Finite Group Databasebeta

← #7228568

Subgroups — #7228568

Order 512.

1154 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46191C211yesmaximal, characteristic, complemented
2#36421C211yesmaximal, characteristic
3#33071C211yesmaximal, characteristic, complemented
4#33071C211yesmaximal, characteristic, complemented
5#32822C211yesmaximal, characteristic
6#32822C211yesmaximal, characteristic
7#32496C211yesmaximal, characteristic, complemented
8#32475C211yesmaximal, characteristic
9#32403C211yesmaximal, characteristic, complemented
10#32389C211yesmaximal, characteristic
11#32365C211yesmaximal, characteristic, complemented
12#32350C211yesmaximal, characteristic, complemented
13#32106C211yesmaximal, characteristic
14#32085C211yesmaximal, characteristic
15#31987C211yesmaximal, characteristic, complemented
16#31963C211yesmaximal, characteristic
17#31591C211yesmaximal, characteristic
18#31575C211yesmaximal, characteristic, complemented
19#27387C211yesmaximal, characteristic, complemented
20#27365C211yesmaximal, characteristic
21#26884C211yesmaximal, characteristic, complemented
22#26867C211yesmaximal, characteristic, complemented
23#26779C211yesmaximal, characteristic
24#26777C211yesmaximal, characteristic
25#26766C211yesmaximal, characteristic
26#26757C211yesmaximal, characteristic, complemented
27#26545C211yesmaximal, characteristic
28#26531C211yesmaximal, characteristic, complemented
29#26098C211yesmaximal, characteristic
30#26095C211yesmaximal, characteristic, complemented
31#23370C211yesmaximal, characteristic, complemented
32#2866—21no—
33#2864C2211yescharacteristic
34#2864C2211yescharacteristic
35#2861C2211yescharacteristic
36#2839—21no—
37#2810—21no—
38#2767—21no—
39#2767—21no—
40#2767—21no—
41#2767—21no—
42#2719—21no—
43#2596—21no—
44#2577—21no—
45#2571C2211yescharacteristic
46#2571C2211yescharacteristic
47#2570C2211yescharacteristic
48#2570C2211yescharacteristic
49#2565C2211yescharacteristic
50#2545C2211yescharacteristic
51#2529—21no—
52#2525—21no—
53#2522—21no—
54#2513C2211yescharacteristic
55#2511C2211yescharacteristic
56#2509C2211yescharacteristic
57#2509C2211yescharacteristic
58#2509C2211yescharacteristic
59#2508C2211yescharacteristic
60#2508C2211yescharacteristic
61#2508C2211yescharacteristic
62#2507C2211yescharacteristic
63#2506C2211yescharacteristic
64#2475—21no—
65#2448C2211yescharacteristic
66#2446C2211yescharacteristic
67#2382—21no—
68#2370C2211yescharacteristic
69#2367C2211yescharacteristic
70#2367C2211yescharacteristic
71#2365C2211yescharacteristic
72#2356C2211yescharacteristic
73#2354C2211yescharacteristic
74C4×#125C2211yescharacteristic
75#2298—21no—
76C42×Q8C2211yescharacteristic
77#2101C2211yescharacteristic
78#2100C2211yescharacteristic
79#2097C2211yescharacteristic
80#2097C2211yescharacteristic
81#2097C2211yescharacteristic
82#2097C2211yescharacteristic
83#2096C2211yescharacteristic
84#2093C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic
88#2086C2211yescharacteristic
89#2085C2211yescharacteristic
90#2084C2211yescharacteristic
91#2084C2211yescharacteristic
92#2084C2211yescharacteristic
93#2074C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2066C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic
114#2059C2211yescharacteristic
115#2059C2211yescharacteristic
116#2059C2211yescharacteristic
117#2043C2211yescharacteristic
118#2043C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#1983C2211yescharacteristic
126#1981C2211yescharacteristic
127#1959C2211yescharacteristic
128#1956C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1947C2211yescharacteristic
137#1943C2211yescharacteristic
138#1942C2211yescharacteristic
139#1940C2211yescharacteristic
140#1940C2211yescharacteristic
141#1939C2211yescharacteristic
142#1939C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1919C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1917C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1916C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1862C2211yescharacteristic
189#1847C2211yescharacteristic
190#1846C2211yescharacteristic
191#1831C2211yescharacteristic
192#1831C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1805C2211yescharacteristic
196#1805C2211yescharacteristic
197#1805C2211yescharacteristic
198#1804C2211yescharacteristic
199#1776C2211yescharacteristic
200C4×#106C2211yescharacteristic
201#1762C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—21no—
