Finite Group Databasebeta

← #6445575

Subgroups — #6445575

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3080C211yesmaximal, characteristic
2C2×C4×#137C211yesmaximal, characteristic
3C2×#2565C211yesmaximal, characteristic, complemented
4C4⋊C4×#41C211yesmaximal, characteristic
5#24826C214yesmaximal, complemented
6#24825C214yesmaximal, complemented
7#24822C214yesmaximal, complemented
8#24821C214yesmaximal, complemented
9#23659C211yesmaximal, characteristic, complemented
10#23658C211yesmaximal, characteristic, complemented
11#23619C211yesmaximal, characteristic, complemented
12#23619C211yesmaximal, characteristic, complemented
13#21325C211yesmaximal, characteristic, complemented
14#21146C211yesmaximal, characteristic, complemented
15#20927C211yesmaximal, characteristic
16#20927C211yesmaximal, characteristic
17#20649C211yesmaximal, characteristic
18#20648C211yesmaximal, characteristic
19#20647C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23C2×C4×#41C2211yescharacteristic
24C2×C4×#41C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26#3080—28no—
27C2×#479C2212yes—
28C2×#479C2212yes—
29C2×#478C2212yes—
30C2×#478C2212yes—
31C4×#137—28no—
32C2×#441C2212yes—
33C2×#440C2212yes—
34C2×C4×Q16C2212yes—
35C2×C4×SD16C2212yes—
36C2×#428C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#423C2211yescharacteristic
40C2×#423C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#419C2211yescharacteristic
48C2×C4×M16C2211yescharacteristic
49#2565—21no—
50#2565—21no—
51#2565—21no—
52#2565—21no—
53#2565C2214yes—
54#2565C2214yes—
55C2×#398—22no—
56#2351C2212yes—
57Q8×C4⋊C4C2212yes—
58#2349—22no—
59#2349C2212yes—
60D4×C4⋊C4—22no—
61D4×C4⋊C4C2212yes—
62#2296—21no—
63#2296—21no—
64#2296C2211yescharacteristic
65#2296C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#391C2211yescharacteristic
68C2×#387—22no—
69#2285—21no—
70#2285C2211yescharacteristic
71C2×#384C2211yescharacteristic
72C2×#382C2211yescharacteristic
73C2×C4×C4⋊C4—21no—
74C2×C4×C4⋊C4C2211yescharacteristic
75#2085C2214yes—
76#2085C2214yes—
77#2084C2214yes—
78#2083C2214yes—
79#2068C2214yes—
80#2068C2214yes—
81#2066C2214yes—
82#2066C2214yes—
83#1992C2214yes—
84#1991C2214yes—
85#1940C2214yes—
86#1939C2214yes—
87#1878C2214yes—
88#1878C2214yes—
89#1877C2214yes—
90#1877C2214yes—
91#1805C2214yes—
92#1805C2214yes—
93#1804C2214yes—
94#1803C2214yes—
95#1803C2214yes—
96#1802C2214yes—
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1736C2211yescharacteristic
102#1736C2211yescharacteristic
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C2×#137—24no—
108C2×#137—24no—
109C2×#137Q818yes—
110C22×Q16C2312yes—
111C22×SD16C2312yes—
112C22×M16C2311yescharacteristic
113C22×M16C2311yescharacteristic
114C22×M16C2311yescharacteristic
115C22×M16C2311yescharacteristic
116C2×#125—21no—
117C2×#125—21no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#125C2312yes—
121C2×#125C2312yes—
122C4×#41—24no—
123C4×#41—24no—
124C4×#41—24no—
125C4×#41—42no—
126C4×#41—42no—
127C4×#41D418yes—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×Q8C2312yes—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2311yescharacteristic
137C2×C4×Q8C2311yescharacteristic
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—22no—
141C2×C4×D4—22no—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2311yescharacteristic
145C2×C4×D4C2311yescharacteristic
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C2×#117C2311yescharacteristic
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—22no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—22no—
157C22×C4⋊C4D412yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C42—21no—
162C22×C42—21no—
163C22×C42—21no—
