Finite Group Databasebeta

← #6440937

Subgroups — #6440937

Order 512.

1851 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35585C211yesmaximal, characteristic, complemented
2#34181C211yesmaximal, characteristic
3#27325C212yesmaximal, complemented
4#27318C212yesmaximal, complemented
5#27317C212yesmaximal, complemented
6#27310C212yesmaximal, complemented
7#27307C212yesmaximal, complemented
8#27304C212yesmaximal, complemented
9#27299C212yesmaximal, complemented
10#27296C212yesmaximal, complemented
11#23747C211yesmaximal, characteristic, complemented
12#23669C211yesmaximal, characteristic, complemented
13#23661C211yesmaximal, characteristic, complemented
14#23656C211yesmaximal, characteristic, complemented
15#21157C211yesmaximal, characteristic, complemented
16#21036C211yesmaximal, characteristic, complemented
17#21026C211yesmaximal, characteristic, complemented
18#20879C211yesmaximal, characteristic
19#20879C211yesmaximal, characteristic
20#20873C211yesmaximal, characteristic
21C2×#1864C211yesmaximal, characteristic
22#20650C211yesmaximal, characteristic
23#20416C211yesmaximal, characteristic
24C2×#518C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C2×#405C2211yescharacteristic
37#2569—22no—
38#2509—21no—
39#2509C2212yescomplemented
40#2508—21no—
41#2508C2212yescomplemented
42#2507—21no—
43#2507C2212yescomplemented
44#2506—21no—
45#2506C2212yescomplemented
46#2442—22no—
47#2349—21no—
48#2349—21no—
49#2349C2212yes—
50#2349C2212yes—
51D4×C4⋊C4—21no—
52D4×C4⋊C4—21no—
53D4×C4⋊C4C2212yes—
54D4×C4⋊C4C2212yes—
55#2317C2211yescharacteristic
56#2316C2211yescharacteristic
57#2316C2211yescharacteristic
58#2316C2211yescharacteristic
59#2316C2211yescharacteristic
60#2315—22no—
61#2296C2211yescharacteristic
62C2×#389C2211yescharacteristic
63#2285C2211yescharacteristic
64#2285C2211yescharacteristic
65C2×#380—22no—
66#2274C2211yescharacteristic
67#2101C2212yescomplemented
68#2101C2212yescomplemented
69#2100C2212yescomplemented
70#2099C2212yescomplemented
71#2088C2212yescomplemented
72#2088C2212yescomplemented
73#2087C2212yescomplemented
74#2086C2212yescomplemented
75#2085C2211yescharacteristic, complemented
76#2085C2211yescharacteristic, complemented
77#2085C2211yescharacteristic, complemented
78#2085C2211yescharacteristic, complemented
79#2085C2212yescomplemented
80#2085C2212yescomplemented
81#2084C2211yescharacteristic, complemented
82#2084C2211yescharacteristic, complemented
83#2084C2212yescomplemented
84#2084C2212yescomplemented
85#2083C2211yescharacteristic, complemented
86#2083C2211yescharacteristic, complemented
87#1944C2212yescomplemented
88#1944C2212yescomplemented
89#1941C2212yescomplemented
90#1941C2212yescomplemented
91#1921C2212yescomplemented
92#1920C2212yescomplemented
93#1919C2212yescomplemented
94#1918C2212yescomplemented
95#1917C2212yescomplemented
96#1917C2212yescomplemented
97#1916C2212yescomplemented
98#1916C2212yescomplemented
99#1864C2212yes—
100#1864C2212yes—
101#1864C2212yes—
102#1864C2212yes—
103#1864C2212yes—
104#1864C2212yes—
105#1864C2212yes—
106#1864C2212yes—
107#1864C2212yes—
108#1864C2212yes—
109#1862C2212yes—
110#1862C2212yes—
111#1862C2212yes—
112#1862C2212yes—
113#1862C2212yes—
114#1862C2212yes—
115#1804C2212yes—
116#1804C2212yes—
117#1802C2212yes—
118#1802C2212yes—
119#1762C2212yes—
120#1762C2212yes—
121C4×#102C2212yes—
122C4×#102C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130C2×#340C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C24×C4—21no—
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C2×#125—22no—
142#518—24no—
143#518—24no—
144#518—42no—
145#518—42no—
146C2×C4×D4—24no—
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—24no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4C2312yes—
155C2×C4×D4C2312yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C22×C4⋊C4—21no—
