Finite Group Databasebeta

← #7505162

Subgroups — #7505162

Order 512.

1714 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35543C211yesmaximal, characteristic, complemented
2#35152C211yesmaximal, characteristic
3#31597C212yesmaximal, complemented
4#31594C212yesmaximal, complemented
5#31593C212yesmaximal, complemented
6#31590C212yesmaximal, complemented
7#31585C212yesmaximal, complemented
8#31582C212yesmaximal, complemented
9#31573C212yesmaximal, complemented
10#31570C212yesmaximal, complemented
11#23735C211yesmaximal, characteristic, complemented
12#23730C211yesmaximal, characteristic, complemented
13#23662C211yesmaximal, characteristic, complemented
14#23634C211yesmaximal, characteristic, complemented
15#23617C211yesmaximal, characteristic, complemented
16#23509C211yesmaximal, characteristic
17#21206C211yesmaximal, characteristic
18#21156C211yesmaximal, characteristic, complemented
19#21067C211yesmaximal, characteristic, complemented
20#21065C211yesmaximal, characteristic, complemented
21#21027C211yesmaximal, characteristic, complemented
22C2×#1862C211yesmaximal, characteristic, complemented
23#20646C211yesmaximal, characteristic, complemented
24C2×#535C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#427C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C22×#107C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C2×#417C2211yescharacteristic
32C2×#417C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C2×#418C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C2×#405C2211yescharacteristic
40#2849—22no—
41#2622—22no—
42#2571C2212yescomplemented
43#2570C2212yescomplemented
44#2570C2212yescomplemented
45#2552C2212yescomplemented
46#2509—21no—
47#2508—21no—
48#2507—21no—
49#2506—21no—
50#2505—22no—
51#2473—22no—
52#2447C2212yes—
53#2447C2212yes—
54#2445C2212yes—
55#2445C2212yes—
56#2422—21no—
57#2422—21no—
58#2420—21no—
59#2420—21no—
60#2317C2211yescharacteristic
61#2317C2211yescharacteristic
62#2317C2211yescharacteristic
63#2317C2211yescharacteristic
64#2311C2211yescharacteristic
65#2309C2211yescharacteristic
66#2297C2211yescharacteristic
67#2296C2211yescharacteristic
68C2×#389C2211yescharacteristic
69#2285C2211yescharacteristic
70#2274C2211yescharacteristic
71#2097C2211yescharacteristic, complemented
72#2097C2211yescharacteristic, complemented
73#2096C2211yescharacteristic, complemented
74#2095C2211yescharacteristic, complemented
75#2094C2212yes—
76#2094C2211yescharacteristic, complemented
77#2093C2212yes—
78#2093C2211yescharacteristic, complemented
79#2092C2212yes—
80#2092C2212yes—
81#2092C2211yescharacteristic, complemented
82#2092C2211yescharacteristic, complemented
83#2085C2212yescomplemented
84#2085C2212yescomplemented
85#2084C2212yescomplemented
86#2083C2212yescomplemented
87#2074C2212yescomplemented
88#2073C2212yescomplemented
89#2072C2212yescomplemented
90#2071C2212yescomplemented
91#2068C2212yescomplemented
92#2067C2212yescomplemented
93#2066C2212yescomplemented
94#2065C2212yescomplemented
95#2042C2212yes—
96#2042C2212yes—
97#2041C2212yes—
98#2041C2212yes—
99#1961C2212yes—
100#1959C2212yes—
101#1958C2212yes—
102#1957C2212yes—
103#1944C2212yescomplemented
104#1944C2212yescomplemented
105#1942C2212yescomplemented
106#1942C2212yescomplemented
107#1928C2212yescomplemented
108#1928C2212yescomplemented
109#1926C2212yes—
110#1926C2212yes—
111#1925C2212yes—
112#1925C2212yes—
113#1925C2212yescomplemented
114#1925C2212yescomplemented
115#1917C2212yescomplemented
116#1917C2212yescomplemented
117#1916C2212yescomplemented
118#1916C2212yescomplemented
119#1862C2212yes—
120#1862C2212yes—
121#1862C2212yes—
122#1862C2212yes—
123#1804C2212yes—
124#1804C2212yes—
125#1802C2212yes—
126#1802C2212yes—
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130C2×#340C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4—21no—
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142#535—24no—
143#535—42no—
144C2×#127C2312yes—
145C2×#125—22no—
146C2×#124C2312yes—
147C2×#123—22no—
148C2×#123—22no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#120—22no—
152C2×C4×D4—24no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—42no—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—21no—
168C22×C42C2311yescharacteristic
169#428—42no—
170#427—24no—
171#427—42no—
172C2×#107—42no—
173C2×#107C2311yescharacteristic
174C2×#107C2311yescharacteristic
175C2×#107C2312yes—
176C2×#107C2311yescharacteristic
177C2×#107C2311yescharacteristic
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#106C2311yescharacteristic
181C2×#106C2311yescharacteristic
182C2×#106C2312yes—
183C2×#106C2311yescharacteristic
184C2×#106C2311yescharacteristic
