Finite Group Databasebeta

← #6574537

Subgroups — #6574537

Order 512.

2074 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C212yesmaximal, complemented
2#36132C211yesmaximal, characteristic, complemented
3C4×#547C211yesmaximal, characteristic
4#33199C211yesmaximal, characteristic, complemented
5#32961C212yesmaximal, complemented
6#28515C211yesmaximal, characteristic, complemented
7#28287C211yesmaximal, characteristic, complemented
8#26466C211yesmaximal, characteristic, complemented
9#26462C211yesmaximal, characteristic, complemented
10#26339C212yesmaximal, complemented
11#26337C212yesmaximal, complemented
12#26044C211yesmaximal, characteristic, complemented
13#26040C211yesmaximal, characteristic, complemented
14#25962C212yesmaximal, complemented
15#25954C212yesmaximal, complemented
16#24840C212yesmaximal, complemented
17#24306C212yesmaximal, complemented
18#22658C211yesmaximal, characteristic, complemented
19#22657C211yesmaximal, characteristic, complemented
20D4×C4⋊C8C211yesmaximal, characteristic, complemented
21#22417C211yesmaximal, characteristic
22#22417C211yesmaximal, characteristic
23C4×#478C211yesmaximal, characteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#533C2212yes—
26C2×C4×#41C2212yes—
27#3076—216no—
28C2×#479C2212yes—
29C2×#479C2212yes—
30C2×#479C2212yes—
31C2×#477C2212yes—
32C2×#475C2212yes—
33C2×#478C2212yes—
34C2×#478C2211yescharacteristic
35C2×#476C2212yes—
36C2×#474C2212yes—
37C2×C8×D4C2211yescharacteristic
38C2×C8×D4C2211yescharacteristic
39C2×#427C2212yes—
40C2×#427C2212yes—
41C22×C4⋊C8C2212yes—
42C2×#416C2212yes—
43C2×#416C2212yes—
44#2859C2211yescharacteristic
45#2851C2212yes—
46#2551C2211yescharacteristic
47#2551C2211yescharacteristic
48#2465—22no—
49#2465—22no—
50#2452—21no—
51#2452—21no—
52#2439C2212yes—
53#2439C2212yes—
54#2365—21no—
55#2365—21no—
56#2365C2211yescharacteristic
57#2362C2212yes—
58#2361—21no—
59#2359—22no—
60#2354C2211yescharacteristic
61#2354C2211yescharacteristic
62#2354C2211yescharacteristic
63D4×C4⋊C4C2211yescharacteristic
64#2344—21no—
65#2339C2212yes—
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68C4×C22⋊Q8C2212yes—
69C4×#123—22no—
70C4×#121—21no—
71C42×D4C2211yescharacteristic
72C42×D4C2211yescharacteristic
73C2×C4×C4⋊C4—21no—
74#2097C2212yes—
75#2097C2212yes—
76#2088C2212yes—
77#2086C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2058C2212yes—
83#2057C2212yes—
84#2024C2212yes—
85#2024C2212yes—
86#1989C2212yes—
87#1989C2211yescharacteristic
88#1981C2211yescharacteristic
89#1981C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1949C2211yescharacteristic
93#1949C2212yes—
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1939C2211yescharacteristic
99#1939C2211yescharacteristic
100#1921C2211yescharacteristic
101#1919C2211yescharacteristic
102#1892C2212yes—
103#1892C2212yes—
104#1873C2212yes—
105#1873C2212yes—
106#1865C2212yes—
107#1864C2212yes—
108#1864C2211yescharacteristic
109#1863C2212yes—
110#1862C2211yescharacteristic
111#1862C2212yes—
112#1854C2212yes—
113#1854C2212yes—
114#1854C2212yes—
115#1854C2212yes—
116#1850C2212yes—
117#1850C2212yes—
118#1845C2211yescharacteristic
119#1844C2211yescharacteristic
120#1842C2211yescharacteristic
121#1808C2212yes—
122#1807C2212yes—
123#1805C2212yes—
124#1804C2212yes—
125#1804C2211yescharacteristic
126#1802C2211yescharacteristic
127#1802C2211yescharacteristic
128#1797C2212yes—
129#1788C2212yes—
130#1788C2212yes—
131C4×#107C2211yescharacteristic
132C4×#106C2211yescharacteristic
133C4×C4⋊C8C2211yescharacteristic
134C4×#102C2211yescharacteristic
135C4×#102C2211yescharacteristic
136C22×#41C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139#547—24no—
140#547Q818yescomplemented
141#533—28no—
142#533—44no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2312yes—
148C2×#125C2312yes—
149C2×#125C2311yescharacteristic
150C2×#123—22no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8C2312yes—
154C2×#121—21no—
155C4×#41—28no—
156C4×#41—44no—
157C2×C4×Q8—22no—
158C2×C4×Q8—22no—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4D411yescharacteristic
164C2×C4×D4D411yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2312yes—
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×#117—22no—
171C2×#117C2312yes—