167C22×C4⋊C4—22no—
168C22×C4⋊C4—22no—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C22⋊C4—21no—
173C22×C22⋊C4—22no—
174C22×C22⋊C4—22no—
175C22×C42C2311yescharacteristic
176#428—24no—
177#427—42no—
178#427—42no—
179C2×#107C2312yes—
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#106—24no—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2311yescharacteristic
191C2×#106C2311yescharacteristic
192#424—42no—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195#418—24no—
196#418—24no—
197C2×#102—24no—
198C2×#102Q818yes—
199C2×#102C2312yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207#405—42no—
208C2×#97C2312yes—
209C2×C4×C8C2312yes—
210#400—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#398—22no—
215#398—22no—
216#398—22no—
217#398—22no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—22no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2312yes—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#385—21no—
251#385—21no—
252#385—22no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#384D411yescharacteristic
262#384D411yescharacteristic
263#384C2312yes—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#382—22no—
267#382D411yescharacteristic
268#382D411yescharacteristic
269#382C2312yes—
270#382C2311yescharacteristic
271#382C2311yescharacteristic
272#380—21no—
273#380—21no—
274#380—22no—
275#380—22no—
276#380—22no—
277#380—22no—
278#380—22no—
279#380—22no—
280#380—22no—
281#380—22no—
282#380D412yes—
283#380D412yes—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C22⋊C4—22no—
295C2×#95—21no—
296C2×#95—22no—
297C2×#95—22no—
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2312yes—
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328C25—21no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4C2×Q814yes—
334C22×D4#4114yes—
335C22×D4#4114yes—
336C22×D4C2412yes—
337C23×C4—28no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—82no—
348C23×C4—82no—
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2411yescharacteristic
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8C2×Q814yes—
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370#125—84no—
371C4×D4—28no—
372C4×D4—28no—
373C4×D4—24no—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—44no—
386C4×D4—44no—
387C4×D4—44no—
388C4×D4—44no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—84no—
429C2×C4⋊C4—84no—
430C2×C4⋊C4—82no—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D412yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×Q814yes—
440C2×C4⋊C4#4114yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C22⋊C4—28no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—48no—
464C2×C22⋊C4—48no—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—24no—
482#107—41no—
483#107—41no—
484#107—41no—
485#107—41no—
486#106—24no—
487#106—24no—
488#106—24no—
489#106—41no—
490#106—41no—
491#106—41no—
492#106—41no—
493C4⋊C8—42no—
494C4⋊C8—42no—
495#102—24no—
496#102—24no—
497#102—24no—
498#102—24no—
499#102—24no—
500#102—24no—
501#102C2×Q818yes—
502#102C2×Q818yes—
503#97—42no—
504C4×C8—42no—
505#95—21no—
506#95—21no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95C2×D412yes—
528#95C2×D412yes—
529#95C2×D412yes—
530#95C2×D412yes—
531C24—22no—
532C24—24no—
533C24—24no—
534C24—24no—
535C24—81no—
536C24—81no—
537C24—81no—
538C24—81no—
539C24C22×D411yescharacteristic
540C2×D4—24no—
541C2×D4—28no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4#125116yescomplemented
550C2×D4C22×Q814yes—
551C2×D4C2×#4114yes—
552C2×D4C2×#4114yes—
553C22×C4—28no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—42no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—816no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×Q812yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C42−1+412yes—
613C22×C4C2511yescharacteristic
