Finite Group Databasebeta

← #6487770

Subgroups — #6487770

Order 512.

2408 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3254C211yesmaximal, characteristic, complemented
2C22×#423C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#32935C214yesmaximal, complemented
6#29784C214yesmaximal, complemented
7#24846C212yesmaximal, complemented
8#24844C212yesmaximal, complemented
9#24837C212yesmaximal, complemented
10#24835C212yesmaximal, complemented
11#24761C212yesmaximal, complemented
12#24759C212yesmaximal, complemented
13#24753C212yesmaximal, complemented
14#24751C212yesmaximal, complemented
15#21964C211yesmaximal, characteristic, complemented
16#21894C211yesmaximal, characteristic, complemented
17#21893C211yesmaximal, characteristic, complemented
18C23×M16C2212yes—
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21C2×#525—21no—
22C23×C42C2211yescharacteristic
23#3254—28no—
24C2×#477C2212yescomplemented
25C2×#474C2212yescomplemented
26C2×#468C2214yes—
27C2×#468C2214yes—
28C2×#465C2214yes—
29C2×#460C2212yescomplemented
30C2×#461C2212yescomplemented
31C2×#423—28no—
32C2×#423C2212yes—
33C2×#423C2212yes—
34C2×#423C2212yes—
35C2×#423C2211yescharacteristic
36C2×#423C2211yescharacteristic
37C22×C4⋊C8C2212yes—
38C22×C4⋊C8C2212yes—
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2856C2211yescharacteristic
46#2856C2211yescharacteristic
47#2855—21no—
48#2855C2212yes—
49#2854—21no—
50#2854C2212yes—
51#2851—21no—
52#2851—21no—
53#2850—21no—
54#2850—21no—
55#2848—21no—
56#2848C2212yes—
57#2847—21no—
58#2847C2212yes—
59C4×C22⋊Q8—21no—
60C4×C22⋊Q8—21no—
61C4×C22⋊Q8C2212yes—
62C4×C22⋊Q8C2212yes—
63C4×#121—21no—
64C4×#121—21no—
65C4×#121C2212yes—
66C4×#121C2212yes—
67#2297—21no—
68#2296—21no—
69#2285C2211yescharacteristic
70#2285C2211yescharacteristic
71#2280—21no—
72#2087C2214yescomplemented
73#2086C2214yescomplemented
74#2068C2214yescomplemented
75#2067C2214yescomplemented
76#2066C2214yescomplemented
77#2065C2214yescomplemented
78#2055C2214yescomplemented
79#2055C2214yescomplemented
80#1988C2212yescomplemented
81#1987C2212yescomplemented
82#1982C2212yescomplemented
83#1981C2212yescomplemented
84#1948C2212yescomplemented
85#1948C2212yescomplemented
86#1947C2212yescomplemented
87#1947C2212yescomplemented
88#1895C2214yes—
89#1895C2214yes—
90#1894C2214yes—
91#1894C2214yes—
92#1893C2214yes—
93#1892C2214yes—
94#1809C2214yes—
95#1809C2214yes—
96#1808C2214yes—
97#1803C2212yescomplemented
98#1803C2212yescomplemented
99#1802C2212yescomplemented
100#1802C2212yescomplemented
101C22×#41—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C22×M16—28no—
107C22×M16—44no—
108C22×M16—44no—
109C22×M16C2314yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112C23×C8C2314yes—
113#533—24no—
114#533—24no—
115#532—24no—
116#532—24no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125—21no—
122C2×#124—21no—
123#525—48no—
124C2×#123—22no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×#121C2312yes—
141C2×#120—22no—
142C2×C4×Q8—21no—
143C2×C4×Q8C2312yes—
144C2×C4×D4—22no—
145C2×C4×D4—22no—
146C2×C4×D4—21no—
147C2×C4×D4C2312yes—
148C2×#117—21no—
149C2×#117—21no—
150C2×#117—21no—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#477—28no—
166#474—28no—
167#468—216no—
168#468—48no—
169#465—48no—
170#461—28no—
171#460—28no—
172C2×#107C2314yes—
173C2×#107C2314yes—
174C2×#106C2314yes—
175#423—28no—
176#423—24no—
177#423—28no—
178#423—28no—
179#423D418yescomplemented
180C2×C4⋊C8—28no—
181C2×C4⋊C8—28no—
182C2×C4⋊C8C2314yes—
183C2×C4⋊C8C2314yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391C2312yes—
199#391C2312yes—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390C2312yes—
205#390C2312yes—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2311yescharacteristic
242#382—21no—
243#382—21no—
244#381—22no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380—21no—
255#380C2312yes—
256#380C2312yes—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#380C2312yes—
261#379—22no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—22no—
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4—22no—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278C25C2×D411yescharacteristic
279C2×#41—44no—
280C2×#41—44no—
281C2×#41—44no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8C2412yes—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4C2412yes—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—22no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C2×SD16—28no—
323C2×SD16—44no—
324C2×SD16—44no—
325C2×M16—24no—
326C2×M16—28no—
327C2×M16—28no—
328C2×M16—42no—
329C2×M16—44no—
330C2×M16—42no—
331C2×M16—42no—
332C2×M16—42no—
333C2×M16—432no—
334C2×M16C2×D418yes—
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—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346#127—22no—
347#127—22no—
348#125—44no—
349#124—44no—
350#123—48no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—44no—
358C22⋊Q8—44no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362#121—24no—
363#121—24no—
364#121—24no—
365#121—24no—
366#121—24no—
