Finite Group Databasebeta

← #6909539

Subgroups — #6909539

Order 512.

1870 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38078C211yesmaximal, characteristic
2#37695C211yesmaximal, characteristic, complemented
3#32813C211yesmaximal, characteristic, complemented
4#32767C211yesmaximal, characteristic, complemented
5#31836C212yesmaximal, complemented
6#31636C212yesmaximal, complemented
7#30742C212yesmaximal, complemented
8#30450C212yesmaximal, complemented
9#30190C211yesmaximal, characteristic, complemented
10#30054C211yesmaximal, characteristic, complemented
11#30050C211yesmaximal, characteristic, complemented
12#29726C211yesmaximal, characteristic, complemented
13#29676C211yesmaximal, characteristic, complemented
14#29104C211yesmaximal, characteristic, complemented
15#28173C211yesmaximal, characteristic, complemented
16#25722C211yesmaximal, characteristic, complemented
17#24532C212yesmaximal, complemented
18#24357C212yesmaximal, complemented
19#23970C212yesmaximal, complemented
20#23944C211yesmaximal, characteristic, complemented
21#23852C212yesmaximal
22C2×#2013C211yesmaximal, characteristic, complemented
23#21997C211yesmaximal, characteristic, complemented
24C23×SD16C2212yes—
25C2×#554C2211yescharacteristic
26C2×#546C2211yescharacteristic
27C2×#541C2211yescharacteristic, complemented
28C22×C4⋊Q8C2211yescharacteristic
29C2×#494C2212yescomplemented
30C2×#464C2212yes—
31C2×#464C2212yes—
32C2×#452C2212yes—
33C2×#452C2212yes—
34C2×#451C2212yes—
35C2×#451C2212yes—
36C22×#103C2212yes—
37#2857C2211yescharacteristic
38#2851C2211yescharacteristic
39#2716—22no—
40#2713—22no—
41#2694—22no—
42#2681—22no—
43#2642C2211yescharacteristic, complemented
44#2640C2211yescharacteristic
45#2621C2211yescharacteristic, complemented
46#2620C2211yescharacteristic
47#2545C2211yescharacteristic
48#2542C2211yescharacteristic
49#2502C2211yescharacteristic
50#2501C2211yescharacteristic
51#2481—22no—
52#2473—22no—
53#2446C2212yescomplemented
54#2437—22no—
55#2435C2211yescharacteristic
56#2432C2211yescharacteristic
57#2429C2212yescomplemented
58#2418—22no—
59#2409C2212yes—
60Q8×C22⋊C4C2212yes—
61#2327C2211yescharacteristic, complemented
62#2326C2211yescharacteristic
63#2311C2211yescharacteristic
64C2×#390C2211yescharacteristic
65#2290C2211yescharacteristic
66#2099C2212yescomplemented
67#2074C2211yescharacteristic, complemented
68#2074C2211yescharacteristic, complemented
69#2073C2211yescharacteristic
70#2073C2211yescharacteristic
71#2072C2212yescomplemented
72#2072C2212yescomplemented
73#2056C2212yescomplemented
74#2056C2212yescomplemented
75#2055C2212yes—
76#2055C2212yes—
77#2043C2212yescomplemented
78#2026C2211yescharacteristic, complemented
79#2026C2211yescharacteristic, complemented
80#2025C2211yescharacteristic
81#2025C2211yescharacteristic
82#2024C2212yescomplemented
83#2024C2212yescomplemented
84#2016C2211yescharacteristic, complemented
85#2016C2211yescharacteristic, complemented
86#2016C2211yescharacteristic, complemented
87#2016C2211yescharacteristic, complemented
88#2015C2212yes—
89#2015C2212yes—
90#2015C2212yes—
91#2015C2212yes—
92#2013C2211yescharacteristic
93#2013C2212yes—
94#2013C2211yescharacteristic
95#2013C2211yescharacteristic
96#2013C2211yescharacteristic
97#2013C2212yes—
98#2001C2212yescomplemented
99#2001C2212yescomplemented
100#2000C2212yes—
101#2000C2212yes—
102#1956C2212yescomplemented
103#1934C2212yes—
104#1934C2212yes—
105#1923C2212yescomplemented
106#1916C2212yescomplemented
107#1892C2212yes—
108#1892C2212yes—
109#1880C2212yes—
110#1880C2212yes—
111#1878C2212yescomplemented
112#1878C2212yescomplemented
113#1878C2212yescomplemented
114#1878C2212yescomplemented