185#423—42no—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188#418—42no—
189#418—42no—
190#417—42no—
191#417—42no—
192#416—24no—
193#416—42no—
194C2×#103C2311yescharacteristic
195C2×#103C2311yescharacteristic
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2311yescharacteristic
199C2×#103C2311yescharacteristic
200C2×#102—24no—
201C2×#102—24no—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2311yescharacteristic
205C2×#102C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2311yescharacteristic
215C2×#102C2311yescharacteristic
216#405—42no—
217C2×#97C2312yes—
218C2×C4×C8C2312yes—
219#400—22no—
220#400—22no—
221#400—22no—
222#400—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#397—22no—
228#397—22no—
229#397—22no—
230#397—22no—
231#394—22no—
232#394—22no—
233#394—22no—
234#394—22no—
235#391C2312yes—
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#390—21no—
239#390—21no—
240#390C2312yes—
241#390C2312yes—
242#390C2312yes—
243#390C2311yescharacteristic
244#390C2311yescharacteristic
245#389—22no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—22no—
251#389—21no—
252#389—21no—
253#389D411yescharacteristic
254#389D411yescharacteristic
255#389D411yescharacteristic
256#389D411yescharacteristic
257#389C2312yes—
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#389C2312yes—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#386—21no—
268#386—21no—
269#386—22no—
270#386—22no—
271#386—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#385—22no—
277#385—22no—
278#385D412yes—
279#385D412yes—
280#384—21no—
281#384—21no—
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2312yes—
285#384C2312yes—
286#382—22no—
287#382—21no—
288#382—21no—
289#382C2311yescharacteristic
290#382C2312yes—
291#382C2312yes—
292#382C2311yescharacteristic
293#381—22no—
294#381—22no—
295#380—21no—
296#380—21no—
297#380—21no—
298#380—21no—
299#379—22no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2312yes—
308C4×C22⋊C4—22no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C2×#95—21no—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328#336C2311yescharacteristic
329#336C2311yescharacteristic
330C25—21no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C22×Q8C2411yescharacteristic
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4#4114yes—
348C22×D4C2411yescharacteristic
349C22×D4C2412yes—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—44no—
357C23×C4—82no—
358C23×C4—82no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2411yescharacteristic
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8#4114yes—
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C22×C8C2412yes—
377C22×C8C2412yes—
378C22×C8C2411yescharacteristic
379C22×C8C2411yescharacteristic
380#127—24no—
381#127—42no—
382#125—84no—
383#124—24no—
384#124—42no—
385#123—84no—
386#123—84no—
387#121—44no—
388#121—44no—
389#120—48no—
390C4×D4—24no—
391C4×D4—24no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—44no—
395C4×D4—44no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—82no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D412yes—
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×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—44no—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—22no—
481#107—22no—
482#107—42no—
483#107—42no—
484#107—41no—
485#107—41no—
486#107—42no—
487#106—22no—
488#106—22no—
489#106—41no—
490#106—41no—
491#106—42no—
492C4⋊C8—42no—
493C4⋊C8—42no—
494#103—22no—
495#103—22no—
496#103—41no—
497#103—41no—
498#103—42no—
499#103—42no—
500#102—24no—
501#102—24no—
502#102—24no—
503#102—24no—
504#102—22no—
505#102—22no—
506#102—41no—
507#102—41no—
508#102—42no—
509#102—42no—
510#102—42no—
511#102—42no—
512#102—42no—
513#102—42no—
514#97—42no—
515C4×C8—42no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
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—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95C2×D412yes—
539#95C2×D412yes—
540#95C2×D412yes—
541#95C2×D412yes—
542C24—22no—
543C24—24no—
544C24—21no—
545C24—42no—
546C24—42no—
547C24—81no—
548C24—81no—
549C24—81no—
550C24—81no—
551C24C22×D411yescharacteristic
552#41—44no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×D4—28no—
563C2×D4—24no—
564C2×D4—28no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—44no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4C2×#4114yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—44no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4—81no—
624C22×C4—816no—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D412yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4H(5,𝔽2)12yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C42−1+412yes—
