Finite Group Databasebeta

← #6617016

Subgroups — #6617016

Order 512.

1537 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36199C211yesmaximal, characteristic
2C2×#2355C211yesmaximal, characteristic
3#33099C211yesmaximal, characteristic
4#33098C211yesmaximal, characteristic
5#32960C211yesmaximal, characteristic
6#27953C211yesmaximal, characteristic
7#27680C211yesmaximal, characteristic
8#27589C211yesmaximal, characteristic
9#27583C211yesmaximal, characteristic
10#27505C212yesmaximal, complemented
11#27487C212yesmaximal, complemented
12#27375C212yesmaximal, complemented
13#27359C212yesmaximal, complemented
14#26100C212yesmaximal, complemented
15#24691C212yesmaximal, complemented
16#24508C211yesmaximal, characteristic
17#24502C211yesmaximal, characteristic
18#23078C212yesmaximal, complemented
19#22818C212yesmaximal, complemented
20#22601C211yesmaximal, characteristic
21#21455C211yesmaximal, characteristic
22#21363C211yesmaximal, characteristic
23#21359C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#479C2212yes—
26C2×#451C2211yescharacteristic
27C2×#441C2212yes—
28C2×#432C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2855C2211yescharacteristic
31#2855C2211yescharacteristic
32#2851C2211yescharacteristic
33#2570C2211yescharacteristic
34#2565C2211yescharacteristic
35#2528—21no—
36#2524—21no—
37#2524—21no—
38#2514C2211yescharacteristic
39#2511C2211yescharacteristic
40#2508C2211yescharacteristic
41#2506C2211yescharacteristic
42#2493—21no—
43#2484—21no—
44#2473—21no—
45#2371—21no—
46#2370C2211yescharacteristic
47#2356C2211yescharacteristic
48#2355—21no—
49#2355—21no—
50#2355—21no—
51#2355—21no—
52#2355C2212yes—
53#2355C2212yes—
54#2355C2212yes—
55#2355C2212yes—
56#2343—21no—
57C4×C22⋊Q8C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#387—21no—
61C2×#387—21no—
62#2285C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2283C2211yescharacteristic
65C2×#382—21no—
66C2×C4×C4⋊C4—21no—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70#2099C2212yes—
71#2097C2212yes—
72#2096C2212yes—
73#2096C2212yes—
74#2084C2212yes—
75#2083C2212yes—
76#2074C2212yes—
77#2072C2212yes—
78#2068C2212yes—
79#2066C2212yes—
80#2056C2212yes—
81#2056C2212yes—
82#1992C2212yes—
83#1971C2212yes—
84#1969C2212yes—
85#1949C2212yes—
86#1949C2212yes—
87#1948C2212yes—
88#1948C2212yes—
89#1948C2212yes—
90#1940C2212yes—
91#1935C2212yes—
92#1933C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1928C2212yes—
96#1927C2212yes—
97#1927C2212yes—
98#1927C2212yes—
99#1927C2212yes—
100#1927C2212yes—
101#1921C2212yes—
102#1921C2212yes—
103#1920C2212yes—
104#1920C2212yes—
105#1917C2212yes—
106#1916C2212yes—
107#1878C2212yes—
108#1872C2211yescharacteristic
109#1872C2211yescharacteristic
110#1872C2211yescharacteristic
111#1865C2212yes—
112#1865C2212yes—
113#1863C2212yes—
114#1853C2211yescharacteristic
115#1853C2211yescharacteristic
116#1853C2211yescharacteristic
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1853C2211yescharacteristic
120#1852C2211yescharacteristic
121#1852C2211yescharacteristic
122#1852C2211yescharacteristic
123#1847C2212yes—
124#1817C2211yescharacteristic
125#1817C2211yescharacteristic
126#1805C2212yes—
127#1803C2212yes—
128#1797C2211yescharacteristic
129#1787C2211yescharacteristic
130#1787C2211yescharacteristic
131#1787C2211yescharacteristic
132#1776C2212yes—
133#1776C2212yes—
134C4×#106C2212yes—
135C4×#106C2212yes—
136#1771C2212yes—
137#1763C2212yes—
138#1749C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C2×#125—21no—
142C2×#125C2311yescharacteristic
143C2×C22⋊Q8C2311yescharacteristic
144C2×C4×Q8—28no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8C2311yescharacteristic
148C2×C4×Q8C2312yes—
149C2×C4×Q8C2312yes—
150C2×#117—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4D411yescharacteristic
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C42—21no—
160C22×C42—21no—
161C22×C42—21no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#479—28no—
166#451—24no—
167#441—28no—
168#432—24no—
169#431—24no—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
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#401—21no—
200#400—21no—
201#400—21no—
202#400—21no—
203#400—21no—
204#400—21no—
205#400—21no—
206#398—21no—
207#398—21no—
208#398—21no—
209#398—21no—
210#398—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391C2311yescharacteristic
216#391C2311yescharacteristic
217#391C2312yes—
218#391C2312yes—
219#391C2311yescharacteristic
220#391C2311yescharacteristic
221#391C2311yescharacteristic
222#391C2312yes—
223#391C2312yes—
224#389—21no—
225#389C2311yescharacteristic
226#389C2311yescharacteristic
227#389C2311yescharacteristic
228#389C2311yescharacteristic
229#389C2311yescharacteristic
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#387—21no—
233#387—21no—
234#387—21no—
235#387—21no—
236#387—21no—
237#387—21no—
238#387—21no—
239#387—21no—
240#387—21no—
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—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—21no—
260#385—21no—
261#385—21no—
262#385—21no—
263#385—21no—
264#385—21no—
265#384—21no—
266#384—21no—
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#384C2312yes—
270#384C2312yes—
271#383—21no—
272#383—21no—