115#1877C2212yes—
116#1877C2212yes—
117#1872C2212yescomplemented
118#1872C2212yescomplemented
119#1869C2212yes—
120#1850C2212yes—
121#1840C2211yescharacteristic, complemented
122#1832C2211yescharacteristic, complemented
123#1824C2212yes—
124#1818C2211yescharacteristic, complemented
125#1803C2212yescomplemented
126#1803C2212yescomplemented
127#1798C2211yescharacteristic, complemented
128#1786C2212yes—
129C4×C22⋊C8C2211yescharacteristic
130C2×#336C2211yescharacteristic
131C22×#41C2311yescharacteristic
132C23×Q8C2312yes—
133C23×D4C2311yescharacteristic
134C22×Q16C2312yes—
135C22×Q16C2312yes—
136C22×Q16C2312yes—
137C22×Q16C2312yes—
138C22×SD16—44no—
139C22×SD16—44no—
140C22×SD16—44no—
141C22×SD16C2312yes—
142C22×SD16C2312yes—
143C22×SD16C2312yes—
144C22×SD16C2312yes—
145C23×C8C2312yes—
146#554—44no—
147#546—44no—
148#541—44no—
149C2×C4⋊Q8—22no—
150C2×C4⋊Q8—44no—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2311yescharacteristic
154C2×C4⋊Q8C2311yescharacteristic
155C2×C4⋊Q8C2311yescharacteristic
156C2×#126—22no—
157C2×#125—22no—
158C2×#125—21no—
159C2×#125C2311yescharacteristic
160C2×#124C2311yescharacteristic
161C2×#124C2311yescharacteristic
162C2×#124C2311yescharacteristic
163C2×#123—21no—
164C2×#123—22no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8C2311yescharacteristic
169C2×C22⋊Q8C2311yescharacteristic
170C2×C22⋊Q8C2312yes—
171C2×C22⋊Q8C2311yescharacteristic
172C2×C22⋊Q8C2312yes—
173C2×#121—21no—
174C2×#121C2311yescharacteristic
175C2×#120—21no—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2311yescharacteristic
179C2×C4×D4—21no—
180C2×C4×D4C2311yescharacteristic
181C2×C4×D4C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C22×C4⋊C4—22no—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C22⋊C4—22no—
187C22×C22⋊C4—21no—
188C22×C42C2311yescharacteristic
189#494—44no—
190#464—44no—
191#464—44no—
192#452—44no—
193#452—44no—
194#451—44no—
195#451—44no—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×#103—44no—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C4×C8C2312yes—
219#400—22no—
220#400—22no—
221#400—22no—
222#399—22no—
223#399—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#398—22no—
228#397—22no—
229#397—22no—
230#396—22no—
231#396—22no—
232#396—22no—
233#395—22no—
234#394—22no—
235#394—22no—
236#394—22no—
237#393—22no—
238#393—22no—
239#391—22no—
240#391—22no—
241#391C2312yes—
242#391C2312yes—
243#391C2311yescharacteristic
244#391C2311yescharacteristic
245#391C2311yescharacteristic
246#391C2311yescharacteristic
247#391C2312yes—
248#391C2312yes—
249#390—22no—
250#390C2311yescharacteristic
251#390C2311yescharacteristic
252#390C2311yescharacteristic
253#390C2311yescharacteristic
254#390C2311yescharacteristic
255#390C2311yescharacteristic
256#389—22no—
257#389—22no—
258#389C2312yes—
259#388—22no—
260#388—22no—
261#388—22no—
262#388D412yes—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#387D412yes—
269#386—22no—
270#386—22no—
271#386D412yes—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#385—22no—
277#385D412yes—
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#382C2311yescharacteristic
282#380—22no—
283#380—22no—
284#380—22no—
285#380C2312yes—
286#379—22no—
287C4×C4⋊C4C2311yescharacteristic
288C4×C22⋊C4—22no—
289C4×C22⋊C4C2311yescharacteristic
290C4×C22⋊C4C2311yescharacteristic
291#376C2311yescharacteristic
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#336C2311yescharacteristic
301#336C2311yescharacteristic
302#336C2312yes—
303#336C2312yes—
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309C25—21no—
310C2×#41—22no—
311C2×#41—42no—
312C2×#41—41no—
313C2×#41—42no—
314C22×Q8—22no—
315C22×Q8—21no—
