Finite Group Databasebeta

← #6794006

Subgroups — #6794006

Order 512.

1394 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36207C211yesmaximal, characteristic
2C2×#2495C211yesmaximal, characteristic
3#33151C211yesmaximal, characteristic, complemented
4#32407C212yesmaximal, complemented
5#32307C212yesmaximal, complemented
6#32199C212yesmaximal, complemented
7#31707C212yesmaximal, complemented
8#29913C211yesmaximal, characteristic, complemented
9#29894C211yesmaximal, characteristic
10#29303C211yesmaximal, characteristic, complemented
11#29240C211yesmaximal, characteristic, complemented
12#28855C212yesmaximal, complemented
13#27846C212yesmaximal, complemented
14#27613C211yesmaximal, characteristic, complemented
15#27602C211yesmaximal, characteristic
16#27483C212yesmaximal, complemented
17#27059C212yesmaximal, complemented
18#24609C211yesmaximal, characteristic, complemented
19#24551C211yesmaximal, characteristic
20#22554C211yesmaximal, characteristic
21#21986C211yesmaximal, characteristic, complemented
22#21941C211yesmaximal, characteristic
23#21579C211yesmaximal, characteristic, complemented
24C2×#483C2211yescharacteristic
25C2×#432C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27#2855C2211yescharacteristic
28#2851C2211yescharacteristic
29#2848C2211yescharacteristic
30#2575—21no—
31#2517—21no—
32#2515—21no—
33#2505—21no—
34#2499C2211yescharacteristic
35#2496C2211yescharacteristic
36#2495—21no—
37#2495—21no—
38#2495—21no—
39#2495—21no—
40#2495C2212yes—
41#2495C2212yes—
42#2495C2211yescharacteristic
43#2495C2212yes—
44#2495C2212yes—
45#2489C2211yescharacteristic
46#2482—21no—
47#2480—21no—
48#2441C2211yescharacteristic
49#2423C2211yescharacteristic
50C2×#400—21no—
51C2×#397—21no—
52#2373—21no—
53#2362C2211yescharacteristic
54#2346C2211yescharacteristic
55#2343—21no—
56C4×C22⋊Q8C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60#2285C2211yescharacteristic
61C2×#383—21no—
62C2×#382C2211yescharacteristic
63#2280C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68#2101C2212yescomplemented
69#2100C2212yescomplemented
70#2097C2212yescomplemented
71#2088C2212yescomplemented
72#2088C2212yescomplemented
73#2085C2212yescomplemented
74#2085C2212yescomplemented
75#2084C2212yescomplemented
76#2077C2212yes—
77#2077C2212yes—
78#2077C2212yes—
79#2076C2212yes—
80#2075C2212yes—
81#2074C2212yescomplemented
82#2068C2212yescomplemented
83#2066C2212yescomplemented
84#2059C2212yescomplemented
85#2036C2212yes—
86#2035C2212yes—
87#2035C2212yes—
88#1989C2212yescomplemented
89#1949C2212yescomplemented
90#1949C2212yescomplemented
91#1949C2212yescomplemented
92#1944C2212yescomplemented
93#1943C2212yescomplemented
94#1943C2212yescomplemented
95#1935C2212yescomplemented
96#1928C2212yescomplemented
97#1924C2212yes—
98#1924C2212yes—
99#1921C2212yescomplemented
100#1919C2212yescomplemented
101#1919C2212yescomplemented
102#1919C2212yescomplemented
103#1919C2212yescomplemented
104#1919C2212yescomplemented
105#1892C2212yes—
106#1872C2211yescharacteristic
107#1872C2211yescharacteristic
108#1872C2211yescharacteristic
109#1865C2212yescomplemented
110#1854C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1853C2211yescharacteristic
114#1853C2211yescharacteristic
115#1853C2211yescharacteristic
116#1853C2211yescharacteristic
117#1853C2211yescharacteristic
118#1852C2211yescharacteristic
119#1852C2211yescharacteristic
120#1852C2211yescharacteristic
121#1852C2211yescharacteristic
122#1850C2212yes—
123#1847C2212yescomplemented
124#1836C2212yescomplemented
125#1825C2212yes—
126#1823C2211yescharacteristic
127#1823C2211yescharacteristic
128#1823C2211yescharacteristic
129#1817C2211yescharacteristic
130#1808C2212yes—
131#1807C2212yes—
132#1807C2212yes—
133#1797C2211yescharacteristic
134#1779C2211yescharacteristic
135#1776C2212yescomplemented
136#1763C2212yescomplemented
137#1752C2212yes—
138#1749C2211yescharacteristic
139C24×C4C2311yescharacteristic
140C23×C8C2312yes—
141C2×#126—21no—
142C2×#125C2311yescharacteristic
143C2×C22⋊Q8C2311yescharacteristic
144C2×C22⋊Q8C2311yescharacteristic
145C2×C22⋊Q8C2311yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×#117—21no—