172C2×#117C2312yes—
173C2×#117C2312yes—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C42—22no—
177C22×C42—21no—
178C22×C42C2312yes—
179#479—28no—
180#479—28no—
181#479—44no—
182#478—28no—
183#478D418yescomplemented
184#477—28no—
185#476—28no—
186#475—28no—
187#474—28no—
188C8×D4—24no—
189C8×D4—24no—
190#427—28no—
191#427—28no—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#107C2311yescharacteristic
197C2×#107C2311yescharacteristic
198C2×#106C2312yes—
199C2×#106C2312yes—
200C2×#106C2312yes—
201C2×#106C2312yes—
202C2×#106C2311yescharacteristic
203C2×#106C2311yescharacteristic
204C2×C4⋊C8—28no—
205C2×C4⋊C8C2312yes—
206C2×C4⋊C8C2312yes—
207C2×C4⋊C8C2312yes—
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2311yescharacteristic
213#416—28no—
214#416—28no—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2311yescharacteristic
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2311yescharacteristic
229C2×C22⋊C8C2312yes—
230C2×C22⋊C8C2312yes—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233#396—22no—
234#396—22no—
235#395—22no—
236#395—22no—
237#393—22no—
238#393—22no—
239#391—22no—
240#391—22no—
241#391C2312yes—
242#391C2312yes—
243#390—21no—
244#390—21no—
245#390—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389—21no—
254#389—21no—
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#388—22no—
261#388—22no—
262#388—22no—
263#388—22no—
264#388—22no—
265#387—21no—
266#387—21no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387—22no—
274#386—22no—
275#386—22no—
276#385—22no—
277#385—22no—
278#385—22no—
279#385—22no—
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#382C2311yescharacteristic
284#382C2312yes—
285#381—22no—
286#380—21no—
287#380C2312yes—
288#380C2312yes—
289#380C2312yes—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C22⋊C4—22no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4D412yes—
313C4×C22⋊C4D412yes—
314C4×C22⋊C4C2312yes—
315C2×#95—22no—
316C43C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2311yescharacteristic
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#340C2311yescharacteristic
331#336C2312yes—
332#336C2312yes—
333#336C2311yescharacteristic
334#336C2311yescharacteristic
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—24no—
338C2×#41—42no—
339C2×#41—42no—
340C2×#41C2×Q818yes—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8C2412yes—
344C22×D4—22no—
345C22×D4C2×D411yescharacteristic
346C22×D4C2411yescharacteristic
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—21no—
350C23×C4—22no—
351C23×C4—21no—
352C23×C4C2×D412yes—
353C23×C4C2×D412yes—
354C23×C4C2412yes—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—24no—
358C22×C8—24no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C4⋊Q8—24no—
368C4⋊Q8—24no—
369C4⋊Q8—22no—
370C4⋊Q8—42no—
371C4⋊Q8—42no—
372C4⋊Q8—44no—
373C4⋊Q8—44no—
374C4⋊Q8C2×Q814yes—
375#125—24no—
376#125—22no—
377#125—24no—
378#125C2×D414yes—
379#123—216no—
380C22⋊Q8—24no—
381C22⋊Q8—48no—
382C22⋊Q8—48no—
383C22⋊Q8C2×Q818yes—
384#121—28no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—42no—
389C4×Q8—48no—
390C4×Q8—48no—
391C4×D4—24no—
392C4×D4—24no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—42no—
397C4×D4—41no—
398C4×D4—42no—
399C4×D4—48no—
400C4×D4—48no—
401C4×D4C2×D414yes—
402C4×D4C2×Q814yes—
403C4×D4C2×Q814yes—
404C4×D4#4114yes—
405#117—24no—
406#117—24no—
407#117—24no—
408#117—48no—
409#117—42no—
410#117—42no—
411#117—42no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4C2×D412yes—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C42—24no—
464C2×C42—24no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—48no—
476C2×C42—44no—
477C2×C42C2×D412yes—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D412yes—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2412yes—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487#107—24no—
488#107—24no—
489#107—24no—
490#107—41no—
491#107—42no—
492#107C2×D414yes—
493#106—24no—
494#106—24no—
495#106—24no—
496#106—41no—
497#106—42no—
498#106C2×D414yes—
499C4⋊C8—24no—
500C4⋊C8—24no—
501C4⋊C8—24no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—42no—
506C4⋊C8C2×D414yes—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#102—24no—
