Finite Group Databasebeta

← #6799728

Subgroups — #6799728

Order 512.

1373 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36560C211yesmaximal, characteristic
2#34951C211yesmaximal, characteristic
3#33067C211yesmaximal, characteristic
4#32630C212yesmaximal
5#32566C212yesmaximal
6#32314C212yesmaximal
7#32082C212yesmaximal
8#29996C211yesmaximal, characteristic
9#29983C211yesmaximal, characteristic
10#29141C211yesmaximal, characteristic
11#29123C211yesmaximal, characteristic
12#29123C211yesmaximal, characteristic
13#29013C212yesmaximal
14#28283C211yesmaximal, characteristic
15#28205C211yesmaximal, characteristic
16#28205C211yesmaximal, characteristic
17#28030C212yesmaximal
18#27128C212yesmaximal
19#26690C212yesmaximal
20#22821C211yesmaximal, characteristic
21#22112C211yesmaximal, characteristic
22#22112C211yesmaximal, characteristic
23C4×#475C211yesmaximal, characteristic
24C2×#557—21no—
25C2×#475C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#475C2211yescharacteristic
28#2868C2211yescharacteristic
29#2859C2211yescharacteristic
30#2859C2211yescharacteristic
31#2585—21no—
32#2585—21no—
33#2582C2211yescharacteristic
34#2568—21no—
35#2568C2211yescharacteristic
36#2565—21no—
37#2565—21no—
38#2552C2211yescharacteristic
39#2546—21no—
40#2546C2212yes—
41#2546C2211yescharacteristic
42#2511C2211yescharacteristic
43#2511C2211yescharacteristic
44#2509—21no—
45#2506—21no—
46#2506—21no—
47#2506C2212yes—
48#2506C2212yes—
49#2453—21no—
50#2446C2211yescharacteristic
51#2446C2211yescharacteristic
52#2402—21no—
53#2402—21no—
54#2365—21no—
55#2365C2212yes—
56C4×C4⋊Q8C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×#125—21no—
63#2295—21no—
64#2295C2211yescharacteristic
65#2295C2211yescharacteristic
66C42×Q8C2211yescharacteristic
67C42×Q8C2211yescharacteristic
68#2100C2212yes—
69#2100C2212yes—
70#2099C2212yes—
71#2096C2212yes—
72#2088C2212yes—
73#2088C2212yes—
74#2084C2212yes—
75#2084C2212yes—
76#2066C2212yes—
77#2066C2212yes—
78#2066C2212yes—
79#2066C2212yes—
80#2058C2212yes—
81#2043C2212yes—
82#2043C2212yes—
83#2043C2212yes—
84#2043C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#1988C2211yescharacteristic
89#1984C2212yes—
90#1981C2212yes—
91#1956C2212yes—
92#1948C2211yescharacteristic
93#1948C2211yescharacteristic
94#1948C2211yescharacteristic
95#1948C2212yes—
96#1941C2212yes—
97#1941C2212yes—
98#1933C2212yes—
99#1933C2212yes—
100#1933C2212yes—
101#1933C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1927C2212yes—
107#1927C2212yes—
108#1927C2212yes—
109#1927C2212yes—
110#1920C2212yes—
111#1920C2212yes—
112#1919C2212yes—
113#1919C2212yes—
114#1919C2212yes—
115#1916C2212yes—
116#1916C2212yes—
117#1865C2212yes—
118#1865C2212yes—
119#1865C2212yes—
120#1842C2211yescharacteristic
121#1834C2212yes—
122#1831C2211yescharacteristic
123#1831C2211yescharacteristic
124#1803C2211yescharacteristic
125#1803C2211yescharacteristic
126#1803C2211yescharacteristic
127#1803C2211yescharacteristic
128#1803C2211yescharacteristic
129#1803C2211yescharacteristic
130#1803C2211yescharacteristic
131#1803C2211yescharacteristic
132#1803C2211yescharacteristic
133C4×#106C2212yes—
134C8×C4⋊C4C2212yes—
135C4×C4⋊C8C2211yescharacteristic
136C4×C4⋊C8C2211yescharacteristic
137C4×C4⋊C8C2211yescharacteristic
138C4×#103C2212yes—
139#557—48no—
140C2×C4⋊Q8—22no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2312yes—
148C2×#125—21no—
149C2×#125—22no—
150C2×#125—22no—
151C2×#125—21no—
152C2×#125—21no—
153C2×C4×Q8—22no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8D411yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165#475—24no—
166#475—24no—
167#475—24no—
168C2×#106C2312yes—
169C2×#106C2312yes—
170C2×#106C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×C4×C8C2312yes—
193C2×C4×C8C2312yes—
194C2×C4×C8C2312yes—
195#400—21no—
196#400—21no—
197#400—21no—
198#400—21no—
199#400—22no—
200#400—22no—
201#400—21no—
202#400—21no—
203#400—21no—
204#400—21no—
205#398—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#398—21no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#398—21no—
217#391—21no—
218#391—21no—
219#391—22no—
220#391—22no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391C2311yescharacteristic
225#391C2311yescharacteristic
226#391C2311yescharacteristic
227#391C2311yescharacteristic
228#391C2311yescharacteristic
229#391C2311yescharacteristic
230#391C2311yescharacteristic
231#391C2311yescharacteristic
232#391C2311yescharacteristic
233#391C2311yescharacteristic
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
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#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2312yes—
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2312yes—
260#389C2312yes—
261#389C2311yescharacteristic
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#387—22no—
275#387—22no—
