Finite Group Databasebeta

← #6855941

Subgroups — #6855941

Order 512.

1504 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36605C211yesmaximal, characteristic
2C2×#2552C211yesmaximal, characteristic, complemented
3#33110C211yesmaximal, characteristic
4#32257C212yesmaximal, complemented
5#32235C212yesmaximal, complemented
6#30834C212yesmaximal, complemented
7#30811C212yesmaximal, complemented
8#29761C211yesmaximal, characteristic
9#29757C211yesmaximal, characteristic, complemented
10#28807C212yesmaximal, complemented
11#27978C211yesmaximal, characteristic
12#27781C212yesmaximal, complemented
13#27681C211yesmaximal, characteristic, complemented
14#26477C212yesmaximal, complemented
15#26039C212yesmaximal, complemented
16#25912C211yesmaximal, characteristic, complemented
17#25907C211yesmaximal, characteristic
18#24307C211yesmaximal, characteristic, complemented
19#24305C211yesmaximal, characteristic
20#22627C211yesmaximal, characteristic, complemented
21#22082C211yesmaximal, characteristic
22#22079C211yesmaximal, characteristic, complemented
23#21581C211yesmaximal, characteristic, complemented
24C22×#125C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C2×#491C2212yes—
27C2×#488C2212yes—
28C2×#484C2211yescharacteristic
29C2×#484C2211yescharacteristic
30C2×#481C2211yescharacteristic
31C2×#479C2212yes—
32C2×#478C2212yes—
33#2857C2211yescharacteristic
34#2850C2211yescharacteristic
35#2850C2211yescharacteristic
36#2594—21no—
37#2579—21no—
38#2573—21no—
39#2570C2211yescharacteristic
40#2552—21no—
41#2552—21no—
42#2552—21no—
43#2552—21no—
44#2552C2212yes—
45#2552C2212yes—
46#2552C2212yes—
47#2552C2212yes—
48#2545C2211yescharacteristic
49#2525—21no—
50#2514C2211yescharacteristic
51#2512C2211yescharacteristic
52#2510—21no—
53#2481—21no—
54#2447C2211yescharacteristic
55#2446C2211yescharacteristic
56C2×#398—21no—
57C2×#398—21no—
58#2373—21no—
59#2367C2211yescharacteristic
60#2356C2211yescharacteristic
61#2353—21no—
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C4×#121C2211yescharacteristic
65C2×#389—21no—
66C2×#389C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#384—21no—
69C2×#384C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72#2100C2212yes—
73#2095C2212yes—
74#2085C2212yes—
75#2083C2212yes—
76#2072C2212yes—
77#2071C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2067C2212yes—
81#2066C2212yes—
82#2059C2212yes—
83#2059C2212yes—
84#2043C2212yes—
85#2042C2212yes—
86#2026C2212yes—
87#2026C2212yes—
88#2026C2212yes—
89#2026C2212yes—
90#2025C2212yes—
91#2025C2212yes—
92#1992C2212yes—
93#1991C2212yes—
94#1989C2212yes—
95#1989C2212yes—
96#1983C2212yes—
97#1959C2212yes—
98#1949C2212yes—
99#1947C2212yes—
100#1944C2212yes—
101#1942C2212yes—
102#1940C2212yes—
103#1936C2212yes—
104#1933C2212yes—
105#1927C2212yes—
106#1927C2212yes—
107#1925C2212yes—
108#1921C2212yes—
109#1919C2212yes—
110#1918C2212yes—
111#1917C2212yes—
112#1916C2212yes—
113#1874C2211yescharacteristic
114#1874C2211yescharacteristic
115#1874C2211yescharacteristic
116#1872C2211yescharacteristic
117#1872C2211yescharacteristic
118#1872C2211yescharacteristic
119#1872C2211yescharacteristic
120#1872C2211yescharacteristic
121#1872C2211yescharacteristic
122#1863C2212yes—
123#1862C2212yes—
124#1853C2211yescharacteristic
125#1852C2211yescharacteristic
126#1852C2211yescharacteristic
127#1836C2212yes—
128#1824C2211yescharacteristic
129#1803C2212yes—
130#1797C2211yescharacteristic
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1776C2212yes—
134#1771C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×#126—21no—
141C2×#125—21no—
142C2×#125—21no—
143C2×#125—21no—
144C2×#125—21no—
145C2×#125—44no—
146C2×#125—44no—
147C2×#125C2312yes—
148C2×#125C2312yes—
149C2×#125C2312yes—
150C2×#125C2312yes—
151C2×#124C2311yescharacteristic
152C2×#124C2311yescharacteristic
153C2×C22⋊Q8C2311yescharacteristic
154C2×C22⋊Q8C2311yescharacteristic
155C2×#121C2311yescharacteristic
156C2×C4×Q8C2311yescharacteristic
157C2×C4×Q8C2311yescharacteristic
158C2×C4×D4—21no—
159C2×C4×D4C2311yescharacteristic
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4D411yescharacteristic
169C22×C4⋊C4D411yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C42—21no—
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#491—44no—
179#488—44no—
180#484—24no—
181#484—24no—
182#481—24no—
183#479—44no—
184#478—44no—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×C22⋊C8C2311yescharacteristic
207C2×C22⋊C8C2311yescharacteristic
208C2×C22⋊C8C2311yescharacteristic
209C2×C22⋊C8C2311yescharacteristic
210C2×#97C2312yes—
211C2×#97C2312yes—
212C2×C4×C8C2312yes—
213#401—21no—
214#400—21no—
215#400—21no—
216#400—21no—
217#398—21no—
218#398—21no—
219#398—22no—
220#398—22no—
221#398—22no—
222#398—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#397—21no—
228#397—21no—
229#397—21no—
230#396—21no—
231#396—21no—
232#396—21no—
233#391C2311yescharacteristic
234#391C2311yescharacteristic
235#391C2311yescharacteristic
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#390C2311yescharacteristic
242#389—22no—
243#389—22no—
244#389—22no—
245#389—22no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2312yes—
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#389C2311yescharacteristic
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—21no—
272#387—21no—
273#387—21no—
274#387—21no—
275#387—21no—
276#387—21no—
277#387—21no—
278#386—21no—
279#386—21no—
280#386—21no—
281#386—21no—
282#386—21no—
283#385—21no—
284#385—21no—
285#385—21no—
286#385—21no—
287#384—22no—
288#384—22no—
289#384—22no—
290#384—22no—
291#384—21no—