516#102—24no—
517#102—22no—
518#102—22no—
519#102C2×D414yes—
520#102C2×D414yes—
521C22⋊C8—24no—
522C22⋊C8—24no—
523C4×C8—22no—
524C4×C8—22no—
525#95—22no—
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—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95C2×D412yes—
547#95C2×D412yes—
548#95C2×D412yes—
549C24—21no—
550C24C22×D412yes—
551#41—216no—
552#41—48no—
553#41—48no—
554#41—48no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—82no—
565C2×Q8—82no—
566C2×Q8C22×Q814yes—
567C2×D4—28no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4C22⋊Q814yes—
576C2×D4C22×D412yes—
577C2×D4C22×Q812yes—
578C2×D42−1+412yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—28no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—44no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—82no—
614C22×C4—81no—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×Q814yes—
625C22×C4C2×#4114yes—
626C22×C4C2511yescharacteristic
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—48no—
644C2×C8—48no—
645C2×C8C22×D412yes—
646C2×C8C22×D412yes—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4C22⋊Q814yes—
687C4⋊C4#13514yes—
688C4⋊C4C22×D412yes—
689C4⋊C4C22×D412yes—
690C4⋊C4C22×D412yes—
691C4⋊C4C22×Q812yes—
692C22⋊C4—28no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—42no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4C22⋊Q818yes—
706C42—24no—
707C42—24no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—41no—
715C42—41no—
716C42—44no—
717C42—44no—
718C42—44no—
719C42—44no—
720C42—42no—
721C42—42no—
722C42—44no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42C22×D412yes—
727C42C22×Q812yes—
728C42C2×#4112yes—
729C42H(5,𝔽2)12yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C2×C22⋊Q814yes—
744C23C23×D411yescharacteristic
745Q8—24no—
746Q8—24no—
747Q8—42no—
748Q8—42no—
749Q8—88no—
750Q8—88no—
751D4—28no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—416no—
756D4D4×Q814yes—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
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—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—416no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—84no—
818C2×C4—88no—
819C2×C4—84no—
820C2×C4C2×C22⋊Q812yes—
821C2×C4C2×C22⋊Q814yes—
822C2×C4C2×C22⋊Q812yes—
823C2×C4D4212yes—
824C2×C4D4212yes—
825C2×C4C2×#13514yes—
826C2×C4C2×#13512yes—
827C2×C4#57512yes—
828C2×C4C23×D411yescharacteristic
829C2×C4C23×Q811yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4#58511yescharacteristic
834C8—22no—
835C8—22no—
836C8—42no—
837C8—42no—
838C8—41no—
839C8—41no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22C22×C22⋊Q811yescharacteristic
855C22C2×D4211yescharacteristic
856C22#348911yescharacteristic
857C22C22×#13511yescharacteristic
858C22C2×#57511yescharacteristic
859C22#358411yescharacteristic
860C22#358611yescharacteristic
861C4—22no—
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—41no—
872C4—41no—
873C4—44no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4#307614yescomplemented
881C4C2×D4×Q811yescharacteristic
882C4D4×#4111yescharacteristic
883C4#350111yescharacteristic
884C4#352011yescharacteristic
885C2—44no—
886C2—44no—
887C2D4×C22⋊Q811yescharacteristic
888C2C2×#307611yescharacteristic
889C2#6049911yescharacteristic
890C2D4×#13511yescharacteristic
891C2#6106711yescharacteristic
892C2#6210511yescharacteristic
893C2#6214111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
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. C2×#3076C2semidirect
2. #36132C2semidirect
4. #33199C2semidirect
5. #32961C2semidirect
6. #28515C2semidirect
7. #28287C2semidirect
8. #26466C2semidirect
9. #26462C2semidirect
10. #26339C2semidirect
11. #26337C2semidirect
12. #26044C2semidirect
13. #26040C2semidirect
14. #25962C2semidirect
15. #25954C2semidirect
16. #24840C2semidirect
17. #24306C2semidirect
18. #22658C2semidirect
19. #22657C2semidirect
20. D4×C4⋊C8C2semidirect
23. C4×#478C2semidirect
140. #547Q8semidirect
183. #478D4semidirect
880. C4#3076semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
#361322
C4×#5472
#331992
#329612
#285152
#282872
#264662
#264622
#263392
#263372
#260442
#260402
#259622
#259542
#248402
#243062
#226582
#226572
D4×C4⋊C82
#224172
C4×#4782