Finite Group Databasebeta

← #6796109

Subgroups — #6796109

Order 512.

1456 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36188C211yesmaximal, characteristic
2#34898C211yesmaximal, characteristic
3#33198C211yesmaximal, characteristic, complemented
4#32419C212yesmaximal, complemented
5#32406C212yesmaximal, complemented
6#31624C212yesmaximal, complemented
7#31604C212yesmaximal, complemented
8#29942C211yesmaximal, characteristic, complemented
9#29939C211yesmaximal, characteristic, complemented
10#29289C211yesmaximal, characteristic, complemented
11#28714C212yesmaximal
12#28694C211yesmaximal, characteristic, complemented
13#27631C211yesmaximal, characteristic, complemented
14#27630C211yesmaximal, characteristic, complemented
15#26521C212yesmaximal, complemented
16#25463C212yesmaximal, complemented
17#25352C212yesmaximal
18#24846C211yesmaximal, characteristic, complemented
19#24837C211yesmaximal, characteristic, complemented
20#22648C211yesmaximal, characteristic
21#21964C211yesmaximal, characteristic, complemented
22#21962C211yesmaximal, characteristic, complemented
23#21616C211yesmaximal, characteristic, complemented
24C2×#556—21no—
25C2×#501C2212yes—
26C2×#477C2211yescharacteristic
27C2×#477C2212yes—
28C2×#435C2212yes—
29C2×#423C2211yescharacteristic
30C22×C4⋊C8C2211yescharacteristic
31#2868C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2577—21no—
35#2575—21no—
36#2570C2211yescharacteristic
37#2568—21no—
38#2565C2211yescharacteristic
39#2562C2211yescharacteristic
40#2547—21no—
41#2547C2212yes—
42#2536C2211yescharacteristic
43#2524—21no—
44#2499—21no—
45#2499—21no—
46#2496—21no—
47#2496—21no—
48#2496C2211yescharacteristic
49#2496C2212yes—
50#2496C2212yes—
51#2495C2211yescharacteristic
52#2468—21no—
53#2423C2211yescharacteristic
54#2421C2211yescharacteristic
55#2402—21no—
56#2395—21no—
57#2365—21no—
58#2365C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#125C2211yescharacteristic
61C4×#126—21no—
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64#2298—21no—
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67#2285C2211yescharacteristic
68#2283C2211yescharacteristic
69C42×Q8C2211yescharacteristic
70C42×D4C2211yescharacteristic
71#2101C2212yes—
72#2100C2212yes—
73#2088C2212yes—
74#2087C2212yes—
75#2086C2212yes—
76#2086C2212yes—
77#2085C2212yes—
78#2084C2212yes—
79#2083C2212yes—
80#2083C2212yes—
81#2077C2212yes—
82#2077C2212yes—
83#2076C2212yes—
84#2076C2212yes—
85#2075C2212yes—
86#2075C2212yes—
87#2068C2212yes—
88#2066C2212yes—
89#2036C2212yes—
90#2035C2212yes—
91#1993C2212yes—
92#1989C2212yes—
93#1987C2211yescharacteristic
94#1987C2211yescharacteristic
95#1987C2212yes—
96#1987C2211yescharacteristic
97#1949C2212yes—
98#1949C2212yes—
99#1949C2212yes—
100#1948C2211yescharacteristic
101#1948C2211yescharacteristic
102#1948C2211yescharacteristic
103#1948C2211yescharacteristic
104#1948C2212yes—
105#1947C2211yescharacteristic
106#1947C2211yescharacteristic
107#1947C2211yescharacteristic
108#1947C2212yes—
109#1947C2212yes—
110#1947C2211yescharacteristic
111#1947C2211yescharacteristic
112#1940C2212yes—
113#1928C2212yes—
114#1927C2212yes—
115#1919C2212yes—
116#1918C2212yes—
117#1918C2212yes—
118#1894C2212yes—
119#1892C2212yes—
120#1865C2212yes—
121#1851C2212yes—
122#1850C2212yes—
123#1842C2211yescharacteristic
124#1809C2212yes—
125#1809C2212yes—
126#1809C2212yes—
127#1808C2212yes—
128#1808C2212yes—
129#1807C2212yes—
130#1803C2211yescharacteristic
131#1803C2211yescharacteristic
132#1803C2211yescharacteristic
133#1803C2212yes—
134#1797C2211yescharacteristic
135#1797C2211yescharacteristic
136#1776C2212yes—
137#1767C2211yescharacteristic
138#1763C2212yes—
139C22×M16C2312yes—
140C23×C8C2312yes—
141#556—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×#126—21no—
