Finite Group Databasebeta

← #6447390

Subgroups — #6447390

Order 512.

1903 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#34932C211yesmaximal, characteristic
2C4×D4×Q8C211yesmaximal, characteristic, complemented
3#27535C212yesmaximal, complemented
4#27115C212yesmaximal, complemented
5#26677C212yesmaximal, complemented
6#26532C211yesmaximal, characteristic, complemented
7#26296C211yesmaximal, characteristic, complemented
8#26112C211yesmaximal, characteristic, complemented
9#25884C211yesmaximal, characteristic, complemented
10#25320C211yesmaximal, characteristic, complemented
11#24965C211yesmaximal, characteristic
12#24910C212yesmaximal, complemented
13#24813C211yesmaximal, characteristic, complemented
14#24239C211yesmaximal, characteristic
15#23762C212yesmaximal, complemented
16#23710C212yesmaximal, complemented
17#21647C211yesmaximal, characteristic, complemented
18#21615C211yesmaximal, characteristic, complemented
19#21504C211yesmaximal, characteristic, complemented
20#21454C212yesmaximal, complemented
21#21270C211yesmaximal, characteristic, complemented
22#20740C212yesmaximal, complemented
23C4×#440C211yesmaximal, characteristic, complemented
24C2×D4×Q8C2211yescharacteristic
25C2×#529—21no—
26C22×C4×Q8C2212yes—
27C2×#487C2211yescharacteristic
28C2×#475C2211yescharacteristic
29C2×#461C2211yescharacteristic
30C2×#448C2212yes—
31C2×#440C2211yescharacteristic
32C2×#440C2211yescharacteristic
33C2×#440C2212yes—
34C2×C4×SD16C2211yescharacteristic
35C2×#432C2212yes—
36#2553—22no—
37#2552C2211yescharacteristic
38#2547C2211yescharacteristic
39#2542C2211yescharacteristic
40#2537C2211yescharacteristic
41#2496C2212yes—
42#2489—21no—
43#2427—21no—
44#2422C2212yes—
45#2395—22no—
46#2365—21no—
47#2365C2211yescharacteristic
48#2360—22no—
49#2360C2212yes—
50Q8×C4⋊C4C2211yescharacteristic
51D4×C4⋊C4—21no—
52D4×C4⋊C4C2211yescharacteristic
53Q8×C22⋊C4C2212yes—
54C4×C4⋊Q8—21no—
55C4×C4⋊Q8C2211yescharacteristic
56C4×C4⋊Q8C2211yescharacteristic
57C4×C22⋊Q8—21no—
58C4×C22⋊Q8—22no—
59C4×C22⋊Q8C2212yes—
60C4×#121C2212yes—
61#2285C2212yes—
62C42×Q8C2211yescharacteristic
63C42×D4—21no—
64C42×D4C2211yescharacteristic
65C42×D4C2211yescharacteristic
66#2100C2212yes—
67#2095C2212yes—
68#2087C2212yes—
69#2084C2212yes—
70#2075C2212yes—
71#2075C2212yes—
72#2075C2212yes—
73#2072C2212yes—
74#2068C2212yes—
75#2065C2212yes—
76#2055C2212yes—
77#2035C2212yes—
78#2035C2212yes—
79#2035C2212yes—
80#2033C2212yes—
81#2000C2212yes—
82#1990C2211yescharacteristic
83#1988C2211yescharacteristic
84#1981C2211yescharacteristic
85#1956C2211yescharacteristic
86#1954C2211yescharacteristic
87#1954C2211yescharacteristic
88#1947C2211yescharacteristic
89#1947C2211yescharacteristic
90#1939C2211yescharacteristic
91#1939C2211yescharacteristic
92#1935C2212yes—
93#1935C2212yes—
94#1928C2212yes—
95#1924C2212yes—
96#1924C2212yes—
97#1920C2212yes—
98#1880C2212yes—
99#1880C2212yes—
100#1877C2212yes—
101#1874C2212yes—
102#1863C2212yes—
103#1863C2212yes—
104#1863C2212yes—
105#1852C2212yes—
106#1834C2211yescharacteristic
107#1823C2212yes—
108#1823C2212yes—
109#1803C2212yes—
110#1803C2211yescharacteristic
111#1803C2212yes—
112#1803C2212yes—
113#1803C2212yes—
114#1802C2211yescharacteristic
115#1787C2212yes—
116#1787C2212yes—
117#1787C2212yes—
118#1776C2211yescharacteristic
119#1776C2211yescharacteristic
120#1776C2212yes—
121C4×#107C2211yescharacteristic
122#1767C2211yescharacteristic
123#1763C2212yes—
124#1763C2211yescharacteristic
125#1763C2212yes—
126#1763C2212yes—
127#1763C2211yescharacteristic
128#1763C2212yes—
129#1762C2211yescharacteristic
130#1762C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#102C2211yescharacteristic
133#1749C2212yes—
134C4×#97C2211yescharacteristic
135C23×Q8C2312yes—
136C22×SD16C2312yes—
137C22×SD16C2311yescharacteristic
138D4×Q8—24no—
139D4×Q8—24no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143#529—48no—
144C2×#126—22no—
145C2×#125—21no—
146C2×#124—21no—
