Finite Group Databasebeta

← #6654225

Subgroups — #6654225

Order 512.

1418 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35283C211yesmaximal, characteristic
2#34938C211yesmaximal, characteristic
3#33148C211yesmaximal, characteristic
4#33108C211yesmaximal, characteristic
5#32376C212yesmaximal, complemented
6#32228C212yesmaximal, complemented
7#31742C212yesmaximal
8#31456C212yesmaximal, complemented
9#31354C212yesmaximal
10#31089C212yesmaximal
11#30949C212yesmaximal, complemented
12#30777C212yesmaximal
13#29938C211yesmaximal, characteristic
14#29922C211yesmaximal, characteristic
15#29347C211yesmaximal, characteristic, complemented
16#29347C211yesmaximal, characteristic, complemented
17#29287C211yesmaximal, characteristic, complemented
18#29273C211yesmaximal, characteristic, complemented
19#29255C211yesmaximal, characteristic, complemented
20#29206C211yesmaximal, characteristic, complemented
21#28687C211yesmaximal, characteristic, complemented
22#28283C211yesmaximal, characteristic, complemented
23#21922C211yesmaximal, characteristic
24C2×#533—21no—
25C2×#498C2212yes—
26C2×#483C2212yes—
27C2×#475C2212yes—
28#2868C2211yescharacteristic
29#2862C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2647—21no—
33#2628—21no—
34#2552C2211yescharacteristic
35#2552C2211yescharacteristic
36#2551C2211yescharacteristic
37#2551C2211yescharacteristic
38#2550—21no—
39#2550—21no—
40#2549—21no—
41#2549—21no—
42#2511—21no—
43#2511C2212yes—
44#2492—21no—
45#2492C2212yes—
46#2451—21no—
47#2451C2212yes—
48#2440C2211yescharacteristic
49#2440C2211yescharacteristic
50#2440C2211yescharacteristic
51#2440C2211yescharacteristic
52#2423—21no—
53#2423C2212yes—
54#2399—21no—
55#2399—21no—
56#2331—21no—
57#2314—21no—
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64#2296—21no—
65#2285C2211yescharacteristic
66C4×#117C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2099C2212yes—
69#2099C2212yes—
70#2096C2212yes—
71#2096C2212yes—
72#2088C2212yes—
73#2088C2212yes—
74#2084C2212yes—
75#2084C2212yes—
76#2084C2212yes—
77#2077C2212yes—
78#2077C2212yes—
79#2072C2212yes—
80#2072C2212yes—
81#2072C2212yes—
82#2066C2212yes—
83#2066C2212yes—
84#2058C2212yes—
85#2058C2212yes—
86#2058C2212yes—
87#2035C2212yes—
88#2035C2212yes—
89#2024C2212yes—
90#2024C2212yes—
91#2024C2212yes—
92#1990C2212yes—
93#1990C2212yes—
94#1988C2212yes—
95#1987C2211yescharacteristic
96#1987C2211yescharacteristic
97#1987C2211yescharacteristic
98#1987C2211yescharacteristic
99#1981C2211yescharacteristic
100#1981C2211yescharacteristic
101#1981C2211yescharacteristic
102#1981C2211yescharacteristic
103#1948C2211yescharacteristic
104#1948C2211yescharacteristic
105#1948C2211yescharacteristic
106#1948C2211yescharacteristic
107#1948C2211yescharacteristic
108#1948C2211yescharacteristic
109#1948C2211yescharacteristic
110#1948C2211yescharacteristic
111#1948C2212yes—
112#1933C2212yes—
113#1933C2212yes—
114#1933C2212yes—
115#1933C2212yes—
116#1927C2212yes—
117#1927C2212yes—
118#1923C2212yes—
119#1923C2212yes—
120#1920C2212yes—
121#1920C2212yes—
122#1919C2212yes—
123#1919C2212yes—
124#1916C2212yes—
125#1916C2212yes—
126#1872C2212yes—
127#1865C2212yes—
128#1865C2212yes—
129#1853C2212yes—
130#1844C2212yes—
131#1842C2211yescharacteristic
132#1831C2211yescharacteristic
133#1823C2212yes—
134#1803C2212yes—
135#1797C2211yescharacteristic
136#1797C2211yescharacteristic
137C4×C4⋊C8C2211yescharacteristic
138C4×C4⋊C8C2211yescharacteristic
139#533—48no—
140C2×C4⋊Q8—21no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×#125—21no—
152C2×#125—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8C2312yes—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8C2312yes—
165C2×#117—21no—
166C2×#117D411yescharacteristic
167C2×#117D411yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C42—21no—
171C22×C42C2311yescharacteristic
172#498—44no—
173#483—44no—
174#475—44no—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×#106C2312yes—
182C2×#106C2312yes—
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2311yescharacteristic
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C4×C8C2312yes—
200C2×C4×C8C2312yes—
201#400—22no—
202#400—22no—
203#400—22no—
204#399—22no—
205#398—22no—
206#398—22no—
207#398—21no—
208#398—21no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#395—22no—
216#395—21no—
217#395—21no—
218#395—21no—
219#395—21no—
220#395—21no—
221#395—21no—
222#395—21no—
223#395—21no—
224#393—22no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—22no—
234#391—22no—
235#391C2312yes—
236#391C2312yes—
237#391C2312yes—
238#391C2312yes—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#389C2311yescharacteristic
262#389C2312yes—
263#388—22no—
264#388—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#387—22no—
269#385—21no—
270#385—21no—
271#385—21no—
272#385—21no—
273#384—21no—
274#384—21no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2312yes—
284#382—21no—
285#382—21no—
286#382—21no—
287#380—21no—
288#380—21no—
289#380—21no—
290#380—21no—
291#380C2312yes—
292#380C2311yescharacteristic
293#380C2311yescharacteristic
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⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C22⋊C4D411yescharacteristic
