Finite Group Databasebeta

← #6997905

Subgroups — #6997905

Order 512.

2004 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59124C211yesmaximal, characteristic
2#39639C211yesmaximal, characteristic, complemented
3#32600C212yesmaximal, complemented
4#32164C212yesmaximal, complemented
5#31574C212yesmaximal, complemented
6#30736C212yesmaximal, complemented
7#28571C211yesmaximal, characteristic, complemented
8#28332C212yesmaximal, complemented
9#27747C212yesmaximal, complemented
10#27064C212yesmaximal, complemented
11#26250C212yesmaximal, complemented
12#25717C211yesmaximal, characteristic, complemented
13#25080C212yesmaximal, complemented
14#24530C212yesmaximal, complemented
15#24188C212yesmaximal, complemented
16C2×#2041C211yesmaximal, characteristic, complemented
17#23237C211yesmaximal, characteristic, complemented
18#22874C212yesmaximal, complemented
19#22076C211yesmaximal, characteristic, complemented
20C2×#550C2211yescharacteristic
21C2×#546—21no—
22C22×#127C2211yescharacteristic
23C2×#492C2212yes—
24C2×#481C2211yescharacteristic
25C2×#465C2212yes—
26C2×#460C2212yescomplemented
27C2×#450C2212yes—
28C2×#450C2212yes—
29C2×C4×SD16C2212yescomplemented
30C22×#102C2212yes—
31C22×#102C2212yes—
32#2857C2211yescharacteristic
33#2809—21no—
34#2802—22no—
35#2726—21no—
36#2673—22no—
37#2646—21no—
38#2582C2212yescomplemented
39#2552C2212yescomplemented
40#2548C2211yescharacteristic
41#2541C2212yes—
42#2541C2211yescharacteristic
43#2511C2212yescomplemented
44#2502C2212yes—
45#2473—22no—
46#2446C2212yescomplemented
47#2445C2212yes—
48#2433C2212yes—
49#2431—21no—
50#2428—21no—
51#2410—22no—
52#2408—21no—
53#2366C2211yescharacteristic
54#2360C2212yes—
55D4×C22⋊C4C2212yes—
56#2329—21no—
57C4×C22⋊Q8C2211yescharacteristic
58C4×#121C2211yescharacteristic
59C2×#389C2211yescharacteristic
60#2094C2212yescomplemented
61#2094C2212yescomplemented
62#2084C2211yescharacteristic, complemented
63#2071C2212yescomplemented
64#2071C2212yescomplemented
65#2071C2211yescharacteristic, complemented
66#2065C2212yescomplemented
67#2055C2212yescomplemented
68#2055C2212yescomplemented
69#2055C2212yescomplemented
70#2043C2211yescharacteristic, complemented
71#2041C2212yes—
72#2041C2212yes—
73#2041C2212yes—
74#2041C2212yes—
75#2041C2212yescomplemented
76#2014C2212yes—
77#2014C2212yes—
78#2014C2212yescomplemented
79#2014C2212yescomplemented
80#2014C2212yescomplemented
81#2013C2211yescharacteristic, complemented
82#1984C2212yescomplemented
83#1982C2212yescomplemented
84#1968C2212yescomplemented
85#1968C2212yescomplemented
86#1968C2212yescomplemented
87#1957C2212yes—
88#1957C2212yescomplemented
89#1957C2212yescomplemented
90#1941C2212yescomplemented
91#1934C2212yescomplemented
92#1934C2212yescomplemented
93#1927C2212yescomplemented
94#1926C2212yescomplemented
95#1926C2212yescomplemented
96#1920C2212yescomplemented
97#1916C2212yescomplemented
98#1916C2212yescomplemented
99#1892C2212yes—
100#1880C2212yescomplemented
101#1880C2212yescomplemented
102#1877C2212yescomplemented
103#1877C2212yescomplemented
104#1877C2212yescomplemented
105#1877C2212yescomplemented
106#1874C2211yescharacteristic
107#1864C2212yescomplemented
108#1864C2212yescomplemented
109#1853C2211yescharacteristic
110#1850C2212yes—
111#1824C2211yescharacteristic
112#1802C2212yescomplemented
113#1802C2212yescomplemented
114C8×C4⋊C4C2212yescomplemented
115C4×#102C2212yescomplemented
116C8×C22⋊C4C2212yes—
117C4×C22⋊C8C2211yescharacteristic
118C2×#336C2211yescharacteristic
119C22×#41—21no—
120C23×D4—21no—
121C23×D4—21no—
122C23×D4C2312yes—
123C22×SD16C2312yes—
124C22×SD16C2312yes—
