Finite Group Databasebeta

← #6499223

Subgroups — #6499223

Order 512.

1426 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35286C211yesmaximal, characteristic, complemented
2#34084C211yesmaximal, characteristic
3#33073C211yesmaximal, characteristic, complemented
4#33072C211yesmaximal, characteristic, complemented
5#33068C211yesmaximal, characteristic, complemented
6#33067C211yesmaximal, characteristic, complemented
7#29998C211yesmaximal, characteristic, complemented
8#29997C211yesmaximal, characteristic, complemented
9#29996C211yesmaximal, characteristic, complemented
10#29995C211yesmaximal, characteristic, complemented
11#29251C212yesmaximal, complemented
12#29250C212yesmaximal, complemented
13#29249C212yesmaximal
14#29248C212yesmaximal
15#29203C212yesmaximal, complemented
16#29199C212yesmaximal, complemented
17#29188C212yesmaximal, complemented
18#29185C212yesmaximal, complemented
19#21988C211yesmaximal, characteristic, complemented
20#21981C211yesmaximal, characteristic, complemented
21#21867C211yesmaximal, characteristic
22#21862C211yesmaximal, characteristic
23#20815C211yesmaximal, characteristic, complemented
24C2×#529C2211yescharacteristic
25C2×#432C2211yescharacteristic
26C2×#431C2211yescharacteristic
27#2859C2211yescharacteristic
28#2859C2211yescharacteristic
29#2859C2211yescharacteristic
30#2859C2211yescharacteristic
31#2647C2212yes—
32#2647C2212yes—
33#2571—21no—
34#2571—21no—
35#2552—21no—
36#2552—21no—
37#2442—21no—
38#2442—21no—
39#2442—21no—
40#2442—21no—
41#2335—21no—
42#2335—21no—
43#2334—21no—
44#2334—21no—
45#2330C2211yescharacteristic
46#2330C2211yescharacteristic
47#2326C2211yescharacteristic
48#2326C2211yescharacteristic
49#2324C2211yescharacteristic
50#2324C2211yescharacteristic
51#2323C2211yescharacteristic
52#2323C2211yescharacteristic
53#2317C2212yes—
54#2316C2212yes—
55#2298—21no—
56#2296—21no—
57#2295C2211yescharacteristic
58#2293—21no—
59#2293C2211yescharacteristic
60#2290—21no—
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C42×Q8C2211yescharacteristic
65C42×D4C2211yescharacteristic
66C4×#117C2211yescharacteristic
67#2088C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2088C2212yes—
71#2088C2212yes—
72#2088C2212yes—
73#2087C2212yes—
74#2086C2212yes—
75#2068C2212yes—
76#2067C2212yes—
77#2066C2212yes—
78#2066C2212yes—
79#2066C2212yes—
80#2065C2212yes—
81#2065C2212yes—
82#2065C2212yes—
83#1992C2212yes—
84#1991C2212yes—
85#1959C2212yes—
86#1958C2212yes—
87#1948C2211yescharacteristic
88#1948C2211yescharacteristic
89#1948C2211yescharacteristic
90#1948C2211yescharacteristic
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1921C2212yes—
96#1920C2212yes—
97#1920C2212yes—
98#1920C2212yes—
99#1919C2212yes—
100#1919C2212yes—
101#1919C2212yes—
102#1918C2212yes—
103#1875C2212yes—
104#1874C2212yes—
105#1873C2212yes—
106#1872C2212yes—
107#1865C2212yes—
108#1865C2212yes—
109#1865C2212yes—
110#1864C2212yes—
111#1864C2212yes—
112#1864C2212yes—
113#1863C2212yes—
114#1862C2212yes—
115#1854C2212yes—
116#1854C2212yes—
117#1853C2212yes—
118#1853C2212yes—
119#1847C2212yes—
120#1844C2212yes—
121#1842C2211yescharacteristic
122#1842C2211yescharacteristic
123#1836C2212yes—
124#1834C2212yes—
125#1831C2211yescharacteristic
126#1831C2211yescharacteristic
127#1803C2211yescharacteristic
128#1803C2211yescharacteristic
129#1803C2211yescharacteristic
130#1803C2211yescharacteristic
131#1802C2211yescharacteristic
132#1802C2211yescharacteristic
133#1802C2211yescharacteristic
134#1802C2211yescharacteristic
135#1798C2212yes—
136#1798C2212yes—
137#1768C2212yes—
138#1768C2212yes—
139#529—24no—
140#529Q818yes—
141C2×#126—21no—
142C2×#125—21no—
143C2×#125—21no—
144C2×#125—21no—
145C2×#125—21no—
146C2×#125C2311yescharacteristic
147C2×#124C2311yescharacteristic
148C2×#123—21no—
149C2×C22⋊Q8C2311yescharacteristic
150C2×#121C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×D4—21no—
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C2×#117—21no—
160C2×#117—21no—
161C2×#117C2312yes—
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4C2312yes—
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169#432—24no—
170#431—24no—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×#97C2312yes—
198C2×C4×C8C2312yes—
199#400—22no—
200#400—22no—
201#400—22no—
202#400—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#391C2311yescharacteristic
208#391C2311yescharacteristic
209#390—21no—
210#390—21no—
211#390C2311yescharacteristic
212#390C2311yescharacteristic
213#389—22no—
214#389—22no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389C2312yes—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#388—21no—
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#388—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#386—21no—
262#386—21no—
263#385—21no—
264#385—21no—
265#385—22no—
266#385—22no—
267#385—21no—
268#385—21no—
269#385—21no—
270#385—21no—
271#384—22no—
272#384—21no—
273#384—21no—
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2312yes—
281#382—22no—
282#382—21no—
283#382—21no—
284#382—21no—
285#382—21no—
286#382—21no—
287#382C2312yes—
288#380—21no—
289#380—21no—
290#380—21no—
291#380—22no—
292#380—22no—
293#380C2311yescharacteristic
294#380C2311yescharacteristic
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⋊C4D411yescharacteristic
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320#376—21no—
321#376C2311yescharacteristic
322#376C2311yescharacteristic
323C43—21no—
324C43C2311yescharacteristic
325C43C2311yescharacteristic
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#340C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8C2411yescharacteristic