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4C2311yescharacteristic
318C4×C22⋊C4C2311yescharacteristic
319#376D411yescharacteristic
320#376D411yescharacteristic
321C2×#95—21no—
322C43C2311yescharacteristic
323C43C2311yescharacteristic
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#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8C2412yes—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372C4⋊Q8—41no—
373C4⋊Q8—41no—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—44no—
377C4⋊Q8—44no—
378C4⋊Q8—44no—
379C4⋊Q8—82no—
380#125—44no—
381#125—44no—
382C22⋊Q8—44no—
383C22⋊Q8—44no—
384C22⋊Q8—44no—
385C22⋊Q8—44no—
386C22⋊Q8—42no—
387C22⋊Q8—42no—
388C22⋊Q8—82no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—44no—
392C4×Q8—44no—
393C4×Q8—44no—
394C4×Q8—44no—
395C4×Q8—82no—
396#117—24no—
397#117—44no—
398#117SD1618yes—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
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—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
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—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
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—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—44no—
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×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#106—24no—
494#106—24no—
495#106—42no—
496#106—42no—
497#106—42no—
498#106—42no—
499#106—42no—
500#106—42no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—42no—
506C4⋊C8—42no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515C22⋊C8—42no—
516C22⋊C8—42no—
517C4×C8—42no—
518C4×C8—42no—
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—22no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555C24C22×D411yescharacteristic
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—81no—
575C2×Q8—81no—
576C2×Q8—81no—
577C2×Q8—81no—
578C2×Q8—82no—
579C2×Q8—82no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×SD1614yes—
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×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C2511yescharacteristic
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—22no—
635C2×C8—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
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—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4C2×SD1614yes—
699C4⋊C4C2×SD1614yes—
700C4⋊C4H(5,𝔽2)12yes—
701C4⋊C42−1+412yes—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4C2×SD1614yes—
709C22⋊C4C2×SD1614yes—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—82no—
734C42—82no—
735C42C2×SD1614yes—
736C42C2×SD1614yes—
737C42#13714yes—
738C422−1+412yes—
739C422−1+412yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23C22×SD1612yes—
747C23C23×D411yescharacteristic
748Q8—42no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—84no—
753Q8—84no—
754Q8—84no—
755Q8—84no—
756Q8—84no—
757Q8—164no—
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—28no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
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—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—82no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#53612yes—
831C2×C4#53612yes—
832C2×C4C22×SD1612yes—
833C2×C4C22×SD1612yes—
834C2×C4C22×SD1612yes—
835C2×C4C22×SD1612yes—
836C2×C4C22×SD1612yes—
837C2×C4C22×SD1612yes—
838C2×C4C2×#13712yes—
839C2×C4C2×#13712yes—
840C2×C4C2×#13712yes—
841C2×C4C2×H(5,𝔽2)11yescharacteristic
842C2×C4C2×2−1+411yescharacteristic
843C2×C4C2×2−1+411yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4#58511yescharacteristic
846C2×C4#58511yescharacteristic
847C8—42no—
848C8—42no—
849C8—42no—
850C8—42no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22C2×#53611yescharacteristic
859C22#348811yescharacteristic
860C22#348911yescharacteristic
861C22C23×SD1611yescharacteristic
862C22C22×#13711yescharacteristic
863C22#358511yescharacteristic
864C22#358611yescharacteristic
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—42no—
879C4—82no—
880C4—82no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4—82no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4#322914yes—
890C4#355011yescharacteristic
891C4#355411yescharacteristic
892C4#355511yescharacteristic
893C4#355711yescharacteristic
894C2—42no—
895C2#3727511yescharacteristic
896C2C2×#322911yescharacteristic
897C2#6087011yescharacteristic
898C2#6194811yescharacteristic
899C2#6196511yescharacteristic
900C2#6209611yescharacteristic
901C2#6211311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
5. #32376C2semidirect
6. #32228C2semidirect
8. #31456C2semidirect
11. #30949C2semidirect
15. #29347C2semidirect
16. #29347C2semidirect
17. #29287C2semidirect
18. #29273C2semidirect
19. #29255C2semidirect
20. #29206C2semidirect
21. #28687C2semidirect
22. #28283C2semidirect

Maximal subgroups

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

subgroupindex
#352832
#349382
#331482
#331082
#323762
#322282
#317422
#314562
#313542
#310892
#309492
#307772
#299382
#299222
#293472
#292872
#292732
#292552
#292062
#286872
#282832
#219222