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4D411yescharacteristic
159C22×C22⋊C4D411yescharacteristic
160C22×C42—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#483—24no—
164#432—24no—
165C2×#107C2312yes—
166C2×#107C2312yes—
167C2×#107C2312yes—
168C2×#107C2312yes—
169C2×#106C2312yes—
170C2×#106C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×C22⋊C8—24no—
182C2×C22⋊C8C2311yescharacteristic
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2311yescharacteristic
189C2×#97C2312yes—
190C2×#97C2312yes—
191#400—21no—
192#400—21no—
193#400—22no—
194#400—22no—
195#400—22no—
196#400—22no—
197#400—21no—
198#399—21no—
199#399—21no—
200#398—21no—
201#397—21no—
202#397—22no—
203#397—22no—
204#397—22no—
205#397—22no—
206#397—21no—
207#397—21no—
208#397—21no—
209#397—21no—
210#396—21no—
211#391C2311yescharacteristic
212#391C2311yescharacteristic
213#391C2311yescharacteristic
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389C2312yes—
220#389C2312yes—
221#389C2311yescharacteristic
222#389C2311yescharacteristic
223#389C2312yes—
224#389C2311yescharacteristic
225#389C2311yescharacteristic
226#389C2311yescharacteristic
227#389C2312yes—
228#388—21no—
229#388—21no—
230#388—21no—
231#388—21no—
232#388—21no—
233#388—21no—
234#388—21no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#387—21no—
240#387—21no—
241#387—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—21no—
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#385—21no—
251#385—21no—
252#385—21no—
253#385—21no—
254#385—21no—
255#385—21no—
256#385—21no—
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#383—21no—
260#383—22no—
261#383—22no—
262#383—22no—
263#383—22no—
264#382—21no—
265#382—21no—
266#382—21no—
267#382—21no—
268#382—21no—
269#382C2312yes—
270#382C2311yescharacteristic
271#382C2312yes—
272#381—21no—
273#381—21no—
274#380—21no—
275#380—21no—
276#380—21no—
277#380—21no—
278#380—21no—
279#380C2311yescharacteristic
280#380C2311yescharacteristic
281#380C2312yes—
282#380C2312yes—
283#380C2311yescharacteristic
284#380C2311yescharacteristic
285#380C2312yes—
286#380C2312yes—
287#380C2311yescharacteristic
288#380C2311yescharacteristic
289#380C2311yescharacteristic
290#379—21no—
291#379—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2312yes—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4D411yescharacteristic
306C4×C22⋊C4D411yescharacteristic
307C4×C22⋊C4D411yescharacteristic
308C4×C22⋊C4D411yescharacteristic
309C4×C22⋊C4C2311yescharacteristic
310C4×C22⋊C4C2311yescharacteristic
311C4×C22⋊C4C2311yescharacteristic
312C4×C22⋊C4C2311yescharacteristic
313#376—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95D411yescharacteristic
322C2×#95D411yescharacteristic
323#340C2312yes—
324#340C2312yes—
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#340C2312yes—
340#340C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345C25C2×D411yescharacteristic
346C22×Q8C2411yescharacteristic
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2411yescharacteristic
365C22×C8—24no—
366C22×C8—42no—
367C22×C8—42no—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372#126—44no—
373#125—42no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—42no—
377C22⋊Q8—42no—
378C4×Q8—42no—
379#117—42no—
380#117—44no—
381#117—42no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—82no—
411C2×C4⋊C4—82no—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2411yescharacteristic
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2411yescharacteristic
420C2×C4⋊C4C2411yescharacteristic
421C2×C4⋊C4C2411yescharacteristic
422C2×C4⋊C4C2411yescharacteristic
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—82no—
443C2×C22⋊C4C2×D411yescharacteristic
444C2×C22⋊C4C2×D411yescharacteristic
445C2×C22⋊C4C2×D411yescharacteristic
446C2×C22⋊C4C2×D411yescharacteristic
447C2×C22⋊C4C2×D411yescharacteristic
448C2×C22⋊C4C2×D411yescharacteristic
449C2×C22⋊C4C2×D411yescharacteristic
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—42no—
462C2×C42—44no—
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471#107—42no—
472#107—42no—
473#107—42no—
474#107—42no—
475#106—24no—
476#106—42no—
477#106—42no—
478#106—42no—
479#106—42no—
