Finite Group Databasebeta

← #6484445

Subgroups — #6484445

Order 512.

1708 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35337C211yesmaximal, characteristic, complemented
2#34275C211yesmaximal, characteristic
3#32965C211yesmaximal, characteristic, complemented
4#32963C211yesmaximal, characteristic, complemented
5#32962C211yesmaximal, characteristic, complemented
6#32962C211yesmaximal, characteristic, complemented
7#29958C212yesmaximal, complemented
8#29956C212yesmaximal, complemented
9#29261C212yesmaximal, complemented
10#29256C212yesmaximal, complemented
11#29203C212yesmaximal, complemented
12#29201C212yesmaximal, complemented
13#29146C211yesmaximal, characteristic, complemented
14#29143C211yesmaximal, characteristic, complemented
15#28521C211yesmaximal, characteristic, complemented
16#28510C211yesmaximal, characteristic, complemented
17#28290C211yesmaximal, characteristic, complemented
18#28290C211yesmaximal, characteristic, complemented
19#28289C211yesmaximal, characteristic, complemented
20#28288C211yesmaximal, characteristic, complemented
21#21992C212yesmaximal, complemented
22#21813C212yesmaximal
23#20813C211yesmaximal, characteristic, complemented
24C2×#535C2211yescharacteristic
25C2×#520C2211yescharacteristic
26C2×#518C2211yescharacteristic
27C2×#477C2211yescharacteristic, complemented
28C2×#475C2211yescharacteristic, complemented
29C2×#476C2211yescharacteristic
30C2×#476C2211yescharacteristic
31C2×#476C2211yescharacteristic, complemented
32C2×#474C2211yescharacteristic
33C2×#474C2211yescharacteristic
34C2×#474C2211yescharacteristic, complemented
35C2×#433C2212yes—
36#2862C2211yescharacteristic, complemented
37#2859C2211yescharacteristic, complemented
38#2851C2212yes—
39#2647C2212yescomplemented
40#2628C2211yescharacteristic
41#2628C2211yescharacteristic
42#2589—22no—
43#2589—22no—
44#2588—22no—
45#2588—22no—
46#2363—22no—
47#2361—22no—
48#2358—22no—
49#2358—22no—
50#2331C2211yescharacteristic, complemented
51#2331C2211yescharacteristic, complemented
52#2328C2211yescharacteristic
53#2328C2211yescharacteristic
54#2326C2211yescharacteristic
55#2326C2211yescharacteristic
56#2317C2211yescharacteristic
57#2314C2212yes—
58C4×#127C2211yescharacteristic
59C4×#127C2211yescharacteristic
60C4×#125C2212yescomplemented
61C4×#124C2211yescharacteristic
62C4×#124C2211yescharacteristic
63#2297C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C4×#117C2211yescharacteristic
66#2097C2212yescomplemented
67#2092C2212yes—
68#2092C2212yes—
69#2092C2212yescomplemented
70#2068C2212yescomplemented
71#2067C2212yes—
72#2067C2212yes—
73#2067C2212yescomplemented
74#2066C2212yescomplemented
75#2065C2212yes—
76#2065C2212yes—
77#2065C2212yescomplemented
78#2026C2212yescomplemented
79#2025C2212yes—
80#2025C2212yes—
81#2025C2212yescomplemented
82#1983C2212yes—
83#1983C2212yes—
84#1982C2212yes—
85#1982C2212yes—
86#1961C2212yes—
87#1959C2212yes—
88#1958C2212yes—
89#1957C2212yes—
90#1949C2212yescomplemented
91#1949C2212yescomplemented
92#1948C2212yescomplemented
93#1947C2212yescomplemented
94#1865C2212yescomplemented
95#1864C2212yes—
96#1864C2212yes—
97#1864C2212yescomplemented
98#1863C2212yescomplemented
99#1862C2212yes—
100#1862C2212yes—
101#1862C2212yescomplemented
102#1854C2212yes—
103#1854C2212yes—
104#1853C2212yes—
105#1852C2212yes—
106#1847C2212yescomplemented
107#1846C2212yescomplemented
108#1843C2211yescharacteristic, complemented
109#1843C2211yescharacteristic, complemented
110#1836C2212yescomplemented
111#1834C2212yescomplemented
112#1831C2212yescomplemented
113#1805C2211yescharacteristic, complemented
114#1805C2211yescharacteristic, complemented
115#1804C2211yescharacteristic
116#1804C2211yescharacteristic
117#1804C2211yescharacteristic
118#1804C2211yescharacteristic
119#1804C2211yescharacteristic, complemented
120#1804C2211yescharacteristic, complemented
121#1798C2211yescharacteristic
122#1798C2211yescharacteristic
123#1797C2212yes—
124#1788C2212yes—
125#1788C2212yes—
126#1786C2212yes—
127#1786C2212yes—
128#1768C2212yescomplemented
129#1767C2211yescharacteristic, complemented
130C4×C4⋊C8C2211yescharacteristic, complemented
131C22×#41C2311yescharacteristic
132C23×D4C2311yescharacteristic
133#535—24no—
134#535Q818yescomplemented
135C2×C4⋊Q8C2311yescharacteristic
136C2×C4⋊Q8C2311yescharacteristic
137C2×#127C2311yescharacteristic
138C2×#127C2311yescharacteristic
139C2×#125C2312yes—
140C2×#124C2311yescharacteristic
141C2×#124C2311yescharacteristic
