Finite Group Databasebeta

← #6451389

Subgroups — #6451389

Order 512.

1888 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34951C211yesmaximal, characteristic, complemented
2C4×#550C211yesmaximal, characteristic
3#27488C212yesmaximal, complemented
4#27192C212yesmaximal, complemented
5#27064C212yesmaximal, complemented
6#26586C212yesmaximal, complemented
7#26530C211yesmaximal, characteristic, complemented
8#26320C211yesmaximal, characteristic, complemented
9#26090C211yesmaximal, characteristic, complemented
10#25627C211yesmaximal, characteristic
11#25368C211yesmaximal, characteristic, complemented
12#25060C211yesmaximal, characteristic, complemented
13#24630C211yesmaximal, characteristic, complemented
14#24188C211yesmaximal, characteristic
15#23799C212yesmaximal, complemented
16#23678C212yesmaximal, complemented
17C4×#492C211yesmaximal, characteristic, complemented
18C4×#460C211yesmaximal, characteristic, complemented
19C4×#461C211yesmaximal, characteristic, complemented
20C4×#461C212yesmaximal, complemented
21#21339C211yesmaximal, characteristic, complemented
22#21117C212yesmaximal, complemented
23C42×SD16C211yesmaximal, characteristic, complemented
24C2×#550C2211yescharacteristic
25C2×C4×#41—21no—
26C2×#492C2211yescharacteristic
27C2×#460C2211yescharacteristic
28C2×#461C2212yes—
29C2×#461C2211yescharacteristic
30C2×C4×SD16C2211yescharacteristic
31C2×C4×SD16C2211yescharacteristic
32C2×C4×SD16C2211yescharacteristic
33C2×C4×SD16C2212yes—
34C2×C4×SD16C2212yes—
35C2×C4×SD16C2212yes—
36C2×C4×SD16C2212yes—
37#2585—22no—
38#2582C2211yescharacteristic
39#2568C2211yescharacteristic
40#2552C2211yescharacteristic
41#2546C2211yescharacteristic
42#2511C2212yes—
43#2509—21no—
44#2453—21no—
45#2446C2212yes—
46#2402—22no—
47#2366C2211yescharacteristic
48#2366C2212yes—
49#2363—22no—
50#2363—21no—
51#2354C2211yescharacteristic
52#2354C2212yes—
53Q8×C4⋊C4C2211yescharacteristic
54#2341—21no—
55C4×C4⋊Q8C2211yescharacteristic
56C4×C4⋊Q8C2212yes—
57C4×#127C2212yes—
58C4×#127C2211yescharacteristic
59C4×#125—21no—
60C4×#121—21no—
61C4×#121—22no—
62#2295—21no—
63#2295C2212yes—
64C42×Q8C2211yescharacteristic
65C42×Q8C2211yescharacteristic
66C42×D4C2211yescharacteristic
67C42×D4C2212yes—
68#2096C2212yes—
69#2096C2212yes—
70#2094C2212yes—
71#2094C2212yes—
72#2084C2212yes—
73#2072C2212yes—
74#2065C2212yes—
75#2065C2212yes—
76#2055C2212yes—
77#2055C2212yes—
78#2041C2212yes—
79#2014C2212yes—
80#2014C2212yes—
81#2014C2212yes—
82#2013C2212yes—
83#2013C2212yes—
84#1984C2211yescharacteristic
85#1984C2211yescharacteristic
86#1982C2211yescharacteristic
87#1981C2211yescharacteristic
88#1981C2212yes—
89#1968C2212yes—
90#1968C2212yes—
91#1957C2211yescharacteristic
92#1956C2211yescharacteristic
93#1948C2212yes—
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1927C2212yes—
99#1927C2212yes—
100#1927C2212yes—
101#1927C2212yes—
102#1927C2212yes—
103#1926C2212yes—
104#1920C2212yes—
105#1920C2212yes—
106#1916C2212yes—
107#1916C2212yes—
108#1880C2212yes—
109#1877C2212yes—
110#1877C2212yes—
111#1877C2212yes—
112#1877C2212yes—
113#1877C2212yes—
114#1864C2212yes—
115#1864C2212yes—
116#1844C2211yescharacteristic
117#1803C2211yescharacteristic
118#1802C2211yescharacteristic
119#1802C2212yes—
120C4×#106C2211yescharacteristic
121C4×#106C2211yescharacteristic
122C4×#106C2211yescharacteristic
123C4×C4⋊C8C2212yes—
124C4×C4⋊C8C2211yescharacteristic
125C4×#103C2211yescharacteristic
126C4×#103C2211yescharacteristic
127C4×#103C2211yescharacteristic
128C4×#103C2212yes—
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131C4×#102C2211yescharacteristic
132C4×#102C2212yes—
133#1744C2212yes—
134C42×C8C2211yescharacteristic
135C22×#41—21no—
136C22×SD16C2311yescharacteristic
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2312yes—
140C22×SD16C2312yes—
141#550—24no—
142#550—24no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2312yes—
145C2×#127C2312yes—
146C2×#127C2311yescharacteristic
147C2×#125—21no—
148C2×#121—21no—
149C2×#121—22no—
150C4×#41—48no—
151C2×C4×Q8—21no—
152C2×C4×Q8D411yescharacteristic
153C2×C4×Q8D411yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×D4—22no—
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4—21no—
