Finite Group Databasebeta

← #6572899

Subgroups — #6572899

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38066C211yesmaximal, characteristic
2#34365C211yesmaximal, characteristic
3#30160C211yesmaximal, characteristic, complemented
4#30102C211yesmaximal, characteristic, complemented
5#29641C211yesmaximal, characteristic
6#29525C211yesmaximal, characteristic, complemented
7#29403C211yesmaximal, characteristic, complemented
8#29323C211yesmaximal, characteristic, complemented
9#29284C211yesmaximal, characteristic, complemented
10#27860C211yesmaximal, characteristic
11#27617C211yesmaximal, characteristic
12#27146C211yesmaximal, characteristic, complemented
13#27131C211yesmaximal, characteristic, complemented
14#27020C211yesmaximal, characteristic, complemented
15#27005C211yesmaximal, characteristic, complemented
16#26877C211yesmaximal, characteristic, complemented
17#26877C211yesmaximal, characteristic, complemented
18#26860C211yesmaximal, characteristic, complemented
19#26860C211yesmaximal, characteristic, complemented
20#25998C211yesmaximal, characteristic
21#25996C211yesmaximal, characteristic
22#24580C211yesmaximal, characteristic
23#24580C211yesmaximal, characteristic
24#23845C211yesmaximal, characteristic, complemented
25#23789C211yesmaximal, characteristic, complemented
26C2×#2058C211yesmaximal, characteristic
27#22934C211yesmaximal, characteristic
28#22920C211yesmaximal, characteristic
29#22615C211yesmaximal, characteristic
30#22609C211yesmaximal, characteristic
31#22595C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C2×#483C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C22×#106C2211yescharacteristic
36C22×#106C2211yescharacteristic
37#2855C2211yescharacteristic
38#2776—21no—
39#2769—21no—
40#2766—21no—
41#2719—21no—
42#2647C2211yescharacteristic
43#2645C2211yescharacteristic
44#2514C2211yescharacteristic
45#2506C2211yescharacteristic
46#2506C2211yescharacteristic
47#2502C2211yescharacteristic
48#2493—21no—
49#2493—21no—
50#2473—21no—
51#2453C2211yescharacteristic
52#2442—21no—
53#2442C2211yescharacteristic
54#2381—21no—
55#2381—21no—
56#2369C2211yescharacteristic
57#2369C2211yescharacteristic
58#2369C2211yescharacteristic
59#2369C2211yescharacteristic
60#2360C2211yescharacteristic
61#2345C2211yescharacteristic
62#2344—21no—
63#2344—21no—
64#2344C2211yescharacteristic
65#2344C2211yescharacteristic
66#2344C2211yescharacteristic
67#2344C2211yescharacteristic
68#2331—21no—
69#2331—21no—
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2331C2211yescharacteristic
73#2331C2211yescharacteristic
74#2330C2211yescharacteristic
75#2320C2211yescharacteristic
76#2310—21no—
77#2310—21no—
78C2×#389C2211yescharacteristic
79#2283C2211yescharacteristic
80#2283C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2097C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2087C2211yescharacteristic
90#2087C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2074C2211yescharacteristic
99#2066C2211yescharacteristic
100#2066C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2058C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2058C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2024C2211yescharacteristic
120#2024C2211yescharacteristic
121#1989C2211yescharacteristic
122#1989C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1948C2211yescharacteristic
127#1948C2211yescharacteristic
128#1948C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1944C2211yescharacteristic
132#1941C2211yescharacteristic
133#1941C2211yescharacteristic
134#1941C2211yescharacteristic
135#1935C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1917C2211yescharacteristic
168#1917C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1865C2211yescharacteristic
174#1863C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1850C2211yescharacteristic
178#1850C2211yescharacteristic
179#1840C2211yescharacteristic
180#1832C2211yescharacteristic
181#1824C2211yescharacteristic
182#1824C2211yescharacteristic
183#1823C2211yescharacteristic
184#1823C2211yescharacteristic
185#1817C2211yescharacteristic
186#1808C2211yescharacteristic
187#1807C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194#1768C2211yescharacteristic
195#1763C2211yescharacteristic
196C4×#103C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199#1746C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8—21no—
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8—24no—
207C2×C4⋊Q8—24no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×#117—21no—
220C2×#117—21no—
221C2×#117—21no—
222C2×#117—21no—
223C22×C4⋊C4—21no—
224C22×C4⋊C4—21no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#483—24no—
231#483—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#106—24no—
237C2×#106—24no—
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×#97C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272#401—21no—
273#401—21no—
274#400—21no—
275#400—21no—
276#400—21no—
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#391—21no—
293#391—21no—
294#391—21no—
295#391—21no—
296#391—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#385—21no—
372#385—21no—
373#385—21no—
374#385—21no—
375#385—21no—
376#384C2311yescharacteristic
377#384C2311yescharacteristic
378#383—21no—
379#383—21no—
380#383—21no—
381#383D411yescharacteristic
382#383D411yescharacteristic
383#382—21no—
