Finite Group Databasebeta

← #6496442

Subgroups — #6496442

Order 512.

2186 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#33210C211yesmaximal, characteristic, complemented
7#33048C211yesmaximal, characteristic, complemented
8#33048C211yesmaximal, characteristic, complemented
9#29877C211yesmaximal, characteristic, complemented
10#29876C211yesmaximal, characteristic, complemented
11#29843C211yesmaximal, characteristic, complemented
12#29842C211yesmaximal, characteristic, complemented
13#24841C214yesmaximal, complemented
14#24706C214yesmaximal, complemented
15#24610C214yesmaximal, complemented
16#24560C214yesmaximal, complemented
17#21984C211yesmaximal, characteristic, complemented
18#21863C211yesmaximal, characteristic, complemented
19#21835C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525—21no—
23C23×C42C2211yescharacteristic
24#3228—28no—
25C2×#500C2211yescharacteristic, complemented
26C2×#498C2211yescharacteristic, complemented
27C2×#486C2211yescharacteristic, complemented
28C2×#486C2211yescharacteristic, complemented
29C2×#482C2214yes—
30C2×#478C2214yescomplemented
31#2920—28no—
32C2×#432C2212yes—
33C2×#432C2212yes—
34C2×#431C2211yescharacteristic
35C2×#431C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C2×#423C2212yes—
39C2×#407C2212yes—
40C2×C4×M16C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2856C2211yescharacteristic
50#2855—21no—
51#2855—21no—
52#2854—21no—
53#2854C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2850—21no—
57#2850—21no—
58#2848—21no—
59#2848—21no—
60#2847—21no—
61#2847C2212yes—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8—21no—
64C4×C22⋊Q8—21no—
65C4×C22⋊Q8—21no—
66C4×#121—21no—
67C4×#121—21no—
68C4×#121C2212yes—
69C4×#121C2212yes—
70#2297—21no—
71#2296C2212yes—
72#2285C2211yescharacteristic
73#2285C2211yescharacteristic
74#2280C2212yes—
75#2088C2214yescomplemented
76#2086C2214yescomplemented
77#2077C2214yes—
78#2075C2214yes—
79#2067C2214yescomplemented
80#2065C2214yescomplemented
81#2034C2214yes—
82#2033C2214yes—
83#1990C2211yescharacteristic, complemented
84#1990C2211yescharacteristic, complemented
85#1990C2211yescharacteristic, complemented
86#1990C2211yescharacteristic, complemented
87#1990C2211yescharacteristic, complemented
88#1990C2211yescharacteristic, complemented
89#1989C2214yescomplemented
90#1957C2211yescharacteristic, complemented
91#1957C2211yescharacteristic, complemented
92#1949C2214yescomplemented
93#1944C2214yescomplemented
94#1943C2214yescomplemented
95#1936C2214yescomplemented
96#1936C2214yescomplemented
97#1895C2214yes—
98#1895C2214yes—
99#1875C2214yes—
100#1854C2214yes—
101#1845C2211yescharacteristic, complemented
102#1844C2211yescharacteristic, complemented
103#1834C2211yescharacteristic, complemented
104#1834C2211yescharacteristic, complemented
105#1825C2214yes—
106#1809C2214yes—
107#1809C2214yes—
108#1804C2214yescomplemented
109C22×#41—21no—
110C24×C4D411yescharacteristic
111C24×C4D411yescharacteristic
112C24×C4C2311yescharacteristic
113C22×M16C2312yes—
114C22×M16C2312yes—
115#533—24no—
116#533—24no—
117#532—24no—
118#532—24no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×#127C2311yescharacteristic
123C2×#125C2312yes—
124C2×#124—21no—
125#525—48no—
126C2×#123—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#120—22no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—21no—
149C2×C4×D4C2312yes—
150C2×#117—21no—
151C2×#117C2312yes—
152C2×#117C2312yes—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#500—24no—
168#498—24no—
169#486—24no—
170#486—24no—
171#482—216no—
172#478—216no—
173#432—28no—
174#432—28no—
175#431—24no—
176#431—24no—
177#431—24no—
178#431D418yescomplemented
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183#423—28no—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192#407—28no—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C4×M16—24no—
198C4×M16—24no—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#390C2312yes—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#385—22no—
244#385—22no—
245#385—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#382—21no—
254#382C2312yes—
255#381—22no—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#379—22no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4C2312yes—
279C4×C22⋊C4—22no—
280C4×C22⋊C4—22no—
281C4×C22⋊C4—22no—
282C4×C22⋊C4—22no—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#340C2314yes—
291C25C2×D411yescharacteristic
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C2412yes—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—24no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
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×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—42no—
338C2×M16—42no—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349#127—22no—
350#127—22no—
351#125—24no—
352#125—24no—
353#124—44no—
354#123—48no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8—44no—
358C22⋊Q8—44no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363#121—24no—
364#121—24no—
365#121—28no—
366#121—44no—
367#121—44no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—44no—