125C22×SD16C2312yes—
126C22×SD16C2312yes—
127C22×SD16C2312yes—
128C23×C8C2312yes—
129#550—44no—
130#546—48no—
131C2×C4⋊Q8C2311yescharacteristic
132C2×#127—21no—
133C2×#127—21no—
134C2×#127—44no—
135C2×#127C2311yescharacteristic
136C2×#127C2312yes—
137C2×#127C2312yes—
138C2×#127C2311yescharacteristic
139C2×#127C2312yes—
140C2×#125—22no—
141C2×#124—21no—
142C2×#123—22no—
143C2×C22⋊Q8D411yescharacteristic
144C2×C22⋊Q8C2312yes—
145C2×#121—21no—
146C2×#121—22no—
147C2×#121—22no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—22no—
151C2×#121C2311yescharacteristic
152C2×#120—22no—
153C2×#120—22no—
154C2×C4×Q8C2312yes—
155C2×C4×Q8C2311yescharacteristic
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×C4×D4C2311yescharacteristic
161C22×C4⋊C4—21no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4—22no—
165C22×C42C2311yescharacteristic
166#492—44no—
167#481—24no—
168#465—44no—
169#460—44no—
170#450—28no—
171#450—44no—
172C4×SD16—44no—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#102—44no—
182C2×#102—44no—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×C22⋊C8C2311yescharacteristic
199C2×C22⋊C8C2311yescharacteristic
200C2×C4×C8C2312yes—
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203#400—22no—
204#400—22no—
205#400—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#398—22no—
210#398—22no—
211#398—22no—
212#398—22no—
213#394—22no—
214#394—22no—
215#394—22no—
216#392—22no—
217#392—22no—
218#392—22no—
219#392—22no—
220#392—22no—
221#391—22no—
222#391D411yescharacteristic
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#390—21no—
228#390—21no—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#390C2312yes—
233#390C2311yescharacteristic
234#389—22no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389D411yescharacteristic
242#389C2312yes—
243#389C2312yes—
244#389C2311yescharacteristic
245#389C2312yes—
246#388—21no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387D412yes—
253#386—21no—
254#386—22no—
255#386—22no—
256#386—22no—
257#386—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385D412yes—
262#384C2312yes—
263#384C2312yes—
264#384C2311yescharacteristic
265#380—21no—
266#380—21no—
267#380D411yescharacteristic
268#380C2311yescharacteristic
269#379—22no—
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2311yescharacteristic
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C22⋊C4—22no—
275C4×C22⋊C4—21no—
276C4×C22⋊C4C2312yes—
277C2×#95—21no—
278#340C2312yes—
279#340C2312yes—
280#340C2312yes—
281#340C2312yes—
282#340C2312yes—
283#340C2312yes—
284#336C2312yes—
285#336C2312yes—
286#336C2311yescharacteristic
287#336C2311yescharacteristic
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C25—22no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C22×Q8C2×D411yescharacteristic
297C22×Q8C2412yes—
298C22×D4—24no—
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—44no—
317C22×D4—44no—
318C22×D4—44no—
319C22×D4—82no—
320C22×D4—82no—
321C22×D4—82no—
322C22×D4C2411yescharacteristic
323C22×D4C2412yes—
324C22×D4C2412yes—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—24no—
334C2×SD16—24no—
335C2×SD16—24no—
336C2×SD16—24no—
337C2×SD16—42no—
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16—42no—
341C2×SD16—42no—
342C2×SD16—42no—
343C2×SD16—42no—
344C2×SD16—42no—
345C2×SD16—42no—
346C2×SD16—42no—
347C2×SD16—42no—
348C22×C8—24no—
349C22×C8—42no—
350C22×C8—42no—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2412yes—
354C22×C8C2412yes—
355C4⋊Q8—42no—
356#127—24no—
357#127—24no—
358#127—24no—
359#127—42no—
360#127—42no—
361#127—42no—
362#127—42no—
