Finite Group Databasebeta

← #6855033

Subgroups — #6855033

Order 512.

1387 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36606C211yesmaximal, characteristic
2C2×#2509C211yesmaximal, characteristic, complemented
3#33106C211yesmaximal, characteristic
4#32496C212yesmaximal, complemented
5#32324C212yesmaximal, complemented
6#32088C212yesmaximal, complemented
7#31989C212yesmaximal, complemented
8#29760C211yesmaximal, characteristic, complemented
9#29760C211yesmaximal, characteristic, complemented
10#29336C211yesmaximal, characteristic, complemented
11#29334C211yesmaximal, characteristic
12#29244C211yesmaximal, characteristic, complemented
13#29234C211yesmaximal, characteristic, complemented
14#29033C212yesmaximal, complemented
15#28049C212yesmaximal, complemented
16#27977C211yesmaximal, characteristic, complemented
17#27684C211yesmaximal, characteristic, complemented
18#27385C212yesmaximal, complemented
19#26783C212yesmaximal, complemented
20#22627C211yesmaximal, characteristic, complemented
21#22081C211yesmaximal, characteristic, complemented
22#22075C211yesmaximal, characteristic, complemented
23#21579C211yesmaximal, characteristic, complemented
24C2×#483C2211yescharacteristic
25C2×#480C2211yescharacteristic
26C2×#480C2211yescharacteristic
27#2856C2211yescharacteristic
28#2850C2211yescharacteristic
29#2850C2211yescharacteristic
30#2595—21no—
31#2593—21no—
32#2591—21no—
33#2570C2211yescharacteristic
34#2544C2211yescharacteristic
35#2516—21no—
36#2513C2211yescharacteristic
37#2511C2211yescharacteristic
38#2509—21no—
39#2509—21no—
40#2509—21no—
41#2509—21no—
42#2509C2212yes—
43#2509C2212yes—
44#2509C2212yes—
45#2509C2212yes—
46#2448C2211yescharacteristic
47#2445C2211yescharacteristic
48#2444—21no—
49#2443—21no—
50C2×#400—21no—
51C2×#400—21no—
52#2374—21no—
53#2367C2211yescharacteristic
54#2364—21no—
55#2357C2211yescharacteristic
56C4×C22⋊Q8C2211yescharacteristic
57C4×#121C2211yescharacteristic
58C4×#121C2211yescharacteristic
59C2×#389—21no—
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#387—21no—
65C2×#382C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2101C2212yes—
69#2101C2212yes—
70#2100C2212yes—
71#2092C2212yes—
72#2086C2212yes—
73#2086C2212yes—
74#2085C2212yes—
75#2085C2212yes—
76#2074C2212yes—
77#2073C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2067C2212yes—
81#2066C2212yes—
82#2065C2212yes—
83#2065C2212yes—
84#2042C2212yes—
85#2042C2212yes—
86#2042C2212yes—
87#2041C2212yes—
88#1982C2212yes—
89#1958C2212yes—
90#1949C2212yes—
91#1947C2212yes—
92#1943C2212yes—
93#1942C2212yes—
94#1940C2212yes—
95#1936C2212yes—
96#1936C2212yes—
97#1936C2212yes—
98#1936C2212yes—
99#1935C2212yes—
100#1934C2212yes—
101#1928C2212yes—
102#1925C2212yes—
103#1925C2212yes—
104#1921C2212yes—
105#1920C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1918C2212yes—
109#1917C2212yes—
110#1916C2212yes—
111#1874C2211yescharacteristic
112#1874C2211yescharacteristic
113#1874C2211yescharacteristic
114#1874C2211yescharacteristic
115#1874C2211yescharacteristic
116#1874C2211yescharacteristic
117#1872C2211yescharacteristic
118#1872C2211yescharacteristic
119#1872C2211yescharacteristic
120#1864C2212yes—
121#1863C2212yes—
122#1862C2212yes—
123#1862C2212yes—
124#1853C2211yescharacteristic
125#1852C2211yescharacteristic
126#1852C2211yescharacteristic
127#1835C2212yes—
128#1823C2211yescharacteristic
129#1804C2212yes—
130#1797C2211yescharacteristic
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1776C2212yes—
134#1771C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C2×#127C2311yescharacteristic
140C2×#124C2311yescharacteristic
141C2×#124C2311yescharacteristic
142C2×#123—21no—
143C2×C22⋊Q8C2311yescharacteristic
144C2×#121—21no—
145C2×#121—21no—
146C2×#121C2311yescharacteristic
147C2×#121C2311yescharacteristic
148C2×C4×Q8C2311yescharacteristic
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4C2311yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4D411yescharacteristic
158C22×C4⋊C4D411yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#483—24no—
168#480—24no—
169#480—24no—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#102C2312yes—
184C2×#102C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×#97C2312yes—
196C2×#97C2312yes—
197C2×C4×C8C2312yes—
198#400—21no—
199#400—21no—
200#400—22no—
201#400—22no—
202#400—22no—
203#400—22no—
204#400—21no—
205#400—22no—
206#400—22no—
207#400—22no—
208#400—22no—
209#399—21no—
210#398—21no—
211#397—21no—
212#397—21no—
213#397—21no—
214#394—21no—
215#394—21no—
216#394—21no—
217#394—21no—
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#391C2311yescharacteristic
221#390—21no—
222#390—21no—
223#390C2311yescharacteristic
224#390C2311yescharacteristic
225#390C2311yescharacteristic
226#390C2311yescharacteristic
227#390C2311yescharacteristic
228#390C2311yescharacteristic
229#389—22no—
230#389—22no—
231#389—22no—
232#389—22no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#389C2312yes—
249#389C2311yescharacteristic
250#389C2312yes—