347C22×D4—21no—
348C22×D4C2411yescharacteristic
349C23×C4—21no—
350C23×C4—22no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2411yescharacteristic
356C22×C8C2412yes—
357C22×C8C2412yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360#126—28no—
361#125—22no—
362#125—82no—
363#125—82no—
364#125—82no—
365#125—82no—
366#125C2×Q814yes—
367#124—22no—
368#124C2×Q814yes—
369#123—28no—
370C22⋊Q8—22no—
371C22⋊Q8C2×Q814yes—
372#121—22no—
373#121C2×Q814yes—
374C4×Q8—22no—
375C4×Q8—41no—
376C4×Q8—41no—
377C4×Q8—41no—
378C4×Q8—41no—
379C4×Q8C2×Q814yes—
380C4×D4—28no—
381C4×D4—22no—
382C4×D4—41no—
383C4×D4—41no—
384C4×D4—41no—
385C4×D4—41no—
386C4×D4C2×Q814yes—
387#117—28no—
388#117—41no—
389#117—41no—
390#117—41no—
391#117—41no—
392#117—42no—
393#117—42no—
394#117—82no—
395#117—82no—
396C2×C4⋊C4—21no—
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—22no—
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—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4—82no—
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
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⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
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—21no—
474C2×C42—21no—
475C2×C42—82no—
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×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×Q814yes—
487C2×C42#4114yes—
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494#107—42no—
495#107—42no—
496#106—42no—
497#106—42no—
498#106—42no—
499#106—42no—
500#106—42no—
501#106—42no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—22no—
506C4⋊C8—42no—
507C4⋊C8—42no—
508C4⋊C8—42no—
509C4⋊C8—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#102—42no—
515#102—42no—
516#102—42no—
517#102—42no—
518C22⋊C8—24no—
519C22⋊C8—24no—
520#97—24no—
521C4×C8—24no—
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—21no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556C24—21no—
557C24C22×D411yescharacteristic
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C22×Q812yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4C22×Q812yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4C22⋊Q814yes—
605C22×C4C22⋊Q814yes—
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×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×Q812yes—
620C22×C4C2×#4112yes—
621C22×C4C2511yescharacteristic
622C2×C8—22no—
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—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
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—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—42no—
661C4⋊C4—44no—
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—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—82no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4C22×Q812yes—
690C4⋊C4C22×Q812yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—44no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—24no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—44no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—81no—
732C42—81no—
733C42—81no—
734C42—81no—
735C42C22⋊Q814yes—
736C42C22⋊Q814yes—
737C42C22×Q812yes—
738C42C22×Q812yes—
739C42C2×#4112yes—
740C42C2×#4112yes—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23C2×C22⋊Q812yes—
755C23C23×D411yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—41no—
759Q8—41no—
760D4—22no—
761D4—22no—
762D4—41no—
763D4—41no—
764D4—84no—
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—28no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—48no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—84no—
838C2×C4—84no—
839C2×C4—164no—
840C2×C4C2×C22⋊Q812yes—
841C2×C4C2×C22⋊Q812yes—
842C2×C4C2×C22⋊Q812yes—
843C2×C4C2×C22⋊Q812yes—
844C2×C4C2×C22⋊Q812yes—
845C2×C4#57712yes—
846C2×C4#57712yes—
847C2×C4C23×Q811yescharacteristic
848C2×C4C22×#4111yescharacteristic
849C2×C4#58511yescharacteristic
850C2×C4#58511yescharacteristic
851C2×C4#58511yescharacteristic
852C2×C4#58511yescharacteristic
853C8—42no—
854C8—42no—
855C8—42no—
856C8—42no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C22×C22⋊Q811yescharacteristic
872C22#344911yescharacteristic
873C22#344911yescharacteristic
874C22C2×#57711yescharacteristic
875C22C2×#57711yescharacteristic
876C22#358511yescharacteristic
877C22#358611yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—82no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4#308414yes—
902C4#350411yescharacteristic
903C4#350411yescharacteristic
904C4#351211yescharacteristic
905C4#351211yescharacteristic
906C2—42no—
907C2—82no—
908C2#3533311yescharacteristic
909C2C2×#308411yescharacteristic
910C2#6049311yescharacteristic
911C2#6098911yescharacteristic
912C2#6099111yescharacteristic
913C2#6099211yescharacteristic
914C2#6099411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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
1. #35286C2semidirect
3. #33073C2semidirect
4. #33072C2semidirect
5. #33068C2semidirect
6. #33067C2semidirect
7. #29998C2semidirect
8. #29997C2semidirect
9. #29996C2semidirect
10. #29995C2semidirect
11. #29251C2semidirect
12. #29250C2semidirect
15. #29203C2semidirect
16. #29199C2semidirect
17. #29188C2semidirect
18. #29185C2semidirect
19. #21988C2semidirect
20. #21981C2semidirect
23. #20815C2semidirect

Maximal subgroups

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

subgroupindex
#352862
#340842
#330732
#330722
#330682
#330672
#299982
#299972
#299962
#299952
#292512
#292502
#292492
#292482
#292032
#291992
#291882
#291852
#219882
#219812
#218672
#218622
#208152