Finite Group Databasebeta

← #6459421

Subgroups — #6459421

Order 512.

2806 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3095C211yesmaximal, characteristic, complemented
2C22×#452C211yesmaximal, characteristic
3#34203C211yesmaximal, characteristic, complemented
4#34044C211yesmaximal, characteristic
5#28133C214yesmaximal, complemented
6#28131C214yesmaximal, complemented
7#28125C214yesmaximal, complemented
8#28122C214yesmaximal, complemented
9#23615C211yesmaximal, characteristic, complemented
10#23614C211yesmaximal, characteristic, complemented
11#23542C211yesmaximal, characteristic, complemented
12#23541C211yesmaximal, characteristic, complemented
13#21064C211yesmaximal, characteristic, complemented
14#21063C211yesmaximal, characteristic, complemented
15#20936C211yesmaximal, characteristic, complemented
16#20935C211yesmaximal, characteristic, complemented
17#20699C211yesmaximal, characteristic, complemented
18#20628C211yesmaximal, characteristic, complemented
19#20600C211yesmaximal, characteristic
20C23×#41C2211yescharacteristic
21C23×Q16C2211yescharacteristic
22C23×SD16C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C2×#519C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#3095—28no—
28C2×#484C2212yescomplemented
29C2×#485C2212yescomplemented
30C2×#485C2212yescomplemented
31C2×#483C2212yescomplemented
32C2×#452—28no—
33C2×#452C2214yes—
34C2×#452C2214yes—
35C2×#428C2211yescharacteristic
36C2×#428C2211yescharacteristic
37C2×#424C2211yescharacteristic
38C2×#424C2211yescharacteristic
39C2×#419C2211yescharacteristic
40C2×#419C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C2×#419C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C2×#407C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49#2362—22no—
50#2360—22no—
51#2344—22no—
52#2342—22no—
53#2323C2214yescomplemented
54#2316C2211yescharacteristic
55#2311—22no—
56#2311C2212yes—
57#2311C2212yes—
58#2310C2211yescharacteristic
59#2310C2211yescharacteristic
60#2310C2211yescharacteristic
61#2309C2211yescharacteristic
62#2309C2211yescharacteristic
63#2308—22no—
64C4×C22⋊Q8C2214yescomplemented
65#2297—22no—
66#2297C2212yes—
67#2297C2212yes—
68#2280—22no—
69#2280C2211yescharacteristic
70#2274C2211yescharacteristic
71#2068C2214yescomplemented
72#2067C2214yescomplemented
73#2066C2214yescomplemented
74#2065C2214yescomplemented
75#2056C2214yescomplemented
76#2056C2214yescomplemented
77#2055C2214yescomplemented
78#2055C2214yescomplemented
79#1928C2214yescomplemented
80#1927C2214yescomplemented
81#1926C2214yescomplemented
82#1925C2214yescomplemented
83#1880C2214yescomplemented
84#1880C2214yescomplemented
85#1878C2214yescomplemented
86#1878C2214yescomplemented
87#1825C2212yescomplemented
88#1825C2212yescomplemented
89#1824C2212yescomplemented
90#1823C2212yescomplemented
91#1798C2214yescomplemented
92#1797C2214yescomplemented
93#1788C2214yes—
94#1788C2214yes—
95#1735C2211yescharacteristic
96#1735C2211yescharacteristic
97#1735C2211yescharacteristic
98#1735C2211yescharacteristic
99#1729C2211yescharacteristic
100#1729C2211yescharacteristic
101C22×#41—24no—
102C22×#41—24no—
103C22×#41—21no—
104C22×#41—21no—
105C22×#41—24no—
106C22×#41—24no—
107C22×#41—42no—
108C22×#41—42no—
109C22×#41C2312yes—
110C22×#41C2312yes—
111C23×Q8C2311yescharacteristic
112C23×Q8C2311yescharacteristic
113C23×D4—21no—
114C23×D4C2311yescharacteristic
115C24×C4—21no—
116C24×C4C2311yescharacteristic
117C22×Q16—24no—
118C22×Q16—24no—
119C22×Q16—42no—
120C22×Q16C2314yes—
121C22×SD16—24no—
122C22×SD16—24no—
123C22×SD16—42no—
124C22×SD16C2314yes—
125C22×M16C2311yescharacteristic
126C22×M16C2311yescharacteristic
127C23×C8C2311yescharacteristic
128C23×C8C2311yescharacteristic
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8D418yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135#519—42no—
136#519—42no—
137C2×C4×Q8—22no—
138C2×C4×Q8C2314yes—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117—22no—
142C2×#117—24no—
143C2×#117—24no—
144C2×#117—42no—
145C2×#117—42no—
146C2×#117D412yes—
147C2×#117D412yes—
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C2×#117C2311yescharacteristic
152C2×#117C2311yescharacteristic
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2312yes—
157C22×C4⋊C4—21no—
158C22×C4⋊C4D412yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4D412yes—
165C22×C42—21no—
166C22×C42C2312yes—
167#485—28no—
168#485—28no—
169#484—28no—
170#483—28no—
171#452—216no—