147C2×#123—22no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8C2312yes—
152C2×#121—21no—
153C2×#121C2312yes—
154C2×C4×Q8—22no—
155C2×C4×Q8—21no—
156C2×C4×Q8—22no—
157C2×C4×Q8—28no—
158C2×C4×Q8—44no—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165C2×C4×D4—21no—
166C2×C4×D4—21no—
167C2×C4×D4—22no—
168C2×C4×D4D411yescharacteristic
169C2×C4×D4D411yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2311yescharacteristic
173C2×C4×D4C2311yescharacteristic
174C2×#117—22no—
175C22×C4⋊C4—22no—
176C22×C4⋊C4C2312yes—
177C22×C42—22no—
178C22×C42—21no—
179C22×C42C2312yes—
180#487—24no—
181#475—24no—
182#461—24no—
183#448—28no—
184#440—24no—
185#440—24no—
186#440—44no—
187C4×SD16—24no—
188#432—44no—
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#107C2312yes—
193C2×#106C2312yes—
194C2×#106C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×#102C2311yescharacteristic
214C2×#102C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2312yes—
219C2×#97C2311yescharacteristic
220C2×#97C2312yes—
221C2×#97C2311yescharacteristic
222C2×#97C2311yescharacteristic
223C2×#97C2311yescharacteristic
224C2×C4×C8C2311yescharacteristic
225C2×C4×C8C2311yescharacteristic
226#400—22no—
227#399—22no—
228#398—22no—
229#397—22no—
230#397—22no—
231#397—22no—
232#394—22no—
233#394—22no—
234#391—21no—
235#391—21no—
236#391—22no—
237#391—22no—
238#391C2312yes—
239#391C2312yes—
240#390C2312yes—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—22no—
248#389—22no—
249#389C2312yes—
250#389C2312yes—
251#389C2312yes—
252#388—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#386—22no—
258#385—22no—
259#385—22no—
260#385—22no—
261#385—22no—
262#384—21no—
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#384C2312yes—
266#384C2312yes—
267#382—22no—
268#380—22no—
269#380—21no—
270#380—22no—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—22no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4D411yescharacteristic
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C22⋊C4—22no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—22no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4D412yes—
303C4×C22⋊C4D412yes—
304C4×C22⋊C4C2312yes—
305C43—21no—
306C43C2311yescharacteristic
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2312yes—
320#340C2312yes—
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8C2412yes—
335C22×Q8C2411yescharacteristic
336C22×D4—22no—
337C22×D4C2×D411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4C2×D412yes—
345C23×C4C2×D412yes—
346C23×C4C2412yes—
347C2×SD16—22no—
348C2×SD16—22no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—42no—
352C2×SD16#4114yes—
353C22×C8C2412yes—
354C22×C8C2411yescharacteristic
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C4⋊Q8—28no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8#4114yes—
364#126—48no—
365#125—44no—
366#124—44no—
367#123—48no—
368C22⋊Q8—216no—
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371C22⋊Q8—44no—
372C22⋊Q8—44no—
373#121—24no—
374#121—42no—
375#121—44no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—24no—
379C4×Q8—22no—
380C4×Q8—24no—
381C4×Q8—24no—
382C4×Q8—24no—
383C4×Q8—48no—
384C4×Q8—42no—
385C4×Q8—42no—
386C4×Q8—41no—
387C4×Q8—48no—
388C4×Q8—44no—
389C4×Q8#4114yes—
390C4×Q8#4114yes—
391C4×D4—28no—
392C4×D4—24no—
393C4×D4—24no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—41no—
402C4×D4—48no—
403C4×D4—44no—
404#117—48no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—48no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D412yes—
455C2×C22⋊C4C2×D412yes—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—24no—
459C2×C42—24no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—48no—
472C2×C42—44no—
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#107—22no—
484#107—22no—
485#107—42no—
486#107—42no—
487#106—22no—
488#106—24no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—42no—
503#103—42no—
504#103—42no—
505#102—22no—
506#102—22no—
