Finite Group Databasebeta

← #7308412

Subgroups — #7308412

Order 512.

1787 conjugacy classes of subgroups.

The subgroup lattice has 1453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59093C211yesmaximal, characteristic, complemented
2#40169C211yesmaximal, characteristic, complemented
3#32188C211yesmaximal, characteristic, complemented
4#32123C211yesmaximal, characteristic, complemented
5#31804C211yesmaximal, characteristic, complemented
6#31653C211yesmaximal, characteristic, complemented
7#31515C211yesmaximal, characteristic, complemented
8#31400C211yesmaximal, characteristic, complemented
9#31217C211yesmaximal, characteristic, complemented
10#31032C211yesmaximal, characteristic, complemented
11#30526C211yesmaximal, characteristic, complemented
12#30524C211yesmaximal, characteristic, complemented
13#30452C211yesmaximal, characteristic, complemented
14#30445C211yesmaximal, characteristic, complemented
15#29719C211yesmaximal, characteristic, complemented
16#29667C211yesmaximal, characteristic, complemented
17#28115C211yesmaximal, characteristic, complemented
18#27526C211yesmaximal, characteristic, complemented
19#27224C211yesmaximal, characteristic, complemented
20#26927C211yesmaximal, characteristic, complemented
21#26908C211yesmaximal, characteristic, complemented
22#26723C211yesmaximal, characteristic, complemented
23#26615C211yesmaximal, characteristic, complemented
24#25373C211yesmaximal, characteristic, complemented
25#25326C211yesmaximal, characteristic, complemented
26#24373C211yesmaximal, characteristic, complemented
27#24366C211yesmaximal, characteristic, complemented
28#24258C211yesmaximal, characteristic, complemented
29#24152C211yesmaximal, characteristic, complemented
30#23866C211yesmaximal, characteristic, complemented
31#23316C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#532C2211yescharacteristic, complemented
35C2×#495C2211yescharacteristic
36C2×#488C2211yescharacteristic, complemented
37C2×#481C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#464C2211yescharacteristic, complemented
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#459C2211yescharacteristic
45C2×#452C2211yescharacteristic
46C2×#451C2211yescharacteristic, complemented
47C2×#448C2211yescharacteristic
48C2×#448C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#447C2211yescharacteristic
51C2×#441C2211yescharacteristic, complemented
52#2850C2211yescharacteristic
53#2779—21no—
54#2749—21no—
55#2735—21no—
56#2712—21no—
57#2700—21no—
58#2697—21no—
59#2636—21no—
60#2566C2211yescharacteristic
61#2544C2211yescharacteristic, complemented
62#2543—21no—
63#2538C2211yescharacteristic
64#2518—21no—
65#2512C2211yescharacteristic
66#2495C2211yescharacteristic
67#2492C2211yescharacteristic
68#2490C2211yescharacteristic
69#2489C2211yescharacteristic
70#2480—21no—
71#2459—21no—
72#2451C2211yescharacteristic, complemented
73#2450—21no—
74#2448C2211yescharacteristic
75#2447C2211yescharacteristic, complemented
76#2444—21no—
77#2436C2211yescharacteristic, complemented
78#2435C2211yescharacteristic
79#2431C2211yescharacteristic
80#2430—21no—
81#2427C2211yescharacteristic
82#2427C2211yescharacteristic
83#2416C2211yescharacteristic
84#2408C2211yescharacteristic
85#2367C2211yescharacteristic
86#2367C2211yescharacteristic, complemented
87#2361C2211yescharacteristic, complemented
88#2339—21no—
89#2339C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2321—21no—
92C4×#123C2211yescharacteristic
93C4×#121C2211yescharacteristic
94C2×#391C2211yescharacteristic, complemented
95#2099C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2074C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic, complemented
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic, complemented
120#2034C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2014C2211yescharacteristic, complemented
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2011C2211yescharacteristic
135#2001C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#2000C2211yescharacteristic, complemented
139#1999C2211yescharacteristic
140#1999C2211yescharacteristic
141#1999C2211yescharacteristic
142#1999C2211yescharacteristic
143#1989C2211yescharacteristic, complemented
144#1987C2211yescharacteristic, complemented
145#1983C2211yescharacteristic, complemented
146#1982C2211yescharacteristic, complemented
147#1972C2211yescharacteristic
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic, complemented
150#1959C2211yescharacteristic, complemented
151#1955C2211yescharacteristic
152#1939C2211yescharacteristic, complemented
153#1939C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1919C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1895C2211yescharacteristic
170#1894C2211yescharacteristic
171#1894C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1874C2211yescharacteristic
183#1872C2211yescharacteristic, complemented
184#1870C2211yescharacteristic
185#1865C2211yescharacteristic, complemented
186#1864C2211yescharacteristic, complemented
187#1864C2211yescharacteristic, complemented
188#1864C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1851C2211yescharacteristic
191#1824C2211yescharacteristic, complemented
192#1804C2211yescharacteristic, complemented
193#1804C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1797C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1787C2211yescharacteristic, complemented
200#1786C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×Q8C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C2×AGL(1,ℤ/8)—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×M16C2311yescharacteristic
