Finite Group Databasebeta

← #7533905

Subgroups — #7533905

Order 512.

1688 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#36477C211yesmaximal, characteristic, complemented
3#31542C212yesmaximal, complemented
4#31523C212yesmaximal, complemented
5#29207C211yesmaximal, characteristic, complemented
6#29149C211yesmaximal, characteristic, complemented
7#28801C212yesmaximal, complemented
8#28273C211yesmaximal, characteristic, complemented
9#28263C211yesmaximal, characteristic, complemented
10#27022C212yesmaximal, complemented
11#27011C212yesmaximal, complemented
12#26538C212yesmaximal, complemented
13#26036C212yesmaximal, complemented
14#25058C211yesmaximal, characteristic, complemented
15#25057C211yesmaximal, characteristic, complemented
16#24326C211yesmaximal, characteristic, complemented
17#24326C211yesmaximal, characteristic, complemented
18#23150C211yesmaximal, characteristic, complemented
19#23108C212yesmaximal
20#22523C211yesmaximal, characteristic, complemented
21Q8×#102C211yesmaximal, characteristic, complemented
22#21613C211yesmaximal, characteristic, complemented
23C4×#459C211yesmaximal, characteristic
24C2×D4×Q8—21no—
25C2×D4×Q8C2211yescharacteristic
26C2×D4×Q8C2211yescharacteristic
27C2×#474C2211yescharacteristic
28C2×#459C2211yescharacteristic
29C2×#446C2211yescharacteristic
30C2×C8×Q8C2211yescharacteristic
31C2×C4×D8C2211yescharacteristic
32C2×C4×D8C2211yescharacteristic
33#2859C2211yescharacteristic
34#2855—21no—
35#2683—22no—
36#2608—22no—
37#2587—22no—
38#2570C2212yes—
39#2566C2212yes—
40#2551C2212yes—
41#2538—21no—
42#2538C2211yescharacteristic
43#2538C2211yescharacteristic
44#2538C2211yescharacteristic
45#2538C2211yescharacteristic
46#2497—21no—
47#2452—22no—
48#2452C2212yes—
49#2452C2212yes—
50#2429—21no—
51#2409—21no—
52#2409—21no—
53#2370C2212yes—
54#2366C2212yes—
55#2357C2212yes—
56#2355C2211yescharacteristic
57Q8×C4⋊C4C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C4×C22⋊Q8—21no—
62C42×D4C2211yescharacteristic
63#2094C2212yes—
64#2092C2212yes—
65#2085C2212yes—
66#2084C2212yes—
67#2067C2212yes—
68#2067C2212yes—
69#2065C2212yes—
70#2065C2212yes—
71#2059C2212yes—
72#2059C2212yes—
73#2057C2212yes—
74#2057C2212yes—
75#2025C2212yes—
76#2025C2212yes—
77#2023C2212yes—
78#2023C2212yes—
79#1993C2212yes—
80#1990C2211yescharacteristic
81#1990C2211yescharacteristic
82#1990C2212yes—
83#1988C2211yescharacteristic
84#1988C2212yes—
85#1987C2212yes—
86#1984C2211yescharacteristic
87#1984C2211yescharacteristic
88#1982C2211yescharacteristic
89#1972C2212yes—
90#1970C2212yes—
91#1961C2212yes—
92#1949C2212yes—
93#1949C2212yes—
94#1948C2211yescharacteristic
95#1947C2211yescharacteristic
96#1944C2212yes—
97#1942C2212yes—
98#1940C2212yes—
99#1926C2212yes—
100#1925C2212yes—
101#1925C2211yescharacteristic
102#1925C2211yescharacteristic
103#1921C2212yes—
104#1921C2212yes—
105#1919C2212yes—
106#1917C2212yes—
107#1916C2212yes—
108#1879C2212yes—
109#1879C2212yes—
110#1879C2211yescharacteristic
111#1879C2211yescharacteristic
112#1864C2212yes—
113#1862C2212yes—
114#1862C2212yes—
115#1845C2211yescharacteristic
116#1844C2211yescharacteristic
117#1836C2212yes—
118#1804C2212yes—
119#1802C2211yescharacteristic
120#1802C2211yescharacteristic
121#1802C2212yes—
122#1802C2211yescharacteristic
123#1802C2211yescharacteristic
124#1802C2211yescharacteristic
125#1802C2211yescharacteristic
126#1776C2212yes—
127#1771C2212yes—
128#1767C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130#1762C2212yes—
131#1762C2212yes—
132C4×#102C2212yes—
133C4×#102C2211yescharacteristic
134C4×#102C2211yescharacteristic
135C23×Q8—21no—
136C23×Q8—21no—
137C22×D8C2311yescharacteristic
138C22×D8C2311yescharacteristic
139D4×Q8—24no—
140D4×Q8—24no—
141D4×Q8—42no—
142D4×Q8—42no—
143D4×Q8—48no—
144C2×C4⋊Q8—22no—
145C2×C4⋊Q8D411yescharacteristic
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2311yescharacteristic
149C2×#127C2311yescharacteristic
150C2×#125C2312yes—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—22no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165C2×C4×D4—22no—
166C2×C4×D4—21no—
167C2×C4×D4—21no—