147C2×#126—22no—
148C2×#126—22no—
149C2×#125C2311yescharacteristic
150C2×#124—22no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8C2311yescharacteristic
154C2×C22⋊Q8C2311yescharacteristic
155C2×C4×Q8—22no—
156C2×C4×Q8—21no—
157C2×C4×Q8C2311yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4D411yescharacteristic
162C2×C4×D4C2311yescharacteristic
163C2×#117—21no—
164C2×#117—21no—
165C2×#117—21no—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#501—44no—
169#477—24no—
170#477—44no—
171#435—44no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#107C2312yes—
176C2×#107C2312yes—
177C2×#107C2312yes—
178C2×#106C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182#423—24no—
183C2×C4⋊C8—24no—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2311yescharacteristic
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2311yescharacteristic
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×#97C2312yes—
199#400—21no—
200#400—21no—
201#400—22no—
202#400—22no—
203#400—21no—
204#400—21no—
205#400—21no—
206#399—21no—
207#398—21no—
208#398—21no—
209#398—21no—
210#398—21no—
211#398—21no—
212#397—21no—
213#397—21no—
214#397—21no—
215#397—22no—
216#397—22no—
217#397—22no—
218#397—22no—
219#394—21no—
220#394—21no—
221#391—22no—
222#391—22no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#389—21no—
229#389—21no—
230#389—21no—
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2312yes—
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2312yes—
237#389C2312yes—
238#388—21no—
239#388—21no—
240#388—21no—
241#388—21no—
242#388—21no—
243#388—21no—
244#388—21no—
245#387—21no—
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—21no—
259#387—21no—
260#385—21no—
261#385—21no—
262#384—21no—
263#384—21no—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#384C2312yes—
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#383—21no—
271#383—21no—
272#382—21no—
273#382—21no—
274#382—21no—
275#382C2311yescharacteristic
276#382C2311yescharacteristic
277#382C2311yescharacteristic
278#381—21no—
279#380—21no—
280#380—21no—
281#380—21no—
282#380—21no—
283#380—21no—
284#380C2311yescharacteristic
285#380C2311yescharacteristic
286#380C2311yescharacteristic
287#380C2311yescharacteristic
288#380C2312yes—
289#380C2311yescharacteristic
290#380C2312yes—
291#380C2311yescharacteristic
292#380C2312yes—
293#380C2312yes—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4D411yescharacteristic
321C4×C22⋊C4D411yescharacteristic
322C4×C22⋊C4D411yescharacteristic
323C4×C22⋊C4C2311yescharacteristic
324C4×C22⋊C4C2311yescharacteristic
325#376—21no—
326C43—21no—
327C43C2311yescharacteristic
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#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8C2411yescharacteristic
352C22×D4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C23×C4C2411yescharacteristic
359C2×M16—24no—
360C2×M16—42no—
361C2×M16—42no—
362C22×C8—24no—
363C22×C8—42no—
364C22×C8—42no—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C4⋊Q8—22no—
370C4⋊Q8—24no—
371C4⋊Q8—24no—
372C4⋊Q8—22no—
373C4⋊Q8—44no—
374C4⋊Q8—44no—
375#126—48no—
376#126—44no—
377#126—48no—
378#125—22no—
379#125—22no—
380#124—48no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385C22⋊Q8—44no—
386C22⋊Q8—44no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—41no—
393C4×Q8—44no—
394C4×Q8—48no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—42no—
399#117—44no—
400#117—44no—
401#117—44no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490#107—24no—
491#107—42no—
492#107—42no—
493#107—42no—
494#107—42no—
495#107—42no—
496#106—42no—
497#106—42no—
498#106—42no—
499#106—42no—
500C4⋊C8—24no—
501C4⋊C8—24no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—24no—