205C2×#125D411yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#124C2311yescharacteristic
208C2×#124C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2311yescharacteristic
212C2×C4×Q8C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×#117—21no—
215C2×#107C2311yescharacteristic
216C2×#107C2311yescharacteristic
217C2×#107C2311yescharacteristic
218C2×#107C2311yescharacteristic
219C2×#107C2311yescharacteristic
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#107C2311yescharacteristic
223C2×#106C2311yescharacteristic
224C2×#106C2311yescharacteristic
225C2×#106C2311yescharacteristic
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2311yescharacteristic
229C2×#106C2311yescharacteristic
230C2×#106C2311yescharacteristic
231C2×C4⋊C8C2311yescharacteristic
232C2×C4⋊C8C2311yescharacteristic
233C2×C4⋊C8C2311yescharacteristic
234C2×C4⋊C8C2311yescharacteristic
235C2×C4⋊C8C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
264C2×#97C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266C2×C4×C8C2311yescharacteristic
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#400—21no—
273#400—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#400—21no—
285#400—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#396—21no—
302#396—21no—
303#391C2311yescharacteristic
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#390C2311yescharacteristic
310#390C2311yescharacteristic
311#390C2311yescharacteristic
312#390C2311yescharacteristic
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#389D411yescharacteristic
322#389D411yescharacteristic
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#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#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#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#387D411yescharacteristic
392#387D411yescharacteristic
393#385—21no—
394#385—21no—
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#382—21no—
400#382—21no—
401#382—21no—
402#382—21no—
403#382—21no—
404#382D411yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#380—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435#376—21no—
436C43—21no—
437C43C2311yescharacteristic
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#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
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
478C22×Q8C2411yescharacteristic
479C22×Q8C2411yescharacteristic
480C22×D4C2411yescharacteristic
481C23×C4—21no—
482C22×C8C2411yescharacteristic
483C22×C8C2411yescharacteristic
484C22×C8C2411yescharacteristic
485C22×C8C2411yescharacteristic
486C22×C8C2411yescharacteristic
487C22×C8C2411yescharacteristic
488C22×C8C2411yescharacteristic
489C22×C8C2411yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8—41no—
492#125—41no—
493#125—41no—
494#125—42no—
495#125—44no—
496#124—22no—
497#124—41no—
498#124—41no—
499#124—41no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8—41no—
504C4×Q8—41no—
505C4×Q8—41no—
506C4×Q8—41no—
507C4×Q8—41no—
508C4×D4—22no—
509C4×D4—41no—
510#117—44no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
544C2×C4⋊C4C2×D411yescharacteristic
545C2×C4⋊C4C2×D411yescharacteristic
546C2×C4⋊C4C2×D411yescharacteristic
547C2×C4⋊C4C2×D411yescharacteristic
548C2×C4⋊C4C2×D411yescharacteristic
549C2×C4⋊C4C2×D411yescharacteristic
550C2×C4⋊C4C2×D411yescharacteristic
551C2×C4⋊C4C2×D411yescharacteristic
552C2×C4⋊C4C2×D411yescharacteristic
553C2×C4⋊C4C2×D411yescharacteristic
554C2×C4⋊C4C2×D411yescharacteristic
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2411yescharacteristic
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2411yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42—21no—
585C2×C42—21no—
586C2×C42—21no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—21no—
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C2×D411yescharacteristic
595C2×C42C2×D411yescharacteristic
596C2×C42C2×D411yescharacteristic
597C2×C42C2×D411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605#107—22no—
606#107—41no—
607#107—41no—
608#107—41no—
609#107—41no—
610#107—41no—
611#107—41no—
612#107—41no—
613#106—22no—
614#106—41no—
615#106—41no—
616#106—41no—
617#106—41no—
618#106—41no—
619#106—41no—
620#106—41no—
621C4⋊C8—41no—
622C4⋊C8—41no—
623C4⋊C8—41no—
624C4⋊C8—41no—
625C4⋊C8—41no—
626C4⋊C8—41no—
627C4⋊C8—41no—
628C4⋊C8—41no—
629#103—22no—
630#103—22no—
631#103—41no—
632#103—41no—
