Finite Group Databasebeta

← #7123983

Subgroups — #7123983

Order 512.

1259 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59893C211yesmaximal, characteristic, complemented
2#59448C211yesmaximal, characteristic, complemented
3#32436C211yesmaximal, characteristic, complemented
4#32356C211yesmaximal, characteristic, complemented
5#32325C211yesmaximal, characteristic, complemented
6#31985C211yesmaximal, characteristic, complemented
7#31651C211yesmaximal, characteristic
8#31541C211yesmaximal, characteristic, complemented
9#31471C211yesmaximal, characteristic, complemented
10#31162C211yesmaximal, characteristic
11#29396C211yesmaximal, characteristic, complemented
12#29375C211yesmaximal, characteristic, complemented
13#28895C211yesmaximal, characteristic, complemented
14#28011C211yesmaximal, characteristic, complemented
15#27581C211yesmaximal, characteristic
16#27562C211yesmaximal, characteristic, complemented
17#27500C211yesmaximal, characteristic
18#27389C211yesmaximal, characteristic, complemented
19#27219C211yesmaximal, characteristic, complemented
20#27200C211yesmaximal, characteristic, complemented
21#27197C211yesmaximal, characteristic
22#27141C211yesmaximal, characteristic, complemented
23#26596C211yesmaximal, characteristic
24#26545C211yesmaximal, characteristic, complemented
25#26378C211yesmaximal, characteristic, complemented
26#26097C211yesmaximal, characteristic, complemented
27#23779C211yesmaximal, characteristic, complemented
28#23072C211yesmaximal, characteristic, complemented
29#22773C211yesmaximal, characteristic, complemented
30#22377C211yesmaximal, characteristic, complemented
31#22149C211yesmaximal, characteristic
32C2×#478C2211yescharacteristic
33C2×#463C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2777—21no—
36#2773—21no—
37#2765—21no—
38#2739—21no—
39#2611—21no—
40#2596—21no—
41#2577—21no—
42#2571C2211yescharacteristic
43#2570C2211yescharacteristic
44#2566C2211yescharacteristic
45#2565C2211yescharacteristic
46#2530—21no—
47#2530—21no—
48#2525—21no—
49#2517—21no—
50#2515—21no—
51#2514C2211yescharacteristic
52#2513C2211yescharacteristic
53#2513C2211yescharacteristic
54#2511C2211yescharacteristic
55#2509C2211yescharacteristic
56#2508C2211yescharacteristic
57#2493—21no—
58#2475—21no—
59#2454C2211yescharacteristic
60#2453C2211yescharacteristic
61#2448C2211yescharacteristic
62#2448C2211yescharacteristic
63#2447C2211yescharacteristic
64#2447C2211yescharacteristic
65#2370C2211yescharacteristic
66#2367C2211yescharacteristic
67#2357C2211yescharacteristic
68#2356C2211yescharacteristic
69#2356C2211yescharacteristic
70#2354C2211yescharacteristic
71#2351C2211yescharacteristic
72#2349C2211yescharacteristic
73#2346—21no—
74#2343—21no—
75C4×#125C2211yescharacteristic
76C4×#125C2211yescharacteristic
77C4×#124C2211yescharacteristic
78#2295C2211yescharacteristic
79#2293C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2099C2211yescharacteristic
85#2097C2211yescharacteristic
86#2097C2211yescharacteristic
87#2095C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2086C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2074C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2055C2211yescharacteristic
112#2054C2211yescharacteristic
113#2042C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2012C2211yescharacteristic
120#1992C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1971C2211yescharacteristic
124#1970C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1968C2211yescharacteristic
128#1959C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1941C2211yescharacteristic
134#1940C2211yescharacteristic
135#1939C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic
142#1928C2211yescharacteristic
143#1928C2211yescharacteristic
144#1927C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1918C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1916C2211yescharacteristic
163#1916C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1865C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1846C2211yescharacteristic
187#1839C2211yescharacteristic
188#1835C2211yescharacteristic
189#1805C2211yescharacteristic
190#1805C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1776C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1771C2211yescharacteristic
197C8×C4⋊C4C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#103C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×#125D411yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117—21no—
221C2×#117—21no—
222#478—24no—
223#463—24no—
224C4×SD16—24no—
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#97C2311yescharacteristic
268C2×#97C2311yescharacteristic
269C2×C4×C8C2311yescharacteristic
270C2×C4×C8C2311yescharacteristic
271C2×C4×C8C2311yescharacteristic
272C2×C4×C8C2311yescharacteristic
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#399—21no—
285#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#391C2311yescharacteristic
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389D411yescharacteristic
328#389D411yescharacteristic
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#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—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#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387D411yescharacteristic
380#387D411yescharacteristic
381#387D411yescharacteristic
382#387D411yescharacteristic
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#383—21no—
394#383—21no—
395#383—21no—
396#382—21no—
397#382—21no—
398#382—21no—
399#382D411yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#381—21no—
407#381—21no—
408#381—21no—
409#380—21no—
410#380—21no—
411#380—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436#376—21no—
437#376—21no—
438#376—21no—
439C2×#95—21no—
440C43C2311yescharacteristic
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#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
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
