Finite Group Databasebeta

← #6763909

Subgroups — #6763909

Order 512.

1802 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37882C211yesmaximal, characteristic, complemented
2#37681C211yesmaximal, characteristic
3#33058C211yesmaximal, characteristic, complemented
4#32085C212yesmaximal, complemented
5#32078C212yesmaximal, complemented
6#31287C212yesmaximal, complemented
7#31286C212yesmaximal, complemented
8#30222C211yesmaximal, characteristic, complemented
9#29849C211yesmaximal, characteristic, complemented
10#29200C211yesmaximal, characteristic, complemented
11#28761C211yesmaximal, characteristic, complemented
12#27909C211yesmaximal, characteristic, complemented
13#27899C211yesmaximal, characteristic, complemented
14#25867C211yesmaximal, characteristic, complemented
15#25858C211yesmaximal, characteristic, complemented
16#24490C212yesmaximal, complemented
17#24490C212yesmaximal, complemented
18#24049C212yesmaximal, complemented
19#24046C212yesmaximal, complemented
20#22228C211yesmaximal, characteristic, complemented
21#21813C211yesmaximal, characteristic, complemented
22#21200C211yesmaximal, characteristic, complemented
23#21106C211yesmaximal, characteristic, complemented
24C2×#550C2211yescharacteristic
25C2×#546C2211yescharacteristic
26C2×#535C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#490C2211yescharacteristic
29C2×#488C2211yescharacteristic
30C2×#488C2211yescharacteristic, complemented
31C2×#480C2212yes—
32C2×#480C2212yescomplemented
33C2×#433C2211yescharacteristic
34C2×#417C2212yes—
35C2×#417C2212yescomplemented
36C2×C4×M16C2211yescharacteristic, complemented
37#2856C2211yescharacteristic
38#2851C2211yescharacteristic, complemented
39#2794—22no—
40#2721—22no—
41#2675—22no—
42#2669—22no—
43#2657C2211yescharacteristic
44#2647C2211yescharacteristic, complemented
45#2629C2211yescharacteristic
46#2620C2211yescharacteristic
47#2545C2211yescharacteristic
48#2541C2211yescharacteristic
49#2506C2212yescomplemented
50#2496C2212yes—
51#2487C2212yes—
52#2481—22no—
53#2473—22no—
54#2456—22no—
55#2433C2211yescharacteristic
56#2432C2211yescharacteristic
57#2431C2211yescharacteristic
58#2431C2211yescharacteristic
59#2424—22no—
60#2345C2212yescomplemented
61#2330C2211yescharacteristic, complemented
62#2326C2211yescharacteristic
63#2314C2211yescharacteristic
64#2290C2211yescharacteristic
65C2×#384C2211yescharacteristic, complemented
66#2093C2212yes—
67#2093C2212yescomplemented
68#2068C2212yescomplemented
69#2068C2212yescomplemented
70#2067C2212yes—
71#2067C2212yescomplemented
72#2043C2212yescomplemented
73#2042C2212yes—
74#2042C2212yes—
75#2042C2212yes—
76#2042C2212yescomplemented
77#2041C2212yes—
78#2041C2212yes—
79#2041C2212yes—
80#2041C2212yescomplemented
81#2041C2212yescomplemented
82#2036C2212yes—
83#2036C2212yes—
84#2033C2212yes—
85#2033C2212yes—
86#1992C2211yescharacteristic, complemented
87#1983C2212yes—
88#1983C2212yescomplemented
89#1982C2212yes—
90#1982C2212yes—
91#1961C2211yescharacteristic
92#1959C2211yescharacteristic
93#1959C2211yescharacteristic
94#1959C2211yescharacteristic, complemented
95#1959C2211yescharacteristic, complemented
96#1958C2211yescharacteristic
97#1958C2211yescharacteristic, complemented
98#1957C2211yescharacteristic
99#1957C2211yescharacteristic
100#1957C2212yes—
101#1956C2212yescomplemented
102#1934C2212yes—
103#1934C2212yescomplemented
104#1928C2212yescomplemented
105#1928C2212yescomplemented
106#1925C2212yes—
107#1925C2212yescomplemented
108#1923C2212yes—
109#1916C2212yescomplemented
110#1895C2212yes—
111#1895C2212yescomplemented
112#1870C2212yes—
