Finite Group Databasebeta

← #6498218

Subgroups — #6498218

Order 512.

1283 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35340C211yesmaximal, characteristic
2#35337C211yesmaximal, characteristic, complemented
3#33211C211yesmaximal, characteristic, complemented
4#33208C211yesmaximal, characteristic, complemented
5#33050C211yesmaximal, characteristic
6#33044C211yesmaximal, characteristic
7#30306C211yesmaximal, characteristic, complemented
8#30282C211yesmaximal, characteristic, complemented
9#30231C211yesmaximal, characteristic, complemented
10#30208C211yesmaximal, characteristic, complemented
11#29589C211yesmaximal, characteristic, complemented
12#29588C211yesmaximal, characteristic, complemented
13#29585C211yesmaximal, characteristic, complemented
14#29584C211yesmaximal, characteristic, complemented
15#29527C211yesmaximal, characteristic, complemented
16#29526C211yesmaximal, characteristic, complemented
17#29525C211yesmaximal, characteristic, complemented
18#29524C211yesmaximal, characteristic, complemented
19#29175C211yesmaximal, characteristic
20#29174C211yesmaximal, characteristic
21#29171C211yesmaximal, characteristic, complemented
22#29170C211yesmaximal, characteristic, complemented
23#27872C211yesmaximal, characteristic, complemented
24#27871C211yesmaximal, characteristic
25#27868C211yesmaximal, characteristic
26#27867C211yesmaximal, characteristic, complemented
27#22249C211yesmaximal, characteristic, complemented
28#22249C211yesmaximal, characteristic, complemented
29#22222C211yesmaximal, characteristic, complemented
30#22222C211yesmaximal, characteristic, complemented
31#20366C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2861C2211yescharacteristic
41#2859C2211yescharacteristic
42#2851C2211yescharacteristic
43#2851C2211yescharacteristic
44#2851C2211yescharacteristic
45#2850C2211yescharacteristic
46#2647C2211yescharacteristic
47#2647C2211yescharacteristic
48#2645C2211yescharacteristic
49#2644C2211yescharacteristic
50#2628C2211yescharacteristic
51#2628C2211yescharacteristic
52#2625C2211yescharacteristic
53#2624C2211yescharacteristic
54#2597—21no—
55#2596—21no—
56#2595—21no—
57#2594—21no—
58#2589—21no—
59#2589—21no—
60#2589—21no—
61#2589—21no—
62#2588—21no—
63#2588—21no—
64#2588—21no—
65#2588—21no—
66#2578—21no—
67#2577—21no—
68#2576—21no—
69#2575—21no—
70#2331C2211yescharacteristic
71#2331C2211yescharacteristic
72#2324C2211yescharacteristic
73#2323C2211yescharacteristic
74#2320C2211yescharacteristic
75#2319C2211yescharacteristic
76#2314C2211yescharacteristic
77#2314C2211yescharacteristic
78C4×#125C2211yescharacteristic
79C4×#125C2211yescharacteristic
80C4×#125C2211yescharacteristic
81C4×#124C2211yescharacteristic
82C4×#117C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2100C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2097C2211yescharacteristic
92#2097C2211yescharacteristic
93#2096C2211yescharacteristic
94#2095C2211yescharacteristic
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#2024C2211yescharacteristic
112#2024C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#1991C2211yescharacteristic
116#1991C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1991C2211yescharacteristic
120#1991C2211yescharacteristic
121#1958C2211yescharacteristic
122#1958C2211yescharacteristic
123#1944C2211yescharacteristic
124#1944C2211yescharacteristic
125#1943C2211yescharacteristic
126#1943C2211yescharacteristic
127#1942C2211yescharacteristic
128#1942C2211yescharacteristic
129#1941C2211yescharacteristic
130#1941C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic
138#1933C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic
166#1894C2211yescharacteristic
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1846C2211yescharacteristic
180#1846C2211yescharacteristic
181#1835C2211yescharacteristic
182#1835C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1746C2211yescharacteristic
192#1746C2211yescharacteristic
193#1746C2211yescharacteristic
194#1746C2211yescharacteristic
195#1744C2211yescharacteristic
196#1744C2211yescharacteristic
197#1744C2211yescharacteristic
198#1744C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C22×C42C2311yescharacteristic
220#499—24no—
221#499—24no—
222#488—24no—
223#488—24no—
224C2×#107C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C4×M16—24no—
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×C4×C8—24no—
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262C2×C4×C8C2311yescharacteristic
263C2×C4×C8C2311yescharacteristic
264C2×C4×C8C2311yescharacteristic
265C2×C4×C8C2311yescharacteristic
266#401—21no—
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#399—21no—
278#399—21no—
279#399—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#397—21no—
286#397—21no—
287#397—21no—
288#397—21no—
289#397—21no—
290#397—21no—
291#396—21no—
292#395—21no—
293#395—21no—
294#394—21no—
295#394—21no—
296#393—21no—
297#393—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#391C2311yescharacteristic
307#391C2311yescharacteristic
308#391C2311yescharacteristic
309#391C2311yescharacteristic
310#390—21no—
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#389—21no—
316#389—21no—
317#389—21no—
318#389—21no—
319#389—21no—
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
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#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
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#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#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#386—21no—
381#386—21no—
382#386—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#383—21no—
393#382—21no—
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#381—21no—
403#380—21no—
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4D411yescharacteristic
417C4×C4⋊C4D411yescharacteristic
418C4×C4⋊C4D411yescharacteristic
419C4×C4⋊C4D411yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4D411yescharacteristic
429C4×C22⋊C4D411yescharacteristic
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432#376C2311yescharacteristic
433#376C2311yescharacteristic
434C43C2311yescharacteristic
435C43C2311yescharacteristic
