Finite Group Databasebeta

← #6799180

Subgroups — #6799180

Order 512.

1365 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C211yesmaximal, characteristic
2C2×#2511C211yesmaximal, characteristic
3#33146C211yesmaximal, characteristic
4#32492C212yesmaximal, complemented
5#32432C212yesmaximal, complemented
6#32228C212yesmaximal, complemented
7#31824C212yesmaximal, complemented
8#29966C211yesmaximal, characteristic
9#29953C211yesmaximal, characteristic
10#29111C211yesmaximal, characteristic
11#29111C211yesmaximal, characteristic
12#29097C212yesmaximal, complemented
13#28124C211yesmaximal, characteristic
14#28124C211yesmaximal, characteristic
15#28048C212yesmaximal, complemented
16#27960C211yesmaximal, characteristic
17#27647C211yesmaximal, characteristic
18#27569C212yesmaximal, complemented
19#27149C212yesmaximal, complemented
20#22627C211yesmaximal, characteristic
21#22084C211yesmaximal, characteristic
22#22044C211yesmaximal, characteristic
23#21579C211yesmaximal, characteristic
24C2×#483C2211yescharacteristic
25C2×#483C2211yescharacteristic
26C2×#451C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2586—21no—
31#2586—21no—
32#2567C2211yescharacteristic
33#2551C2211yescharacteristic
34#2549—21no—
35#2549—21no—
36#2511—21no—
37#2511—21no—
38#2511—21no—
39#2511—21no—
40#2511C2212yes—
41#2511C2212yes—
42#2511C2212yes—
43#2511C2212yes—
44#2507—21no—
45#2507C2211yescharacteristic
46#2507C2211yescharacteristic
47#2451C2211yescharacteristic
48#2451C2211yescharacteristic
49#2440—21no—
50C2×#400—21no—
51C2×#400—21no—
52#2369—21no—
53#2369C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55#2345—21no—
56C4×C22⋊Q8C2211yescharacteristic
57C4×C22⋊Q8C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#387—21no—
64C2×#387—21no—
65C2×#384C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2099C2212yes—
69#2099C2212yes—
70#2099C2212yes—
71#2095C2212yes—
72#2086C2212yes—
73#2086C2212yes—
74#2084C2212yes—
75#2072C2212yes—
76#2072C2212yes—
77#2072C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2057C2212yes—
83#2056C2212yes—
84#2056C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#1990C2212yes—
89#1988C2212yes—
90#1969C2212yes—
91#1948C2212yes—
92#1947C2212yes—
93#1944C2212yes—
94#1940C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1935C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1933C2212yes—
101#1928C2212yes—
102#1928C2212yes—
103#1927C2212yes—
104#1927C2212yes—
105#1920C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1918C2212yes—
109#1917C2212yes—
110#1916C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1878C2212yes—
114#1872C2211yescharacteristic
115#1863C2212yes—
116#1852C2211yescharacteristic
117#1852C2211yescharacteristic
118#1852C2211yescharacteristic
119#1834C2212yes—
120#1823C2211yescharacteristic
121#1823C2211yescharacteristic
122#1823C2211yescharacteristic
123#1823C2211yescharacteristic
124#1823C2211yescharacteristic
125#1823C2211yescharacteristic
126#1803C2212yes—
127#1797C2211yescharacteristic
128#1797C2211yescharacteristic
129#1797C2211yescharacteristic
130#1787C2211yescharacteristic
131#1787C2211yescharacteristic
132#1787C2211yescharacteristic
133#1776C2212yes—
134#1771C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C42—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#483—24no—
165#483—24no—
166#451—24no—
167C2×#107C2312yes—
168C2×#107C2312yes—
169C2×#107C2312yes—
170C2×#106C2312yes—
171C2×#106C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×C22⋊C8C2311yescharacteristic
186C2×C22⋊C8C2311yescharacteristic
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×C4×C8C2312yes—
192#400—22no—
193#400—22no—
194#400—22no—
195#400—22no—
196#400—22no—
197#400—22no—
198#400—22no—
199#400—22no—
200#398—21no—
201#398—21no—
202#398—21no—
203#398—21no—
204#398—21no—
205#398—21no—
206#395—21no—
207#395—21no—
208#395—21no—
209#395—21no—
210#395—21no—
211#395—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391C2311yescharacteristic
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#391C2312yes—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389C2312yes—
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—22no—
270#387—22no—
271#387—22no—
272#387—22no—
273#385—21no—
274#385—21no—
275#385—21no—
276#384—21no—
277#384—21no—
278#384—21no—
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2312yes—
282#384C2311yescharacteristic
283#384C2312yes—
284#380—21no—
285#380—21no—
286#380—21no—
287#380C2311yescharacteristic
288#380C2311yescharacteristic
289#380C2311yescharacteristic
