Finite Group Databasebeta

← #6801713

Subgroups — #6801713

Order 512.

1428 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36586C211yesmaximal, characteristic
2C2×#2511C211yesmaximal, characteristic, complemented
3#33110C211yesmaximal, characteristic
4#32530C212yesmaximal, complemented
5#32399C212yesmaximal, complemented
6#32187C212yesmaximal, complemented
7#31908C212yesmaximal, complemented
8#29757C211yesmaximal, characteristic, complemented
9#29719C211yesmaximal, characteristic
10#28884C212yesmaximal, complemented
11#28315C211yesmaximal, characteristic
12#28304C211yesmaximal, characteristic, complemented
13#28121C211yesmaximal, characteristic, complemented
14#28115C211yesmaximal, characteristic
15#28028C212yesmaximal, complemented
16#27913C211yesmaximal, characteristic
17#27648C211yesmaximal, characteristic, complemented
18#27509C212yesmaximal, complemented
19#27085C212yesmaximal, complemented
20#22629C211yesmaximal, characteristic, complemented
21#22076C211yesmaximal, characteristic
22#22050C211yesmaximal, characteristic, complemented
23#21581C211yesmaximal, characteristic, complemented
24C2×#484C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#484C2211yescharacteristic
27C2×#484C2211yescharacteristic
28C2×#481C2211yescharacteristic
29C2×#481C2211yescharacteristic
30C2×#451C2211yescharacteristic
31C2×#451C2211yescharacteristic
32C2×#448C2211yescharacteristic
33#2857C2211yescharacteristic
34#2850C2211yescharacteristic
35#2850C2211yescharacteristic
36#2596—21no—
37#2596—21no—
38#2571C2211yescharacteristic
39#2547C2211yescharacteristic
40#2514C2211yescharacteristic
41#2514C2211yescharacteristic
42#2511—21no—
43#2511—21no—
44#2511—21no—
45#2511—21no—
46#2511C2212yes—
47#2511C2212yes—
48#2511C2212yes—
49#2511C2212yes—
50#2510—21no—
51#2510—21no—
52#2494—21no—
53#2487—21no—
54#2448C2211yescharacteristic
55#2448C2211yescharacteristic
56C2×#400—21no—
57C2×#400—21no—
58#2365C2211yescharacteristic
59#2354C2211yescharacteristic
60#2352—21no—
61#2347—21no—
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C4×#121C2211yescharacteristic
65C2×#391C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#391C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#387—21no—
70C2×#387—21no—
71C2×#384C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2211yescharacteristic
74#2097C2212yes—
75#2096C2212yes—
76#2095C2212yes—
77#2093C2212yes—
78#2083C2212yes—
79#2083C2212yes—
80#2074C2212yes—
81#2072C2212yes—
82#2068C2212yes—
83#2068C2212yes—
84#2068C2212yes—
85#2066C2212yes—
86#2056C2212yes—
87#2056C2212yes—
88#2055C2212yes—
89#2055C2212yes—
90#2043C2212yes—
91#2016C2212yes—
92#2015C2212yes—
93#2015C2212yes—
94#1983C2212yes—
95#1973C2212yes—
96#1971C2212yes—
97#1971C2212yes—
98#1969C2212yes—
99#1969C2212yes—
100#1959C2212yes—
101#1949C2212yes—
102#1947C2212yes—
103#1941C2212yes—
104#1939C2212yes—
105#1935C2212yes—
106#1934C2212yes—
107#1928C2212yes—
108#1927C2212yes—
109#1927C2212yes—
110#1927C2212yes—
111#1927C2212yes—
112#1925C2212yes—
113#1920C2212yes—
114#1918C2212yes—
115#1917C2212yes—
116#1917C2212yes—
117#1878C2212yes—
118#1878C2212yes—
119#1877C2212yes—
120#1874C2211yescharacteristic
121#1872C2211yescharacteristic
122#1872C2211yescharacteristic
123#1864C2212yes—
124#1853C2211yescharacteristic
125#1847C2212yes—
126#1824C2211yescharacteristic
127#1824C2211yescharacteristic
128#1803C2212yes—
129#1797C2211yescharacteristic
130#1797C2211yescharacteristic
131#1797C2211yescharacteristic
132#1787C2211yescharacteristic
133#1776C2212yes—
134#1770C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C22×Q16C2312yes—
142C22×SD16C2312yes—
143C2×C4⋊Q8C2311yescharacteristic
144C2×#124C2311yescharacteristic
145C2×#124C2311yescharacteristic
146C2×C22⋊Q8C2311yescharacteristic
147C2×C22⋊Q8C2311yescharacteristic