113#1863C2212yescomplemented
114#1863C2212yescomplemented
115#1862C2212yes—
116#1862C2212yes—
117#1851C2212yescomplemented
118#1845C2211yescharacteristic, complemented
119#1845C2211yescharacteristic, complemented
120#1836C2211yescharacteristic, complemented
121#1788C2212yes—
122#1788C2212yes—
123#1788C2212yes—
124#1788C2212yescomplemented
125#1786C2212yes—
126#1786C2212yes—
127#1768C2211yescharacteristic, complemented
128#1750C2211yescharacteristic
129C4×C22⋊C8C2211yescharacteristic, complemented
130#1746C2211yescharacteristic, complemented
131C22×#41C2311yescharacteristic
132C22×#41C2311yescharacteristic
133C22×#41C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C22×M16C2312yes—
136#550—44no—
137#546—44no—
138#535—24no—
139#535—42no—
140#532—24no—
141#532—42no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×#127—21no—
144C2×#127C2311yescharacteristic
145C2×#127C2311yescharacteristic
146C2×#127C2311yescharacteristic
147C2×#127C2311yescharacteristic
148C2×#127C2311yescharacteristic
149C2×#126—22no—
150C2×#125—22no—
151C2×#125C2311yescharacteristic
152C2×#124C2311yescharacteristic
153C2×#124C2311yescharacteristic
154C2×#124C2311yescharacteristic
155C2×#124C2311yescharacteristic
156C2×#124C2311yescharacteristic
157C2×#123—21no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×#121—22no—
160C2×#121—22no—
161C2×#121—22no—
162C2×#121—22no—
163C2×#121—21no—
164C2×#121—21no—
165C2×#121—21no—
166C2×#121C2311yescharacteristic
167C2×#121C2311yescharacteristic
168C2×#121C2311yescharacteristic
169C2×#120—21no—
170C2×#120—22no—
171C2×#120—22no—
172C2×C4×Q8C2311yescharacteristic
173C2×C4×D4—21no—
174C2×C4×D4—22no—
175C2×C4×D4C2311yescharacteristic
176C2×C4×D4C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C22×C4⋊C4—22no—
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—21no—
181C22×C42C2311yescharacteristic
182#490—42no—
183#488—24no—
184#488—42no—
185#480—44no—
186#480—44no—
187#433—42no—
188C2×#107C2312yes—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194#417—44no—
195#417—44no—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2312yes—
217C2×#102C2312yes—
218C2×#102C2312yes—
219C2×#102C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222C2×C22⋊C8C2312yes—
223C4×M16—42no—
224C2×#97C2311yescharacteristic
225C2×#97C2311yescharacteristic
226C2×C4×C8C2311yescharacteristic
227C2×C4×C8C2311yescharacteristic
228C2×C4×C8C2312yes—
229#400—22no—
230#400—22no—
231#400—22no—
232#400—22no—
233#399—22no—
234#398—22no—
235#398—22no—
236#398—22no—
237#397—22no—
238#396—22no—
239#396—22no—
240#396—22no—
241#394—22no—
242#394—22no—
243#392—22no—
244#392—22no—
245#392—22no—
246#392—22no—
247#392—22no—
248#392—22no—
249#391C2311yescharacteristic
250#391C2311yescharacteristic
251#390—22no—
252#390C2311yescharacteristic
253#390C2311yescharacteristic
254#390C2311yescharacteristic
255#390C2311yescharacteristic
256#389—22no—
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#388—22no—
263#388—22no—
264#388—22no—
265#388D412yes—
266#387—22no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387D412yes—
274#386—22no—
275#386—22no—
276#386—22no—
277#386D412yes—
278#385—22no—
279#385—22no—
280#385—22no—
281#385—22no—
282#385D412yes—
283#384—22no—
284#384C2311yescharacteristic
285#384C2311yescharacteristic
286#384C2312yes—
287#384C2311yescharacteristic
288#382C2311yescharacteristic
289#380—22no—
290#380C2312yes—
291#380C2312yes—
292#380C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2311yescharacteristic
296C4×C22⋊C4—22no—
297C4×C22⋊C4C2311yescharacteristic
298C4×C22⋊C4C2311yescharacteristic