639C22×C42−1+412yes—
640C22×C4C2511yescharacteristic
641M16—44no—
642M16—44no—
643C2×C8—28no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—44no—
661C2×C8C2×#4112yes—
662C2×C8C2×#4112yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—24no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—44no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4—82no—
697C4⋊C4—81no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4—82no—
704C4⋊C4—82no—
705C4⋊C4—82no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—82no—
718C22⋊C4—81no—
719C22⋊C4—82no—
720C22⋊C4—81no—
721C22⋊C4—82no—
722C22⋊C4—82no—
723C22⋊C4—82no—
724C22⋊C4—82no—
725C42—22no—
726C42—22no—
727C42—21no—
728C42—21no—
729C42—22no—
730C42—22no—
731C42—21no—
732C42—21no—
733C42—22no—
734C42—22no—
735C42—42no—
736C42—42no—
737C42—42no—
738C42—82no—
739C42—82no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—24no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—48no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23#53612yes—
766C23#54612yes—
767C23#55012yes—
768C23C23×D411yescharacteristic
769Q8—41no—
770Q8—41no—
771Q8—41no—
772Q8—41no—
773D4—24no—
774D4—24no—
775D4—42no—
776D4—41no—
777D4—41no—
778D4—48no—
779D4—41no—
780D4—42no—
781D4—41no—
782D4—84no—
783D4—164no—
784D4—164no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—44no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
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—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—88no—
840C2×C4—82no—
841C2×C4—88no—
842C2×C4—84no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4—162no—
846C2×C4#53612yes—
847C2×C4#53914yes—
848C2×C4#53914yes—
849C2×C4#54612yes—
850C2×C4#55012yes—
851C2×C4#55214yes—
852C2×C4#56214yes—
853C2×C4#57612yes—
854C2×C4C22×#4111yescharacteristic
855C2×C4C22×#4111yescharacteristic
856C2×C4C2×H(5,𝔽2)11yescharacteristic
857C2×C4C2×H(5,𝔽2)11yescharacteristic
858C2×C4C2×2−1+411yescharacteristic
859C2×C4C2×2−1+411yescharacteristic
860C8—22no—
861C8—22no—
862C8—41no—
863C8—41no—
864C8—42no—
865C8—42no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—816no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—82no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22#269414yes—
888C22C2×#53611yescharacteristic
889C22C2×#54611yescharacteristic
890C22C2×#55011yescharacteristic
891C22C2×#57611yescharacteristic
892C22#358411yescharacteristic
893C22#358511yescharacteristic
894C22#358611yescharacteristic
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—41no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—81no—
907C4—82no—
908C4—81no—
909C4—81no—
910C4—81no—
911C4—82no—
912C4—82no—
913C4#269414yes—
914C4C2×#53911yescharacteristic
915C4C2×#53911yescharacteristic
916C4C2×#55211yescharacteristic
917C4C2×#56211yescharacteristic
918C2—24no—
919C2—84no—
920C2—161no—
921C2C2×#269411yescharacteristic
922C2#6088811yescharacteristic
923C2#6089011yescharacteristic
924C2#6118311yescharacteristic
925C2#6118811yescharacteristic
926C2#6140611yescharacteristic
927C2#6141511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35543C2semidirect
3. #31597C2semidirect
4. #31594C2semidirect
5. #31593C2semidirect
6. #31590C2semidirect
7. #31585C2semidirect
8. #31582C2semidirect
9. #31573C2semidirect
10. #31570C2semidirect
11. #23735C2semidirect
12. #23730C2semidirect
13. #23662C2semidirect
14. #23634C2semidirect
15. #23617C2semidirect
18. #21156C2semidirect
19. #21067C2semidirect
20. #21065C2semidirect
21. #21027C2semidirect
22. C2×#1862C2semidirect
23. #20646C2semidirect
42. #2571C22semidirect
43. #2570C22semidirect
44. #2570C22semidirect
45. #2552C22semidirect
71. #2097C22semidirect
72. #2097C22semidirect
73. #2096C22semidirect
74. #2095C22semidirect
76. #2094C22semidirect
78. #2093C22semidirect
81. #2092C22semidirect
82. #2092C22semidirect
83. #2085C22semidirect
84. #2085C22semidirect
85. #2084C22semidirect
86. #2083C22semidirect
87. #2074C22semidirect
88. #2073C22semidirect
89. #2072C22semidirect
90. #2071C22semidirect
91. #2068C22semidirect
92. #2067C22semidirect
93. #2066C22semidirect
94. #2065C22semidirect
103. #1944C22semidirect
104. #1944C22semidirect
105. #1942C22semidirect
106. #1942C22semidirect
107. #1928C22semidirect
108. #1928C22semidirect
113. #1925C22semidirect
114. #1925C22semidirect
115. #1917C22semidirect
116. #1917C22semidirect
117. #1916C22semidirect
118. #1916C22semidirect

Maximal subgroups

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

subgroupindex
#355432
#351522
#315972
#315942
#315932
#315902
#315852
#315822
#315732
#315702
#237352
#237302
#236622
#236342
#236172
#235092
#212062
#211562
#210672
#210652
#210272
C2×#18622
#206462