316C22×Q8—24no—
317C22×Q8—24no—
318C22×Q8—24no—
319C22×Q8—42no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C2411yescharacteristic
323C22×Q8C2411yescharacteristic
324C22×Q8C2412yes—
325C22×Q8C2412yes—
326C22×D4—22no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—24no—
331C22×D4—42no—
332C22×D4—41no—
333C22×D4C2×D411yescharacteristic
334C22×D4C2411yescharacteristic
335C22×D4C2411yescharacteristic
336C23×C4—22no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4C2×D412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C2×Q16—24no—
345C2×Q16—24no—
346C2×Q16—42no—
347C2×Q16—42no—
348C2×Q16—42no—
349C2×Q16—42no—
350C2×Q16—42no—
351C2×Q16—42no—
352C2×Q16—42no—
353C2×Q16—42no—
354C2×Q16—42no—
355C2×Q16—42no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×SD16—24no—
359C2×SD16—24no—
360C2×SD16—42no—
361C2×SD16—42no—
362C2×SD16—42no—
363C2×SD16—42no—
364C2×SD16—42no—
365C2×SD16—42no—
366C2×SD16—42no—
367C2×SD16—42no—
368C2×SD16—432no—
369C22×C8—24no—
370C22×C8—42no—
371C22×C8—42no—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C4⋊Q8—24no—
377C4⋊Q8—24no—
378C4⋊Q8—42no—
379C4⋊Q8—42no—
380C4⋊Q8—42no—
381C4⋊Q8—42no—
382C4⋊Q8—48no—
383#126—48no—
384#125—42no—
385#125—48no—
386#125—44no—
387#124—22no—
388#124—41no—
389#124—42no—
390#124—42no—
391#123—44no—
392#123—84no—
393C22⋊Q8—24no—
394C22⋊Q8—24no—
395C22⋊Q8—24no—
396C22⋊Q8—44no—
397C22⋊Q8—44no—
398C22⋊Q8—42no—
399C22⋊Q8—42no—
400C22⋊Q8—42no—
401C22⋊Q8—42no—
402C22⋊Q8—84no—
403#121—44no—
404#121—42no—
405#120—44no—
406C4×Q8—24no—
407C4×Q8—42no—
408C4×Q8—42no—
409C4×Q8—42no—
410C4×Q8—42no—
411C4×D4—24no—
412C4×D4—42no—
413C4×D4—44no—
414#117—42no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
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—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—48no—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—44no—
467C2×C22⋊C4—84no—
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C22⋊C4C2×D412yes—
471C2×C22⋊C4C2×D412yes—
472C2×C22⋊C4C2×D412yes—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—42no—
477C2×C42C2×D412yes—
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C4⋊C8—42no—
484C4⋊C8—42no—
485#103—42no—
486#103—42no—
487#103—42no—
488#103—42no—
489#103—42no—
490#103—42no—
491#103—42no—
492#103—42no—
493#103—42no—
494#103—42no—
495#103—42no—
496#103—42no—
497#102—24no—
498#102—42no—
499#102—42no—
500#102—42no—
501C22⋊C8—24no—
502C22⋊C8—42no—
503C22⋊C8—42no—
504C4×C8—42no—
505#95—22no—
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#95—22no—
520#95C2×D412yes—
521#95C2×D412yes—
522#95C2×D412yes—
523#95C2×D412yes—
524#95C2×D412yes—
525C24—21no—
526C24—21no—
527C24—42no—
528C24—42no—
529C24—44no—
530C24—82no—
531C24—81no—
532C24C22×D411yescharacteristic
533C24C22×D411yescharacteristic
534#41—84no—
535#41—84no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—44no—
556C2×Q8—42no—
557C2×Q8—48no—
558C2×Q8—48no—
559C2×Q8—44no—
560C2×Q8—82no—
561C2×Q8—82no—
562C2×Q8—84no—
563C2×Q8—84no—
564C2×Q8H(5,𝔽2)14yes—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—48no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—84no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—82no—
584C2×D4H(5,𝔽2)12yes—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4H(5,𝔽2)14yes—
626C22×C4C2511yescharacteristic
627Q16—84no—
628Q16—84no—
629Q16—84no—
630Q16—84no—
631SD16—48no—
632SD16—48no—
633SD16—48no—
634SD16—48no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—48no—
648C4⋊C4—28no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C22⋊C4—22no—
681C22⋊C4—24no—
682C22⋊C4—22no—