299#376C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309C25—21no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—24no—
314C2×#41—24no—
315C2×#41—41no—
316C2×#41—41no—
317C2×#41—41no—
318C2×#41—42no—
319C2×#41—42no—
320C2×#41—42no—
321C2×#41—42no—
322C22×Q8C2411yescharacteristic
323C22×Q8C2411yescharacteristic
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4—41no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4C2×D411yescharacteristic
342C22×D4C2411yescharacteristic
343C22×D4C2411yescharacteristic
344C22×D4C2411yescharacteristic
345C22×D4C2411yescharacteristic
346C23×C4—22no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4C2×D412yes—
352C23×C4C2411yescharacteristic
353C23×C4C2411yescharacteristic
354C2×M16—24no—
355C2×M16—42no—
356C2×M16—42no—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C4⋊Q8—22no—
362C4⋊Q8—41no—
363#127—22no—
364#127—22no—
365#127—22no—
366#127—22no—
367#127—41no—
368#127—41no—
369#127—42no—
370#127—42no—
371#127—44no—
372#126—84no—
373#125—22no—
374#125—22no—
375#125—84no—
376#124—22no—
377#124—22no—
378#124—22no—
379#124—22no—
380#124—41no—
381#124—42no—
382#124—42no—
383#124#4114yes—
384#123—44no—
385C22⋊Q8—42no—
386#121—24no—
387#121—24no—
388#121—48no—
389#121—48no—
390#121—44no—
391#121—44no—
392#121—44no—
393#121—42no—
394#121—84no—
395#121—84no—
396#120—48no—
397#120—44no—
398#120—84no—
399C4×Q8—42no—
400C4×D4—24no—
401C4×D4—48no—
402C4×D4—42no—
403C4×D4—44no—
404#117—22no—
405#117—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—84no—
424C2×C4⋊C4C2×D412yes—
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C22⋊C4C2×D412yes—
454C2×C22⋊C4C2×D411yescharacteristic
455C2×C22⋊C4C2×D412yes—
456C2×C22⋊C4C2×D412yes—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42C2×D412yes—
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C2×C42C2411yescharacteristic
468#107—42no—
469#107—42no—
470#107—42no—
471#107—42no—
472C4⋊C8—42no—
473C4⋊C8—42no—
474#103—24no—
475#103—42no—
476#103—42no—
477#103—42no—
478#103—42no—
479#103—42no—
480#103—42no—
481#103—42no—
482#102—24no—
483#102—42no—
484#102—42no—
485#102—42no—
486#102—42no—
487#102—42no—
488#102—42no—
489#102—42no—
490#102—42no—
491#102—42no—
492#102—42no—
493#102—42no—
494#102—42no—
495#102—42no—
496#102—42no—
497#102—42no—
498C22⋊C8—24no—
499C22⋊C8—42no—
500C22⋊C8—42no—
501#97—22no—
502#97—22no—
503C4×C8—22no—
504C4×C8—22no—
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—22no—
519#95C2×D412yes—
520#95C2×D412yes—
521#95C2×D412yes—
522#95C2×D412yes—
523#95C2×D412yes—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—81no—
531C24—82no—
532C24—82no—
533C24C22×D411yescharacteristic
534C24C22×D411yescharacteristic
535#41—48no—
536#41—48no—
537#41—84no—
538#41—84no—
539#41—84no—
540#41—84no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8C2×#4112yes—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—81no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4—82no—
590C2×D4—82no—
591C2×D4—82no—
592C2×D4—82no—
593C2×D4—82no—
594C2×D4—84no—
595C2×D4—84no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—82no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4C2×#4112yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4—82no—
633C22×C4—82no—
634C22×C4—82no—
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4H(5,𝔽2)14yes—
644C22×C4C2511yescharacteristic
645M16—48no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C4⋊C4—22no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—28no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—42no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C42—24no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—22no—