172#452—216no—
173#428—24no—
174#428—24no—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179#424—42no—
180#424—42no—
181C2×C4⋊C8C2314yes—
182C2×C4⋊C8C2314yes—
183#419—24no—
184#419—24no—
185#419—24no—
186#419—42no—
187#418—24no—
188#418—42no—
189C2×#103—24no—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#102—24no—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×#102C2314yes—
201#407—24no—
202C2×C22⋊C8—24no—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2312yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207#391—22no—
208#391—22no—
209#391—22no—
210#391C2314yes—
211#391C2312yes—
212#391C2312yes—
213#391C2312yes—
214#391C2312yes—
215#390—22no—
216#390—22no—
217#390C2312yes—
218#390C2312yes—
219#390C2312yes—
220#390C2312yes—
221#389—22no—
222#389—24no—
223#389C2314yes—
224#388—24no—
225#388—24no—
226#387—24no—
227#387—24no—
228#386—24no—
229#386—24no—
230#386—24no—
231#386—24no—
232#385—24no—
233#381—21no—
234#381—22no—
235#381—22no—
236#381—22no—
237#380—24no—
238#380—24no—
239#380—22no—
240#380C2312yes—
241#380C2312yes—
242#379—21no—
243#379—22no—
244#379—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—24no—
247C4×C4⋊C4C2314yes—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—24no—
253C4×C22⋊C4—24no—
254#340C2312yes—
255#340C2312yes—
256#340C2312yes—
257#340C2312yes—
258#340C2312yes—
259#340C2312yes—
260#340C2312yes—
261#340C2312yes—
262#336C2314yes—
263#336C2314yes—
264C25—21no—
265C25C2×D411yescharacteristic
266C2×#41—28no—
267C2×#41—28no—
268C2×#41—24no—
269C2×#41—24no—
270C2×#41—24no—
271C2×#41—24no—
272C2×#41—24no—
273C2×#41—24no—
274C2×#41—24no—
275C2×#41—24no—
276C2×#41—42no—
277C2×#41—42no—
278C2×#41—42no—
279C2×#41—42no—
280C2×#41—416no—
281C2×#41—416no—
282C2×#41—416no—
283C2×#41—416no—
284C2×#41—44no—
285C2×#41—44no—
286C2×#41—44no—
287C2×#41—44no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8C2×D414yes—
301C22×Q8#4114yes—
302C22×Q8C2412yes—
303C22×Q8C2412yes—
304C22×D4—28no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—44no—
314C22×D4—44no—
315C22×D4#4114yes—
316C22×D4C2412yes—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—28no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—44no—
330C23×C4—44no—
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D411yescharacteristic
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D414yes—
335C23×C4C2×D414yes—
336C23×C4#4114yes—
337C23×C4C2411yescharacteristic
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C2×Q16—28no—
341C2×Q16—28no—
342C2×Q16—44no—
343C2×Q16—416no—
344C2×SD16—28no—
345C2×SD16—28no—
346C2×SD16—44no—
347C2×SD16—416no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C22⋊Q8—28no—
365C22⋊Q8—28no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8C2×D418yes—
369C22⋊Q8C2×D418yes—
370C4×Q8—44no—
371C4×Q8—44no—
372C4×Q8—48no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—22no—
384#117—22no—
385#117—22no—
386#117—22no—
387#117—22no—
388#117—22no—
389#117—42no—
390#117—42no—
391#117—44no—
392#117—48no—
393#117—44no—
394#117—44no—
395#117—44no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
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—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C2×D412yes—
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2×D414yes—
413C2×C4⋊C4C2×D414yes—
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D414yes—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—24no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—24no—
449C2×C42—42no—
450C2×C42—42no—
451C2×C42—44no—
452C2×C42C2×D414yes—
453C2×C42C2412yes—
454C2×C42C2412yes—
455#107—24no—
456#107—24no—
457#106—24no—
458#106—24no—
459C4⋊C8—44no—
460C4⋊C8—44no—
461#103—24no—
462#103—24no—
463#103—24no—
464#103—24no—
465#103—28no—
466#103—28no—
467#103—44no—
468#102—28no—
469#102—28no—
470#102—44no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475#95—22no—
476#95—24no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—24no—
482#95—22no—
483#95—24no—
484#95—24no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—24no—
489C24—42no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24—82no—
494C24—82no—
495C24#12114yes—
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499#41—48no—
500#41—48no—
501#41—48no—
502#41—48no—
503#41—48no—
504#41—48no—
505#41—48no—
506#41—48no—
507#41—432no—
508#41—432no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—28no—
514C2×Q8—28no—
515C2×Q8—28no—