251#389C2312yes—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—21no—
256#388—21no—
257#388—21no—
258#388—21no—
259#388—21no—
260#388—21no—
261#388—21no—
262#388—21no—
263#388—21no—
264#388—21no—
265#388—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—21no—
271#387—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#386—21no—
276#386—21no—
277#386—21no—
278#386—21no—
279#386—21no—
280#386—21no—
281#386—21no—
282#386—21no—
283#386—21no—
284#385—21no—
285#385—21no—
286#384C2311yescharacteristic
287#382—21no—
288#382—21no—
289#382C2311yescharacteristic
290#382C2311yescharacteristic
291#382C2312yes—
292#382C2312yes—
293#381—21no—
294#380C2311yescharacteristic
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2312yes—
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95D411yescharacteristic
324C2×#95D411yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345C22×Q8C2411yescharacteristic
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4C2411yescharacteristic
351C22×D4C2411yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369#127—42no—
370#124—42no—
371#124—42no—
372#123—44no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375#121—22no—
376#121—22no—
377#121—22no—
378#121—22no—
379#121—44no—
380#121—82no—
381C4×Q8—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—82no—
385C4×D4—82no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—82no—
414C2×C4⋊C4—82no—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D411yescharacteristic
419C2×C4⋊C4C2×D411yescharacteristic
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4#4114yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—42no—
462C2×C42—42no—
463C2×C42—42no—
464C2×C42—82no—
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2411yescharacteristic
477#107—24no—
478#107—24no—
479#107—42no—
480#107—42no—
481#106—24no—
482#106—42no—
483C4⋊C8—42no—
484C4⋊C8—42no—
485C4⋊C8—42no—
486#103—24no—
487#103—42no—
488#103—42no—
489#103—42no—
490#102—24no—
491#102—24no—
492#102—42no—
493#102—42no—
494#102—42no—
495#102—42no—
496#102—42no—
497#102—42no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502#97—42no—
503#97—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—21no—
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—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544C24—21no—
545C24—21no—
546C24C22×D411yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2×#4112yes—
633C22×C42−1+412yes—
634C22×C4C2511yescharacteristic
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—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4C2×#4114yes—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C42—22no—
713C42—22no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—41no—
719C42—41no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—41no—
724C42—81no—
725C42—82no—
726C42—82no—
727C42—81no—
728C42—81no—
729C42—81no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23#54812yes—
749C23#57512yes—
750C23#57612yes—
751C23C23×D411yescharacteristic
752Q8—42no—
753Q8—42no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—84no—
759D4—84no—
760D4—162no—
761D4—162no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—48no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—84no—
839C2×C4—84no—
840C2×C4—84no—
841C2×C4—162no—
842C2×C4—162no—
843C2×C4#54812yes—
844C2×C4#57512yes—
845C2×C4C22×#4111yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C2×C4#58512yes—
848C2×C4#58512yes—
849C8—42no—
850C8—42no—
851C8—42no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22#337014yes—
874C22#344911yescharacteristic
875C22C2×#54811yescharacteristic
876C22#348511yescharacteristic
877C22C2×#57511yescharacteristic
878C22C2×#57511yescharacteristic
879C22C2×#57611yescharacteristic
880C22#358611yescharacteristic
881C4—22no—
882C4—22no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—44no—
895C4—82no—
896C4—81no—
897C4—81no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4#351212yes—
905C4#355312yes—
906C2—24no—
907C2—161no—
908C2—161no—
909C2#3971711yescharacteristic
910C2#6097011yescharacteristic
911C2#6097611yescharacteristic
912C2C2×#337011yescharacteristic
913C2#6132011yescharacteristic
914C2#6171211yescharacteristic
915C2#6172711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2509C2semidirect
4. #32496C2semidirect
5. #32324C2semidirect
6. #32088C2semidirect
7. #31989C2semidirect
8. #29760C2semidirect
9. #29760C2semidirect
10. #29336C2semidirect
12. #29244C2semidirect
13. #29234C2semidirect
14. #29033C2semidirect
15. #28049C2semidirect
16. #27977C2semidirect
17. #27684C2semidirect
18. #27385C2semidirect
19. #26783C2semidirect
20. #22627C2semidirect
21. #22081C2semidirect
22. #22075C2semidirect
23. #21579C2semidirect

Maximal subgroups

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

subgroupindex
#366062
C2×#25092
#331062
#324962
#323242
#320882
#319892
#297602
#293362
#293342
#292442
#292342
#290332
#280492
#279772
#276842
#273852
#267832
#226272
#220812
#220752
#215792