507#102—22no—
508#102—42no—
509C22⋊C8—24no—
510C22⋊C8—42no—
511C22⋊C8—42no—
512C22⋊C8—42no—
513#97—22no—
514#97—22no—
515#97—22no—
516#97—24no—
517#97—41no—
518C4×C8—22no—
519C4×C8—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541C24—21no—
542C24C22×D412yes—
543C2×Q8—28no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—48no—
555C2×Q8—48no—
556C2×Q8—48no—
557C2×Q8—48no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8C2×#4114yes—
562C2×Q8C2×#4112yes—
563C2×Q8C2×#4112yes—
564C2×Q8C2×#4112yes—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4AGL(1,ℤ/8)14yes—
576C2×D4C2×#4112yes—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—82no—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C2511yescharacteristic
625SD16—28no—
626SD16—48no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8C2×#4112yes—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4#13714yes—
686C4⋊C4C2×#4112yes—
687C4⋊C4C2×#4112yes—
688C22⋊C4—28no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—42no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C42—24no—
703C42—24no—
704C42—24no—
705C42—24no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—22no—
710C42—22no—
711C42—21no—
712C42—41no—
713C42—41no—
714C42—44no—
715C42—44no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—42no—
720C42—44no—
721C42—44no—
722C42—42no—
723C42—42no—
724C42—81no—
725C42C2×#4112yes—
726C42C2×#4112yes—
727C42C2×#4112yes—
728C42H(5,𝔽2)12yes—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23C2×AGL(1,ℤ/8)14yes—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—24no—
748Q8—24no—
749Q8—416no—
750Q8—42no—
751Q8—42no—
752Q8—84no—
753Q8#52914yescomplemented
754D4—28no—
755D4—22no—
756D4—22no—
757D4—41no—
758D4—41no—
759D4—88no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—416no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—88no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4#52512yes—
825C2×C4#52512yes—
826C2×C4#54612yes—
827C2×C4#54612yes—
828C2×C4C2×AGL(1,ℤ/8)12yes—
829C2×C4C2×#13714yes—
830C2×C4C2×#13712yes—
831C2×C4C22×#4111yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4#58511yescharacteristic
837C8—22no—
838C8—41no—
839C8—42no—
840C8—41no—
841C8—41no—
842C8—42no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C2×#52511yescharacteristic
858C22C2×#54611yescharacteristic
859C22D4×#4111yescharacteristic
860C22C22×AGL(1,ℤ/8)11yescharacteristic
861C22C22×#13711yescharacteristic
862C22#358611yescharacteristic
863C22#358611yescharacteristic
864C4—24no—
865C4—22no—
866C4—22no—
867C4—24no—
868C4—22no—
869C4—41no—
870C4—41no—
871C4—42no—
872C4—44no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4—81no—
880C4—82no—
881C4—82no—
882C4—81no—
883C4#311214yes—
884C4C2×#52911yescharacteristic
885C4#346011yescharacteristic
886C4#347511yescharacteristic
887C4#348111yescharacteristic
888C2—44no—
889C2—82no—
890C2#3470011yescharacteristic
891C2C2×#311211yescharacteristic
892C2#6057711yescharacteristic
893C2#6115711yescharacteristic
894C2#6116111yescharacteristic
895C2#6145211yescharacteristic
896C2#6147011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
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
2. C4×D4×Q8C2semidirect
3. #27535C2semidirect
4. #27115C2semidirect
5. #26677C2semidirect
6. #26532C2semidirect
7. #26296C2semidirect
8. #26112C2semidirect
9. #25884C2semidirect
10. #25320C2semidirect
12. #24910C2semidirect
13. #24813C2semidirect
15. #23762C2semidirect
16. #23710C2semidirect
17. #21647C2semidirect
18. #21615C2semidirect
19. #21504C2semidirect
20. #21454C2semidirect
21. #21270C2semidirect
22. #20740C2semidirect
23. C4×#440C2semidirect
753. Q8#529semidirect

Maximal subgroups

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

subgroupindex
#349322
C4×D4×Q82
#275352
#271152
#266772
#265322
#262962
#261122
#258842
#253202
#249652
#249102
#248132
#242392
#237622
#237102
#216472
#216152
#215042
#214542
#212702
#207402
C4×#4402