633#103—41no—
634#103—41no—
635#103—41no—
636#103—41no—
637#103—41no—
638#103—41no—
639#103—41no—
640#103—41no—
641#103—41no—
642#103—41no—
643#103—41no—
644#103—41no—
645#102—41no—
646#102—41no—
647#102—41no—
648#102—41no—
649#102—41no—
650#102—41no—
651#102—41no—
652#102—41no—
653#97—41no—
654#97—41no—
655C4×C8—41no—
656C4×C8—41no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666#95—21no—
667#95—21no—
668#95—21no—
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#95C2×D411yescharacteristic
711#95C2×D411yescharacteristic
712#95C2×D411yescharacteristic
713#95C2×D411yescharacteristic
714#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24—21no—
723C2×Q8—21no—
724C2×Q8—21no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q82−1+412yes—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—81no—
759C22×C4C22×D411yescharacteristic
760C22×C4C22×D411yescharacteristic
761C22×C4C22×D411yescharacteristic
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D411yescharacteristic
773C22×C4C2511yescharacteristic
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—41no—
830C4⋊C4—41no—
831C4⋊C4—41no—
832C4⋊C4—41no—
833C4⋊C4—41no—
834C4⋊C4—41no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—81no—
850C4⋊C4—81no—
851C4⋊C4—81no—
852C4⋊C4—81no—
853C4⋊C4—81no—
854C4⋊C4—81no—
855C4⋊C4—81no—
856C4⋊C4—81no—
857C4⋊C4—81no—
858C4⋊C4—81no—
859C4⋊C4—81no—
860C4⋊C4—81no—
861C4⋊C4—81no—
862C4⋊C4—81no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C42−1+412yes—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—81no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C22⋊C4—81no—
880C22⋊C4—81no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42—21no—
889C42—21no—
890C42—21no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42—41no—
896C42—41no—
897C42—41no—
898C42—41no—
899C42—42no—
900C42—42no—
901C42—42no—
902C42—42no—
903C42—42no—
904C42—42no—
905C42—42no—
906C42—81no—
907C42—81no—
908C42—81no—
909C42—81no—
910C42—81no—
911C42—81no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23C23×D411yescharacteristic
920Q8—22no—
921Q8—22no—
922Q8—41no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
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—84no—
1019C2×C4#57512yes—
1020C2×C4C2×2−1+411yescharacteristic
1021C2×C4C2×2−1+411yescharacteristic
1022C2×C4#58511yescharacteristic
1023C2×C4#58511yescharacteristic
1024C2×C4#58511yescharacteristic
1025C2×C4#58511yescharacteristic
1026C8—41no—
1027C8—41no—
1028C8—41no—
1029C8—41no—
1030C8—41no—
1031C8—41no—
1032C8—41no—
1033C8—41no—
1034C22—81no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—81no—
1040C22—81no—
1041C22#348711yescharacteristic
1042C22#348911yescharacteristic
1043C22#348911yescharacteristic
1044C22C2×#57511yescharacteristic
1045C22#358411yescharacteristic
1046C22#358411yescharacteristic
1047C22#358611yescharacteristic
1048C4—22no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—42no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—41no—
1058C4—42no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—41no—
1063C4—41no—
1064C4—81no—
1065C4—81no—
1066C4—81no—
1067C4—81no—
1068C4—81no—
1069C4—81no—
1070C4—81no—
1071C4—81no—
1072C4—81no—
1073C4—81no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4#353111yescharacteristic
1078C4#355311yescharacteristic
1079C4#356311yescharacteristic
1080C4#356711yescharacteristic
1081C2—161no—
1082C2#4613511yescharacteristic
1083C2#6190811yescharacteristic
1084C2#6191811yescharacteristic
1085C2#6212011yescharacteristic
1086C2#6214111yescharacteristic
1087C2#6217811yescharacteristic
1088C2#6221011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
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. #46191C2semidirect
3. #33071C2semidirect
4. #33071C2semidirect
7. #32496C2semidirect
9. #32403C2semidirect
11. #32365C2semidirect
12. #32350C2semidirect
15. #31987C2semidirect
18. #31575C2semidirect
19. #27387C2semidirect
21. #26884C2semidirect
22. #26867C2semidirect
26. #26757C2semidirect
28. #26531C2semidirect
30. #26095C2semidirect
31. #23370C2semidirect

Maximal subgroups

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

subgroupindex
#461912
#364212
#330712
#328222
#324962
#324752
#324032
#323892
#323652
#323502
#321062
#320852
#319872
#319632
#315912
#315752
#273872
#273652
#268842
#268672
#267792
#267772
#267662
#267572
#265452
#265312
#260982
#260952
#233702