Finite Group Databasebeta

← #6624398

Subgroups — #6624398

Order 512.

1543 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36571C211yesmaximal, characteristic
2C2×#2355C211yesmaximal, characteristic
3#33150C211yesmaximal, characteristic
4#33147C211yesmaximal, characteristic
5#32960C211yesmaximal, characteristic
6#29112C211yesmaximal, characteristic
7#29105C211yesmaximal, characteristic
8#28121C211yesmaximal, characteristic
9#28121C211yesmaximal, characteristic
10#27965C211yesmaximal, characteristic
11#27648C211yesmaximal, characteristic
12#27441C212yesmaximal, complemented
13#27425C212yesmaximal, complemented
14#27375C212yesmaximal, complemented
15#27361C212yesmaximal, complemented
16#26034C212yesmaximal, complemented
17#24691C212yesmaximal, complemented
18#23074C212yesmaximal, complemented
19#22777C212yesmaximal, complemented
20#22627C211yesmaximal, characteristic
21#21581C211yesmaximal, characteristic
22C4×#484C211yesmaximal, characteristic
23#21455C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#484C2211yescharacteristic
27C2×#479C2212yes—
28C2×#451C2211yescharacteristic
29C2×#441C2212yes—
30#2857C2211yescharacteristic
31#2851C2211yescharacteristic
32#2851C2211yescharacteristic
33#2588—21no—
34#2585—21no—
35#2583—21no—
36#2565C2211yescharacteristic
37#2550C2211yescharacteristic
38#2520—21no—
39#2509C2211yescharacteristic
40#2506C2211yescharacteristic
41#2505—21no—
42#2473—21no—
43#2453C2211yescharacteristic
44#2451C2211yescharacteristic
45#2370—21no—
46#2370C2211yescharacteristic
47#2368—21no—
48#2355—21no—
49#2355—21no—
50#2355—21no—
51#2355—21no—
52#2355C2212yes—
53#2355C2212yes—
54#2355C2212yes—
55#2355C2212yes—
56#2351C2211yescharacteristic
57C4×C22⋊Q8C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C4×C22⋊Q8C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#387—21no—
63C2×#387—21no—
64C2×#384C2211yescharacteristic
65C2×#382—21no—
66C2×C4×C4⋊C4—21no—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70#2099C2212yes—
71#2099C2212yes—
72#2083C2212yes—
73#2074C2212yes—
74#2072C2212yes—
75#2072C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2056C2212yes—
79#2056C2212yes—
80#2026C2212yes—
81#2024C2212yes—
82#1992C2212yes—
83#1989C2212yes—
84#1988C2212yes—
85#1949C2212yes—
86#1948C2212yes—
87#1947C2212yes—
88#1940C2212yes—
89#1935C2212yes—
90#1935C2212yes—
91#1933C2212yes—
92#1933C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1928C2212yes—
96#1927C2212yes—
97#1921C2212yes—
98#1920C2212yes—
99#1919C2212yes—
100#1919C2212yes—
101#1918C2212yes—
102#1918C2212yes—
103#1917C2212yes—
104#1916C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1878C2212yes—
108#1872C2211yescharacteristic
109#1865C2212yes—
110#1865C2212yes—
111#1863C2212yes—
112#1853C2211yescharacteristic
113#1853C2211yescharacteristic
114#1852C2211yescharacteristic
115#1836C2212yes—
116#1824C2211yescharacteristic
117#1824C2211yescharacteristic
118#1824C2211yescharacteristic
119#1824C2211yescharacteristic
120#1824C2211yescharacteristic
121#1824C2211yescharacteristic
122#1805C2212yes—
123#1803C2212yes—
124#1797C2211yescharacteristic
125#1797C2211yescharacteristic
126#1797C2211yescharacteristic
127#1787C2211yescharacteristic
128#1787C2211yescharacteristic
129#1787C2211yescharacteristic
130#1776C2212yes—
131C4×#107C2212yes—
132#1771C2212yes—
133#1763C2212yes—
134#1763C2212yes—
135C4×#103C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—21no—
143C2×#125C2311yescharacteristic
144C2×#125C2311yescharacteristic
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8C2311yescharacteristic
147C2×C4×Q8—28no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4D411yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C42—21no—
164C22×C42—21no—
165C22×C42—21no—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#484—24no—
170#484—24no—
171#479—28no—
172#451—24no—
173#441—28no—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2311yescharacteristic
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×C4×C8C2312yes—
199#400—21no—
200#400—21no—
201#400—21no—
202#400—21no—
203#398—21no—
204#398—21no—
205#398—21no—
206#398—21no—
207#398—21no—
208#398—21no—
209#395—21no—
210#395—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#391C2312yes—
221#391C2312yes—
222#391C2311yescharacteristic
223#391C2312yes—
224#391C2312yes—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#387—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—21no—
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—21no—
264#385—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#385—21no—
269#385—21no—
270#385—21no—