292#384—21no—
293#384C2311yescharacteristic
294#384C2312yes—
295#384C2312yes—
296#383—21no—
297#383—21no—
298#382C2311yescharacteristic
299#382C2311yescharacteristic
300#381—21no—
301#380—21no—
302#380—21no—
303#380C2311yescharacteristic
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4D411yescharacteristic
311C4×C4⋊C4D411yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2312yes—
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319C4×C4⋊C4C2311yescharacteristic
320C4×C4⋊C4C2311yescharacteristic
321C4×C22⋊C4—21no—
322C4×C22⋊C4—21no—
323C4×C22⋊C4—21no—
324C4×C22⋊C4—21no—
325#376—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95D411yescharacteristic
330C2×#95D411yescharacteristic
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#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8C2411yescharacteristic
352C22×Q8C2411yescharacteristic
353C22×D4—21no—
354C22×D4C2411yescharacteristic
355C23×C4—21no—
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—
372#126—44no—
373#125—24no—
374#125—24no—
375#125—24no—
376#125—24no—
377#125—42no—
378#125—42no—
379#125—42no—
380#125—42no—
381#125—44no—
382#125—44no—
383#125—44no—
384#125—44no—
385#124—24no—
386#124—42no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391#121—22no—
392#121—22no—
393C4×Q8—24no—
394C4×Q8—42no—
395C4×D4—42no—
396C4×D4—44no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
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—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
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—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—44no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—82no—
440C2×C4⋊C4—82no—
441C2×C4⋊C4—82no—
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⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4#4114yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2412yes—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C42—24no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—42no—
484C2×C42—42no—
485C2×C42—44no—
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498#107—24no—
499#107—24no—
500#107—42no—
501#107—42no—
502#106—24no—
503#106—24no—
504C4⋊C8—24no—
505C4⋊C8—42no—
506C4⋊C8—42no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#102—24no—
516#102—24no—
517#102—42no—
518#102—42no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—24no—
524#97—42no—
525C4×C8—42no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
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#95—21no—
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563C24—21no—
564C24C22×D411yescharacteristic
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—81no—
625C22×C4—81no—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C2×#4112yes—
640C22×C42−1+412yes—
641C22×C4C2511yescharacteristic
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—81no—
697C4⋊C4—81no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C4⋊C4C2×#4114yes—
708C4⋊C4H(5,𝔽2)14yes—
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—42no—
718C22⋊C4—42no—
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—22no—
731C42—41no—
732C42—41no—
733C42—41no—
734C42—41no—
735C42—44no—
736C42—42no—
737C42—42no—
738C42—42no—
739C42—44no—
740C42—81no—
741C42—81no—
742C422−1+414yes—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23#54812yes—
755C23#57512yes—
756C23#57812yes—
757C23C23×D411yescharacteristic
758Q8—42no—
759Q8—42no—
760Q8—42no—
761Q8—42no—
762D4—42no—
763D4—42no—
764D4—84no—
765C2×C4—28no—
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—24no—
775C2×C4—24no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—24no—
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—24no—
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—44no—
806C2×C4—48no—
807C2×C4—48no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4—162no—
846C2×C4#53612yes—
847C2×C4#53612yes—
848C2×C4#54812yes—
849C2×C4#57512yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C2×H(5,𝔽2)12yes—
852C2×C4C2×2−1+412yes—
853C2×C4C2×2−1+411yescharacteristic
854C8—42no—
855C8—42no—
856C8—42no—
857C8—42no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#337714yes—
872C22C2×#53611yescharacteristic
873C22C2×#54811yescharacteristic
874C22#348411yescharacteristic
875C22C2×#57511yescharacteristic
876C22C2×#57511yescharacteristic
877C22C2×#57811yescharacteristic
878C22#358511yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—44no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—44no—
893C4—41no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—82no—
901C4—81no—
902C4—81no—
903C4#351112yes—
904C4#355212yes—
905C2—24no—
906C2—161no—
907C2#3972011yescharacteristic
908C2#6086111yescharacteristic
909C2#6087411yescharacteristic
910C2C2×#337711yescharacteristic
911C2#6131811yescharacteristic
912C2#6157711yescharacteristic
913C2#6159511yescharacteristic
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×#2552C2semidirect
4. #32257C2semidirect
5. #32235C2semidirect
6. #30834C2semidirect
7. #30811C2semidirect
9. #29757C2semidirect
10. #28807C2semidirect
12. #27781C2semidirect
13. #27681C2semidirect
14. #26477C2semidirect
15. #26039C2semidirect
16. #25912C2semidirect
18. #24307C2semidirect
20. #22627C2semidirect
22. #22079C2semidirect
23. #21581C2semidirect

Maximal subgroups

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

subgroupindex
#366052
C2×#25522
#331102
#322572
#322352
#308342
#308112
#297612
#297572
#288072
#279782
#277812
#276812
#264772
#260392
#259122
#259072
#243072
#243052
#226272
#220822
#220792
#215812