Finite Group Databasebeta

← #6796104

Subgroups — #6796104

Order 512.

1378 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#36210C211yesmaximal, characteristic
2#34941C211yesmaximal, characteristic
3#33200C211yesmaximal, characteristic, complemented
4#32418C212yesmaximal, complemented
5#32415C212yesmaximal, complemented
6#31623C212yesmaximal, complemented
7#31615C212yesmaximal, complemented
8#29939C211yesmaximal, characteristic, complemented
9#29938C211yesmaximal, characteristic, complemented
10#29287C211yesmaximal, characteristic, complemented
11#28715C212yesmaximal
12#28693C211yesmaximal, characteristic, complemented
13#27631C211yesmaximal, characteristic, complemented
14#27628C211yesmaximal, characteristic, complemented
15#26522C212yesmaximal, complemented
16#25467C212yesmaximal, complemented
17#25357C212yesmaximal
18#24846C211yesmaximal, characteristic, complemented
19#24837C211yesmaximal, characteristic, complemented
20#22648C211yesmaximal, characteristic
21#21964C211yesmaximal, characteristic, complemented
22#21959C211yesmaximal, characteristic, complemented
23#21616C211yesmaximal, characteristic, complemented
24C2×#501C2212yes—
25C2×#479C2212yes—
26C2×#477C2211yescharacteristic
27C2×#435C2212yes—
28C2×#423C2211yescharacteristic
29C22×C4⋊C8C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2574—21no—
34#2574—21no—
35#2567C2211yescharacteristic
36#2563C2211yescharacteristic
37#2562C2212yes—
38#2552C2211yescharacteristic
39#2538C2211yescharacteristic
40#2514—21no—
41#2509—21no—
42#2508—21no—
43#2497C2211yescharacteristic
44#2497C2211yescharacteristic
45#2495C2212yes—
46#2494—21no—
47#2494C2212yes—
48#2485—21no—
49#2454—21no—
50#2423C2211yescharacteristic
51#2423C2211yescharacteristic
52#2421—21no—
53#2415—21no—
54#2396—21no—
55#2396—21no—
56#2370C2212yes—
57#2362—21no—
58#2347—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125—21no—
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64#2293—21no—
65#2285C2211yescharacteristic
66#2285C2211yescharacteristic
67#2285C2211yescharacteristic
68#2285C2211yescharacteristic
69C42×Q8C2211yescharacteristic
70C42×D4C2211yescharacteristic
71#2100C2212yes—
72#2099C2212yes—
73#2088C2212yes—
74#2088C2212yes—
75#2087C2212yes—
76#2086C2212yes—
77#2085C2212yes—
78#2085C2212yes—
79#2084C2212yes—
80#2083C2212yes—
81#2077C2212yes—
82#2077C2212yes—
83#2077C2212yes—
84#2076C2212yes—
85#2076C2212yes—
86#2075C2212yes—
87#2068C2212yes—
88#2066C2212yes—
89#2035C2212yes—
90#2035C2212yes—
91#1992C2212yes—
92#1989C2212yes—
93#1988C2212yes—
94#1987C2211yescharacteristic
95#1987C2211yescharacteristic
96#1987C2211yescharacteristic
97#1949C2212yes—
98#1948C2212yes—
99#1948C2211yescharacteristic
100#1948C2211yescharacteristic
101#1948C2211yescharacteristic
102#1948C2211yescharacteristic
103#1948C2211yescharacteristic
104#1948C2212yes—
105#1948C2212yes—
106#1948C2212yes—
107#1948C2211yescharacteristic
108#1947C2211yescharacteristic
109#1947C2211yescharacteristic
110#1947C2212yes—
111#1947C2211yescharacteristic
112#1940C2212yes—
113#1928C2212yes—
114#1927C2212yes—
115#1920C2212yes—
116#1919C2212yes—
117#1918C2212yes—
118#1894C2212yes—
119#1892C2212yes—
120#1865C2212yes—
121#1851C2212yes—
122#1850C2212yes—
123#1842C2211yescharacteristic
124#1809C2212yes—
125#1809C2212yes—
126#1809C2212yes—
127#1808C2212yes—
128#1807C2212yes—
129#1807C2212yes—
130#1805C2212yes—
131#1803C2211yescharacteristic
132#1803C2211yescharacteristic
133#1803C2211yescharacteristic
134#1797C2211yescharacteristic
135#1797C2211yescharacteristic
136#1776C2212yes—
137#1767C2211yescharacteristic
138#1763C2212yes—
139C22×M16C2312yes—
140C23×C8C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125—21no—
144C2×#125C2312yes—
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8C2311yescharacteristic
148C2×C22⋊Q8C2311yescharacteristic
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C2×#117—21no—
159C2×#117—21no—
160C2×#117—21no—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#501—44no—
164#479—44no—
165#477—24no—
166#435—44no—
167C2×#107C2312yes—
168C2×#107C2312yes—
169C2×#107C2312yes—
170C2×#107C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177#423—24no—
178C2×C4⋊C8—24no—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2311yescharacteristic
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×#97C2312yes—
194#401—22no—
195#400—22no—
196#400—21no—
197#400—21no—
198#400—22no—
199#399—21no—
200#399—21no—
201#398—21no—
202#398—21no—
203#398—21no—
204#398—21no—
205#397—22no—
206#397—22no—
207#396—21no—
208#396—21no—
209#396—21no—
210#396—21no—
211#395—21no—
212#395—21no—
213#394—22no—
214#393—21no—
215#393—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391C2311yescharacteristic
221#391C2311yescharacteristic
222#390—21no—
223#390—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—22no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#388—22no—
245#388—22no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—22no—
251#388—22no—
252#387—22no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—22no—
260#387—22no—
261#385—21no—
262#385—21no—
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#384C2311yescharacteristic
270#384C2311yescharacteristic
271#383—22no—
272#382—21no—
273#382—21no—
274#382—21no—
275#382—21no—
276#382—21no—
277#382C2312yes—
278#380—21no—
279#380—21no—
280#380—21no—
281#380—21no—
282#380—21no—
283#380—21no—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287#380C2312yes—
288#380C2311yescharacteristic
289#380C2311yescharacteristic
290#380C2311yescharacteristic
291#380C2311yescharacteristic
