Finite Group Databasebeta

← #6528507

Subgroups — #6528507

Order 512.

1468 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35239C211yesmaximal, characteristic
2C2×#2565C211yesmaximal, characteristic
3#29112C211yesmaximal, characteristic
4#29111C211yesmaximal, characteristic
5#29106C211yesmaximal, characteristic
6#29105C211yesmaximal, characteristic
7#27969C211yesmaximal, characteristic
8#27965C211yesmaximal, characteristic
9#27964C211yesmaximal, characteristic
10#27961C211yesmaximal, characteristic
11#27831C212yesmaximal, complemented
12#27827C212yesmaximal, complemented
13#27820C212yesmaximal, complemented
14#27818C212yesmaximal, complemented
15#27745C212yesmaximal, complemented
16#27741C212yesmaximal, complemented
17#27734C212yesmaximal, complemented
18#27732C212yesmaximal, complemented
19#21838C211yesmaximal, characteristic
20#21836C211yesmaximal, characteristic
21#20741C211yesmaximal, characteristic
22#20734C211yesmaximal, characteristic
23#20535C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#432C2211yescharacteristic
27C2×#431C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2851C2211yescharacteristic
31#2851C2211yescharacteristic
32#2666—21no—
33#2666—21no—
34#2571C2211yescharacteristic
35#2570C2211yescharacteristic
36#2570C2211yescharacteristic
37#2565—21no—
38#2565—21no—
39#2565—21no—
40#2565—21no—
41#2565C2212yes—
42#2565C2212yes—
43#2565C2212yes—
44#2565C2212yes—
45#2552C2211yescharacteristic
46#2552C2211yescharacteristic
47#2551C2211yescharacteristic
48#2550C2211yescharacteristic
49#2550C2211yescharacteristic
50#2442—21no—
51#2440—21no—
52#2438—21no—
53#2438—21no—
54C2×#398—21no—
55C2×#398—21no—
56#2331—21no—
57#2330—21no—
58C2×#391C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#387—21no—
61C2×#387—21no—
62#2285C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2283C2211yescharacteristic
65C2×#382C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67#2101C2212yes—
68#2101C2212yes—
69#2101C2212yes—
70#2101C2212yes—
71#2100C2212yes—
72#2100C2212yes—
73#2099C2212yes—
74#2099C2212yes—
75#2074C2212yes—
76#2074C2212yes—
77#2072C2212yes—
78#2072C2212yes—
79#2026C2212yes—
80#2026C2212yes—
81#2024C2212yes—
82#2024C2212yes—
83#1993C2212yes—
84#1992C2212yes—
85#1992C2212yes—
86#1992C2212yes—
87#1991C2212yes—
88#1991C2212yes—
89#1991C2212yes—
90#1990C2212yes—
91#1989C2212yes—
92#1989C2212yes—
93#1989C2212yes—
94#1989C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1935C2212yes—
98#1935C2212yes—
99#1933C2212yes—
100#1933C2212yes—
101#1933C2212yes—
102#1933C2212yes—
103#1836C2212yes—
104#1836C2212yes—
105#1835C2212yes—
106#1834C2212yes—
107#1824C2211yescharacteristic
108#1824C2211yescharacteristic
109#1824C2211yescharacteristic
110#1824C2211yescharacteristic
111#1824C2211yescharacteristic
112#1824C2211yescharacteristic
113#1824C2211yescharacteristic
114#1824C2211yescharacteristic
115#1823C2211yescharacteristic
116#1823C2211yescharacteristic
117#1823C2211yescharacteristic
118#1823C2211yescharacteristic
119#1805C2212yes—
120#1805C2212yes—
121#1803C2212yes—
122#1803C2212yes—
123#1787C2211yescharacteristic
124#1787C2211yescharacteristic
125#1787C2211yescharacteristic
126#1787C2211yescharacteristic
127#1771C2212yes—
128#1771C2212yes—
129#1770C2212yes—
130C8×C4⋊C4C2212yes—
131#1763C2212yes—
132#1763C2212yes—
133C4×#103C2212yes—
134C4×#103C2212yes—
135#1749C2211yescharacteristic
136#1749C2211yescharacteristic
137C4×C22⋊C8C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125—21no—
144C2×#125—21no—
145C2×#125—21no—
146C2×#125—24no—
147C2×#125—24no—
148C2×#125C2312yes—
149C2×#125C2312yes—
150C2×#125C2311yescharacteristic
151C2×#125C2311yescharacteristic
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—24no—
157C2×C4×Q8—24no—
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2312yes—
160C2×#117—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4D411yescharacteristic
167C22×C4⋊C4D411yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#432—24no—
176#431—24no—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2311yescharacteristic
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×C4×C8C2312yes—
195C2×C4×C8C2312yes—
196C2×C4×C8C2312yes—
197#400—21no—
198#400—21no—
199#400—21no—
200#400—21no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#398—21no—
217#395—21no—
218#395—21no—
219#395—21no—
220#395—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#385—21no—
269#384—21no—
270#384—21no—
271#384—21no—
272#384C2312yes—
273#384C2312yes—
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#383—21no—
279#382—21no—
280#382—21no—
281#382—21no—
282#382—21no—
283#382C2312yes—
284#382C2312yes—
285#382C2311yescharacteristic
286#382C2311yescharacteristic
287#382C2311yescharacteristic
288#382C2311yescharacteristic
289#381—21no—
290#380—21no—
291#380—21no—
292#380—21no—
293#380C2311yescharacteristic
294#380C2311yescharacteristic
295#380C2311yescharacteristic
296#380C2311yescharacteristic