276#387—22no—
277#387—22no—
278#384—21no—
279#384—21no—
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#384C2311yescharacteristic
286#384C2312yes—
287#382—21no—
288#382—21no—
289#382—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319#376—21no—
320#376—21no—
321C43—21no—
322C43C2311yescharacteristic
323C43C2311yescharacteristic
324C43C2311yescharacteristic
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—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—22no—
348C22×Q8C2×D411yescharacteristic
349C22×Q8C2411yescharacteristic
350C22×Q8C2411yescharacteristic
351C22×Q8C2411yescharacteristic
352C22×C8C2412yes—
353C22×C8C2412yes—
354C22×C8C2412yes—
355C22×C8C2412yes—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359C4⋊Q8—42no—
360C4⋊Q8—42no—
361C4⋊Q8—41no—
362C4⋊Q8—41no—
363C4⋊Q8—41no—
364C4⋊Q8—41no—
365C4⋊Q8—44no—
366C4⋊Q8—48no—
367C4⋊Q8—44no—
368C4⋊Q8#4114yes—
369#125—44no—
370#125—48no—
371#125—48no—
372#125—44no—
373#125—44no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—41no—
382C4×Q8—41no—
383C4×Q8—42no—
384C4×Q8—41no—
385C4×Q8—41no—
386C4×Q8—41no—
387C4×Q8—48no—
388C4×Q8—44no—
389C4×Q8—44no—
390C4×Q8—44no—
391C4×Q8SD1618yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
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—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
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—22no—
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—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⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D411yescharacteristic
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
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
477C2×C42C2411yescharacteristic
478#106—24no—
479#106—24no—
480#106—24no—
481#106—42no—
482#106—42no—
483#106—42no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—42no—
489C4⋊C8—42no—
490#103—24no—
491#103—24no—
492#103—24no—
493#103—24no—
494#103—42no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103—42no—
500#103—42no—
501#103—42no—
502C4×C8—42no—
503C4×C8—42no—
504C4×C8—42no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
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—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—21no—
534#95—21no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548C2×Q8—24no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8—44no—
572C2×Q8—42no—
573C2×Q8C2×SD1614yes—
574C2×Q82−1+412yes—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C2511yescharacteristic
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4C2×SD1614yes—
676C4⋊C4C2×SD1614yes—
677C4⋊C4C2×SD1614yes—
678C4⋊C4C2×#4114yes—
679C42—22no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—41no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—44no—
707C42—44no—
708C42—44no—
709C42—42no—
710C42—81no—
711C42C2×SD1614yes—
712C42C2×SD1614yes—
713C42C2×SD1614yes—
714C42C2×#4112yes—
715C422−1+412yes—
716C23C23×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—44no—
720Q8—48no—
721Q8—41no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—88no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—24no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
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—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4#54812yes—
800C2×C4#54812yes—
801C2×C4C22×SD1612yes—
802C2×C4C22×SD1612yes—
803C2×C4C22×SD1612yes—
804C2×C4C22×SD1612yes—
805C2×C4C22×SD1612yes—
806C2×C4C22×SD1612yes—
807C2×C4C22×SD1612yes—
808C2×C4#57512yes—
809C2×C4#57812yes—
810C2×C4C22×#4111yescharacteristic
811C2×C4C2×2−1+411yescharacteristic
812C2×C4C2×2−1+411yescharacteristic
813C2×C4#58511yescharacteristic
814C2×C4#58511yescharacteristic
815C2×C4#58511yescharacteristic
816C8—42no—
817C8—42no—
818C8—42no—
819C8—42no—
820C22#344911yescharacteristic
821C22C2×#54811yescharacteristic
822C22#348911yescharacteristic
823C22C23×SD1611yescharacteristic
824C22C2×#57511yescharacteristic
825C22C2×#57811yescharacteristic
826C22#358611yescharacteristic
827C4—22no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—44no—
839C4—41no—
840C4—41no—
841C4—42no—
842C4—82no—
843C4—82no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4—82no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4#335914yes—
853C4#351611yescharacteristic
854C4#352411yescharacteristic
855C4#356311yescharacteristic
856C4#356511yescharacteristic
857C2#3911911yescharacteristic
858C2#6094111yescharacteristic
859C2#6099511yescharacteristic
860C2C2×#335911yescharacteristic
861C2#6132011yescharacteristic
862C2#6209911yescharacteristic
863C2#6213011yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#365602
#349512
#330672
#326302
#325662
#323142
#320822
#299962
#299832
#291412
#291232
#290132
#282832
#282052
#280302
#271282
#266902
#228212
#221122
C4×#4752