Finite Group Databasebeta

← #7090587

Subgroups — #7090587

Order 512.

1789 conjugacy classes of subgroups.

The subgroup lattice has 1450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59416C211yesmaximal, characteristic, complemented
2#39525C211yesmaximal, characteristic, complemented
3#32662C211yesmaximal, characteristic, complemented
4#32597C211yesmaximal, characteristic, complemented
5#31955C211yesmaximal, characteristic, complemented
6#31309C211yesmaximal, characteristic, complemented
7#31001C211yesmaximal, characteristic, complemented
8#30564C211yesmaximal, characteristic, complemented
9#30468C211yesmaximal, characteristic, complemented
10#30421C211yesmaximal, characteristic, complemented
11#29502C211yesmaximal, characteristic, complemented
12#29496C211yesmaximal, characteristic, complemented
13#28850C211yesmaximal, characteristic, complemented
14#28361C211yesmaximal, characteristic, complemented
15#26971C211yesmaximal, characteristic, complemented
16#26960C211yesmaximal, characteristic, complemented
17#26627C211yesmaximal, characteristic, complemented
18#25787C211yesmaximal, characteristic, complemented
19#25638C211yesmaximal, characteristic, complemented
20#25417C211yesmaximal, characteristic, complemented
21#25160C211yesmaximal, characteristic, complemented
22#25150C211yesmaximal, characteristic, complemented
23#24900C211yesmaximal, characteristic, complemented
24#24450C211yesmaximal, characteristic, complemented
25#24193C211yesmaximal, characteristic, complemented
26#23850C211yesmaximal, characteristic, complemented
27#23796C211yesmaximal, characteristic, complemented
28#23270C211yesmaximal, characteristic, complemented
29#22880C211yesmaximal, characteristic, complemented
30#22449C211yesmaximal, characteristic, complemented
31#22272C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#497C2211yescharacteristic, complemented
36C2×#496C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#470C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#452C2211yescharacteristic, complemented
44C2×#449C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#447C2211yescharacteristic
49C2×C4×SD16C2211yescharacteristic, complemented
50C2×C4×SD16C2211yescharacteristic, complemented
51C2×C4×SD16C2211yescharacteristic, complemented
52C2×C4×D8C2211yescharacteristic
53C2×C4×D8C2211yescharacteristic
54C2×#418C2211yescharacteristic
55#2863C2211yescharacteristic, complemented
56#2797—21no—
57#2752—21no—
58#2751—21no—
59#2714—21no—
60#2687—21no—
61#2685—21no—
62#2631—21no—
63#2592C2211yescharacteristic, complemented
64#2580C2211yescharacteristic
65#2580C2211yescharacteristic, complemented
66#2559—21no—
67#2553—21no—
68#2536C2211yescharacteristic
69#2499C2211yescharacteristic
70#2496C2211yescharacteristic, complemented
71#2480—21no—
72#2476—21no—
73#2472—21no—
74#2467—21no—
75#2444—21no—
76#2435C2211yescharacteristic
77#2432C2211yescharacteristic
78#2431C2211yescharacteristic, complemented
79#2429C2211yescharacteristic
80#2428C2211yescharacteristic
81#2427C2211yescharacteristic
82#2427C2211yescharacteristic
83#2421C2211yescharacteristic
84#2420C2211yescharacteristic
85#2420C2211yescharacteristic, complemented
86#2414C2211yescharacteristic
87#2407C2211yescharacteristic
88#2363C2211yescharacteristic
89#2342—21no—
90#2341C2211yescharacteristic
91#2339C2211yescharacteristic, complemented
92D4×C22⋊C4C2211yescharacteristic
93#2318—21no—
94C4×#127C2211yescharacteristic, complemented
95C4×#124C2211yescharacteristic
96C4×#124C2211yescharacteristic
97C4×#124C2211yescharacteristic
98#2095C2211yescharacteristic, complemented
99#2094C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic, complemented
102#2092C2211yescharacteristic, complemented
103#2085C2211yescharacteristic, complemented
104#2085C2211yescharacteristic, complemented
105#2085C2211yescharacteristic, complemented
106#2077C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2074C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2036C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2014C2211yescharacteristic, complemented
127#2013C2211yescharacteristic, complemented
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2011C2211yescharacteristic
133#2001C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1985C2211yescharacteristic, complemented
139#1984C2211yescharacteristic, complemented
140#1981C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1972C2211yescharacteristic
143#1971C2211yescharacteristic, complemented
144#1969C2211yescharacteristic, complemented
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1961C2211yescharacteristic, complemented
148#1959C2211yescharacteristic
149#1958C2211yescharacteristic
150#1944C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic, complemented
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1873C2211yescharacteristic
181#1870C2211yescharacteristic
182#1869C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic, complemented
189#1854C2211yescharacteristic
190#1836C2211yescharacteristic, complemented