142C2×#121—22no—
143C2×#120—22no—
144#520—42no—
145#520—42no—
146#518—42no—
147#518—42no—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—22no—
155C2×C4×D4—22no—
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×C4×D4C2311yescharacteristic
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×#117—21no—
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C22⋊C4—22no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C42C2311yescharacteristic
172#477—42no—
173#476—42no—
174#476—42no—
175#476—42no—
176#475—42no—
177#474—42no—
178#474—42no—
179#474—42no—
180#433—28no—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×C4⋊C8C2311yescharacteristic
190C2×C4⋊C8C2311yescharacteristic
191C2×C4⋊C8C2311yescharacteristic
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#102C2312yes—
202C2×#102C2312yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×#97C2312yes—
216C2×C4×C8C2312yes—
217#400—21no—
218#400—21no—
219#400—22no—
220#400—22no—
221#399—21no—
222#399—21no—
223#398—22no—
224#398—22no—
225#395—21no—
226#395—21no—
227#393—21no—
228#393—21no—
229#391—22no—
230#391—22no—
231#391—22no—
232#391—22no—
233#391C2311yescharacteristic
234#391C2311yescharacteristic
235#390—22no—
236#390—22no—
237#390—22no—
238#390C2311yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#390C2311yescharacteristic
242#390C2311yescharacteristic
243#390C2311yescharacteristic
244#389—22no—
245#389—22no—
246#389—22no—
247#389C2312yes—
248#389C2312yes—
249#389C2312yes—
250#389C2312yes—
251#388—22no—
252#388—22no—
253#388—22no—
254#388—22no—
255#388—22no—
256#388—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#386—22no—
266#386—22no—
267#386—22no—
268#386—22no—
269#386—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2312yes—
278#382C2312yes—
279#382C2312yes—
280#382C2311yescharacteristic
281#382C2311yescharacteristic
282#382C2311yescharacteristic
283#382C2311yescharacteristic
284#380C2312yes—
285#380C2312yes—
286C4×C4⋊C4—22no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4D412yes—
289C4×C4⋊C4D412yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294C4×C22⋊C4—22no—
295C4×C22⋊C4D412yes—
296C4×C22⋊C4D412yes—
297#376C2311yescharacteristic
298#376C2311yescharacteristic
299C43C2311yescharacteristic
300C43C2311yescharacteristic
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313C25—21no—
314C2×#41—22no—
315C2×#41—41no—
316C2×#41—41no—
317C2×#41—41no—
318C2×#41—41no—
319C2×#41C2×Q814yes—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8C2411yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4C2×Q814yes—
333C22×D4C2411yescharacteristic
334C22×D4C2411yescharacteristic
335C22×D4C2411yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4C2×D412yes—
345C23×C4C2411yescharacteristic
346C22×C8C2412yes—
347C22×C8C2412yes—
348C22×C8C2412yes—
349C22×C8C2412yes—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354#127—22no—
355#127—22no—
356#127C2×Q814yes—
357#127C2×Q814yes—
358#125—42no—
359#125—42no—
360#124—22no—
361#124—22no—
362#124C2×Q814yes—
363#124C2×Q814yes—
364#121—216no—
365#120—216no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—41no—
369C4×Q8—41no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—41no—
377C4×D4—41no—
378C4×D4—41no—
379C4×D4—41no—
380C4×D4—41no—
381C4×D4—41no—
382C4×D4—44no—
383C4×D4—44no—
384C4×D4—44no—
385C4×D4—44no—
386C4×D4—84no—
387C4×D4—84no—
388#117—22no—
389#117—22no—
390#117—41no—
391#117—41no—
392#117—44no—
393#117C2×Q814yes—
394#117#4114yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
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—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—84no—
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D412yes—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—41no—
453C2×C42—41no—
454C2×C42C2×D412yes—
455C2×C42C2×D412yes—
456C2×C42C2×D412yes—
457C2×C42C2×D412yes—
458C2×C42C2×D412yes—
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465#107—42no—
466#107—42no—
467#107—42no—
468#107—42no—
469#106—42no—
470#106—42no—
471#106—42no—
472#106—42no—
473C4⋊C8—24no—
474C4⋊C8—24no—
475C4⋊C8—22no—
476C4⋊C8—22no—
477C4⋊C8—22no—
478C4⋊C8—22no—
479C4⋊C8—42no—
480C4⋊C8—42no—
481#103—42no—
482#103—42no—
483#103—42no—
484#103—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—
497C22⋊C8—24no—
498C22⋊C8—24no—
499#97—24no—
500C4×C8—24no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
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—21no—