505C4⋊C8—22no—
506C4⋊C8—42no—
507C4⋊C8#4114yes—
508#103—24no—
509#103—24no—
510#103—42no—
511#103—42no—
512C22⋊C8—42no—
513C22⋊C8—42no—
514#97—24no—
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—22no—
531#95—22no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—22no—
543#95—22no—
544#95—21no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556C24C22×D411yescharacteristic
557C24C22×D411yescharacteristic
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—42no—
567C2×Q8—44no—
568C2×Q8—42no—
569C2×Q82−1+412yes—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—41no—
573C22×C4—22no—
574C22×C4—21no—
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—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
622M16—84no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
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—84no—
635C2×C8C2×#4114yes—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
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—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—41no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4AGL(1,ℤ/8)14yes—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—41no—
721C42—42no—
722C42—44no—
723C42—44no—
724C42—42no—
725C42—42no—
726C42—44no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—81no—
732C42C2×#4112yes—
733C42H(5,𝔽2)12yes—
734C422−1+412yes—
735C422−1+412yes—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23C2×AGL(1,ℤ/8)12yes—
750C23C23×D411yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755Q8—84no—
756Q8—88no—
757D4—44no—
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—22no—
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—44no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4#53712yes—
835C2×C4#53712yes—
836C2×C4#54712yes—
837C2×C4#54712yes—
838C2×C4C2×AGL(1,ℤ/8)12yes—
839C2×C4C2×AGL(1,ℤ/8)12yes—
840C2×C4#57512yes—
841C2×C4#57812yes—
842C2×C4C22×#4111yescharacteristic
843C2×C4C2×H(5,𝔽2)11yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4C2×2−1+411yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C2×C4#58511yescharacteristic
848C8—24no—
849C8—42no—
850C8—42no—
851C8—42no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22C2×#53711yescharacteristic
867C22C2×#54711yescharacteristic
868C22#348911yescharacteristic
869C22C22×AGL(1,ℤ/8)11yescharacteristic
870C22C2×#57511yescharacteristic
871C22C2×#57811yescharacteristic
872C22#358611yescharacteristic
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—41no—
879C4—41no—
880C4—42no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—81no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—82no—
895C4—81no—
896C4#334914yes—
897C4#351411yescharacteristic
898C4#352311yescharacteristic
899C4#355211yescharacteristic
900C4#355511yescharacteristic
901C2—42no—
902C2—81no—
903C2#3892311yescharacteristic
904C2#6091611yescharacteristic
905C2#6092511yescharacteristic
906C2C2×#334911yescharacteristic
907C2#6125211yescharacteristic
908C2#6211811yescharacteristic
909C2#6213211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33198C2semidirect
4. #32419C2semidirect
5. #32406C2semidirect
6. #31624C2semidirect
7. #31604C2semidirect
8. #29942C2semidirect
9. #29939C2semidirect
10. #29289C2semidirect
12. #28694C2semidirect
13. #27631C2semidirect
14. #27630C2semidirect
15. #26521C2semidirect
16. #25463C2semidirect
18. #24846C2semidirect
19. #24837C2semidirect
21. #21964C2semidirect
22. #21962C2semidirect
23. #21616C2semidirect

Maximal subgroups

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

subgroupindex
#361882
#348982
#331982
#324192
#324062
#316242
#316042
#299422
#299392
#292892
#287142
#286942
#276312
#276302
#265212
#254632
#253522
#248462
#248372
#226482
#219642
#219622
#216162