Finite Group Databasebeta

← #7504944

Subgroups — #7504944

Order 512.

1774 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35667C211yesmaximal, characteristic
2#35267C211yesmaximal, characteristic
3#31516C212yesmaximal, complemented
4#31512C212yesmaximal, complemented
5#31509C212yesmaximal, complemented
6#31505C212yesmaximal, complemented
7#31501C212yesmaximal, complemented
8#31497C212yesmaximal, complemented
9#31492C212yesmaximal, complemented
10#31488C212yesmaximal, complemented
11#23670C211yesmaximal, characteristic, complemented
12#23633C211yesmaximal, characteristic, complemented
13#23615C211yesmaximal, characteristic, complemented
14C2×#2043C211yesmaximal, characteristic, complemented
15#23487C211yesmaximal, characteristic
16#23484C211yesmaximal, characteristic
17#21259C211yesmaximal, characteristic, complemented
18#21032C211yesmaximal, characteristic, complemented
19#20974C211yesmaximal, characteristic
20#20974C211yesmaximal, characteristic
21#20880C211yesmaximal, characteristic, complemented
22#20839C211yesmaximal, characteristic
23#20651C211yesmaximal, characteristic, complemented
24C22×#131C2211yescharacteristic
25C2×#536C2211yescharacteristic
26C2×#536C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C2×#519C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#423C2211yescharacteristic
33C2×#419C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C2×#419C2211yescharacteristic
36C2×#419C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C2×#408C2211yescharacteristic
42#2863—21no—
43#2860—21no—
44#2645—21no—
45#2644—21no—
46#2546—21no—
47#2546—21no—
48#2545—21no—
49#2545—21no—
50#2510—22no—
51#2497C2212yes—
52#2496C2212yes—
53#2495C2212yes—
54#2494C2212yes—
55#2481—22no—
56#2429C2212yes—
57#2429C2212yes—
58#2429C2212yes—
59#2429C2212yes—
60#2413—22no—
61#2413—22no—
62#2317C2211yescharacteristic
63#2316C2211yescharacteristic
64#2311C2211yescharacteristic
65#2311C2211yescharacteristic
66#2310C2211yescharacteristic
67#2297C2211yescharacteristic
68#2296C2211yescharacteristic
69C2×#389C2211yescharacteristic
70C4×#117C2211yescharacteristic
71#2088C2212yes—
72#2088C2212yes—
73#2087C2212yes—
74#2086C2212yes—
75#2074C2212yes—
76#2074C2212yes—
77#2072C2212yes—
78#2072C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2066C2212yes—
83#2043C2212yes—
84#2043C2212yes—
85#2043C2212yes—
86#2043C2212yes—
87#2036C2212yes—
88#2036C2212yes—
89#2036C2212yes—
90#2036C2212yes—
91#2035C2212yes—
92#2035C2212yes—
93#2035C2212yes—
94#2035C2212yes—
95#1981C2212yes—
96#1981C2212yes—
97#1981C2212yes—
98#1981C2212yes—
99#1921C2211yescharacteristic
100#1921C2211yescharacteristic
101#1920C2211yescharacteristic
102#1920C2211yescharacteristic
103#1919C2211yescharacteristic
104#1919C2211yescharacteristic
105#1918C2211yescharacteristic
106#1918C2211yescharacteristic
107#1894C2212yes—
108#1894C2212yes—
109#1894C2212yes—
110#1894C2212yes—
111#1892C2212yes—
112#1892C2212yes—
113#1892C2212yes—
114#1892C2212yes—
115#1865C2212yes—
116#1865C2212yes—
117#1863C2212yes—
118#1863C2212yes—
119#1851C2212yes—
120#1851C2212yes—
121#1850C2212yes—
122#1850C2212yes—
123#1805C2212yes—
124#1805C2212yes—
125#1803C2212yes—
126#1803C2212yes—
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1735C2211yescharacteristic
131#1735C2211yescharacteristic
132#1735C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C2×#131—42no—
139C2×#131—42no—
140C2×#131—42no—
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143C22×M16C2312yes—
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146C23×C8C2312yes—
147#536—24no—
148#536—24no—
149#536—42no—
150#536—42no—
151C2×C4⋊Q8—21no—
152C2×C4⋊Q8—21no—
153C2×C4⋊Q8—24no—
154C2×C4⋊Q8—21no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—42no—
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2312yes—
159C2×#126—22no—
160C2×#124—21no—
161C2×#124—21no—
162C2×#123—22no—
163C2×#123—22no—
164C2×C22⋊Q8C2312yes—
165C2×C22⋊Q8C2312yes—
166C2×C22⋊Q8C2312yes—
167C2×C22⋊Q8C2312yes—
168#519—24no—
169#519—42no—
170C2×C4×Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×#117—22no—
175C2×#117C2311yescharacteristic
176C2×#117C2311yescharacteristic