715C42—22no—
716C42—42no—
717C42—82no—
718C42—82no—
719C42C2×#4112yes—
720C42H(5,𝔽2)12yes—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—84no—
751C23—84no—
752C23—164no—
753C23—162no—
754C23—164no—
755C23#53512yes—
756C23C23×D411yescharacteristic
757Q8—24no—
758Q8—42no—
759Q8—42no—
760Q8—42no—
761D4—24no—
762D4—42no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—88no—
770D4—82no—
771D4—84no—
772D4—84no—
773D4—84no—
774D4—84no—
775D4—84no—
776D4—164no—
777D4—164no—
778D4—162no—
779D4—164no—
780D4—162no—
781D4—162no—
782D4—162no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—48no—
806C2×C4—41no—
807C2×C4—41no—
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—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—162no—
833C2×C4—164no—
834C2×C4#53512yes—
835C2×C4#54614yes—
836C2×C4#57614yes—
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×H(5,𝔽2)12yes—
839C2×C4C2×H(5,𝔽2)11yescharacteristic
840C2×C4#58512yes—
841C8—42no—
842C8—42no—
843C8—42no—
844C8—42no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—42no—
852C22—41no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—81no—
858C22—81no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—168no—
876C22C2×#53511yescharacteristic
877C22C2×#54611yescharacteristic
878C22#350011yescharacteristic
879C22C2×#57612yes—
880C22#358612yes—
881C4—24no—
882C4—24no—
883C4—22no—
884C4—42no—
885C4—41no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—82no—
896C4—81no—
897C4#351312yes—
898C4#354212yes—
899C2—42no—
900C2—81no—
901C2—82no—
902C2—161no—
903C2—161no—
904C2—161no—
905C2#3808411yescharacteristic
906C2#6080911yescharacteristic
907C2#6081711yescharacteristic
908C2#6119112yes—
909C2#6261812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37681C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #37882C2semidirect
3. #33058C2semidirect
4. #32085C2semidirect
5. #32078C2semidirect
6. #31287C2semidirect
7. #31286C2semidirect
8. #30222C2semidirect
9. #29849C2semidirect
10. #29200C2semidirect
11. #28761C2semidirect
12. #27909C2semidirect
13. #27899C2semidirect
14. #25867C2semidirect
15. #25858C2semidirect
16. #24490C2semidirect
17. #24490C2semidirect
18. #24049C2semidirect
19. #24046C2semidirect
20. #22228C2semidirect
21. #21813C2semidirect
22. #21200C2semidirect
23. #21106C2semidirect
30. C2×#488C22semidirect
32. C2×#480C22semidirect
35. C2×#417C22semidirect
36. C2×C4×M16C22semidirect
38. #2851C22semidirect
44. #2647C22semidirect
49. #2506C22semidirect
60. #2345C22semidirect
61. #2330C22semidirect
65. C2×#384C22semidirect
67. #2093C22semidirect
68. #2068C22semidirect
69. #2068C22semidirect
71. #2067C22semidirect
72. #2043C22semidirect
76. #2042C22semidirect
80. #2041C22semidirect
81. #2041C22semidirect
86. #1992C22semidirect
88. #1983C22semidirect
94. #1959C22semidirect
95. #1959C22semidirect
97. #1958C22semidirect
101. #1956C22semidirect
103. #1934C22semidirect
104. #1928C22semidirect
105. #1928C22semidirect
107. #1925C22semidirect
109. #1916C22semidirect
111. #1895C22semidirect
113. #1863C22semidirect
114. #1863C22semidirect
117. #1851C22semidirect
118. #1845C22semidirect
119. #1845C22semidirect
120. #1836C22semidirect
124. #1788C22semidirect
127. #1768C22semidirect
129. C4×C22⋊C8C22semidirect
130. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#378822
#376812
#330582
#320852
#320782
#312872
#312862
#302222
#298492
#292002
#287612
#279092
#278992
#258672
#258582
#244902
#240492
#240462
#222282
#218132
#212002
#211062