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⋊C4—21no—
305C4×C4⋊C4—22no—
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2312yes—
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
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
325C43—21no—
326C43C2311yescharacteristic
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#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8C2411yescharacteristic
351C22×D4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2411yescharacteristic
357C23×C4C2411yescharacteristic
358C2×M16—24no—
359C2×M16—42no—
360C2×M16—42no—
361C22×C8—24no—
362C22×C8—42no—
363C22×C8—42no—
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372#125—24no—
373#125—24no—
374#125—44no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—41no—
378C22⋊Q8—41no—
379C22⋊Q8—44no—
380C22⋊Q8—82no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—82no—
388C4×Q8—82no—
389C4×D4—24no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—42no—
393#117—44no—
394#117—82no—
395#117—82no—
396#117—82no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
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—22no—
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—22no—
414C2×C4⋊C4—22no—
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—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4C2×D411yescharacteristic
456C2×C22⋊C4C2×D411yescharacteristic
457C2×C22⋊C4C2×D411yescharacteristic
458C2×C22⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489#107—24no—
490#107—42no—
491#107—42no—
492#107—42no—
493#106—42no—
494#106—42no—
495#106—42no—
496#106—42no—
497#106—42no—
498#106—42no—
499C4⋊C8—24no—
500C4⋊C8—24no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—24no—
504C4⋊C8—22no—
505C4⋊C8—42no—
506C4⋊C8#4114yes—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511C22⋊C8—42no—
512C22⋊C8—42no—
513#97—24no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—22no—
525#95—21no—
526#95—21no—
527#95—22no—
528#95—21no—
529#95—21no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551C24C22×D411yescharacteristic
552C24C22×D411yescharacteristic
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—81no—
563C2×Q8—81no—
564C2×Q82−1+412yes—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—41no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4#13714yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2511yescharacteristic
617M16—84no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—84no—
630C2×C8C2×#4114yes—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
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—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—82no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—41no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—82no—
701C22⋊C4—81no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—82no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—41no—
719C42—41no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—44no—
725C42—42no—
726C42—42no—
727C42—42no—
728C42—81no—
729C42—82no—
730C42—82no—
731C42C2×#4112yes—
732C42H(5,𝔽2)12yes—
733C422−1+412yes—
734C422−1+412yes—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23C2×#13712yes—
749C23C23×D411yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—41no—
753Q8—41no—
754Q8—84no—
755Q8—84no—
756D4—44no—
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—28no—
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—41no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—41no—
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—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—82no—
833C2×C4#53712yes—
834C2×C4#53712yes—
835C2×C4#54712yes—
836C2×C4#54712yes—
837C2×C4C2×#13712yes—
838C2×C4C2×#13712yes—
839C2×C4#57512yes—
840C2×C4#57712yes—
841C2×C4C22×#4111yescharacteristic
842C2×C4C2×H(5,𝔽2)11yescharacteristic
843C2×C4C2×2−1+411yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4C2×2−1+411yescharacteristic
846C2×C4#58511yescharacteristic
847C8—24no—
848C8—42no—
849C8—42no—
850C8—42no—
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—
865C22C2×#53711yescharacteristic
866C22C2×#54711yescharacteristic
867C22#348911yescharacteristic
868C22C22×#13711yescharacteristic
869C22C2×#57511yescharacteristic
870C22C2×#57711yescharacteristic
871C22#358511yescharacteristic
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—41no—
878C4—41no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—82no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—82no—
895C4#334414yes—
896C4#351411yescharacteristic
897C4#352311yescharacteristic
898C4#355211yescharacteristic
899C4#355511yescharacteristic
900C2—42no—
901C2—81no—
902C2#3892311yescharacteristic
903C2#6091811yescharacteristic
904C2#6092911yescharacteristic
905C2C2×#334411yescharacteristic
906C2#6125511yescharacteristic
907C2#6211411yescharacteristic
908C2#6213511yescharacteristic
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. #33200C2semidirect
4. #32418C2semidirect
5. #32415C2semidirect
6. #31623C2semidirect
7. #31615C2semidirect
8. #29939C2semidirect
9. #29938C2semidirect
10. #29287C2semidirect
12. #28693C2semidirect
13. #27631C2semidirect
14. #27628C2semidirect
15. #26522C2semidirect
16. #25467C2semidirect
18. #24846C2semidirect
19. #24837C2semidirect
21. #21964C2semidirect
22. #21959C2semidirect
23. #21616C2semidirect

Maximal subgroups

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

subgroupindex
#362102
#349412
#332002
#324182
#324152
#316232
#316152
#299392
#299382
#292872
#287152
#286932
#276312
#276282
#265222
#254672
#253572
#248462
#248372
#226482
#219642
#219592
#216162