191#1807C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1745C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×#135—24no—
207C2×#135—42no—
208C2×#135—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×M16C2311yescharacteristic
222C23×C8C2311yescharacteristic
223#556—42no—
224#556—42no—
225#546—42no—
226#546—42no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#126—21no—
230C2×#126—21no—
231C2×#126—21no—
232C2×#124D411yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×#117—21no—
264C2×#117C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267#497—42no—
268#496—24no—
269#485—42no—
270#470—42no—
271#468—42no—
272#465—42no—
273#463—42no—
274#463—42no—
275#452—42no—
276#450—42no—
277#449—42no—
278#449—42no—
279#447—24no—
280#447—42no—
281C4×SD16—42no—
282C4×SD16—42no—
283C4×SD16—42no—
284C4×D8—42no—
285C4×D8—42no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#418—42no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341#400—21no—
342#400—21no—
343#399—21no—
344#399—21no—
345#398—21no—
346#398—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#396—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#393—21no—
370#393—21no—
371#393—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#391D411yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390D411yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388D411yescharacteristic
419#388D411yescharacteristic
420#388D411yescharacteristic
421#388D411yescharacteristic
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#384C2311yescharacteristic
450#383—21no—
451#382D411yescharacteristic
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#381—21no—
457#381—21no—
458#380—21no—
459#380—21no—
460#380—21no—
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#379—21no—
466#379—21no—
467#379—21no—
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4—21no—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479C2×#95—21no—
480C43C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505C25—21no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552#135—416no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—41no—
582C2×D8—41no—
583C2×D8—41no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8#4114yes—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8—22no—
593C22×C8—22no—
594C22×C8—41no—
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C4⋊Q8—22no—
604C4⋊Q8—41no—
605#127—22no—
606#127—41no—
607#126—44no—
608#126—44no—
609#126—82no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—22no—
614#124—42no—
615#124—41no—
616#124—41no—
617#124—41no—
618#124—41no—
619#123—44no—
620C22⋊Q8—22no—
621C22⋊Q8—44no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629#121—22no—
630#121—22no—
631#121—44no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121—82no—
639#120—44no—
640C4×Q8—22no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×D4—22no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—44no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—82no—
664#117—44no—
665#117—41no—
666#117—41no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—44no—
741C2×C22⋊C4—44no—
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C22⋊C4C2×D411yescharacteristic
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42C2×D411yescharacteristic
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766#107—41no—
767#107—41no—
768#107—41no—
769#107—41no—
770#106—22no—
771#106—22no—
772#106—41no—
773#106—41no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776#103—22no—
777#103—22no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808C22⋊C8—22no—
809C22⋊C8—22no—
810C22⋊C8—22no—
811C22⋊C8—41no—
812C22⋊C8—41no—
813C22⋊C8—41no—
814#97—22no—
815#97—41no—
816#97—41no—
817C4×C8—22no—
818C4×C8—22no—
819C4×C8—41no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95—21no—
846#95—21no—
847#95—21no—
848#95—21no—
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855#95C2×D411yescharacteristic
856#95C2×D411yescharacteristic
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—42no—
862C24—42no—
863C24—42no—
864C24—81no—
865C24—81no—
866C24—81no—
867C24—81no—
868C24C22×D411yescharacteristic
869C24C22×D411yescharacteristic
870#41—44no—
871#41—44no—
872#41—82no—
873#41—82no—
874#41—82no—
875#41—82no—
876#41—82no—
877#41—82no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—41no—
896C2×Q8—41no—
897C2×Q8—41no—
898C2×Q8H(5,𝔽2)12yes—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—41no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—82no—
939C2×D4—82no—
940C2×D4—82no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4C2×#4112yes—
955C2×D4C2×#4112yes—
956C2×D4H(5,𝔽2)12yes—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4—81no—
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C2511yescharacteristic
1018Q16—44no—
1019Q16—82no—
1020SD16—28no—
1021SD16—44no—
1022SD16—44no—
1023SD16—82no—
1024SD16—82no—
1025SD16—82no—
1026D8—44no—
1027D8—44no—
1028D8—44no—
1029D8—82no—
1030M16—82no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—44no—
1053C2×C8C2×#4112yes—
1054C2×C8H(5,𝔽2)12yes—
