41—28no—
561#41—24no—
562#41—28no—
563#41—28no—
564#41—24no—
565#41—28no—
566#41—24no—
567#41—816no—
568C2×Q8—28no—
569C2×Q8—24no—
570C2×Q8—84no—
571C2×Q8C23×C412yes—
572C2×Q8C23×C414yes—
573C2×Q8C23×C412yes—
574C2×Q8C23×C414yes—
575C2×Q8C23×C418yes—
576C2×Q8C23×C418yes—
577C2×D4—28no—
578C2×D4—216no—
579C2×D4—28no—
580C2×D4—24no—
581C2×D4—84no—
582C2×D4C23×C414yes—
583C2×D4C23×C418yes—
584C2×D4C23×C414yes—
585C2×D4C23×C418yes—
586C2×D4C23×C412yes—
587C2×D4C23×C414yes—
588C2×D4C23×C412yes—
589C2×D4C23×C414yes—
590C2×D4C23×C418yes—
591C2×D4C23×C4132yes—
592C2×D4C23×C418yes—
593C22×C4—28no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—28no—
597C22×C4—82no—
598C22×C4—84no—
599C22×C4C23×C412yes—
600C22×C4C23×C414yes—
601C22×C4C23×C414yes—
602C22×C4C23×C418yes—
603C22×C4C23×C412yes—
604C22×C4C23×C412yes—
605C22×C4C23×C414yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C23×C412yes—
609C22×C4C23×C412yes—
610C22×C4C23×C418yes—
611C22×C4C23×C418yes—
612C22×C4C23×C418yes—
613C22×C4C23×C4132yes—
614C22×C4C23×C411yescharacteristic
615C22×C4C23×C411yescharacteristic
616C22×C4C23×C411yescharacteristic
617C22×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2518yes—
620C22×C4C2514yes—
621C22×C4C2511yescharacteristic
622C22×C4C2511yescharacteristic
623C22×C4C2511yescharacteristic
624M16—28no—
625M16—24no—
626M16—28no—
627M16—28no—
628M16—24no—
629M16—28no—
630M16—216no—
631M16—232no—
632M16—216no—
633M16—216no—
634M16—216no—
635M16C2×#4118yes—
636M16C2×#4118yes—
637C2×C8—22no—
638C2×C8—28no—
639C2×C8—22no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—28no—
644C2×C8—216no—
645C2×C8—216no—
646C2×C8—216no—
647C2×C8—216no—
648C2×C8—232no—
649C2×C8C2×#4118yes—
650C2×C8C2×#4114yes—
651C2×C8C2×#4118yes—
652C2×C8C2×#4114yes—
653C2×C8C2×#4118yes—
654C2×C8C2518yes—
655C2×C8C2512yes—
656C2×C8C2514yes—
657C2×C8C2518yes—
658C2×C8C2512yes—
659C2×C8C2514yes—
660C2×C8C2512yes—
661C2×C8C2512yes—
662C4⋊C4C23×C414yes—
663C4⋊C4C23×C418yes—
664C4⋊C4C23×C418yes—
665C4⋊C4C23×C4116yes—
666C4⋊C4C23×C418yes—
667C4⋊C4C23×C414yes—
668C4⋊C4C23×C418yes—
669C4⋊C4C23×C418yes—
670C4⋊C4C23×C4132yes—
671C4⋊C4C23×C418yes—
672C4⋊C4C23×C418yes—
673C4⋊C4C23×C4116yes—
674C4⋊C4C23×C418yes—
675C4⋊C4C23×C4132yes—
676C22⋊C4C23×C414yes—
677C22⋊C4C23×C418yes—
678C22⋊C4C23×C4116yes—
679C22⋊C4C23×C414yes—
680C22⋊C4C23×C418yes—
681C22⋊C4C23×C418yes—
682C22⋊C4C23×C4132yes—
683C22⋊C4C23×C418yes—
684C22⋊C4C23×C4116yes—
685C22⋊C4C23×C4132yes—
686C22⋊C4C23×C4132yes—
687C42C23×C411yescharacteristic
688C42C23×C411yescharacteristic
689C42C23×C414yes—
690C42C23×C418yes—
691C42C23×C411yescharacteristic
692C42C23×C411yescharacteristic
693C42C23×C412yes—
694C42C23×C412yes—
695C42C23×C418yes—
696C42C23×C412yes—
697C42C23×C412yes—
698C42C23×C4132yes—
699C42C23×C418yes—
700C42C2514yes—
701C42C2512yes—
702C42C2518yes—
703C42C2512yes—
704C23—24no—
705C23—28no—
706C23—42no—
707C23—44no—
708C23—48no—
709C23C4×#4114yes—
710C23C24×C418yes—
711C23C24×C414yes—
712C23C24×C411yescharacteristic
713C23C24×C411yescharacteristic
714C23C24×C411yescharacteristic
715Q8—24no—
716Q8—28no—
717Q8—28no—
718Q8—24no—
719Q8—48no—
720Q8—48no—
721D4—28no—
722D4—216no—
723D4—28no—
724D4—216no—
725D4—24no—
726D4—28no—
727D4—24no—
728D4—28no—