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2312yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2311yescharacteristic
174C2×C4×D4C2311yescharacteristic
175C22×C42—21no—
176#474—24no—
177#459Q818yescomplemented
178#446—42no—
179C8×Q8—42no—
180C4×D8—42no—
181C4×D8—42no—
182C2×#107C2312yes—
183C2×#107C2311yescharacteristic
184C2×#107C2311yescharacteristic
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2311yescharacteristic
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2311yescharacteristic
199C2×#102C2312yes—
200C2×#102C2311yescharacteristic
201C2×#102C2312yes—
202C2×#102C2311yescharacteristic
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2311yescharacteristic
206C2×#102C2311yescharacteristic
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#97C2312yes—
211C2×#97C2312yes—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2312yes—
215#400—22no—
216#398—22no—
217#396—22no—
218#396—22no—
219#396—22no—
220#396—22no—
221#396—22no—
222#396—22no—
223#396—22no—
224#396—22no—
225#395—22no—
226#395—22no—
227#393—22no—
228#393—22no—
229#391—21no—
230#391—21no—
231#391D411yescharacteristic
232#391D411yescharacteristic
233#390—22no—
234#390—21no—
235#390—21no—
236#390C2311yescharacteristic
237#390C2311yescharacteristic
238#390C2312yes—
239#390C2312yes—
240#390C2312yes—
241#390C2312yes—
242#389—22no—
243#389—21no—
244#389—22no—
245#389—22no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389D412yes—
252#389D412yes—
253#389C2312yes—
254#389C2312yes—
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#388—22no—
259#388—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#386—22no—
266#386—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#384D411yescharacteristic
272#384C2311yescharacteristic
273#384C2311yescharacteristic
274#384C2312yes—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#382C2312yes—
278#382C2312yes—
279#381—22no—
280#380—21no—
281#380—21no—
282#380—21no—
283#380—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C22⋊C4—21no—
296C4×C22⋊C4—21no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—22no—
299C43C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323C22×Q8—21no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—44no—
327C22×Q8—44no—
328C22×Q8—44no—
329C22×Q8—44no—
330C22×Q8—82no—
331C22×Q8—82no—
332C22×Q8C2×D411yescharacteristic
333C22×Q8C2×D411yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C2411yescharacteristic
337C22×D4C2411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—21no—
346C2×D8—41no—
347C2×D8—41no—
348C2×D8—41no—
349C2×D8—41no—
350C2×D8C2×Q814yescomplemented
351C2×D8C2×Q814yescomplemented
352C22×C8C2412yes—
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C4⋊Q8—24no—
359C4⋊Q8—24no—
360C4⋊Q8—24no—
361C4⋊Q8—22no—
362C4⋊Q8—42no—
363C4⋊Q8—42no—
364C4⋊Q8—48no—
365C4⋊Q8#4114yes—
366#127—22no—
367#127C2×Q814yes—
368#125—42no—
369#125—42no—
370C22⋊Q8—48no—
371C22⋊Q8—48no—
372C22⋊Q8—44no—
373C22⋊Q8—44no—
374C22⋊Q8—48no—
375C22⋊Q8—48no—
376C22⋊Q8—44no—
377C22⋊Q8—44no—
378C22⋊Q8—44no—
379C22⋊Q8—82no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—44no—
385C4×Q8—82no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—41no—
396C4×D4—41no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—44no—
400C4×D4—48no—
401C4×D4—82no—
402C4×D4C2×Q814yescomplemented
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4C2×D412yes—
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2×D412yes—
428C2×C4⋊C4C2×D412yes—
429C2×C4⋊C4C2×D412yes—
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C42—22no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—82no—
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2412yes—
471C2×C42C2412yes—
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475#107—24no—
476#107—42no—
477#107—42no—
478#107—41no—
479#107—41no—
480#106—42no—
481#106—42no—
482#106—42no—
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—42no—
487C4⋊C8—42no—
488C4⋊C8C2×Q814yescomplemented
489#102—24no—
490#102—41no—
491#102—41no—
492#102—42no—
493#102—42no—
494#102—42no—
495#102—42no—
496#102—42no—
497#102—41no—
498#102—41no—
499#102—41no—