223#548—42no—
224#548—42no—
225#532—42no—
226#532—42no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#126—21no—
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124—21no—
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#123D411yescharacteristic
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#120—21no—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#495—42no—
268#488—42no—
269#481—42no—
270#476—42no—
271#464—42no—
272#463—42no—
273#463—42no—
274#463—42no—
275#463—42no—
276#459—42no—
277#452—42no—
278#451—42no—
279#450—42no—
280#448—42no—
281#448—42no—
282#447—42no—
283#441—42no—
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#395—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#393—21no—
368#393—21no—
369#393—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#391—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#389—21no—
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
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#388D411yescharacteristic
416#388D411yescharacteristic
417#387—21no—
418#387D411yescharacteristic
419#387D411yescharacteristic
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—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#386D411yescharacteristic
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385D411yescharacteristic
445#384C2311yescharacteristic
446#383—21no—
447#382—21no—
448#382C2311yescharacteristic
449#381—21no—
450#381—21no—
451#381D411yescharacteristic
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461#379—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C2×#95—21no—
474C2×#95—21no—
475C2×#95—21no—
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—44no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—44no—
511C2×#41—82no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—22no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—22no—
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×D4—41no—
538C22×D4C2×D411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4C2×D411yescharacteristic
552C23×C4C2×D411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555AGL(1,ℤ/8)—416no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—41no—
568C2×SD16—41no—
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×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8—41no—
589C2×D8—41no—
590C2×D8—41no—
591C2×D8—41no—
592C2×M16—41no—
593C2×M16—41no—
594C2×M16—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—82no—
608#125—41no—
609#125—41no—
610#124—22no—
611#124—22no—
612#124—22no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—41no—
618#124—41no—
619#124—41no—
620#124—44no—
621#124—44no—
622#123—42no—
623C22⋊Q8—22no—
624C22⋊Q8—44no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630#121—22no—
631#121—22no—
632#121—22no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—44no—
637#121—44no—
638#121—41no—
639#121—41no—
640#121—41no—
641#121—41no—
642#121—82no—
643#120—44no—
644C4×Q8—22no—
645C4×Q8—41no—
646C4×Q8—41no—
647C4×Q8—41no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—44no—
661C4×D4—44no—
662C4×D4—82no—
663C4×D4—82no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
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—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
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—82no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—41no—
753C2×C42—41no—
754C2×C42C2×D411yescharacteristic
755C2×C42C2×D411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761#106—22no—
762#106—41no—
763#106—41no—
764#106—41no—
765C4⋊C8—41no—
766C4⋊C8—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771C4⋊C8—41no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
776#103—41no—
777#103—41no—
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#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802#102—41no—
803#102—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C22⋊C8—41no—
808C22⋊C8—41no—
809C22⋊C8—41no—
810C22⋊C8—41no—
811#97—41no—
812C4×C8—41no—
813C4×C8—41no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
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#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—42no—
858C24—42no—
859C24—81no—
860C24—81no—
861C24—81no—
862C24—81no—
863C24—81no—
864C24C22×D411yescharacteristic
865C24C22×D411yescharacteristic
866#41—44no—
867#41—82no—
868#41—82no—
869#41—82no—
870#41—816no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
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—42no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8—82no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8—82no—
898C2×Q8H(5,𝔽2)12yes—
899C2×D4—24no—
900C2×D4—22no—
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—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—41no—
924C2×D4—41no—
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—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—81no—
954C2×D4—81no—
955C2×D4H(5,𝔽2)12yes—
956C2×D4H(5,𝔽2)12yes—
957C22×C4—22no—
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—22no—
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—21no—
982C22×C4—21no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
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×C4—81no—
1006C22×C4—81no—
1007C22×C4—81no—
1008C22×C4—81no—
1009C22×C4—81no—
1010C22×C4—81no—
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C2511yescharacteristic