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—21no—
485C22×Q8—21no—
486C22×Q8C2411yescharacteristic
487C22×D4—21no—
488C22×D4C2411yescharacteristic
489C23×C4—21no—
490C23×C4C2×D411yescharacteristic
491C23×C4C2×D411yescharacteristic
492C23×C4C2411yescharacteristic
493C2×M16—22no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—41no—
498C2×M16—41no—
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—41no—
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#125—22no—
518#125—22no—
519#125—22no—
520#125—22no—
521#125—22no—
522#125—22no—
523#124—22no—
524#124—22no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527#121—22no—
528#121—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—41no—
532C4×D4—41no—
533#117—22no—
534#117—22no—
535#117—41no—
536#117—41no—
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⋊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⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
605C2×C22⋊C4C2×D411yescharacteristic
606C2×C22⋊C4C2×D411yescharacteristic
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633#107—22no—
634#107—22no—
635#107—22no—
636#107—22no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#106—22no—
642#106—22no—
643#106—22no—
644#106—22no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#103—22no—
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#103—41no—
656#103—41no—
657#102—22no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665#97—22no—
666#97—22no—
667C4×C8—22no—
668C4×C8—22no—
669C4×C8—22no—
670C4×C8—22no—
671C4×C8#4114yes—
672C4×C8#4114yes—
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#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728#95C2×D411yescharacteristic
729#95C2×D411yescharacteristic
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733C24—21no—
734C24C22×D411yescharacteristic
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—42no—
742C2×Q8—42no—
743C2×Q8—81no—
744C2×Q8—81no—
745C2×Q8—81no—
746C2×Q8—81no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—42no—
754C2×D4—81no—
755C2×D4—81no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
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—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—42no—
782C22×C4—81no—
783C22×C4—81no—
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C22×D411yescharacteristic
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C42−1+412yes—
798C22×C42−1+412yes—
799C22×C4C2511yescharacteristic
800M16—44no—
801M16—44no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
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—44no—
823C2×C8—44no—
824C2×C8C2×#4112yes—
825C2×C8C2×#4112yes—
826C2×C8C2×#4112yes—
827C2×C8C2×#4112yes—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
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—41no—
859C4⋊C4—41no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
877C4⋊C4—81no—
878C4⋊C4—81no—
879C4⋊C4—81no—
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—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—41no—
893C22⋊C4—41no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—81no—
900C22⋊C4—81no—
901C22⋊C4—81no—
902C22⋊C4—81no—
903C22⋊C4—81no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
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—41no—
926C42—41no—
927C42—41no—
928C42—41no—
929C42—41no—
930C42—41no—
931C42—41no—
932C42—41no—
933C42—42no—
934C42—81no—
935C42—81no—
936C42—81no—
937C42—81no—
938C42—81no—
939C42—81no—
940C42C2×#4112yes—
941C42C2×#4112yes—
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23#53612yes—
956C23C23×D411yescharacteristic
957Q8—41no—
958Q8—41no—
959Q8—41no—
960Q8—41no—
961Q8—162no—
962Q8—162no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—162no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
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—21no—
1008C2×C4—44no—
1009C2×C4—44no—
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—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—162no—
1056C2×C4#53212yes—
1057C2×C4#53212yes—
1058C2×C4#53612yes—
1059C2×C4C22×#4111yescharacteristic
1060C2×C4C22×#4111yescharacteristic
1061C2×C4C2×2−1+411yescharacteristic
1062C2×C4C2×2−1+411yescharacteristic
1063C2×C4#58511yescharacteristic
1064C2×C4#58511yescharacteristic
1065C8—22no—
1066C8—22no—
1067C8—22no—
1068C8—22no—
1069C8—41no—
1070C8—41no—
1071C8—41no—
1072C8—41no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—41no—
1077C22—41no—
1078C22—41no—
1079C22—41no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22C2×#53211yescharacteristic
1088C22C2×#53611yescharacteristic
1089C22#344911yescharacteristic
1090C22#358411yescharacteristic
1091C22#358411yescharacteristic
1092C22#358411yescharacteristic
1093C22#358411yescharacteristic
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4—81no—
1121C4—81no—
1122C4#349511yescharacteristic
1123C4#349511yescharacteristic
1124C4#349511yescharacteristic
1125C4#349511yescharacteristic
1126C2—42no—
1127C2—161no—
1128C2#3532611yescharacteristic
1129C2#6068211yescharacteristic
1130C2#6068511yescharacteristic
1131C2#6087911yescharacteristic
1132C2#6088211yescharacteristic
1133C2#6100711yescharacteristic
1134C2#6101011yescharacteristic
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
2. #35337C2semidirect
3. #33211C2semidirect
4. #33208C2semidirect
7. #30306C2semidirect
8. #30282C2semidirect
9. #30231C2semidirect
10. #30208C2semidirect
11. #29589C2semidirect
12. #29588C2semidirect
13. #29585C2semidirect
14. #29584C2semidirect
15. #29527C2semidirect
16. #29526C2semidirect
17. #29525C2semidirect
18. #29524C2semidirect
21. #29171C2semidirect
22. #29170C2semidirect
23. #27872C2semidirect
26. #27867C2semidirect
27. #22249C2semidirect
28. #22249C2semidirect
29. #22222C2semidirect
30. #22222C2semidirect
31. #20366C2semidirect

Maximal subgroups

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

subgroupindex
#353402
#353372
#332112
#332082
#330502
#330442
#303062
#302822
#302312
#302082
#295892
#295882
#295852
#295842
#295272
#295262
#295252
#295242
#291752
#291742
#291712
#291702
#278722
#278712
#278682
#278672
#222492
#222222
#203662