614M16—44no—
615M16—44no—
616C2×C8—28no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8C22×Q812yes—
635C2×C8C22×Q812yes—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—82no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4C22×Q814yes—
688C4⋊C4C2×#4114yes—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C42—22no—
702C42—22no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—82no—
716C42—82no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—216no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23#52512yes—
736C23#54612yes—
737C23D4×Q812yes—
738C23C23×D411yescharacteristic
739D4—24no—
740D4—24no—
741D4—24no—
742D4—216no—
743D4C2×#12518yes—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—44no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—82no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—88no—
806C2×C4—164no—
807C2×C4—164no—
808C2×C4—164no—
809C2×C4—164no—
810C2×C4—162no—
811C2×C4#52512yes—
812C2×C4C2×#12514yes—
813C2×C4#53914yes—
814C2×C4#54612yes—
815C2×C4D4×Q812yes—
816C2×C4#55214yes—
817C2×C4#55414yes—
818C2×C4#57712yes—
819C2×C4C23×Q811yescharacteristic
820C2×C4C22×#4111yescharacteristic
821C2×C4C22×#4111yescharacteristic
822C2×C4C22×#4111yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×2−1+411yescharacteristic
825C8—22no—
826C8—22no—
827C8—41no—
828C8—41no—
829C8—42no—
830C8—42no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—28no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—816no—
845C22#247314yes—
846C22C2×#52511yescharacteristic
847C22C2×#54611yescharacteristic
848C22C2×D4×Q811yescharacteristic
849C22C2×#57711yescharacteristic
850C22#358411yescharacteristic
851C22#358511yescharacteristic
852C22#358511yescharacteristic
853C4—22no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—41no—
859C4—44no—
860C4—41no—
861C4—41no—
862C4—44no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—82no—
872C4#247314yes—
873C4C22×#12511yescharacteristic
874C4C2×#53911yescharacteristic
875C4C2×#55211yescharacteristic
876C4C2×#55411yescharacteristic
877C2—24no—
878C2—48no—
879C2C2×#247311yescharacteristic
880C2#6057911yescharacteristic
881C2#6058011yescharacteristic
882C2#6120011yescharacteristic
883C2#6120111yescharacteristic
884C2#6137111yescharacteristic
885C2#6137811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35585C2semidirect
3. #27325C2semidirect
4. #27318C2semidirect
5. #27317C2semidirect
6. #27310C2semidirect
7. #27307C2semidirect
8. #27304C2semidirect
9. #27299C2semidirect
10. #27296C2semidirect
11. #23747C2semidirect
12. #23669C2semidirect
13. #23661C2semidirect
14. #23656C2semidirect
15. #21157C2semidirect
16. #21036C2semidirect
17. #21026C2semidirect
39. #2509C22semidirect
41. #2508C22semidirect
43. #2507C22semidirect
45. #2506C22semidirect
67. #2101C22semidirect
68. #2101C22semidirect
69. #2100C22semidirect
70. #2099C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2087C22semidirect
74. #2086C22semidirect
75. #2085C22semidirect
76. #2085C22semidirect
77. #2085C22semidirect
78. #2085C22semidirect
79. #2085C22semidirect
80. #2085C22semidirect
81. #2084C22semidirect
82. #2084C22semidirect
83. #2084C22semidirect
84. #2084C22semidirect
85. #2083C22semidirect
86. #2083C22semidirect
87. #1944C22semidirect
88. #1944C22semidirect
89. #1941C22semidirect
90. #1941C22semidirect
91. #1921C22semidirect
92. #1920C22semidirect
93. #1919C22semidirect
94. #1918C22semidirect
95. #1917C22semidirect
96. #1917C22semidirect
97. #1916C22semidirect
98. #1916C22semidirect
549. C2×D4#125semidirect

Maximal subgroups

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

subgroupindex
#355852
#341812
#273252
#273182
#273172
#273102
#273072
#273042
#272992
#272962
#237472
#236692
#236612
#236562
#211572
#210362
#210262
#208792
#208732
C2×#18642
#206502
#204162