148C2×#121C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×D4—21no—
152C2×C4×D4C2311yescharacteristic
153C2×#117—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4D411yescharacteristic
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C42—21no—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#484—24no—
167#484—42no—
168#484—42no—
169#484—42no—
170#481—24no—
171#481—42no—
172#451—24no—
173#451—42no—
174#448—42no—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2311yescharacteristic
202C2×C22⋊C8C2311yescharacteristic
203C2×#97C2312yes—
204C2×#97C2312yes—
205C2×C4×C8C2312yes—
206#401—21no—
207#401—21no—
208#400—21no—
209#400—21no—
210#400—22no—
211#400—22no—
212#400—22no—
213#400—22no—
214#400—21no—
215#400—21no—
216#400—22no—
217#400—22no—
218#400—22no—
219#400—22no—
220#399—21no—
221#399—21no—
222#397—21no—
223#397—21no—
224#397—21no—
225#397—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391C2312yes—
233#391C2312yes—
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#391C2312yes—
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#391C2311yescharacteristic
240#391C2312yes—
241#391C2311yescharacteristic
242#391C2312yes—
243#391C2312yes—
244#390C2311yescharacteristic
245#390C2311yescharacteristic
246#390C2311yescharacteristic
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2312yes—
257#389C2312yes—
258#388—21no—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#388—21no—
265#388—21no—
266#388—21no—
267#388—21no—
268#388—21no—
269#387—21no—
270#387—21no—
271#387—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#387—21no—
276#387—21no—
277#387—21no—
278#387—21no—
279#387—22no—
280#387—22no—
281#387—22no—
282#387—22no—
283#386—21no—
284#386—21no—
285#386—21no—
286#386—21no—
287#386—21no—
288#385—21no—
289#385—21no—
290#384—21no—
291#384—21no—
292#384C2312yes—
293#384C2311yescharacteristic
294#384C2312yes—
295#383—21no—
296#383—21no—
297#382—21no—
298#382C2311yescharacteristic
299#382C2311yescharacteristic
300#380—21no—
301#380—21no—
302#380—21no—
303#380—21no—
304#380—21no—
305#380C2311yescharacteristic
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4D411yescharacteristic
312C4×C4⋊C4D411yescharacteristic
313C4×C4⋊C4D411yescharacteristic
314C4×C4⋊C4D411yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2311yescharacteristic
321C4×C4⋊C4C2311yescharacteristic
322C4×C4⋊C4C2311yescharacteristic
323C4×C4⋊C4C2311yescharacteristic
324C4×C22⋊C4—21no—
325C4×C22⋊C4—21no—
326C4×C22⋊C4—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95—21no—
332C2×#95—21no—
333C2×#95—21no—
334C2×#95—21no—
335C2×#95D411yescharacteristic
336C2×#95D411yescharacteristic
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—21no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—42no—
355C22×Q8—42no—
356C22×Q8C2411yescharacteristic
357C22×Q8C2411yescharacteristic
358C22×Q8C2412yes—
359C22×D4—21no—
360C22×D4C2411yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2411yescharacteristic
373C2×Q16—24no—
374C2×Q16—42no—
375C2×Q16—42no—
376C2×Q16—42no—
377C2×Q16—42no—
378C2×Q16—42no—
379C2×SD16—42no—
380C2×SD16—42no—
381C2×SD16—42no—
382C22×C8C2412yes—
383C22×C8C2412yes—
384C22×C8C2412yes—
385C22×C8C2412yes—
386C4⋊Q8—42no—
387#124—42no—
388#124—42no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393#121—22no—
394#121—22no—
395C4×Q8—42no—
396C4×Q8—42no—
397C4×D4—42no—
398C4×D4—44no—
399#117—44no—
400C2×C4⋊C4—24no—
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—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—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4—82no—
429C2×C4⋊C4—82no—
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⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—42no—
469C2×C42—42no—
470C2×C42—42no—