480#106—42no—
481C4⋊C8—24no—
482C4⋊C8—42no—
483#103—24no—
484#103—42no—
485#103—42no—
486#103—42no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—24no—
491C22⋊C8—42no—
492C22⋊C8—42no—
493C22⋊C8#4114yes—
494#97—24no—
495#97—42no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
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—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
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#95C2×D411yescharacteristic
534#95C2×D411yescharacteristic
535#95C2×D411yescharacteristic
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—41no—
546C24—41no—
547C24—41no—
548C24C22×D411yescharacteristic
549C24C22×D411yescharacteristic
550C24C22×D411yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
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—42no—
609C22×C4—42no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C2×#4112yes—
624C22×C42−1+412yes—
625C22×C4C2511yescharacteristic
626C2×C8—22no—
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—84no—
638C2×C8C2×#4114yes—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—81no—
667C4⋊C4—81no—
668C4⋊C4—81no—
669C4⋊C4—81no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—81no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—82no—
699C22⋊C4—82no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—22no—
703C42—22no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—22no—
709C42—22no—
710C42—41no—
711C42—41no—
712C42—44no—
713C42—44no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—81no—
719C42—81no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—82no—
742C23—82no—
743C23—82no—
744C23#54712yes—
745C23#57512yes—
746C23#57512yes—
747C23#57712yes—
748C23C23×D411yescharacteristic
749Q8—42no—
750Q8—42no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
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—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—82no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4#54712yes—
837C2×C4C22×#4111yescharacteristic
838C2×C4C2×2−1+411yescharacteristic
839C2×C4#58512yes—
840C2×C4#58512yes—
841C8—24no—
842C8—42no—
843C8—42no—
844C8—42no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—88no—
866C22#334814yes—
867C22#344911yescharacteristic
868C22C2×#54711yescharacteristic
869C22#348511yescharacteristic
870C22C2×#57511yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57711yescharacteristic
873C22#358611yescharacteristic
874C4—22no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4#352112yes—
898C4#356412yes—
899C2—24no—
900C2—42no—
901C2—81no—
902C2#3891311yescharacteristic
903C2#6095911yescharacteristic
904C2#6097711yescharacteristic
905C2C2×#334811yescharacteristic
906C2#6125311yescharacteristic
907C2#6171111yescharacteristic
908C2#6173611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33151C2semidirect
4. #32407C2semidirect
5. #32307C2semidirect
6. #32199C2semidirect
7. #31707C2semidirect
8. #29913C2semidirect
10. #29303C2semidirect
11. #29240C2semidirect
12. #28855C2semidirect
13. #27846C2semidirect
14. #27613C2semidirect
16. #27483C2semidirect
17. #27059C2semidirect
18. #24609C2semidirect
21. #21986C2semidirect
23. #21579C2semidirect
68. #2101C22semidirect
69. #2100C22semidirect
70. #2097C22semidirect
71. #2088C22semidirect
72. #2088C22semidirect
73. #2085C22semidirect
74. #2085C22semidirect
75. #2084C22semidirect
81. #2074C22semidirect
82. #2068C22semidirect
83. #2066C22semidirect
84. #2059C22semidirect
88. #1989C22semidirect
89. #1949C22semidirect
90. #1949C22semidirect
91. #1949C22semidirect
92. #1944C22semidirect
93. #1943C22semidirect
94. #1943C22semidirect
95. #1935C22semidirect
96. #1928C22semidirect
99. #1921C22semidirect
100. #1919C22semidirect
101. #1919C22semidirect
102. #1919C22semidirect
103. #1919C22semidirect
104. #1919C22semidirect
109. #1865C22semidirect
123. #1847C22semidirect
124. #1836C22semidirect
135. #1776C22semidirect
136. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#362072
C2×#24952
#331512
#324072
#323072
#321992
#317072
#299132
#298942
#293032
#292402
#288552
#278462
#276132
#276022
#274832
#270592
#246092
#245512
#225542
#219862
#219412
#215792