177C2×#117C2311yescharacteristic
178C2×#117C2311yescharacteristic
179C2×#117C2311yescharacteristic
180C22×C4⋊C4—21no—
181C22×C4⋊C4—21no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C42C2311yescharacteristic
186#428—42no—
187#427—24no—
188C2×#107C2311yescharacteristic
189C2×#107C2311yescharacteristic
190C2×#107C2312yes—
191C2×#106C2311yescharacteristic
192C2×#106C2311yescharacteristic
193C2×#106C2312yes—
194#424—42no—
195#423—42no—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2312yes—
200#419—42no—
201#419—42no—
202#419—42no—
203#419—42no—
204C2×#103—24no—
205C2×#103—42no—
206C2×#103—42no—
207C2×#103—42no—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224#408—42no—
225C2×C22⋊C8C2312yes—
226C2×C22⋊C8C2312yes—
227#401—22no—
228#400—22no—
229#400—22no—
230#400—22no—
231#398—22no—
232#398—22no—
233#398—22no—
234#398—22no—
235#397—22no—
236#397—22no—
237#397—22no—
238#396—22no—
239#396—22no—
240#396—22no—
241#396—22no—
242#396—22no—
243#391—21no—
244#391—21no—
245#391—21no—
246#391—21no—
247#391D411yescharacteristic
248#391D411yescharacteristic
249#391C2312yes—
250#391C2312yes—
251#390—21no—
252#390—21no—
253#390D411yescharacteristic
254#390D411yescharacteristic
255#389—21no—
256#389—21no—
257#389—21no—
258#389—21no—
259#389—21no—
260#389—21no—
261#389—22no—
262#389—22no—
263#389—22no—
264#389—22no—
265#389C2312yes—
266#389C2312yes—
267#389C2311yescharacteristic
268#389C2312yes—
269#389C2311yescharacteristic
270#389C2312yes—
271#389C2311yescharacteristic
272#389C2311yescharacteristic
273#388—22no—
274#388—22no—
275#388—22no—
276#388—22no—
277#388—22no—
278#388—22no—
279#388—22no—
280#387—22no—
281#387—22no—
282#387—22no—
283#386—22no—
284#386—22no—
285#386D412yes—
286#386D412yes—
287#385—21no—
288#385—21no—
289#385—22no—
290#384C2312yes—
291#383—22no—
292#382C2312yes—
293#381—22no—
294#380—22no—
295#380C2312yes—
296#380C2312yes—
297#380C2312yes—
298#380C2312yes—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C22⋊C4—21no—
306C4×C22⋊C4—21no—
307C4×C22⋊C4C2312yes—
308C4×C22⋊C4C2312yes—
309#376—21no—
310C2×#95—21no—
311C43—21no—
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2312yes—
325#340C2312yes—
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#336C2312yes—
331#336C2312yes—
332#336C2311yescharacteristic
333#336C2311yescharacteristic
334#336C2311yescharacteristic
335#336C2311yescharacteristic
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C22×Q8—21no—
343C22×Q8—21no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8C2×D411yescharacteristic
356C22×Q8#4114yes—
357C22×Q8C2412yes—
358C22×Q8C2412yes—
359C22×D4C2×D412yes—
360C22×D4C2×D411yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2412yes—
368C23×C4C2411yescharacteristic
369#131—416no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—42no—
377C2×M16—42no—
378C2×M16—42no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—22no—
384C22×C8—22no—
385C22×C8—42no—
386C22×C8—42no—
387C22×C8—42no—
388C22×C8C2411yescharacteristic
389C22×C8C2411yescharacteristic
390C22×C8C2412yes—
391C22×C8C2411yescharacteristic
392C22×C8C2411yescharacteristic
393C22×C8C2412yes—
394C4⋊Q8—24no—
395C4⋊Q8—24no—
396C4⋊Q8—42no—
397C4⋊Q8—42no—
398C4⋊Q8—44no—
399C4⋊Q8—44no—
400C4⋊Q8—44no—
401C4⋊Q8—44no—
402#126—84no—
403#124—44no—
404#124—44no—
405#123—48no—
406#123—48no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8—24no—
411C22⋊Q8—42no—
412C22⋊Q8—42no—
413C22⋊Q8—42no—
414C22⋊Q8—42no—
415C4×Q8—24no—
416C4×Q8—24no—
417C4×Q8—42no—
418C4×Q8—42no—
419C4×Q8—44no—
420C4×Q8—44no—
421#117—22no—
422#117—22no—
423#117—22no—
424#117—22no—
425#117—22no—
426#117—22no—
427#117—22no—
428#117—22no—
429#117—22no—
430#117—48no—
431#117#4114yes—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4—82no—
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4C2×D412yes—
486C2×C22⋊C4C2×D412yes—
487C2×C22⋊C4C2×D412yes—
488C2×C22⋊C4C2×D412yes—
489C2×C22⋊C4C2×D412yes—
490C2×C42—21no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2412yes—
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507#107—22no—
508#107—22no—
509#107—42no—
510#106—22no—
511#106—22no—
512#106—42no—
513C4⋊C8—42no—