471C2×C42—82no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#107—24no—
485#107—42no—
486#107—42no—
487#107—42no—
488#106—24no—
489#106—42no—
490#106—42no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493C4⋊C8—42no—
494#103—24no—
495#103—24no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103—42no—
500#103—42no—
501#103—42no—
502#103—42no—
503#103—42no—
504#103—42no—
505#102—24no—
506#102—42no—
507#102—42no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8#4114yes—
512#97—42no—
513#97—42no—
514C4×C8—42no—
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#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
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#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562C24—21no—
563C24C22×D411yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—42no—
581C2×Q8—84no—
582C2×Q8—84no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4#13714yes—
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C2×#4112yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C4C2511yescharacteristic
652Q16—84no—
653Q16—84no—
654SD16—84no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8C2×#4114yes—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—41no—
688C4⋊C4—41no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—44no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—81no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C4⋊C4—82no—
707C4⋊C4—81no—
708C4⋊C4—81no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4—81no—
723C22⋊C4—81no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—41no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—41no—
736C42—42no—
737C42—42no—
738C42—42no—
739C42—82no—
740C42—82no—
741C42—81no—
742C42—81no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23#55012yes—
755C23C2×#13712yes—
756C23#57812yes—
757C23C23×D411yescharacteristic
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762Q8—42no—
763Q8—42no—
764Q8—42no—
765Q8—42no—
766Q8—84no—
767D4—42no—
768D4—42no—
769D4—84no—
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—24no—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4—84no—
851C2×C4#55012yes—
852C2×C4C2×#13712yes—
853C2×C4C2×#13712yes—
854C2×C4#57512yes—
855C2×C4C22×#4111yescharacteristic
856C2×C4C2×H(5,𝔽2)11yescharacteristic
857C2×C4#58512yes—
858C2×C4#58512yes—
859C8—24no—
860C8—42no—
861C8—42no—
862C8—42no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22#339814yes—
877C22#344911yescharacteristic
878C22C2×#55011yescharacteristic
879C22#348511yescharacteristic
880C22C22×#13711yescharacteristic
881C22C2×#57511yescharacteristic
882C22C2×#57811yescharacteristic
883C22#358511yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—81no—
901C4—82no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—82no—
908C4#352112yes—
909C4#356012yes—
910C2—24no—
911C2—161no—
912C2#3912911yescharacteristic
913C2#6096011yescharacteristic
914C2#6098111yescharacteristic
915C2C2×#339811yescharacteristic
916C2#6140511yescharacteristic
917C2#6171911yescharacteristic
918C2#6173811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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
2. C2×#2511C2semidirect
4. #32530C2semidirect
5. #32399C2semidirect
6. #32187C2semidirect
7. #31908C2semidirect
8. #29757C2semidirect
10. #28884C2semidirect
12. #28304C2semidirect
13. #28121C2semidirect
15. #28028C2semidirect
17. #27648C2semidirect
18. #27509C2semidirect
19. #27085C2semidirect
20. #22629C2semidirect
22. #22050C2semidirect
23. #21581C2semidirect

Maximal subgroups

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

subgroupindex
#365862
C2×#25112
#331102
#325302
#323992
#321872
#319082
#297572
#297192
#288842
#283152
#283042
#281212
#281152
#280282
#279132
#276482
#275092
#270852
#226292
#220762
#220502
#215812