Finite Group Databasebeta

← #6491711

Subgroups — #6491711

Order 512.

2338 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3215C211yesmaximal, characteristic, complemented
2C22×#432C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4C2×#2850C211yesmaximal, characteristic
5#33184C212yesmaximal, complemented
6#33051C212yesmaximal, complemented
7#29854C212yesmaximal, complemented
8#29815C212yesmaximal, complemented
9#24755C214yesmaximal, complemented
10#24657C214yesmaximal, complemented
11#24508C212yesmaximal, complemented
12#24507C212yesmaximal, complemented
13#24380C212yesmaximal, complemented
14#24379C212yesmaximal
15#21986C211yesmaximal, characteristic, complemented
16#21866C211yesmaximal, characteristic, complemented
17#21808C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#3215—28no—
24C2×#497C2212yescomplemented
25C2×#489C2212yescomplemented
26C2×#467C2214yescomplemented
27C2×#465C2214yes—
28C2×#464C2214yescomplemented
29C2×#451C2212yes—
30C2×#450C2212yes—
31C2×#432—28no—
32C2×#432C2211yescharacteristic
33C2×#432C2212yes—
34C2×#432C2211yescharacteristic
35C2×#432C2212yescomplemented
36C2×#432C2212yescomplemented
37C22×C4⋊C8C2212yescomplemented
38C22×C22⋊C8C2212yes—
39C22×#97C2212yescomplemented
40#2857C2211yescharacteristic, complemented
41#2857C2211yescharacteristic, complemented
42#2857C2211yescharacteristic, complemented
43#2857C2211yescharacteristic, complemented
44#2855—21no—
45#2855C2212yes—
46#2851—21no—
47#2851—21no—
48#2850—21no—
49#2850—21no—
50#2850—21no—
51#2850—21no—
52#2850C2212yes—
53#2850C2212yes—
54#2850C2212yes—
55#2850C2212yes—
56#2848—21no—
57#2848C2212yes—
58C4×C22⋊Q8—21no—
59C4×C22⋊Q8—21no—
60C4×C22⋊Q8C2212yescomplemented
61C4×C22⋊Q8C2212yescomplemented
62#2296—21no—
63C2×#391C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#388—21no—
66C2×#388—21no—
67C2×#386—21no—
68C2×#386—21no—
69#2285C2211yescharacteristic
70C2×#382C2211yescharacteristic
71#2280—21no—
72#2067C2214yescomplemented
73#2066C2214yescomplemented
74#2056C2214yescomplemented
75#2055C2214yescomplemented
76#2036C2214yescomplemented
77#2034C2214yes—
78#2001C2214yescomplemented
79#2000C2214yes—
80#1993C2212yescomplemented
81#1983C2214yescomplemented
82#1973C2214yescomplemented
83#1971C2214yescomplemented
84#1960C2212yescomplemented
85#1959C2212yescomplemented
86#1959C2212yescomplemented
87#1949C2214yescomplemented
88#1936C2214yescomplemented
89#1935C2214yescomplemented
90#1893C2214yes—
91#1892C2214yescomplemented
92#1872C2212yes—
93#1872C2212yes—
94#1853C2212yes—
95#1852C2212yes—
96#1847C2212yescomplemented
97#1836C2212yescomplemented
98#1805C2214yescomplemented
99#1787C2212yes—
100#1786C2212yes—
101C23×Q8C2311yescharacteristic
102C23×D4—21no—
103C23×D4C2311yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4C2311yescharacteristic
107C22×Q16C2314yes—
108C22×SD16C2314yes—
109C23×C8C2314yes—
110#533—24no—
111#533—24no—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#125—21no—
115C2×#124—21no—
116C2×#124—21no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124C2312yes—
120C2×#124C2312yes—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—44no—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—44no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8C2312yes—
139C2×#117—21no—
140C2×#117—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#497—28no—
165#489—28no—
166#467—48no—
167#465—48no—
168#464—216no—
169#451—28no—
170#450—28no—
171#432—24no—
172#432—28no—
173#432—28no—
174#432—28no—
175#432D418yescomplemented
176C2×#107C2314yes—
177C2×#106C2314yes—
178C2×C4⋊C8—28no—
179C2×C4⋊C8C2314yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×C22⋊C8—28no—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2314yes—
193C2×C22⋊C8C2312yes—
194C2×#97—28no—
195C2×#97C2314yes—
196C2×#97C2312yes—
197C2×#97C2312yes—
198#391—21no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391C2312yes—
203#391C2312yes—
204#391C2312yes—
205#391C2312yes—
206#390—21no—
207#390—21no—
208#390C2312yes—
209#390C2312yes—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#385—22no—
242#385—22no—
243#385—22no—
244#384C2311yescharacteristic
245#384C2311yescharacteristic
246#382—21no—
247#382—21no—
248#382—21no—
249#382C2312yes—
250#382C2312yes—
251#381—22no—
252#380—21no—
253#380—21no—
254#380—21no—
255#380—21no—
256#380—21no—
257#380—21no—
258#380—21no—
259#380C2312yes—
260#380C2312yes—
261#380C2312yes—
262#379—22no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4C2312yes—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C2×#95—21no—
270C2×#95—21no—
271C2×#95—21no—
272C2×#95—21no—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277C25—21no—
278C25C2×D411yescharacteristic
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—42no—
284C22×Q8—42no—
285C22×Q8C2412yes—
286C22×Q8C2412yes—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—22no—
292C22×D4—42no—
293C22×D4—42no—
294C22×D4—44no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4C2412yes—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—24no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C2×Q16—28no—
330C2×Q16—44no—
331C2×Q16—44no—
332C2×SD16—28no—
333C2×SD16—44no—
334C2×SD16—44no—
335C22×C8—28no—
336C22×C8—28no—