729D4—48no—
730D4—48no—
731D4—432no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—28no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—432no—
751C2×C4C4×#4114yes—
752C2×C4C4×#4114yes—
753C2×C4C4×#4114yes—
754C2×C4C24×C412yes—
755C2×C4C24×C418yes—
756C2×C4C24×C412yes—
757C2×C4C24×C414yes—
758C2×C4C24×C418yes—
759C2×C4C24×C412yes—
760C2×C4C24×C4116yes—
761C2×C4C24×C412yes—
762C2×C4C24×C411yescharacteristic
763C2×C4C24×C411yescharacteristic
764C2×C4C24×C411yescharacteristic
765C2×C4C22×#4112yes—
766C2×C4C22×#4112yes—
767C2×C4C22×#4112yes—
768C2×C4C22×#4112yes—
769C2×C4C22×#4112yes—
770C2×C4C22×#4112yes—
771C2×C4C2611yescharacteristic
772C8—22no—
773C8—22no—
774C8—28no—
775C8—24no—
776C8—28no—
777C8C22×#4114yes—
778C8C22×#4118yes—
779C8C22×#4114yes—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—216no—
785C22—24no—
786C22—28no—
787C22—44no—
788C22—48no—
789C22—88no—
790C22C2×C4×#4112yes—
791C22C2×C4×#4112yes—
792C22C2×C4×#4112yes—
793C22C25×C411yescharacteristic
794C4—22no—
795C4—28no—
796C4—22no—
797C4—22no—
798C4—216no—
799C4—22no—
800C4—28no—
801C4—24no—
802C4C2×C4×#4112yes—
803C4C2×C4×#4112yes—
804C4C2×C4×#4112yes—
805C4C23×#4111yescharacteristic
806C4C23×#4111yescharacteristic
807C2—22no—
808C2—22no—
809C2—22no—
810C2—44no—
811C2—48no—
812C2C22×C4×#4111yescharacteristic
813C2#6307612yes—
subgroupG/H
center, Frattini, cosocleC2×C4C26
commutator, socleC22C25×C4
prime radical#62815C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60219C2semidirect
3. #60216C2semidirect
4. #60209C2semidirect
5. #60207C2semidirect
6. #60206C2semidirect
7. #60205C2semidirect
8. #60192C2semidirect
9. C2×#2961C2semidirect
10. #60144C2semidirect
11. #60142C2semidirect
12. #60140C2semidirect
13. C2×#2932C2semidirect
14. #60126C2semidirect
15. #60125C2semidirect
16. #60058C2semidirect
17. C2×#2875C2semidirect
39. #2970C22semidirect
40. #2969C22semidirect
41. #2968C22semidirect
42. #2968C22semidirect
43. #2967C22semidirect
44. #2967C22semidirect
45. #2966C22semidirect
46. #2965C22semidirect
47. Q8×M16C22semidirect
48. #2962C22semidirect
49. #2961C22semidirect
50. #2961C22semidirect
51. #2961C22semidirect
52. #2961C22semidirect
53. #2961C22semidirect
54. #2961C22semidirect
55. #2960C22semidirect
56. C2×#446C22semidirect
57. #2935C22semidirect
58. #2935C22semidirect
59. D4×M16C22semidirect
66. #2932C22semidirect
67. #2932C22semidirect
69. #2931C22semidirect
71. #2930C22semidirect
72. #2930C22semidirect
74. #2929C22semidirect
75. #2929C22semidirect
76. C2×#435C22semidirect
78. #2925C22semidirect
79. #2925C22semidirect
80. #2924C22semidirect
81. #2923C22semidirect
82. #2922C22semidirect
83. #2921C22semidirect
84. #2920C22semidirect
93. #2875C22semidirect
94. #2875C22semidirect
95. #2875C22semidirect
96. C4×#131C22semidirect
97. C4×#131C22semidirect
100. #2873C22semidirect
104. C2×#405C22semidirect
105. C2×#405C22semidirect
106. C2×#405C22semidirect
108. C2×C4×M16C22semidirect
110. C22×#97C22semidirect
362. C2×M16#41semidirect
380. C22×C8#41semidirect

Maximal subgroups

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

subgroupindex
#628152
#602192
#602162
#602092
#602072
#602062
#602052
#601922
C2×#29612
#601442
#601422
#601402
C2×#29322
#601262
#601252
#600582
C2×#28752