Finite Group Databasebeta

← #6597268

Subgroups — #6597268

Order 512.

1949 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36261C211yesmaximal, characteristic, complemented
2C4×#550C211yesmaximal, characteristic
3#33069C211yesmaximal, characteristic, complemented
4#32955C212yesmaximal, complemented
5#29258C211yesmaximal, characteristic, complemented
6#29238C212yesmaximal, complemented
7#29190C211yesmaximal, characteristic, complemented
8#29163C212yesmaximal, complemented
9#26526C211yesmaximal, characteristic, complemented
10#26460C211yesmaximal, characteristic, complemented
11#26427C212yesmaximal, complemented
12#26357C212yesmaximal, complemented
13#26108C211yesmaximal, characteristic, complemented
14#26042C211yesmaximal, characteristic, complemented
15#25975C212yesmaximal, complemented
16#25967C212yesmaximal, complemented
17#22713C211yesmaximal, characteristic, complemented
18#22700C211yesmaximal, characteristic, complemented
19#22663C211yesmaximal, characteristic, complemented
20#22432C211yesmaximal, characteristic
21#22432C211yesmaximal, characteristic
22C4×#477C211yesmaximal, characteristic, complemented
23#20875C212yesmaximal, complemented
24C2×#554—21no—
25C2×#550C2211yescharacteristic
26C2×C4×#41C2212yes—
27C2×#477C2211yescharacteristic
28C2×#475C2212yes—
29C2×#474C2212yes—
30C2×#436C2211yescharacteristic
31C2×#436C2211yescharacteristic
32C2×#428C2212yes—
33C2×#417C2212yes—
34C2×#417C2212yes—
35#2859C2211yescharacteristic
36#2857C2212yes—
37#2584—21no—
38#2583—22no—
39#2552C2211yescharacteristic
40#2551C2211yescharacteristic
41#2550—21no—
42#2549—22no—
43#2440C2212yes—
44#2440C2212yes—
45#2366—21no—
46#2366C2211yescharacteristic
47#2363—22no—
48#2363C2212yes—
49#2354—21no—
50#2354C2211yescharacteristic
51Q8×C4⋊C4C2211yescharacteristic
52#2349—21no—
53D4×C4⋊C4C2211yescharacteristic
54D4×C4⋊C4C2211yescharacteristic
55#2341C2212yes—
56C4×C4⋊Q8C2211yescharacteristic
57C4×#127—21no—
58C4×#127C2211yescharacteristic
59C4×#121—22no—
60C4×#121C2212yes—
61C2×#389C2212yes—
62C42×Q8C2211yescharacteristic
63C42×D4—21no—
64C42×D4C2211yescharacteristic
65#2099C2212yes—
66#2094C2212yes—
67#2093C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2067C2212yes—
71#2067C2212yes—
72#2065C2212yes—
73#2065C2212yes—
74#2058C2212yes—
75#2023C2212yes—
76#2023C2212yes—
77#1987C2211yescharacteristic
78#1982C2211yescharacteristic
79#1982C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1948C2211yescharacteristic
83#1948C2211yescharacteristic
84#1947C2211yescharacteristic
85#1947C2211yescharacteristic
86#1947C2211yescharacteristic
87#1939C2211yescharacteristic
88#1939C2211yescharacteristic
89#1921C2212yes—
90#1921C2212yes—
91#1921C2211yescharacteristic
92#1921C2211yescharacteristic
93#1895C2212yes—
94#1895C2212yes—
95#1874C2212yes—
96#1874C2212yes—
97#1865C2212yes—
98#1865C2212yes—
99#1864C2212yes—
100#1864C2212yes—
101#1864C2212yes—
102#1864C2212yes—
103#1863C2212yes—
104#1863C2212yes—
105#1863C2211yescharacteristic
106#1863C2211yescharacteristic
107#1862C2212yes—
108#1862C2212yes—
109#1854C2212yes—
110#1854C2212yes—
111#1853C2212yes—
112#1852C2212yes—
113#1851C2212yes—
114#1851C2212yes—
115#1844C2211yescharacteristic
116#1834C2211yescharacteristic
117#1831C2211yescharacteristic
118#1809C2212yes—
119#1809C2212yes—
120#1803C2211yescharacteristic
121#1803C2211yescharacteristic
122#1803C2211yescharacteristic
123#1803C2212yes—
124#1802C2212yes—
125#1797C2212yes—
126#1788C2212yes—
127#1788C2212yes—
128C4×#107C2211yescharacteristic
129C4×#107C2211yescharacteristic
130C4×C4⋊C8C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133#1736C2212yes—
134#1728C2212yes—
135C22×#41C2312yes—
136C22×M16C2312yes—
137C22×M16C2312yes—
138#554—48no—
139#550—24no—
140#550Q818yescomplemented
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2312yes—
144C2×#127—21no—
145C2×#127C2311yescharacteristic
146C2×#125—21no—
147C2×#125—21no—
148C2×C22⋊Q8—22no—
149C2×C22⋊Q8—22no—
150C2×C22⋊Q8—22no—
151C2×#121—22no—
152C2×#121C2312yes—
153C4×#41—44no—
154C4×#41—44no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×D4—21no—
161C2×C4×D4—21no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4—22no—
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4—21no—
169C2×C4×D4D411yescharacteristic
170C2×C4×D4D411yescharacteristic