1055C2×C8H(5,𝔽2)12yes—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C4⋊C4—81no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C22⋊C4—81no—
1146C22⋊C4—81no—
1147C22⋊C4—81no—
1148C42—22no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—41no—
1160C42—41no—
1161C42—41no—
1162C42—42no—
1163C42—42no—
1164C42—81no—
1165C42—81no—
1166C42—81no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—22no—
1174C23—22no—
1175C23—21no—
1176C23—21no—
1177C23—22no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—84no—
1210C23—84no—
1211C23—84no—
1212C23—162no—
1213C23—162no—
1214C23—162no—
1215C23—162no—
1216C23C23×D411yescharacteristic
1217Q8—22no—
1218Q8—22no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8—41no—
1229Q8—82no—
1230D4—22no—
1231D4—22no—
1232D4—22no—
1233D4—22no—
1234D4—22no—
1235D4—22no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—82no—
1247D4—84no—
1248D4—84no—
1249D4—84no—
1250D4—84no—
1251D4—84no—
1252D4—162no—
1253D4—162no—
1254D4—162no—
1255D4—162no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—162no—
1339C2×C4—162no—
1340C2×C4—162no—
1341C2×C4—162no—
1342C2×C4—162no—
1343C2×C4#57512yes—
1344C2×C4C22×#4111yescharacteristic
1345C2×C4C2×H(5,𝔽2)11yescharacteristic
1346C2×C4C2×H(5,𝔽2)11yescharacteristic
1347C2×C4C2×H(5,𝔽2)11yescharacteristic
1348C2×C4C2×H(5,𝔽2)11yescharacteristic
1349C2×C4#58511yescharacteristic
1350C8—22no—
1351C8—22no—
1352C8—22no—
1353C8—41no—
1354C8—41no—
1355C8—41no—
1356C8—41no—
1357C8—41no—
1358C22—42no—
1359C22—41no—
1360C22—41no—
1361C22—42no—
1362C22—42no—
1363C22—41no—
1364C22—41no—
1365C22—42no—
1366C22—42no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—41no—
1380C22—42no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—168no—
1401C22D4×#4111yescharacteristic
1402C22#348411yescharacteristic
1403C22#349811yescharacteristic
1404C22C2×#57511yescharacteristic
1405C22#358411yescharacteristic
1406C22#358411yescharacteristic
1407C22#358511yescharacteristic
1408C4—22no—
1409C4—41no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—42no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—81no—
1422C4—81no—
1423C4—81no—
1424C4—81no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4#349011yescharacteristic
1433C4#351911yescharacteristic
1434C4#353411yescharacteristic
1435C4#354211yescharacteristic
1436C2—81no—
1437C2—81no—
1438C2—82no—
1439C2—82no—
1440C2—82no—
1441C2—161no—
1442C2#4422811yescharacteristic
1443C2#6144211yescharacteristic
1444C2#6153611yescharacteristic
1445C2#6159911yescharacteristic
1446C2#6169011yescharacteristic
1447C2#6243311yescharacteristic
1448C2#6244911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59416C2semidirect
2. #39525C2semidirect
3. #32662C2semidirect
4. #32597C2semidirect
5. #31955C2semidirect
6. #31309C2semidirect
7. #31001C2semidirect
8. #30564C2semidirect
9. #30468C2semidirect
10. #30421C2semidirect
11. #29502C2semidirect
12. #29496C2semidirect
13. #28850C2semidirect
14. #28361C2semidirect
15. #26971C2semidirect
16. #26960C2semidirect
17. #26627C2semidirect
18. #25787C2semidirect
19. #25638C2semidirect
20. #25417C2semidirect
21. #25160C2semidirect
22. #25150C2semidirect
23. #24900C2semidirect
24. #24450C2semidirect
25. #24193C2semidirect
26. #23850C2semidirect
27. #23796C2semidirect
28. #23270C2semidirect
29. #22880C2semidirect
30. #22449C2semidirect
31. #22272C2semidirect
35. C2×#497C22semidirect
40. C2×#465C22semidirect
43. C2×#452C22semidirect
49. C2×C4×SD16C22semidirect
50. C2×C4×SD16C22semidirect
51. C2×C4×SD16C22semidirect
55. #2863C22semidirect
63. #2592C22semidirect
65. #2580C22semidirect
70. #2496C22semidirect
78. #2431C22semidirect
85. #2420C22semidirect
91. #2339C22semidirect
94. C4×#127C22semidirect
98. #2095C22semidirect
101. #2092C22semidirect
102. #2092C22semidirect
103. #2085C22semidirect
104. #2085C22semidirect
105. #2085C22semidirect
106. #2077C22semidirect
107. #2074C22semidirect
108. #2074C22semidirect
109. #2068C22semidirect
111. #2067C22semidirect
113. #2043C22semidirect
116. #2042C22semidirect
118. #2036C22semidirect
119. #2036C22semidirect
122. #2033C22semidirect
126. #2014C22semidirect
127. #2013C22semidirect
138. #1985C22semidirect
139. #1984C22semidirect
140. #1981C22semidirect
143. #1971C22semidirect
144. #1969C22semidirect
147. #1961C22semidirect
150. #1944C22semidirect
152. #1935C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
158. #1924C22semidirect
160. #1923C22semidirect
161. #1919C22semidirect
164. #1880C22semidirect
165. #1880C22semidirect
166. #1880C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
183. #1865C22semidirect
186. #1863C22semidirect
188. #1862C22semidirect
190. #1836C22semidirect
191. #1807C22semidirect
192. #1805C22semidirect
195. #1788C22semidirect
199. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1745C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#594162
#395252
#326622
#325972
#319552
#313092
#310012
#305642
#304682
#304212
#295022
#294962
#288502
#283612
#269712
#269602
#266272
#257872
#256382
#254172
#251602
#251502
#249002
#244502
#241932
#238502
#237962
#232702
#228802
#224492
#222722