164C22×C42—21no—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#479—28no—
169#479—28no—
170#478—28no—
171#478—28no—
172#441—28no—
173#440—28no—
174C4×Q16—28no—
175C4×SD16—28no—
176#428—24no—
177#428—24no—
178#428—24no—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#106C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185#423—24no—
186#423—42no—
187#423—42no—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2314yes—
191C2×C4⋊C8C2314yes—
192#419—24no—
193#419—42no—
194#419—42no—
195#417—24no—
196#417—24no—
197#417—24no—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2314yes—
204C2×#103C2314yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C4×M16—24no—
209C2×#97C2312yes—
210C2×C4×C8C2312yes—
211#398—24no—
212#398—24no—
213#398—24no—
214#398—24no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391C2314yes—
220#391C2314yes—
221#389—22no—
222#389—22no—
223#389—22no—
224#389—22no—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#387—24no—
230#387—24no—
231#387—24no—
232#387—24no—
233#385—22no—
234#385—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#385—22no—
239#384—22no—
240#384—21no—
241#384—21no—
242#384C2314yes—
243#384C2312yes—
244#382—21no—
245#382—21no—
246#382—22no—
247#382C2314yes—
248#382C2312yes—
249#380—21no—
250#380—21no—
251#380—22no—
252#380—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4D411yescharacteristic
264C4×C4⋊C4D411yescharacteristic
265C4×C4⋊C4C2312yes—
266C4×C4⋊C4C2312yes—
267C2×#95—22no—
268C2×#95—22no—
269C2×#95—22no—
270C2×#95—22no—
271C2×#95D412yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2314yes—
279#336C2314yes—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41C2×D414yes—
284C2×#41C2×Q814yes—
285C2×#41#4114yes—
286C22×Q8—21no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8C2×Q814yes—
293C22×Q8C2412yes—
294C22×Q8C2411yescharacteristic
295C22×D4—21no—
296C22×D4C2411yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311#137—232no—
312C2×Q16—24no—
313C2×Q16—24no—
314C2×Q16C2×Q818yes—
315C2×SD16—24no—
316C2×SD16—24no—
317C2×SD16C2×Q818yes—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16C2×Q814yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334#125—24no—
335#125—24no—
336#125—24no—
337#125—24no—
338#125—44no—
339#125—44no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—24no—
343C4×Q8—24no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×Q8C2×D414yes—
353C4×Q8C2×D414yes—
354C4×D4—28no—
355C4×D4—28no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—42no—
361C4×D4—42no—
362C4×D4—48no—
363C4×D4—48no—
364C4×D4C2×D414yes—
365C4×D4C2×D414yes—
366#117—22no—
367#117—28no—
368#117—22no—
369#117—22no—
370#117—22no—
371#117—22no—
372#117—44no—
373#117—44no—
374#117C2×D414yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—48no—
404C2×C4⋊C4—48no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4C2×D412yes—
409C2×C4⋊C4C2×D412yes—
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—28no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—44no—
441C2×C42—44no—
442C2×C42—44no—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D414yes—
450C2×C42#4114yes—
451C2×C42C2412yes—
452C2×C42C2412yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—24no—
456#107—24no—
457#107—24no—
458#106—24no—
459#106—24no—
460#106—24no—
461C4⋊C8—24no—
462C4⋊C8—24no—
463C4⋊C8—44no—
464C4⋊C8—44no—
465#103—24no—
466#103—24no—
467#103—24no—
468#103—24no—
469#103—24no—
470#103—44no—
471#103—44no—
472#102—24no—
473#102—24no—
474#102—24no—
475#97—24no—
476C4×C8—24no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—24no—
481#95—24no—
482#95—24no—
483#95—24no—
484#95—24no—
485#95—24no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95C2×D412yes—
490#95C2×D412yes—