514#95—21no—
515#95—22no—
516#95—22no—
517#95—21no—
518#95—21no—
519#95—22no—
520#95—22no—
521#95C2×D412yes—
522#95C2×D412yes—
523#95C2×D412yes—
524#95C2×D412yes—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—24no—
529C24—42no—
530C24—42no—
531C24—82no—
532C24—82no—
533C24C22×D411yescharacteristic
534#41—44no—
535#41—44no—
536#41—44no—
537#41—44no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—82no—
547C2×Q8C22×Q812yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—82no—
579C2×D4C22×Q812yes—
580C2×D4C22×Q812yes—
581C2×D4C22×Q812yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×Q812yes—
625C22×C4C2×#4112yes—
626C22×C4C2511yescharacteristic
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4C22⋊Q818yes—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4C22⋊Q818yes—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—82no—
708C42—82no—
709C42C22×Q812yes—
710C42C22×Q812yes—
711C42C2×#4112yes—
712C42C2×#4112yes—
713C42H(5,𝔽2)12yes—
714C42H(5,𝔽2)12yes—
715C23—22no—
716C23—22no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—48no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—88no—
736C23—164no—
737C23—162no—
738C23—162no—
739C23C2×C22⋊Q812yes—
740C23C23×D411yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—162no—
746Q8—162no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—48no—
754D4—48no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—88no—
762D4—88no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—162no—
811C2×C4—162no—
812C2×C4—162no—
813C2×C4—162no—
814C2×C4—162no—
815C2×C4—162no—
816C2×C4—162no—
817C2×C4C2×C22⋊Q814yes—
818C2×C4C2×C22⋊Q814yes—
819C2×C4C2×C22⋊Q812yes—
820C2×C4#53512yes—
821C2×C4#53512yes—
822C2×C4C23×Q811yescharacteristic
823C2×C4C22×#4111yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×H(5,𝔽2)11yescharacteristic
826C2×C4#58511yescharacteristic
827C2×C4#58511yescharacteristic
828C8—42no—
829C8—42no—
830C8—42no—
831C8—42no—
832C22—24no—
833C22—22no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—168no—
853C22C22×C22⋊Q811yescharacteristic
854C22C2×#53511yescharacteristic
855C22#344911yescharacteristic
856C22#358412yes—
857C22#358512yes—
858C4—24no—
859C4—24no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—41no—
867C4—41no—
868C4—82no—
869C4—82no—
870C4—81no—
871C4—82no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—82no—
876C4#350111yescharacteristic
877C4#350111yescharacteristic
878C4#350611yescharacteristic
879C4#350611yescharacteristic
880C2—42no—
881C2—82no—
882C2—82no—
883C2—82no—
884C2#3517211yescharacteristic
885C2#6049612yes—
886C2#6081911yescharacteristic
887C2#6082711yescharacteristic
888C2#6098612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35337C2semidirect
3. #32965C2semidirect
4. #32963C2semidirect
5. #32962C2semidirect
6. #32962C2semidirect
7. #29958C2semidirect
8. #29956C2semidirect
9. #29261C2semidirect
10. #29256C2semidirect
11. #29203C2semidirect
12. #29201C2semidirect
13. #29146C2semidirect
14. #29143C2semidirect
15. #28521C2semidirect
16. #28510C2semidirect
17. #28290C2semidirect
18. #28290C2semidirect
19. #28289C2semidirect
20. #28288C2semidirect
21. #21992C2semidirect
23. #20813C2semidirect
27. C2×#477C22semidirect
28. C2×#475C22semidirect
31. C2×#476C22semidirect
34. C2×#474C22semidirect
36. #2862C22semidirect
37. #2859C22semidirect
39. #2647C22semidirect
50. #2331C22semidirect
51. #2331C22semidirect
60. C4×#125C22semidirect
66. #2097C22semidirect
69. #2092C22semidirect
70. #2068C22semidirect
73. #2067C22semidirect
74. #2066C22semidirect
77. #2065C22semidirect
78. #2026C22semidirect
81. #2025C22semidirect
90. #1949C22semidirect
91. #1949C22semidirect
92. #1948C22semidirect
93. #1947C22semidirect
94. #1865C22semidirect
97. #1864C22semidirect
98. #1863C22semidirect
101. #1862C22semidirect
106. #1847C22semidirect
107. #1846C22semidirect
108. #1843C22semidirect
109. #1843C22semidirect
110. #1836C22semidirect
111. #1834C22semidirect
112. #1831C22semidirect
113. #1805C22semidirect
114. #1805C22semidirect
119. #1804C22semidirect
120. #1804C22semidirect
128. #1768C22semidirect
129. #1767C22semidirect
130. C4×C4⋊C8C22semidirect
134. #535Q8semidirect

Maximal subgroups

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

subgroupindex
#353372
#342752
#329652
#329632
#329622
#299582
#299562
#292612
#292562
#292032
#292012
#291462
#291432
#285212
#285102
#282902
#282892
#282882
#219922
#218132
#208132