372#120—48no—
373C4×Q8—44no—
374C4×Q8—44no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—48no—
378C4×D4—48no—
379C4×D4—44no—
380#117—24no—
381#117—24no—
382#117—44no—
383#117—44no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C22⋊C4—22no—
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×C42—24no—
428C2×C42—24no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—22no—
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×C42C2×D411yescharacteristic
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×D414yes—
459C2×C42#4114yes—
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464#107—28no—
465#107—44no—
466#106—28no—
467#106—44no—
468C4⋊C8—24no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471C4⋊C8C2×D418yes—
472#102—28no—
473#102—28no—
474#102—44no—
475#102—44no—
476C22⋊C8—24no—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C22⋊C8C2×D418yes—
480#97—24no—
481#97—24no—
482C4×C8—22no—
483C4×C8—22no—
484C4×C8C2×D414yes—
485C4×C8C2×D414yes—
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—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—41no—
507C24—41no—
508C24—41no—
509C24—41no—
510C24C22×D411yescharacteristic
511C24C22×D411yescharacteristic
512C24C22×D411yescharacteristic
513#41—816no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—44no—
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—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C22×C4—22no—
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—48no—
601C22×C4—48no—
602C22×C4—416no—
603C22×C4—416no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4#12114yes—
608C22×C4#12114yes—
609C22×C4AGL(1,ℤ/8)14yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4112yes—
623C22×C42−1+414yes—
624C22×C4C2511yescharacteristic
625M16—48no—
626M16—48no—
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×C8C22×D414yes—
638C2×C8C22×D414yes—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
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—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—44no—
700C42—44no—
701C42—44no—
702C42#12114yes—
703C42#12114yes—
704C42C22×D412yes—
705C42C22×D412yes—
706C42C2×#4112yes—
707C42C2×#4112yes—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23C2×#12112yes—
741C23#53612yes—
742C23C2×AGL(1,ℤ/8)12yes—
743C23C23×D411yescharacteristic
744Q8—84no—
745Q8—84no—
746Q8—84no—
747D4—44no—
748D4—44no—
749D4—88no—
750D4—88no—
751D4—88no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
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—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
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—88no—
819C2×C4C2×#12112yes—
820C2×C4C2×#12112yes—
821C2×C4C2×#12112yes—
822C2×C4C2×#12112yes—
823C2×C4C2×#12112yes—
824C2×C4#53612yes—
825C2×C4C2×AGL(1,ℤ/8)12yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4#57512yes—
828C2×C4#57512yes—
829C2×C4#57512yes—
830C2×C4C23×D411yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C2×2−1+412yes—
833C2×C4#58512yes—
834C8—24no—
835C8—24no—
836C8—42no—
837C8—42no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—416no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22C22×#12111yescharacteristic
868C22C2×#53611yescharacteristic
869C22#344911yescharacteristic
870C22C22×AGL(1,ℤ/8)11yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57511yescharacteristic
873C22C2×#57511yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4#305414yes—
891C4#305514yes—
892C4#348912yes—
893C4#349512yes—
894C2—42no—
895C2—42no—
896C2—42no—
897C2—162no—
898C2#3530611yescharacteristic
899C2C2×#305411yescharacteristic
900C2C2×#305511yescharacteristic
901C2#6086211yescharacteristic
902C2#6086411yescharacteristic
903C2#6096511yescharacteristic
904C2#6097211yescharacteristic
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×#3228C2semidirect
2. C2×#2920C2semidirect
3. #36625C2semidirect
5. #33212C2semidirect
6. #33210C2semidirect
7. #33048C2semidirect
8. #33048C2semidirect
9. #29877C2semidirect
10. #29876C2semidirect
11. #29843C2semidirect
12. #29842C2semidirect
13. #24841C2semidirect
14. #24706C2semidirect
15. #24610C2semidirect
16. #24560C2semidirect
17. #21984C2semidirect
18. #21863C2semidirect
19. #21835C2semidirect
25. C2×#500C22semidirect
26. C2×#498C22semidirect
27. C2×#486C22semidirect
28. C2×#486C22semidirect
30. C2×#478C22semidirect
75. #2088C22semidirect
76. #2086C22semidirect
79. #2067C22semidirect
80. #2065C22semidirect
83. #1990C22semidirect
84. #1990C22semidirect
85. #1990C22semidirect
86. #1990C22semidirect
87. #1990C22semidirect
88. #1990C22semidirect
89. #1989C22semidirect
90. #1957C22semidirect
91. #1957C22semidirect
92. #1949C22semidirect
93. #1944C22semidirect
94. #1943C22semidirect
95. #1936C22semidirect
96. #1936C22semidirect
101. #1845C22semidirect
102. #1844C22semidirect
103. #1834C22semidirect
104. #1834C22semidirect
108. #1804C22semidirect
178. #431D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#29202
#366252
#366242
#332122
#332102
#330482
#298772
#298762
#298432
#298422
#248412
#247062
#246102
#245602
#219842
#218632
#218352