514C4⋊C8—42no—
515C4⋊C8—42no—
516C4⋊C8—42no—
517#103—24no—
518#103—24no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103—42no—
526#103—42no—
527#103—42no—
528#103—42no—
529#103—42no—
530#103—42no—
531#103—42no—
532#103—42no—
533C22⋊C8—42no—
534C22⋊C8—42no—
535#95—22no—
536#95—22no—
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—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95C2×D412yes—
558#95C2×D412yes—
559#95C2×D412yes—
560#95C2×D412yes—
561C24C22×D412yes—
562C24C22×D411yescharacteristic
563#41—44no—
564#41—44no—
565#41—44no—
566#41—44no—
567C2×Q8—22no—
568C2×Q8—24no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—28no—
573C2×Q8—28no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—42no—
586C2×Q8—44no—
587C2×Q8—42no—
588C2×Q8—42no—
589C2×Q8—42no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8C2×#4114yes—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4H(5,𝔽2)12yes—
649C22×C4H(5,𝔽2)12yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C42−1+412yes—
652C22×C4C2511yescharacteristic
653M16—48no—
654M16—44no—
655M16—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—22no—
674C2×C8—48no—
675C2×C8—44no—
676C2×C8—44no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—44no—
713C4⋊C4—42no—
714C4⋊C4—82no—
715C4⋊C4—82no—
716C4⋊C4—82no—
717C4⋊C4—82no—
718C4⋊C4—82no—
719C4⋊C4C2×#4112yes—
720C4⋊C4C2×#4112yes—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—82no—
735C22⋊C4—82no—
736C22⋊C4—82no—
737C22⋊C4—82no—
738C42—22no—
739C42—22no—
740C42—24no—
741C42—21no—
742C42—21no—
743C42—22no—
744C42—21no—
745C42—21no—
746C42—22no—
747C42—44no—
748C42—44no—
749C42—42no—
750C42—42no—
751C42—42no—
752C42—42no—
753C42—42no—
754C42—81no—
755C42—81no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23#53712yes—
768C23#54612yes—
769C23#54612yes—
770C23C23×D411yescharacteristic
771Q8—24no—
772Q8—24no—
773Q8—42no—
774Q8—48no—
775Q8—44no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8—42no—
780Q8—42no—
781Q8—84no—
782D4—48no—
783D4—44no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—48no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—84no—
847C2×C4—84no—
848C2×C4—162no—
849C2×C4#53712yes—
850C2×C4#53914yes—
851C2×C4#54214yes—
852C2×C4#54612yes—
853C2×C4#54612yes—
854C2×C4#55314yes—
855C2×C4#56014yes—
856C2×C4#57712yes—
857C2×C4#57812yes—
858C2×C4C22×#4111yescharacteristic
859C2×C4C22×#4111yescharacteristic
860C2×C4C2×H(5,𝔽2)11yescharacteristic
861C2×C4C2×H(5,𝔽2)11yescharacteristic
862C2×C4C2×H(5,𝔽2)11yescharacteristic
863C2×C4C2×2−1+411yescharacteristic
864C8—41no—
865C8—41no—
866C8—41no—
867C8—41no—
868C8—42no—
869C8—42no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22#269114yes—
884C22C2×#53711yescharacteristic
885C22C2×#54611yescharacteristic
886C22C2×#54611yescharacteristic
887C22C2×#57711yescharacteristic
888C22C2×#57811yescharacteristic
889C22#358611yescharacteristic
890C22#358611yescharacteristic
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—44no—
901C4—81no—
902C4—82no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—81no—
908C4—82no—
909C4—81no—
910C4#269114yes—
911C4C2×#53911yescharacteristic
912C4C2×#54211yescharacteristic
913C4C2×#55311yescharacteristic
914C4C2×#56011yescharacteristic
915C2—24no—
916C2—82no—
917C2C2×#269111yescharacteristic
918C2#6092311yescharacteristic
919C2#6092511yescharacteristic
920C2#6118511yescharacteristic
921C2#6118611yescharacteristic
922C2#6121711yescharacteristic
923C2#6122411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #31516C2semidirect
4. #31512C2semidirect
5. #31509C2semidirect
6. #31505C2semidirect
7. #31501C2semidirect
8. #31497C2semidirect
9. #31492C2semidirect
10. #31488C2semidirect
11. #23670C2semidirect
12. #23633C2semidirect
13. #23615C2semidirect
14. C2×#2043C2semidirect
17. #21259C2semidirect
18. #21032C2semidirect
21. #20880C2semidirect
23. #20651C2semidirect

Maximal subgroups

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

subgroupindex
#356672
#352672
#315162
#315122
#315092
#315052
#315012
#314972
#314922
#314882
#236702
#236332
#236152
C2×#20432
#234872
#234842
#212592
#210322
#209742
#208802
#208392
#206512