171C2×C4×D4C2312yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2311yescharacteristic
174C2×#117—22no—
175C2×#117C2312yes—
176C22×C4⋊C4—22no—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C42—22no—
180C22×C42C2312yes—
181#477—24no—
182#475—44no—
183#474—44no—
184#436—24no—
185#436—24no—
186#428—44no—
187C2×#107C2311yescharacteristic
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#107C2312yes—
191C2×#107C2311yescharacteristic
192C2×#107C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×#106C2312yes—
196C2×#106C2312yes—
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×C4⋊C8C2312yes—
201C2×C4⋊C8C2312yes—
202C2×C4⋊C8C2311yescharacteristic
203#417—28no—
204#417—44no—
205C2×#103C2311yescharacteristic
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#103C2312yes—
209C2×#103C2311yescharacteristic
210C2×#103C2311yescharacteristic
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2312yes—
217C2×#102C2312yes—
218C2×#102C2312yes—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C4×C8C2311yescharacteristic
222C2×C4×C8C2311yescharacteristic
223#398—22no—
224#398—22no—
225#398—22no—
226#395—22no—
227#395—22no—
228#395—22no—
229#391—21no—
230#391—22no—
231#390—21no—
232#390—21no—
233#390—22no—
234#390—22no—
235#390—22no—
236#390—21no—
237#390—21no—
238#390C2312yes—
239#390C2312yes—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—22no—
247#389—22no—
248#389—21no—
249#389—22no—
250#389—22no—
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#388—22no—
259#388—22no—
260#388—22no—
261#386—22no—
262#386—22no—
263#386—22no—
264#385—22no—
265#385—22no—
266#385—22no—
267#385—22no—
268#384—21no—
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#384C2312yes—
272#384C2311yescharacteristic
273#384C2311yescharacteristic
274#382—21no—
275#380—22no—
276#380—22no—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4D411yescharacteristic
287C4×C4⋊C4D411yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C22⋊C4—22no—
295C4×C22⋊C4—22no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4D412yes—
298C4×C22⋊C4D412yes—
299C4×C22⋊C4C2312yes—
300C2×#95—22no—
301C43—21no—
302C43C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2312yes—
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2311yescharacteristic
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2311yescharacteristic
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—24no—
328C2×#41—42no—
329C2×#41—42no—
330C2×#41C2×Q818yes—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8C2411yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4C2×D411yescharacteristic
339C22×D4C2412yes—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4C2×D412yes—
346C23×C4C2×D412yes—
347C23×C4C2412yes—
348C2×M16—24no—
349C2×M16—24no—
350C2×M16—24no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—42no—
354C22×C8C2411yescharacteristic
355C22×C8C2412yes—
356C22×C8C2412yes—
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C4⋊Q8—22no—
361C4⋊Q8—41no—
362C4⋊Q8—42no—
363C4⋊Q8—42no—
364C4⋊Q8—44no—
365#127—28no—
366#127—22no—
367#127C2×Q814yes—
368#125—44no—
369#125—44no—
370C22⋊Q8—48no—
371C22⋊Q8—48no—
372C22⋊Q8—48no—
373#121—24no—
374#121—216no—
375#121C2×Q818yes—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—24no—
381C4×Q8—41no—
382C4×Q8—42no—
383C4×Q8—44no—
384C4×Q8C2×Q814yes—
385C4×D4—28no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—42no—
390C4×D4—42no—
391C4×D4—42no—
392C4×D4—48no—
393C4×D4—48no—
394C4×D4—44no—
395C4×D4—44no—
396C4×D4—44no—
397C4×D4—44no—
398C4×D4—82no—
399C4×D4—84no—
400C4×D4C2×Q814yes—
401C4×D4#4114yes—
402#117—24no—
403#117—42no—
404#117—48no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—48no—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4C2×D412yes—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—42no—
473C2×C42—42no—
474C2×C42—48no—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D412yes—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D412yes—
480C2×C42C2×D411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2412yes—
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107—22no—
486#107—22no—
487#107—22no—
488#107—24no—
489#107—22no—
490#107—42no—
491#106—42no—
492#106—42no—
493#106—42no—
494#106—42no—
495C4⋊C8—22no—
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—41no—
499C4⋊C8—42no—