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×#117—22no—
172C2×#117—21no—
173C22×C42—21no—
174C22×C42—22no—
175#492—24no—
176#461—24no—
177#461—28no—
178#460—24no—
179C4×SD16—24no—
180C4×SD16—24no—
181C4×SD16—24no—
182C4×SD16—28no—
183C4×SD16—44no—
184C4×SD16—44no—
185C4×SD16—44no—
186C2×#106C2311yescharacteristic
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2312yes—
197C2×#103C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2311yescharacteristic
206C2×#102C2311yescharacteristic
207C2×#102C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2311yescharacteristic
222#400—22no—
223#400—22no—
224#400—22no—
225#400—22no—
226#398—22no—
227#398—22no—
228#398—22no—
229#398—22no—
230#391—21no—
231#391—21no—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#391C2312yes—
236#391C2312yes—
237#390—21no—
238#390—22no—
239#390—21no—
240#390—22no—
241#390—21no—
242#390—22no—
243#390C2312yes—
244#390C2312yes—
245#390C2312yes—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—22no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389—22no—
254#389—22no—
255#389—21no—
256#389C2312yes—
257#389C2312yes—
258#388—22no—
259#388—22no—
260#388—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#386—22no—
268#386—22no—
269#386—22no—
270#384C2311yescharacteristic
271#384C2312yes—
272#384C2311yescharacteristic
273#384C2312yes—
274#382—21no—
275#380—21no—
276#380—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—22no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4D412yes—
287C4×C4⋊C4D411yescharacteristic
288C4×C4⋊C4D412yes—
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2311yescharacteristic
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—22no—
305#376—22no—
306C43—21no—
307C43C2311yescharacteristic
308C43C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C2×#41—28no—
327C2×#41—44no—
328C2×#41—44no—
329C22×Q8C2×D411yescharacteristic
330C22×Q8C2412yes—
331C22×Q8C2411yescharacteristic
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—21no—
336C22×D4C2411yescharacteristic
337C22×D4C2412yes—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—24no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—22no—
352C2×SD16—24no—
353C2×SD16—24no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×SD16—42no—
357C2×SD16—42no—
358C2×SD16—42no—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C4⋊Q8—24no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—42no—
369#127—24no—
370#127—24no—
371#127—22no—
372#127#4114yes—
373#125—44no—
374#121—28no—
375#121—216no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—24no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—24no—
385C4×Q8—42no—
386C4×Q8—41no—
387C4×Q8—44no—
388C4×Q8SD1618yescomplemented
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—24no—
398C4×D4—41no—
399C4×D4—42no—
400C4×D4—48no—
401C4×D4—44no—
402C4×D4—48no—
403C4×D4—44no—
404C4×D4—82no—
405C4×D4—84no—
406C4×D4#4114yes—
407#117—48no—
408#117—44no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C22⋊C4—22no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C42—21no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—48no—
466C2×C42—44no—
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D412yes—
470C2×C42C2×D412yes—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D412yes—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D412yes—
475C2×C42C2412yes—
476C2×C42C2411yescharacteristic
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#106—22no—
481#106—24no—
482#106—22no—
483#106—22no—
484#106—42no—
485#106—42no—
486#106—42no—
487C4⋊C8—24no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—42no—
491#103—24no—
492#103—22no—
493#103—22no—
494#103—24no—
495#103—24no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103#4114yescomplemented
500#102—22no—
501#102—24no—
502#102—22no—
503#102—24no—
504#102—22no—
505#102—42no—
506#102—42no—
507#102—42no—
508#102—42no—
509C4×C8—22no—
510C4×C8—22no—
511C4×C8—22no—
512C4×C8—22no—
513C4×C8—24no—
514C4×C8—41no—
515C4×C8#4114yescomplemented
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—21no—
521#95—21no—
522#95—22no—
523#95—22no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95C2×D412yes—