516C2×Q8—28no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8C22×D414yes—
534C2×Q8C2×#4114yes—
535C2×D4—28no—
536C2×D4—28no—
537C2×D4—24no—
538C2×D4—28no—
539C2×D4—28no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—432no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4C2×#4114yes—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—432no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4#12114yes—
605C22×C4#12114yes—
606C22×C4#12114yes—
607C22×C4C22×D414yes—
608C22×C4C22×D414yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C4C2511yescharacteristic
623Q16—416no—
624SD16—416no—
625M16—44no—
626M16—44no—
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—22no—
639C2×C8—44no—
640C2×C8—44no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—44no—
660C4⋊C4—48no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—84no—
664C4⋊C4C22×D414yes—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—84no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C22⋊C4—84no—
681C22⋊C4—82no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—44no—
687C42—48no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42—42no—
694C42—84no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—28no—
706C23—24no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—48no—
714C23—84no—
715C23—84no—
716C23—88no—
717C23—84no—
718C23—84no—
719C23—88no—
720C23C2×#12112yes—
721C23C2×#12112yes—
722C23C2×#12112yes—
723C23#52512yes—
724C23#53412yes—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—24no—
729Q8—24no—
730Q8—42no—
731Q8—42no—
732Q8—42no—
733Q8—42no—
734Q8—48no—
735Q8—48no—
736D4—24no—
737D4—24no—
738D4—416no—
739D4—416no—
740D4—42no—
741D4—42no—
742D4—48no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—416no—
768C2×C4—416no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—84no—
791C2×C4—88no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4C2×#12112yes—
795C2×C4C2×#12112yes—
796C2×C4C2×#12112yes—
797C2×C4#52512yes—
798C2×C4#53412yes—
799C2×C4#54614yes—
800C2×C4#54614yes—
801C2×C4#55114yes—
802C2×C4#55114yes—
803C2×C4C23×D411yescharacteristic
804C2×C4C22×#4111yescharacteristic
805C2×C4C22×#4111yescharacteristic
806C2×C4C22×#4111yescharacteristic
807C2×C4C2×H(5,𝔽2)11yescharacteristic
808C2×C4C2×H(5,𝔽2)11yescharacteristic
809C8—42no—
810C8—42no—
811C8—42no—
812C8—42no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—24no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—48no—
829C22—88no—
830C22—816no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22#253414yes—
835C22C22×#12111yescharacteristic
836C22C2×#52511yescharacteristic
837C22C2×#53411yescharacteristic
838C22#358412yes—
839C22#358612yes—
840C4—22no—
841C4—22no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—81no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—82no—
852C4—82no—
853C4#253414yes—
854C4C2×#54611yescharacteristic
855C4C2×#54611yescharacteristic
856C4C2×#55111yescharacteristic
857C4C2×#55111yescharacteristic
858C2—24no—
859C2—42no—
860C2—42no—
861C2—84no—
862C2C2×#253411yescharacteristic
863C2#6042211yescharacteristic
864C2#6042411yescharacteristic
865C2#6058112yes—
866C2#6076112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3095C2semidirect
3. #34203C2semidirect
5. #28133C2semidirect
6. #28131C2semidirect
7. #28125C2semidirect
8. #28122C2semidirect
9. #23615C2semidirect
10. #23614C2semidirect
11. #23542C2semidirect
12. #23541C2semidirect
13. #21064C2semidirect
14. #21063C2semidirect
15. #20936C2semidirect
16. #20935C2semidirect
17. #20699C2semidirect
18. #20628C2semidirect
28. C2×#484C22semidirect
29. C2×#485C22semidirect
30. C2×#485C22semidirect
31. C2×#483C22semidirect
53. #2323C22semidirect
64. C4×C22⋊Q8C22semidirect
71. #2068C22semidirect
72. #2067C22semidirect
73. #2066C22semidirect
74. #2065C22semidirect
75. #2056C22semidirect
76. #2056C22semidirect
77. #2055C22semidirect
78. #2055C22semidirect
79. #1928C22semidirect
80. #1927C22semidirect
81. #1926C22semidirect
82. #1925C22semidirect
83. #1880C22semidirect
84. #1880C22semidirect
85. #1878C22semidirect
86. #1878C22semidirect
87. #1825C22semidirect
88. #1825C22semidirect
89. #1824C22semidirect
90. #1823C22semidirect
91. #1798C22semidirect
92. #1797C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30952
C22×#4522
#342032
#340442
#281332
#281312
#281252
#281222
#236152
#236142
#235422
#235412
#210642
#210632
#209362
#209352
#206992
#206282
#206002