491#95C2×D412yes—
492#95C2×D412yes—
493C24—21no—
494C24C22×D411yescharacteristic
495#41—28no—
496#41—28no—
497#41—28no—
498#41C22⋊Q8116yes—
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—22no—
504C2×Q8—28no—
505C2×Q8—28no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—42no—
511C2×Q8—44no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8C22×D412yes—
515C2×Q8C22×Q814yes—
516C2×Q8C22×Q812yes—
517C2×Q8C2×#4112yes—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4C22×D412yes—
525C2×D4C22×Q812yes—
526C2×D4C2×#4112yes—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4#12114yes—
567C22×C4#12114yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D412yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D412yes—
578C22×C4C22×Q812yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C42−1+412yes—
583C22×C4C2511yescharacteristic
584Q16—216no—
585SD16—216no—
586M16—28no—
587M16—44no—
588M16—44no—
589M16—44no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8C22×Q814yes—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—48no—
636C4⋊C4—82no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4C22×D412yes—
640C4⋊C4C22×D412yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C42—24no—
649C42—24no—
650C42—24no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—42no—
664C42—42no—
665C42#12114yes—
666C42#12114yes—
667C42C22×D412yes—
668C42C22×D412yes—
669C42C2×#4112yes—
670C42C2×#4112yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23C2×#12112yes—
679C23#54612yes—
680C23D4×Q812yes—
681C23C23×D411yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—24no—
686Q8—24no—
687Q8—48no—
688Q8—42no—
689Q8—42no—
690Q8C2×C22⋊Q814yes—
691D4—216no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4C2×C22⋊Q814yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—216no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—84no—
740C2×C4—88no—
741C2×C4—84no—
742C2×C4—88no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4C2×#12112yes—
747C2×C4C2×#12112yes—
748C2×C4C2×#12112yes—
749C2×C4C2×#12112yes—
750C2×C4C2×#12112yes—
751C2×C4C2×C22⋊Q814yes—
752C2×C4#53714yes—
753C2×C4#54612yes—
754C2×C4D4×Q812yes—
755C2×C4#55214yes—
756C2×C4#55414yes—
757C2×C4#57514yes—
758C2×C4C23×D411yescharacteristic
759C2×C4C23×Q811yescharacteristic
760C2×C4C22×#4111yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4C2×2−1+411yescharacteristic
764C8—24no—
765C8—42no—
766C8—42no—
767C8—42no—
768C22—22no—
769C22—24no—
770C22—24no—
771C22—22no—
772C22—24no—
773C22—42no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22#241714yes—
778C22C22×#12111yescharacteristic
779C22C2×#54611yescharacteristic
780C22C2×D4×Q811yescharacteristic
781C22C2×#57512yes—
782C22#358612yes—
783C4—22no—
784C4—22no—
785C4—24no—
786C4—24no—
787C4—22no—
788C4—22no—
789C4—42no—
790C4—44no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#241714yes—
801C4C22×C22⋊Q811yescharacteristic
802C4C2×#53711yescharacteristic
803C4C2×#55211yescharacteristic
804C4C2×#55411yescharacteristic
805C2—24no—
806C2—44no—
807C2C2×#241711yescharacteristic
808C2#6041511yescharacteristic
809C2#6042711yescharacteristic
810C2#6116312yes—
811C2#6136912yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2565C2semidirect
5. #24826C2semidirect
6. #24825C2semidirect
7. #24822C2semidirect
8. #24821C2semidirect
9. #23659C2semidirect
10. #23658C2semidirect
11. #23619C2semidirect
12. #23619C2semidirect
13. #21325C2semidirect
14. #21146C2semidirect
19. #20647C2semidirect

Maximal subgroups

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

subgroupindex
C2×#30802
C2×C4×#1372
C2×#25652
C4⋊C4×#412
#248262
#248252
#248222
#248212
#236592
#236582
#236192
#213252
#211462
#209272
#206492
#206482
#206472