297C4×C4⋊C4—21no—
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
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×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C22⋊C4—21no—
311#376—21no—
312C2×#95—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95D411yescharacteristic
319C2×#95D411yescharacteristic
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
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#340C2312yes—
343#340C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—24no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—42no—
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
367C22×C8C2412yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C4⋊Q8—42no—
372C4⋊Q8—42no—
373C4⋊Q8—44no—
374#125—24no—
375#125—24no—
376#125—24no—
377#125—24no—
378#125—42no—
379#125—42no—
380#125—44no—
381#125—44no—
382#125—44no—
383C22⋊Q8—82no—
384C22⋊Q8—82no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×Q8—24no—
389C4×Q8—44no—
390C4×Q8—44no—
391#117—82no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
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—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
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—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
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—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—44no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42#4114yes—
479C2×C42#4114yes—
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C4⋊C8—24no—
487C4⋊C8—24no—
488#103—24no—
489#103—24no—
490#103—24no—
491#103—24no—
492#103—42no—
493#103—42no—
494#103—42no—
495#103—42no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—24no—
501#97—42no—
502#97—42no—
503C4×C8—24no—
504C4×C8—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#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550C24C22×D411yescharacteristic
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—48no—
558C2×Q8—48no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—81no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8—81no—
567C2×Q82−1+414yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
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#12414yes—
611C22×C4#12414yes—
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×C4C22×D411yescharacteristic
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2511yescharacteristic
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×C8—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—81no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C42—42no—
710C42—42no—
711C42—44no—
712C42—44no—
713C42—81no—
714C42—81no—
715C42#12414yes—
716C42#12414yes—
717C42C2×#4112yes—
718C42C2×#4112yes—
719C42C2×#4112yes—
720C42C2×#4112yes—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23C2×#12412yes—
726C23#57712yes—
727C23#57812yes—
728C23C23×D411yescharacteristic
729Q8—24no—
730Q8—24no—
731Q8—48no—
732Q8—42no—
733Q8—42no—
734Q8—162no—
735Q8—162no—
736C2×C4—28no—
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—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—21no—
758C2×C4—21no—
759C2×C4—24no—
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—44no—
774C2×C4—44no—
775C2×C4—48no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
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—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—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×#12412yes—
817C2×C4C2×#12412yes—
818C2×C4C2×#12412yes—
819C2×C4C2×#12412yes—
820C2×C4C2×#12412yes—
821C2×C4#57512yes—
822C2×C4#57512yes—
823C2×C4C22×#4111yescharacteristic
824C2×C4C22×#4111yescharacteristic
825C2×C4C2×2−1+412yes—
826C2×C4#58512yes—
827C8—42no—
828C8—42no—
829C8—42no—
830C8—42no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22#313714yes—
838C22C22×#12411yescharacteristic
839C22#348511yescharacteristic
840C22#348611yescharacteristic
841C22C2×#57511yescharacteristic
842C22C2×#57511yescharacteristic
843C22C2×#57711yescharacteristic
844C22C2×#57811yescharacteristic
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—44no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4#349512yes—
871C4#349512yes—
872C2—24no—
873C2#3564411yescharacteristic
874C2C2×#313711yescharacteristic
875C2#6061811yescharacteristic
876C2#6172911yescharacteristic
877C2#6173811yescharacteristic
878C2#6183611yescharacteristic
879C2#6184211yescharacteristic
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
11. #27831C2semidirect
12. #27827C2semidirect
13. #27820C2semidirect
14. #27818C2semidirect
15. #27745C2semidirect
16. #27741C2semidirect
17. #27734C2semidirect
18. #27732C2semidirect

Maximal subgroups

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

subgroupindex
#352392
C2×#25652
#291122
#291112
#291062
#291052
#279692
#279652
#279642
#279612
#278312
#278272
#278202
#278182
#277452
#277412
#277342
#277322
#218382
#218362
#207412
#207342
#205352