537#95C2×D412yes—
538#95C2×D412yes—
539C24—22no—
540C24—21no—
541#41—432no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8C2×SD1614yes—
556C2×Q8C2×#4112yes—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—81no—
576C2×D4—82no—
577C2×D4—81no—
578C2×D4—82no—
579C2×D4C2×#4114yes—
580C2×D4C2×#4112yes—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—82no—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2511yescharacteristic
620SD16—28no—
621SD16—48no—
622SD16—48no—
623SD16—48no—
624SD16—48no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8C2×#4112yes—
641C2×C8C2×#4112yes—
642C2×C8C2×#4112yes—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—82no—
675C4⋊C4—81no—
676C4⋊C4—82no—
677C4⋊C4—81no—
678C4⋊C4—82no—
679C4⋊C4C2×SD1618yes—
680C4⋊C4C2×SD1614yes—
681C4⋊C4C2×#4112yes—
682C4⋊C4C2×#4112yes—
683C22⋊C4—28no—
684C22⋊C4—24no—
685C22⋊C4—42no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C42—22no—
696C42—22no—
697C42—24no—
698C42—21no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—21no—
703C42—22no—
704C42—41no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—44no—
711C42—42no—
712C42—42no—
713C42—44no—
714C42—44no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—81no—
719C42C2×SD1618yes—
720C42C2×SD1614yes—
721C42C2×#4112yes—
722C42C2×#4112yes—
723C42C2×#4112yes—
724C42H(5,𝔽2)12yes—
725C23—24no—
726C23—22no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—41no—
737C23—42no—
738C23—41no—
739C23C23×D411yescharacteristic
740Q8—28no—
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749D4—22no—
750D4—22no—
751D4—24no—
752D4—24no—
753D4—416no—
754D4—48no—
755D4—42no—
756D4—42no—
757D4—41no—
758D4—41no—
759D4—84no—
760D4—88no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—416no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—84no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4#52512yes—
817C2×C4#52512yes—
818C2×C4#55012yes—
819C2×C4#55012yes—
820C2×C4C22×SD1612yes—
821C2×C4C22×SD1614yes—
822C2×C4C22×SD1614yes—
823C2×C4C22×SD1612yes—
824C2×C4C22×SD1612yes—
825C2×C4#57512yes—
826C2×C4#57712yes—
827C2×C4C22×#4111yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C22×#4111yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4#58511yescharacteristic
833C8—22no—
834C8—22no—
835C8—22no—
836C8—41no—
837C8—42no—
838C8—42no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—81no—
846C22—82no—
847C22—82no—
848C22—81no—
849C22—82no—
850C22—81no—
851C22—81no—
852C22—82no—
853C22C2×#52511yescharacteristic
854C22C2×#55011yescharacteristic
855C22D4×#4111yescharacteristic
856C22C23×SD1611yescharacteristic
857C22C2×#57511yescharacteristic
858C22C2×#57711yescharacteristic
859C22#358411yescharacteristic
860C4—24no—
861C4—22no—
862C4—22no—
863C4—22no—
864C4—24no—
865C4—41no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—82no—
875C4—81no—
876C4—81no—
877C4—82no—
878C4#310114yes—
879C4#339214yes—
880C4#344411yescharacteristic
881C4#346011yescharacteristic
882C4#347511yescharacteristic
883C4#348111yescharacteristic
884C2—84no—
885C2—82no—
886C2#3472711yescharacteristic
887C2C2×#310111yescharacteristic
888C2#6057111yescharacteristic
889C2C2×#339211yescharacteristic
890C2#6140111yescharacteristic
891C2SD16×#4111yescharacteristic
892C2#6145011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#550C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #34951C2semidirect
3. #27488C2semidirect
4. #27192C2semidirect
5. #27064C2semidirect
6. #26586C2semidirect
7. #26530C2semidirect
8. #26320C2semidirect
9. #26090C2semidirect
11. #25368C2semidirect
12. #25060C2semidirect
13. #24630C2semidirect
15. #23799C2semidirect
16. #23678C2semidirect
17. C4×#492C2semidirect
18. C4×#460C2semidirect
19. C4×#461C2semidirect
20. C4×#461C2semidirect
21. #21339C2semidirect
22. #21117C2semidirect
23. C42×SD16C2semidirect
388. C4×Q8SD16semidirect
499. #103#41semidirect
515. C4×C8#41semidirect

Maximal subgroups

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

subgroupindex
#349512
C4×#5502
#274882
#271922
#270642
#265862
#265302
#263202
#260902
#256272
#253682
#250602
#246302
#241882
#237992
#236782
C4×#4922
C4×#4602
C4×#4612
#213392
#211172
C42×SD162