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⋊C4D411yescharacteristic
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95D411yescharacteristic
322C2×#95D411yescharacteristic
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#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—42no—
352C22×Q8—42no—
353C22×Q8C2412yes—
354C22×Q8C2411yescharacteristic
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—42no—
368C2×Q16—42no—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—44no—
377C22⋊Q8—22no—
378C22⋊Q8—82no—
379C22⋊Q8—82no—
380C22⋊Q8—82no—
381C22⋊Q8#4114yes—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—42no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
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—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
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—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—82no—
425C2×C4⋊C4—82no—
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—42no—
457C2×C42—42no—
458C2×C42—42no—
459C2×C42—82no—
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472#107—42no—
473#107—42no—
474#107—42no—
475#106—24no—
476#106—24no—
477C4⋊C8—42no—
478C4⋊C8—42no—
479C4⋊C8—42no—
480#103—24no—
481#103—24no—
482#103—24no—
483#103—42no—
484#103—42no—
485#103—42no—
486#103—42no—
487#103—42no—
488#103—42no—
489#103—42no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494#97—42no—
495#97—42no—
496C4×C8—42no—
497#95—22no—
498#95—22no—
499#95—22no—
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—22no—
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#95C2×D411yescharacteristic
535#95C2×D411yescharacteristic
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541#95C2×D411yescharacteristic
542C24C22×D411yescharacteristic
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—81no—
559C2×Q8—81no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8—81no—
564C2×Q8—84no—
565C2×Q8—84no—
566C2×Q8C2×#4112yes—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—42no—
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#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—84no—
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—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
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—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
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#13714yes—
692C4⋊C4C2×#4112yes—
693C22⋊C4—24no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—41no—
704C42—41no—
705C42—41no—
706C42—41no—
707C42—41no—
708C42—41no—
709C42—42no—
710C42—42no—
711C42—81no—
712C42—81no—
713C42—82no—
714C42—82no—
715C42—81no—
716C42—81no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23#54812yes—
722C23C2×#13712yes—
723C23#57612yes—
724C23C23×D411yescharacteristic
725Q8—24no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—42no—
730Q8—42no—
731Q8—84no—
732Q8—162no—
733Q8—162no—
734Q8—162no—
735C2×C4—21no—
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—21no—
756C2×C4—22no—
757C2×C4—22no—
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—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4#54812yes—
817C2×C4C2×#13712yes—
818C2×C4C2×#13712yes—
819C2×C4C2×#13712yes—
820C2×C4C2×#13712yes—
821C2×C4C2×#13712yes—
822C2×C4C22×#4111yescharacteristic
823C2×C4C2×2−1+411yescharacteristic
824C2×C4#58512yes—
825C2×C4#58512yes—
826C8—42no—
827C8—42no—
828C8—42no—
829C8—42no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22#337514yes—
837C22#344911yescharacteristic
838C22C2×#54811yescharacteristic
839C22#348511yescharacteristic
840C22C22×#13711yescharacteristic
841C22C22×#13711yescharacteristic
842C22C2×#57611yescharacteristic
843C22#358611yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—82no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4#352112yes—
870C4#356412yes—
871C2—24no—
872C2#3911711yescharacteristic
873C2#6097111yescharacteristic
874C2#6097611yescharacteristic
875C2C2×#337511yescharacteristic
876C2#6132211yescharacteristic
877C2#6170511yescharacteristic
878C2#6172611yescharacteristic
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
4. #32492C2semidirect
5. #32432C2semidirect
6. #32228C2semidirect
7. #31824C2semidirect
12. #29097C2semidirect
15. #28048C2semidirect
18. #27569C2semidirect
19. #27149C2semidirect

Maximal subgroups

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

subgroupindex
#365642
C2×#25112
#331462
#324922
#324322
#322282
#318242
#299662
#299532
#291112
#290972
#281242
#280482
#279602
#276472
#275692
#271492
#226272
#220842
#220442
#215792