481C22×Q8C2411yescharacteristic
482C22×Q8C2411yescharacteristic
483C22×D4C2411yescharacteristic
484C22×D4C2411yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C2×Q16—22no—
490C2×Q16—41no—
491C2×Q16—41no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—41no—
496C2×SD16—41no—
497C2×SD16—41no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509#125—22no—
510#125—42no—
511#125—41no—
512#125—41no—
513#125—41no—
514#124—22no—
515#124—22no—
516#124—41no—
517#124—41no—
518C4×Q8—22no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—41no—
522C4×Q8—41no—
523C4×Q8—41no—
524C4×Q8—41no—
525C4×Q8—41no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—41no—
532C4×D4—41no—
533C4×D4—41no—
534#117—44no—
535#117—44no—
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—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
561C2×C4⋊C4C2×D411yescharacteristic
562C2×C4⋊C4C2×D411yescharacteristic
563C2×C4⋊C4C2×D411yescharacteristic
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C42—21no—
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×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631#107—22no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#106—22no—
638#106—22no—
639#106—41no—
640#106—41no—
641#106—41no—
642#106—41no—
643C4⋊C8—22no—
644C4⋊C8—22no—
645C4⋊C8—41no—
646C4⋊C8—41no—
647C4⋊C8—41no—
648C4⋊C8—41no—
649#103—22no—
650#103—22no—
651#103—41no—
652#103—41no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#103—41no—
658#103—41no—
659#103—41no—
660#103—41no—
661#102—22no—
662#102—41no—
663#102—41no—
664#102—41no—
665#102—41no—
666#102—41no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671#102—41no—
672#102#4114yes—
673#97—41no—
674#97—41no—
675C4×C8—22no—
676C4×C8—41no—
677C4×C8—41no—
678C4×C8—41no—
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#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
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
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739C24—21no—
740C24—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q82−1+412yes—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4C2×#4112yes—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—81no—
786C22×C4—81no—
787C22×C4—81no—
788C22×C4—81no—
789C22×C4—81no—
790C22×C4—81no—
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
806Q16—82no—
807SD16—44no—
808SD16—82no—
809D8—82no—
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—21no—
833C2×C8C2×#4112yes—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
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—41no—
860C4⋊C4—41no—
861C4⋊C4—41no—
862C4⋊C4—41no—
863C4⋊C4—41no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—41no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—42no—
870C4⋊C4—42no—
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⋊C4C2×#4112yes—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C42—22no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—21no—
926C42—21no—
927C42—21no—
928C42—21no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—41no—
934C42—41no—
935C42—41no—
936C42—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42—42no—
941C42—42no—
942C42—42no—
943C42—81no—
944C42—81no—
945C42—81no—
946C42—81no—
947C42—81no—
948C23—22no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23C23×D411yescharacteristic
963Q8—22no—
964Q8—22no—
965Q8—41no—
966Q8—41no—
967Q8—41no—
968Q8—41no—
969Q8—41no—
970Q8—41no—
971D4—22no—
972D4—22no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
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—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
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—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—162no—
1065C2×C4—162no—
1066C2×C4#57512yes—
1067C2×C4C22×#4111yescharacteristic
1068C2×C4C2×2−1+411yescharacteristic
1069C2×C4#58511yescharacteristic
1070C2×C4#58511yescharacteristic
1071C2×C4#58511yescharacteristic
1072C2×C4#58511yescharacteristic
1073C8—22no—
1074C8—41no—
1075C8—41no—
1076C8—41no—
1077C8—41no—
1078C8—41no—
1079C8—41no—
1080C8—41no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22D4×#4111yescharacteristic
1096C22#348711yescharacteristic
1097C22#348911yescharacteristic
1098C22C2×#57511yescharacteristic
1099C22#358411yescharacteristic
1100C22#358411yescharacteristic
1101C22#358411yescharacteristic
1102C4—22no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—42no—
1107C4—41no—
1108C4—41no—
1109C4—41no—
1110C4—41no—
1111C4—41no—
1112C4—41no—
1113C4—41no—
1114C4—41no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C4—81no—
1127C4—81no—
1128C4—81no—
1129C4—81no—
1130C4#349511yescharacteristic
1131C4#352111yescharacteristic
1132C4#356411yescharacteristic
1133C4#356711yescharacteristic
1134C2—82no—
1135C2—161no—
1136C2#4475111yescharacteristic
1137C2#6144211yescharacteristic
1138C2#6148611yescharacteristic
1139C2#6190811yescharacteristic
1140C2#6193011yescharacteristic
1141C2#6214011yescharacteristic
1142C2#6221011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59893C2semidirect
2. #59448C2semidirect
3. #32436C2semidirect
4. #32356C2semidirect
5. #32325C2semidirect
6. #31985C2semidirect
8. #31541C2semidirect
9. #31471C2semidirect
11. #29396C2semidirect
12. #29375C2semidirect
13. #28895C2semidirect
14. #28011C2semidirect
16. #27562C2semidirect
18. #27389C2semidirect
19. #27219C2semidirect
20. #27200C2semidirect
22. #27141C2semidirect
24. #26545C2semidirect
25. #26378C2semidirect
26. #26097C2semidirect
27. #23779C2semidirect
28. #23072C2semidirect
29. #22773C2semidirect
30. #22377C2semidirect

Maximal subgroups

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

subgroupindex
#598932
#594482
#324362
#323562
#323252
#319852
#316512
#315412
#314712
#311622
#293962
#293752
#288952
#280112
#275812
#275622
#275002
#273892
#272192
#272002
#271972
#271412
#265962
#265452
#263782
#260972
#237792
#230722
#227732
#223772
#221492