367#121—24no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—44no—
372#121—44no—
373#120—48no—
374C4×Q8—24no—
375C4×Q8—24no—
376C4×Q8—44no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—48no—
380C4×D4—48no—
381C4×D4—44no—
382#117—44no—
383#117—44no—
384#117—44no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D414yes—
460C2×C42#4114yes—
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465#107—28no—
466#107—44no—
467#106—44no—
468C4⋊C8—28no—
469C4⋊C8—28no—
470C4⋊C8—24no—
471C4⋊C8—24no—
472C4⋊C8C2×D418yes—
473C4⋊C8C2×D418yes—
474#103—28no—
475#103—44no—
476#103—44no—
477#102—28no—
478#102—44no—
479#102—44no—
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—
493#95—22no—
494#95—22no—
495#95—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—41no—
503C24—41no—
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507#41—816no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
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—21no—
563C22×C4—21no—
564C22×C4—21no—
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—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—416no—
606C22×C4—416no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4#12114yes—
611C22×C4#12114yes—
612C22×C4AGL(1,ℤ/8)14yes—
613C22×C4#13714yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C2×#4112yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C42−1+412yes—
630C22×C42−1+412yes—
631C22×C4C2511yescharacteristic
632SD16—88no—
633M16—48no—
634M16—416no—
635M16—48no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—416no—
642C2×C8C22×D418yes—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—44no—
707C42—44no—
708C42—44no—
709C42#12114yes—
710C42#12114yes—
711C42C22×D412yes—
712C42C22×D412yes—
713C42C2×#4112yes—
714C42C2×#4112yes—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—28no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23C2×#12112yes—
746C23#53712yes—
747C23#53712yes—
748C23C2×AGL(1,ℤ/8)12yes—
749C23C2×#13712yes—
750C23C23×D411yescharacteristic
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—84no—
756Q8—84no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—84no—
762D4—88no—
763D4—88no—
764D4—88no—
765D4—84no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
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—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—88no—
835C2×C4C2×#12112yes—
836C2×C4C2×#12112yes—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4C2×#12112yes—
840C2×C4#53712yes—
841C2×C4#53712yes—
842C2×C4C2×AGL(1,ℤ/8)12yes—
843C2×C4C2×AGL(1,ℤ/8)12yes—
844C2×C4C2×#13712yes—
845C2×C4C2×#13712yes—
846C2×C4#57512yes—
847C2×C4#57512yes—
848C2×C4C23×D411yescharacteristic
849C2×C4C22×#4111yescharacteristic
850C2×C4C2×H(5,𝔽2)11yescharacteristic
851C2×C4C2×H(5,𝔽2)11yescharacteristic
852C2×C4C2×2−1+411yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C8—28no—
855C8—44no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—416no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22#325414yescomplemented
885C22C22×#12111yescharacteristic
886C22C2×#53711yescharacteristic
887C22C2×#53711yescharacteristic
888C22C22×AGL(1,ℤ/8)11yescharacteristic
889C22C22×#13711yescharacteristic
890C22C2×#57511yescharacteristic
891C22C2×#57511yescharacteristic
892C4—22no—
893C4—22no—
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4#305514yes—
909C4#305614yes—
910C4#348411yescharacteristic
911C4#348611yescharacteristic
912C4#349211yescharacteristic
913C4#349211yescharacteristic
914C2—24no—
915C2—42no—
916C2—42no—
917C2—162no—
918C2#3522311yescharacteristic
919C2C2×#305511yescharacteristic
920C2C2×#305611yescharacteristic
921C2C2×#325411yescharacteristic
922C2#6090711yescharacteristic
923C2#6091611yescharacteristic
924C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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×#3254C2semidirect
2. C22×#423C2semidirect
3. #36625C2semidirect
5. #32935C2semidirect
6. #29784C2semidirect
7. #24846C2semidirect
8. #24844C2semidirect
9. #24837C2semidirect
10. #24835C2semidirect
11. #24761C2semidirect
12. #24759C2semidirect
13. #24753C2semidirect
14. #24751C2semidirect
15. #21964C2semidirect
16. #21894C2semidirect
17. #21893C2semidirect
24. C2×#477C22semidirect
25. C2×#474C22semidirect
29. C2×#460C22semidirect
30. C2×#461C22semidirect
72. #2087C22semidirect
73. #2086C22semidirect
74. #2068C22semidirect
75. #2067C22semidirect
76. #2066C22semidirect
77. #2065C22semidirect
78. #2055C22semidirect
79. #2055C22semidirect
80. #1988C22semidirect
81. #1987C22semidirect
82. #1982C22semidirect
83. #1981C22semidirect
84. #1948C22semidirect
85. #1948C22semidirect
86. #1947C22semidirect
87. #1947C22semidirect
97. #1803C22semidirect
98. #1803C22semidirect
99. #1802C22semidirect
100. #1802C22semidirect
179. #423D4semidirect
884. C22#3254semidirect

Maximal subgroups

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

subgroupindex
C2×#32542
C22×#4232
#366252
#366242
#329352
#297842
#248462
#248442
#248372
#248352
#247612
#247592
#247532
#247512
#219642
#218942
#218932