500C4⋊C8—42no—
501#103—24no—
502#103—22no—
503#103—22no—
504#103—24no—
505#103—22no—
506#103#4114yes—
507#102—24no—
508#102—24no—
509#102—42no—
510#102—42no—
511#102—42no—
512#102—42no—
513#102—42no—
514#102—42no—
515C22⋊C8—24no—
516C22⋊C8—24no—
517C4×C8—22no—
518C4×C8—22no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95C2×D412yes—
535#95C2×D412yes—
536#95C2×D412yes—
537C24—22no—
538C24C22×D412yes—
539#41—216no—
540#41—48no—
541#41—48no—
542#41—48no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8—44no—
549C2×Q8—81no—
550C2×Q8—82no—
551C2×Q8—82no—
552C2×Q8C22×Q812yes—
553C2×Q8C2×#4112yes—
554C2×Q8H(5,𝔽2)12yes—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4C22⋊Q814yes—
575C2×D4C22×Q814yes—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—28no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×Q814yes—
622C22×C4C2×#4114yes—
623C22×C4C2511yescharacteristic
624M16—48no—
625M16—84no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8C2×#4112yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
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—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—81no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4C22⋊Q814yes—
688C4⋊C4AGL(1,ℤ/8)14yes—
689C4⋊C4C22×Q812yes—
690C4⋊C4C2×#4112yes—
691C4⋊C4H(5,𝔽2)12yes—
692C22⋊C4—28no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4C22⋊Q818yes—
706C42—24no—
707C42—24no—
708C42—22no—
709C42—21no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—42no—
716C42—42no—
717C42—41no—
718C42—41no—
719C42—44no—
720C42—44no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—81no—
727C42#13714yes—
728C42C22×Q812yes—
729C42C2×#4112yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—24no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23C2×C22⋊Q814yes—
744C23C23×D411yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—84no—
749Q8—164no—
750Q8#55414yescomplemented
751D4—28no—
752D4—24no—
753D4—24no—
754D4—416no—
755D4—48no—
756D4—42no—
757D4—42no—
758D4—84no—
759D4—88no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—416no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4—88no—
821C2×C4—88no—
822C2×C4—164no—
823C2×C4C2×C22⋊Q812yes—
824C2×C4C2×C22⋊Q814yes—
825C2×C4C2×C22⋊Q812yes—
826C2×C4C2×AGL(1,ℤ/8)14yes—
827C2×C4C2×AGL(1,ℤ/8)12yes—
828C2×C4C2×#13712yes—
829C2×C4C2×#13712yes—
830C2×C4C2×#13712yes—
831C2×C4C23×Q811yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4#58511yescharacteristic
837C8—22no—
838C8—41no—
839C8—42no—
840C8—41no—
841C8—42no—
842C8—41no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22C22×C22⋊Q811yescharacteristic
858C22D4×#4111yescharacteristic
859C22#348411yescharacteristic
860C22C22×AGL(1,ℤ/8)11yescharacteristic
861C22C22×#13711yescharacteristic
862C22#358411yescharacteristic
863C22#358511yescharacteristic
864C4—22no—
865C4—22no—
866C4—24no—
867C4—24no—
868C4—22no—
869C4—24no—
870C4—41no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—41no—
875C4—42no—
876C4—81no—
877C4—82no—
878C4—81no—
879C4—82no—
880C4—81no—
881C4—82no—
882C4—81no—
883C4#307914yes—
884C4C2×#55411yescharacteristic
885C4#348111yescharacteristic
886C4#350111yescharacteristic
887C4#351311yescharacteristic
888C2—44no—
889C2—84no—
890C2#3621511yescharacteristic
891C2C2×#307911yescharacteristic
892C2#6049611yescharacteristic
893C2#6144011yescharacteristic
894C2#6146511yescharacteristic
895C2#6158811yescharacteristic
896C2#6159811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#550C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36261C2semidirect
3. #33069C2semidirect
4. #32955C2semidirect
5. #29258C2semidirect
6. #29238C2semidirect
7. #29190C2semidirect
8. #29163C2semidirect
9. #26526C2semidirect
10. #26460C2semidirect
11. #26427C2semidirect
12. #26357C2semidirect
13. #26108C2semidirect
14. #26042C2semidirect
15. #25975C2semidirect
16. #25967C2semidirect
17. #22713C2semidirect
18. #22700C2semidirect
19. #22663C2semidirect
22. C4×#477C2semidirect
23. #20875C2semidirect
140. #550Q8semidirect
750. Q8#554semidirect

Maximal subgroups

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

subgroupindex
#362612
C4×#5502
#330692
#329552
#292582
#292382
#291902
#291632
#265262
#264602
#264272
#263572
#261082
#260422
#259752
#259672
#227132
#227002
#226632
#224322
C4×#4772
#208752