683C22⋊C4—24no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—82no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C42—22no—
704C42—21no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—21no—
709C42—42no—
710C42—44no—
711C42—42no—
712C42—82no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—41no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—84no—
732C23—88no—
733C23—84no—
734C23—162no—
735C23—164no—
736C23#53512yes—
737C23#57814yes—
738C23C23×D411yescharacteristic
739Q8—24no—
740Q8—24no—
741Q8—42no—
742Q8—42no—
743Q8—42no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749Q8—42no—
750Q8—42no—
751Q8—88no—
752Q8—162no—
753D4—24no—
754D4—44no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—84no—
759D4—84no—
760D4—162no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—88no—
813C2×C4—84no—
814C2×C4—162no—
815C2×C4—162no—
816C2×C4—162no—
817C2×C4#53512yes—
818C2×C4#57714yes—
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×H(5,𝔽2)12yes—
821C2×C4C2×H(5,𝔽2)12yes—
822C2×C4#58511yescharacteristic
823C8—42no—
824C8—42no—
825C8—42no—
826C8—42no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—42no—
832C22—44no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—82no—
841C22—82no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—82no—
846C22—168no—
847C22#322314yes—
848C22C2×#53511yescharacteristic
849C22#348411yescharacteristic
850C22#348811yescharacteristic
851C22C2×#57712yes—
852C22C2×#57812yes—
853C4—22no—
854C4—24no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—44no—
859C4—41no—
860C4—42no—
861C4—42no—
862C4—82no—
863C4—81no—
864C4—82no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—82no—
871C4#353212yes—
872C4#353412yes—
873C2—24no—
874C2—81no—
875C2—82no—
876C2—161no—
877C2#4058811yescharacteristic
878C2C2×#322311yescharacteristic
879C2#6081811yescharacteristic
880C2#6163212yes—
881C2#6205412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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
2. #37695C2semidirect
3. #32813C2semidirect
4. #32767C2semidirect
5. #31836C2semidirect
6. #31636C2semidirect
7. #30742C2semidirect
8. #30450C2semidirect
9. #30190C2semidirect
10. #30054C2semidirect
11. #30050C2semidirect
12. #29726C2semidirect
13. #29676C2semidirect
14. #29104C2semidirect
15. #28173C2semidirect
16. #25722C2semidirect
17. #24532C2semidirect
18. #24357C2semidirect
19. #23970C2semidirect
20. #23944C2semidirect
22. C2×#2013C2semidirect
23. #21997C2semidirect
27. C2×#541C22semidirect
29. C2×#494C22semidirect
43. #2642C22semidirect
45. #2621C22semidirect
53. #2446C22semidirect
57. #2429C22semidirect
61. #2327C22semidirect
66. #2099C22semidirect
67. #2074C22semidirect
68. #2074C22semidirect
71. #2072C22semidirect
72. #2072C22semidirect
73. #2056C22semidirect
74. #2056C22semidirect
77. #2043C22semidirect
78. #2026C22semidirect
79. #2026C22semidirect
82. #2024C22semidirect
83. #2024C22semidirect
84. #2016C22semidirect
85. #2016C22semidirect
86. #2016C22semidirect
87. #2016C22semidirect
98. #2001C22semidirect
99. #2001C22semidirect
102. #1956C22semidirect
105. #1923C22semidirect
106. #1916C22semidirect
111. #1878C22semidirect
112. #1878C22semidirect
113. #1878C22semidirect
114. #1878C22semidirect
117. #1872C22semidirect
118. #1872C22semidirect
121. #1840C22semidirect
122. #1832C22semidirect
124. #1818C22semidirect
125. #1803C22semidirect
126. #1803C22semidirect
127. #1798C22semidirect

Maximal subgroups

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

subgroupindex
#380782
#376952
#328132
#327672
#318362
#316362
#307422
#304502
#301902
#300542
#300502
#297262
#296762
#291042
#281732
#257222
#245322
#243572
#239702
#239442
#238522
C2×#20132
#219972