337C22×C8—44no—
338C22×C8C2414yes—
339C22×C8C2414yes—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344#125—44no—
345#124—24no—
346#124—24no—
347#124—24no—
348#124—24no—
349#124—44no—
350#124—44no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—28no—
354C22⋊Q8—28no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8—44no—
358C22⋊Q8—44no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362#121—28no—
363#121—44no—
364#121—44no—
365#121—44no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—44no—
369#117—44no—
370#117—44no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D414yes—
451C2×C42#4114yes—
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—44no—
457#106—44no—
458C4⋊C8—28no—
459C4⋊C8—24no—
460C4⋊C8C2×D418yescomplemented
461#103—28no—
462#103—44no—
463#103—44no—
464#103—44no—
465#103—44no—
466#102—28no—
467#102—44no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—28no—
471C22⋊C8C2×D418yes—
472#97—28no—
473#97—24no—
474#97C2×D418yescomplemented
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—41no—
499C24—41no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24#13714yes—
508C24C22×D411yescharacteristic
509C24C22×D411yescharacteristic
510C24C22×D411yescharacteristic
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8—24no—
518C2×Q8—24no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—84no—
526C2×Q8—84no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—84no—
541C2×D4—84no—
542C2×D4—816no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
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—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—416no—
605C22×C4—416no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4#12114yes—
616C22×C4#12114yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C2×#4112yes—
630C22×C4H(5,𝔽2)14yes—
631C22×C4C2511yescharacteristic
632Q16—88no—
633SD16—88no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—416no—
640C2×C8C22×D418yes—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—44no—
697C42—44no—
698C42#12114yes—
699C42#12114yes—
700C42C22×D412yes—
701C42C22×D412yes—
702C42C2×#4112yes—
703C42C2×#4112yes—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—28no—
716C23—28no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23C2×#12112yes—
740C23#53512yes—
741C23C2×#13712yes—
742C23C2×#13712yes—
743C23C2×#13712yes—
744C23#57512yes—
745C23#57512yes—
746C23C23×D411yescharacteristic
747Q8—44no—
748Q8—44no—
749Q8—44no—
750Q8—44no—
751Q8—84no—
752Q8—84no—
753D4—44no—
754D4—44no—
755D4—84no—
756D4—88no—
757D4—88no—
758C2×C4—28no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—28no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4C2×#12112yes—
830C2×C4C2×#12112yes—
831C2×C4C2×#12112yes—
832C2×C4C2×#12112yes—
833C2×C4C2×#12112yes—
834C2×C4#53512yes—
835C2×C4#57512yes—
836C2×C4C23×D411yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×H(5,𝔽2)12yes—
839C2×C4#58512yes—
840C8—28no—
841C8—44no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—416no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—168no—
870C22#305614yes—
871C22#321514yescomplemented
872C22C22×#12111yescharacteristic
873C22C2×#53511yescharacteristic
874C22#344911yescharacteristic
875C22C22×#13711yescharacteristic
876C22C2×#57511yescharacteristic
877C22C2×#57511yescharacteristic
878C22C2×#57511yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4#348812yes—
898C4#349412yes—
899C2—24no—
900C2—24no—
901C2—42no—
902C2—162no—
903C2#3525211yescharacteristic
904C2C2×#305611yescharacteristic
905C2#6044411yescharacteristic
906C2C2×#321511yescharacteristic
907C2#6079011yescharacteristic
908C2#6095911yescharacteristic
909C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3215C2semidirect
2. C22×#432C2semidirect
3. #36625C2semidirect
5. #33184C2semidirect
6. #33051C2semidirect
7. #29854C2semidirect
8. #29815C2semidirect
9. #24755C2semidirect
10. #24657C2semidirect
11. #24508C2semidirect
12. #24507C2semidirect
13. #24380C2semidirect
15. #21986C2semidirect
16. #21866C2semidirect
17. #21808C2semidirect
24. C2×#497C22semidirect
25. C2×#489C22semidirect
26. C2×#467C22semidirect
28. C2×#464C22semidirect
35. C2×#432C22semidirect
36. C2×#432C22semidirect
37. C22×C4⋊C8C22semidirect
39. C22×#97C22semidirect
40. #2857C22semidirect
41. #2857C22semidirect
42. #2857C22semidirect
43. #2857C22semidirect
60. C4×C22⋊Q8C22semidirect
61. C4×C22⋊Q8C22semidirect
72. #2067C22semidirect
73. #2066C22semidirect
74. #2056C22semidirect
75. #2055C22semidirect
76. #2036C22semidirect
78. #2001C22semidirect
80. #1993C22semidirect
81. #1983C22semidirect
82. #1973C22semidirect
83. #1971C22semidirect
84. #1960C22semidirect
85. #1959C22semidirect
86. #1959C22semidirect
87. #1949C22semidirect
88. #1936C22semidirect
89. #1935C22semidirect
91. #1892C22semidirect
96. #1847C22semidirect
97. #1836C22semidirect
98. #1805C22semidirect
175. #432D4semidirect
460. C4⋊C8C2×D4semidirect
474. #97C2×D4semidirect
871. C22#3215semidirect

Maximal subgroups

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

subgroupindex
C2×#32152
C22×#4322
#366252
C2×#28502
#331842
#330512
#298542
#298152
#247552
#246572
#245082
#245072
#243802
#243792
#219862
#218662
#218082