273#383—21no—
274#382—22no—
275#382—22no—
276#382—22no—
277#382—22no—
278#382—21no—
279#382—21no—
280#382C2311yescharacteristic
281#382C2311yescharacteristic
282#382C2311yescharacteristic
283#381—21no—
284#381—21no—
285#381—21no—
286#380—21no—
287#380C2311yescharacteristic
288#380C2311yescharacteristic
289#380C2311yescharacteristic
290C4×C4⋊C4—22no—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—22no—
293C4×C4⋊C4—22no—
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⋊C4—21no—
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4D411yescharacteristic
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320#376—21no—
321#376—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95D411yescharacteristic
329C2×#95D411yescharacteristic
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—22no—
351C22×Q8—22no—
352C22×Q8—42no—
353C22×Q8C2411yescharacteristic
354C22×Q8C2412yes—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2411yescharacteristic
366C2×Q16—24no—
367C2×Q16—24no—
368C2×Q16—42no—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373#125—24no—
374#125—44no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C4×Q8—28no—
378C4×Q8—28no—
379C4×Q8—24no—
380C4×Q8—24no—
381C4×Q8—24no—
382C4×Q8—24no—
383C4×Q8#4118yes—
384#117—44no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—82no—
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—28no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—24no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—82no—
458C2×C42—82no—
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471#107—24no—
472#107—42no—
473#107—42no—
474#106—24no—
475#106—24no—
476#106—42no—
477#106—42no—
478#106—42no—
479#106—42no—
480C4⋊C8—24no—
481C4⋊C8—24no—
482C4⋊C8—24no—
483#103—24no—
484#103—24no—
485#103—24no—
486#103—24no—
487#103—24no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103—42no—
492#103—42no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8#4114yes—
497#97—24no—
498#97—24no—
499C4×C8—24no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
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—22no—
555C2×Q8—22no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—48no—
563C2×Q8—48no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8C2×#4114yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4#13714yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
625C22×C42−1+412yes—
626C22×C4C2511yescharacteristic
627Q16—48no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
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×C8C2×#4114yes—
640C4⋊C4—24no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
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—41no—
663C4⋊C4—41no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—42no—
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—44no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4C2×#4114yes—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C42—28no—
691C42—28no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—22no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—81no—
712C42—81no—
713C42—82no—
714C42—82no—
715C42—82no—
716C42—82no—
717C42C2×#4114yes—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#54712yes—
723C23C2×#13712yes—
724C23#57712yes—
725C23C23×D411yescharacteristic
726Q8—24no—
727Q8—24no—
728Q8—48no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732Q8—42no—
733C2×C4—28no—
734C2×C4—21no—
735C2×C4—28no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
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—24no—
748C2×C4—24no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
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—44no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4#52512yes—
815C2×C4#52512yes—
816C2×C4#54712yes—
817C2×C4C2×#13712yes—
818C2×C4C2×#13712yes—
819C2×C4#57512yes—
820C2×C4C22×#4111yescharacteristic
821C2×C4C22×#4112yes—
822C2×C4C2×2−1+411yescharacteristic
823C2×C4#58512yes—
824C8—24no—
825C8—42no—
826C8—42no—
827C8—42no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22#334414yes—
835C22C2×#52511yescharacteristic
836C22C2×#54711yescharacteristic
837C22#348711yescharacteristic
838C22C22×#13711yescharacteristic
839C22C2×#57511yescharacteristic
840C22C2×#57711yescharacteristic
841C22#358611yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—44no—
855C4—41no—
856C4—44no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—82no—
866C4—82no—
867C4#347512yes—
868C4#349512yes—
869C2—24no—
870C2#3642711yescharacteristic
871C2#6056011yescharacteristic
872C2#6058511yescharacteristic
873C2C2×#334411yescharacteristic
874C2#6125711yescharacteristic
875C2#6189311yescharacteristic
876C2#6190411yescharacteristic
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
10. #27505C2semidirect
11. #27487C2semidirect
12. #27375C2semidirect
13. #27359C2semidirect
14. #26100C2semidirect
15. #24691C2semidirect
18. #23078C2semidirect
19. #22818C2semidirect

Maximal subgroups

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

subgroupindex
#361992
C2×#23552
#330992
#330982
#329602
#279532
#276802
#275892
#275832
#275052
#274872
#273752
#273592
#261002
#246912
#245082
#245022
#230782
#228182
#226012
#214552
#213632
#213592