384#382D411yescharacteristic
385#382D411yescharacteristic
386#382C2311yescharacteristic
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#381—21no—
390#381—21no—
391#381—21no—
392#381—21no—
393#381—21no—
394#381—21no—
395#381D411yescharacteristic
396#381D411yescharacteristic
397#380—21no—
398#380—21no—
399#380D411yescharacteristic
400#380D411yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4C2311yescharacteristic
427C4×C22⋊C4C2311yescharacteristic
428#376—21no—
429#376C2311yescharacteristic
430#376C2311yescharacteristic
431C2×#95—21no—
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—28no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—82no—
490C22×Q8—82no—
491C22×Q8C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2411yescharacteristic
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C4⋊Q8—28no—
514C4⋊Q8—28no—
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523#125—22no—
524#125—41no—
525#125—82no—
526#125—82no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C4×Q8—22no—
530C4×Q8—41no—
531#117—82no—
532#117—82no—
533#117—82no—
534#117—82no—
535C2×C4⋊C4—28no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—82no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4#4114yes—
583C2×C4⋊C4#4114yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4C2×D411yescharacteristic
604C2×C22⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631#107—22no—
632#107—22no—
633#107—41no—
634#107—41no—
635#106—22no—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—22no—
640#106—22no—
641#106—22no—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—22no—
646#106—22no—
647#106—22no—
648#106—22no—
649#106—41no—
650#106—41no—
651C4⋊C8—22no—
652C4⋊C8—22no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655#103—22no—
656#103—22no—
657#103—22no—
658#103—22no—
659#103—22no—
660#103—22no—
661#103—41no—
662#103—41no—
663C22⋊C8—22no—
664C22⋊C8—22no—
665#97—22no—
666#97—41no—
667C4×C8—22no—
668C4×C8—41no—
669#95—21no—
670#95—21no—
671#95—21no—
672#95—21no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736C24C22×D411yescharacteristic
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—81no—
748C2×Q8—81no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8—816no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—41no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—81no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C2×#4112yes—
808C22×C4C2×#4112yes—
809C22×C4C2511yescharacteristic
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—44no—
833C2×C8—44no—
834C2×C82−1+412yes—
835C2×C82−1+412yes—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—41no—
870C4⋊C4—41no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—42no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4C2×#4112yes—
901C4⋊C4C2×#4112yes—
902C4⋊C4C2×#4112yes—
903C4⋊C4C2×#4112yes—
904C4⋊C42−1+412yes—
905C22⋊C4—22no—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—42no—
910C22⋊C4—42no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C42—22no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—42no—
928C42—42no—
929C42—42no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42—81no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—21no—
945C23#52512yes—
946C23#57712yes—
947C23#57712yes—
948C23C23×D411yescharacteristic
949Q8—41no—
950Q8—41no—
951Q8—41no—
952Q8—41no—
953Q8—84no—
954Q8—84no—
955Q8—84no—
956Q8—84no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—84no—
1051C2×C4—162no—
1052C2×C4#52512yes—
1053C2×C4#57712yes—
1054C2×C4C22×#4111yescharacteristic
1055C2×C4C22×#4111yescharacteristic
1056C2×C4C2×2−1+411yescharacteristic
1057C2×C4C2×2−1+411yescharacteristic
1058C2×C4C2×2−1+411yescharacteristic
1059C2×C4#58511yescharacteristic
1060C8—22no—
1061C8—22no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C8—41no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22#312314yes—
1075C22C2×#52511yescharacteristic
1076C22#348911yescharacteristic
1077C22#349911yescharacteristic
1078C22C2×#57711yescharacteristic
1079C22C2×#57711yescharacteristic
1080C22C2×#57711yescharacteristic
1081C22#358611yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—41no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—42no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4#349511yescharacteristic
1112C4#349511yescharacteristic
1113C4#350911yescharacteristic
1114C4#350911yescharacteristic
1115C2—24no—
1116C2#3608611yescharacteristic
1117C2C2×#312311yescharacteristic
1118C2#6058211yescharacteristic
1119C2#6215711yescharacteristic
1120C2#6220211yescharacteristic
1121C2#6248611yescharacteristic
1122C2#6251311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #30160C2semidirect
4. #30102C2semidirect
6. #29525C2semidirect
7. #29403C2semidirect
8. #29323C2semidirect
9. #29284C2semidirect
12. #27146C2semidirect
13. #27131C2semidirect
14. #27020C2semidirect
15. #27005C2semidirect
16. #26877C2semidirect
17. #26877C2semidirect
18. #26860C2semidirect
19. #26860C2semidirect
24. #23845C2semidirect
25. #23789C2semidirect

Maximal subgroups

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

subgroupindex
#380662
#343652
#301602
#301022
#296412
#295252
#294032
#293232
#292842
#278602
#276172
#271462
#271312
#270202
#270052
#268772
#268602
#259982
#259962
#245802
#238452
#237892
C2×#20582
#229342
#229202
#226152
#226092
#225952