271#384—21no—
272#384—21no—
273#384C2311yescharacteristic
274#384C2312yes—
275#384C2312yes—
276#382—22no—
277#382—22no—
278#382—22no—
279#382—22no—
280#382—21no—
281#382C2311yescharacteristic
282#382C2311yescharacteristic
283#380—21no—
284#380C2311yescharacteristic
285#380C2311yescharacteristic
286#380C2311yescharacteristic
287C4×C4⋊C4—22no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4—22no—
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—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4D411yescharacteristic
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95D411yescharacteristic
325C2×#95D411yescharacteristic
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—24no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—42no—
354C22×Q8C2411yescharacteristic
355C22×Q8C2412yes—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2411yescharacteristic
367C2×Q16—24no—
368C2×Q16—24no—
369C2×Q16—42no—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C4⋊Q8—42no—
375#125—24no—
376#125—42no—
377#125—44no—
378C22⋊Q8—22no—
379C22⋊Q8—44no—
380C22⋊Q8#4114yes—
381C4×Q8—28no—
382C4×Q8—28no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—42no—
388C4×Q8—42no—
389C4×Q8#4118yes—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4—82no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C42—28no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—24no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—42no—
466C2×C42—42no—
467C2×C42—82no—
468C2×C42—82no—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—24no—
482#107—24no—
483#107—24no—
484#106—24no—
485#106—24no—
486C4⋊C8—24no—
487C4⋊C8—42no—
488C4⋊C8—42no—
489#103—24no—
490#103—24no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—24no—
495#103—24no—
496#103—42no—
497#103—42no—
498#103—42no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503#97—24no—
504#97—42no—
505C4×C8—42no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551C24C22×D411yescharacteristic
552C2×Q8—24no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—48no—
562C2×Q8—48no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×Q8C2×#4112yes—
569C2×Q8C2×#4114yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4#13714yes—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C2×#4112yes—
628C22×C42−1+412yes—
629C22×C4C2511yescharacteristic
630Q16—48no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C4⋊C4—24no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4C2×#4112yes—
693C4⋊C4C2×#4114yes—
694C22⋊C4—24no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C42—28no—
699C42—28no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—41no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—42no—
712C42—42no—
713C42—81no—
714C42—81no—
715C42—82no—
716C42—82no—
717C42—82no—
718C42—82no—
719C42—81no—
720C42—81no—
721C42C2×#4114yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23#54812yes—
727C23C2×#13712yes—
728C23#57812yes—
729C23C23×D411yescharacteristic
730Q8—24no—
731Q8—24no—
732Q8—24no—
733Q8—48no—
734Q8—42no—
735Q8—42no—
736Q8—42no—
737Q8—162no—
738C2×C4—28no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4#52512yes—
820C2×C4#52512yes—
821C2×C4#54812yes—
822C2×C4C2×#13712yes—
823C2×C4C2×#13712yes—
824C2×C4#57512yes—
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4112yes—
827C2×C4C2×2−1+411yescharacteristic
828C2×C4#58512yes—
829C8—42no—
830C8—42no—
831C8—42no—
832C8—42no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22#337414yes—
840C22C2×#52511yescharacteristic
841C22C2×#54811yescharacteristic
842C22#348511yescharacteristic
843C22C22×#13711yescharacteristic
844C22C2×#57511yescharacteristic
845C22C2×#57811yescharacteristic
846C22#358511yescharacteristic
847C4—22no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—41no—
863C4—44no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4#347512yes—
873C4#349512yes—
874C2—24no—
875C2#3651611yescharacteristic
876C2#6056011yescharacteristic
877C2#6058911yescharacteristic
878C2C2×#337411yescharacteristic
879C2#6132411yescharacteristic
880C2#6170911yescharacteristic
881C2#6173011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #27441C2semidirect
13. #27425C2semidirect
14. #27375C2semidirect
15. #27361C2semidirect
16. #26034C2semidirect
17. #24691C2semidirect
18. #23074C2semidirect
19. #22777C2semidirect

Maximal subgroups

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

subgroupindex
#365712
C2×#23552
#331502
#331472
#329602
#291122
#291052
#281212
#279652
#276482
#274412
#274252
#273752
#273612
#260342
#246912
#230742
#227772
#226272
#215812
C4×#4842
#214552