363#127—42no—
364#127—44no—
365#127—44no—
366#125—84no—
367#124—44no—
368#123—48no—
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371C22⋊Q8SD1618yescomplemented
372#121—22no—
373#121—22no—
374#121—44no—
375#121—48no—
376#121—44no—
377#121—48no—
378#121—84no—
379#121—82no—
380#120—48no—
381#120—84no—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—42no—
385C4×D4—24no—
386C4×D4—42no—
387C4×D4—42no—
388C4×D4—42no—
389C4×D4—42no—
390C4×D4—44no—
391C4×D4—44no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—82no—
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2411yescharacteristic
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—48no—
441C2×C22⋊C4C2×D412yes—
442C2×C22⋊C4C2×D412yes—
443C2×C42—21no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—42no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2412yes—
450C2×C42C2411yescharacteristic
451C2×C42C2412yes—
452C2×C42C2411yescharacteristic
453#106—24no—
454#106—42no—
455#106—42no—
456C4⋊C8—42no—
457C4⋊C8—42no—
458#103—42no—
459#103—42no—
460#103—42no—
461#102—24no—
462#102—24no—
463#102—24no—
464#102—24no—
465#102—24no—
466#102—42no—
467#102—42no—
468#102—42no—
469#102—42no—
470#102—42no—
471#102—42no—
472#102—42no—
473#102—42no—
474#102—42no—
475#102—42no—
476C22⋊C8—22no—
477C22⋊C8#4114yescomplemented
478C4×C8—42no—
479C4×C8—42no—
480C4×C8—42no—
481#95—22no—
482#95—22no—
483#95—21no—
484#95—21no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—21no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95C2×D412yes—
497#95C2×D412yes—
498#95C2×D412yes—
499#95C2×D412yes—
500#95C2×D412yes—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—82no—
509C24—82no—
510C24—82no—
511C24C22×D411yescharacteristic
512#41—816no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—41no—
520C2×Q8—41no—
521C2×Q8C2×SD1614yes—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—22no—
525C2×D4—21no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—48no—
540C2×D4—48no—
541C2×D4—42no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—44no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—42no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—84no—
561C2×D4—84no—
562C2×D4—82no—
563C2×D4—82no—
564C2×D4—82no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—82no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4—82no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—816no—
578C2×D4—816no—
579C2×D4H(5,𝔽2)14yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×SD1614yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4C2511yescharacteristic
622SD16—48no—
623SD16—84no—
624SD16—84no—
625SD16—84no—
626SD16—84no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—84no—
639C2×C8C2×#4114yes—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—41no—
652C4⋊C4—42no—
653C4⋊C4—41no—
654C4⋊C4—42no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4—82no—
661C4⋊C4—82no—
662C4⋊C4—81no—
663C4⋊C4—82no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—81no—
669C4⋊C4—81no—
670C4⋊C4C2×SD1614yes—
671C4⋊C4C2×SD1618yes—
672C22⋊C4—24no—
673C22⋊C4—44no—
674C22⋊C4—42no—
675C22⋊C4—44no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—82no—
685C22⋊C4—82no—
686C22⋊C4—82no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4C2×SD1618yes—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—41no—
697C42—41no—
698C42—42no—
699C42—82no—
700C42—82no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—24no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—88no—
727C23—88no—
728C23—88no—
729C23—88no—
730C23—164no—
731C23—164no—
732C23—164no—