500#102—41no—
501#102C2×Q814yescomplemented
502#102C2×Q814yescomplemented
503#97—24no—
504#97—42no—
505C4×C8—22no—
506C4×C8—22no—
507C4×C8—42no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95C2×D412yes—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527C24—21no—
528C24—21no—
529C24—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—24no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—42no—
540C2×Q8—44no—
541C2×Q8—42no—
542C2×Q8—82no—
543C2×Q8—82no—
544C2×Q8—816no—
545C2×Q8—816no—
546C2×Q8AGL(1,ℤ/8)14yes—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C22×Q812yes—
569C2×D4C22×Q812yes—
570C2×D4C22×Q812yes—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C2511yescharacteristic
612D8—44no—
613D8—44no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—22no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8C22×Q812yes—
631C2×C8C22×Q812yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—81no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—82no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4C22×Q812yes—
677C4⋊C4C2×#4114yes—
678C22⋊C4—24no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—44no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42—41no—
707C42—44no—
708C42—42no—
709C42—82no—
710C42—81no—
711C42—81no—
712C42—82no—
713C42C22×Q812yes—
714C42C2×#4112yes—
715C42H(5,𝔽2)12yes—
716C422−1+412yes—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23C23×D411yescharacteristic
739Q8—28no—
740Q8—44no—
741Q8—48no—
742Q8—88no—
743Q8—88no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—84no—
758C2×C4—21no—
759C2×C4—21no—
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—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
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—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—84no—
809C2×C4—88no—
810C2×C4—88no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4#54612yes—
816C2×C4#54612yes—
817C2×C4D4×Q812yes—
818C2×C4D4×Q812yes—
819C2×C4C2×AGL(1,ℤ/8)14yes—
820C2×C4C2×AGL(1,ℤ/8)12yes—
821C2×C4#57612yes—
822C2×C4C23×Q811yescharacteristic
823C2×C4C22×#4111yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×2−1+411yescharacteristic
826C2×C4#58511yescharacteristic
827C2×C4#58511yescharacteristic
828C8—22no—
829C8—22no—
830C8—42no—
831C8—41no—
832C8—41no—
833C8—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×#54611yescharacteristic
856C22C2×D4×Q811yescharacteristic
857C22#348711yescharacteristic
858C22C22×AGL(1,ℤ/8)11yescharacteristic
859C22C2×#57611yescharacteristic
860C22#358411yescharacteristic
861C22#358611yescharacteristic
862C4—22no—
863C4—22no—
864C4—22no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—44no—
871C4—41no—
872C4—41no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—81no—
880C4#331814yes—
881C4Q8×#4111yescharacteristic
882C4#350111yescharacteristic
883C4#351811yescharacteristic
884C4#354711yescharacteristic
885C2—82no—
886C2—82no—
887C2—82no—
888C2#5903611yescharacteristic
889C2C2×#331811yescharacteristic
890C2#6120411yescharacteristic
891C2Q8×AGL(1,ℤ/8)11yescharacteristic
892C2#6137011yescharacteristic
893C2#6190311yescharacteristic
894C2#6191211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#459C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #36477C2semidirect
3. #31542C2semidirect
4. #31523C2semidirect
5. #29207C2semidirect
6. #29149C2semidirect
7. #28801C2semidirect
8. #28273C2semidirect
9. #28263C2semidirect
10. #27022C2semidirect
11. #27011C2semidirect
12. #26538C2semidirect
13. #26036C2semidirect
14. #25058C2semidirect
15. #25057C2semidirect
16. #24326C2semidirect
17. #24326C2semidirect
18. #23150C2semidirect
20. #22523C2semidirect
21. Q8×#102C2semidirect
22. #21613C2semidirect
177. #459Q8semidirect
350. C2×D8C2×Q8semidirect
351. C2×D8C2×Q8semidirect
402. C4×D4C2×Q8semidirect
488. C4⋊C8C2×Q8semidirect
501. #102C2×Q8semidirect
502. #102C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598172
#364772
#315422
#315232
#292072
#291492
#288012
#282732
#282632
#270222
#270112
#265382
#260362
#250582
#250572
#243262
#231502
#231082
#225232
Q8×#1022
#216132
C4×#4592