733C23#55012yes—
734C23C22×SD1612yes—
735C23#57712yes—
736C23C23×D411yescharacteristic
737Q8—44no—
738Q8—42no—
739Q8—42no—
740Q8—42no—
741Q8—42no—
742D4—24no—
743D4—24no—
744D4—48no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—88no—
754D4—88no—
755D4—88no—
756D4—88no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—164no—
762D4—164no—
763D4—164no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—164no—
814C2×C4—162no—
815C2×C4#55012yes—
816C2×C4C22×SD1612yes—
817C2×C4C22×SD1614yes—
818C2×C4C22×SD1614yes—
819C2×C4C22×SD1612yes—
820C2×C4#57612yes—
821C2×C4C22×#4111yescharacteristic
822C2×C4C2×H(5,𝔽2)12yes—
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4#58512yes—
825C8—24no—
826C8—42no—
827C8—42no—
828C8—42no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—81no—
843C22—82no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—82no—
849C22—81no—
850C22—81no—
851C22—82no—
852C22—81no—
853C22—82no—
854C22—82no—
855C22—81no—
856C22—1616no—
857C22#339214yes—
858C22C2×#55011yescharacteristic
859C22#348411yescharacteristic
860C22#350011yescharacteristic
861C22C23×SD1611yescharacteristic
862C22C2×#57611yescharacteristic
863C22C2×#57711yescharacteristic
864C22#358511yescharacteristic
865C4—24no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—41no—
873C4—42no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4#351312yes—
882C4#353412yes—
883C2—24no—
884C2—84no—
885C2—161no—
886C2—162no—
887C2#4300611yescharacteristic
888C2C2×#339211yescharacteristic
889C2#6141911yescharacteristic
890C2#6156011yescharacteristic
891C2#6162911yescharacteristic
892C2#6252511yescharacteristic
893C2#6259611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59124C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39639C2semidirect
3. #32600C2semidirect
4. #32164C2semidirect
5. #31574C2semidirect
6. #30736C2semidirect
7. #28571C2semidirect
8. #28332C2semidirect
9. #27747C2semidirect
10. #27064C2semidirect
11. #26250C2semidirect
12. #25717C2semidirect
13. #25080C2semidirect
14. #24530C2semidirect
15. #24188C2semidirect
16. C2×#2041C2semidirect
17. #23237C2semidirect
18. #22874C2semidirect
19. #22076C2semidirect
26. C2×#460C22semidirect
29. C2×C4×SD16C22semidirect
38. #2582C22semidirect
39. #2552C22semidirect
43. #2511C22semidirect
46. #2446C22semidirect
60. #2094C22semidirect
61. #2094C22semidirect
62. #2084C22semidirect
63. #2071C22semidirect
64. #2071C22semidirect
65. #2071C22semidirect
66. #2065C22semidirect
67. #2055C22semidirect
68. #2055C22semidirect
69. #2055C22semidirect
70. #2043C22semidirect
75. #2041C22semidirect
78. #2014C22semidirect
79. #2014C22semidirect
80. #2014C22semidirect
81. #2013C22semidirect
82. #1984C22semidirect
83. #1982C22semidirect
84. #1968C22semidirect
85. #1968C22semidirect
86. #1968C22semidirect
88. #1957C22semidirect
89. #1957C22semidirect
90. #1941C22semidirect
91. #1934C22semidirect
92. #1934C22semidirect
93. #1927C22semidirect
94. #1926C22semidirect
95. #1926C22semidirect
96. #1920C22semidirect
97. #1916C22semidirect
98. #1916C22semidirect
100. #1880C22semidirect
101. #1880C22semidirect
102. #1877C22semidirect
103. #1877C22semidirect
104. #1877C22semidirect
105. #1877C22semidirect
107. #1864C22semidirect
108. #1864C22semidirect
112. #1802C22semidirect
113. #1802C22semidirect
114. C8×C4⋊C4C22semidirect
115. C4×#102C22semidirect
371. C22⋊Q8SD16semidirect
477. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#591242
#396392
#326002
#321642
#315742
#307362
#285712
#283322
#277472
#270642
#262502
#257172
#250802
#245302
#241882
C2×#20412
#232372
#228742
#220762