1024Q16—44no—
1025Q16—82no—
1026SD16—44no—
1027SD16—44no—
1028SD16—82no—
1029SD16—82no—
1030SD16—82no—
1031SD16—82no—
1032D8—44no—
1033D8—44no—
1034D8—82no—
1035D8—82no—
1036M16—44no—
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—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C4⋊C4—22no—
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—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
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—
1095C4⋊C4—81no—
1096C4⋊C4—81no—
1097C4⋊C4—81no—
1098C4⋊C4H(5,𝔽2)12yes—
1099C22⋊C4—24no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—41no—
1107C22⋊C4—41no—
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—42no—
1122C22⋊C4—42no—
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—
1148C22⋊C4—81no—
1149C22⋊C4—81no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—21no—
1155C42—21no—
1156C42—21no—
1157C42—21no—
1158C42—21no—
1159C42—21no—
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—21no—
1174C23—21no—
1175C23—22no—
1176C23—21no—
1177C23—22no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—41no—
1183C23—41no—
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—84no—
1209C23—84no—
1210C23—162no—
1211C23—162no—
1212C23—162no—
1213C23—162no—
1214C23—162no—
1215C23#57512yes—
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—84no—
1230Q8—84no—
1231D4—22no—
1232D4—22no—
1233D4—22no—
1234D4—22no—
1235D4—48no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—84no—
1249D4—82no—
1250D4—84no—
1251D4—84no—
1252D4—84no—
1253D4—84no—
1254D4—84no—
1255D4—162no—
1256D4—162no—
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—22no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—21no—
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—21no—
1293C2×C4—21no—
1294C2×C4—44no—
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—41no—
1336C2×C4—41no—
1337C2×C4—82no—
1338C2×C4—84no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—84no—
1342C2×C4—162no—
1343C2×C4—162no—
1344C2×C4—162no—
1345C2×C4—162no—
1346C2×C4#57712yes—
1347C2×C4C2×H(5,𝔽2)11yescharacteristic
1348C2×C4C2×H(5,𝔽2)11yescharacteristic
1349C2×C4C2×H(5,𝔽2)11yescharacteristic
1350C2×C4C2×H(5,𝔽2)11yescharacteristic
1351C2×C4#58511yescharacteristic
1352C2×C4#58511yescharacteristic
1353C8—41no—
1354C8—41no—
1355C8—41no—
1356C8—41no—
1357C8—41no—
1358C8—41no—
1359C8—41no—
1360C8—41no—
1361C22—22no—
1362C22—22no—
1363C22—22no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—42no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—42no—
1374C22—42no—
1375C22—41no—
1376C22—42no—
1377C22—41no—
1378C22—41no—
1379C22—42no—
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—81no—
1401C22—81no—
1402C22—81no—
1403C22—168no—
1404C22#348411yescharacteristic
1405C22#348811yescharacteristic
1406C22#348811yescharacteristic
1407C22C2×#57511yescharacteristic
1408C22C2×#57711yescharacteristic
1409C22#358411yescharacteristic
1410C22#358511yescharacteristic
1411C4—22no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—42no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—41no—
1424C4—42no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4—81no—
1433C4—81no—
1434C4—81no—
1435C4#353211yescharacteristic
1436C4#354211yescharacteristic
1437C4#355811yescharacteristic
1438C4#356011yescharacteristic
1439C2—42no—
1440C2—81no—
1441C2—82no—
1442C2—82no—
1443C2—161no—
1444C2—161no—
1445C2#4784411yescharacteristic
1446C2#6158111yescharacteristic
1447C2#6164111yescharacteristic
1448C2#6197811yescharacteristic
1449C2#6199211yescharacteristic
1450C2#6204511yescharacteristic
1451C2#6204711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59093C2semidirect
2. #40169C2semidirect
3. #32188C2semidirect
4. #32123C2semidirect
5. #31804C2semidirect
6. #31653C2semidirect
7. #31515C2semidirect
8. #31400C2semidirect
9. #31217C2semidirect
10. #31032C2semidirect
11. #30526C2semidirect
12. #30524C2semidirect
13. #30452C2semidirect
14. #30445C2semidirect
15. #29719C2semidirect
16. #29667C2semidirect
17. #28115C2semidirect
18. #27526C2semidirect
19. #27224C2semidirect
20. #26927C2semidirect
21. #26908C2semidirect
22. #26723C2semidirect
23. #26615C2semidirect
24. #25373C2semidirect
25. #25326C2semidirect
26. #24373C2semidirect
27. #24366C2semidirect
28. #24258C2semidirect
29. #24152C2semidirect
30. #23866C2semidirect
31. #23316C2semidirect
34. C2×#532C22semidirect
36. C2×#488C22semidirect
39. C2×#464C22semidirect
46. C2×#451C22semidirect
51. C2×#441C22semidirect
61. #2544C22semidirect
72. #2451C22semidirect
75. #2447C22semidirect
77. #2436C22semidirect
86. #2367C22semidirect
87. #2361C22semidirect
94. C2×#391C22semidirect
95. #2099C22semidirect
96. #2088C22semidirect
99. #2074C22semidirect
100. #2074C22semidirect
101. #2071C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
107. #2056C22semidirect
116. #2042C22semidirect
119. #2034C22semidirect
120. #2034C22semidirect
121. #2026C22semidirect
122. #2025C22semidirect
123. #2024C22semidirect
128. #2015C22semidirect
129. #2014C22semidirect
137. #2000C22semidirect
138. #2000C22semidirect
143. #1989C22semidirect
144. #1987C22semidirect
145. #1983C22semidirect
146. #1982C22semidirect
149. #1968C22semidirect
150. #1959C22semidirect
152. #1939C22semidirect
153. #1939C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
166. #1919C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
174. #1880C22semidirect
183. #1872C22semidirect
185. #1865C22semidirect
186. #1864C22semidirect
187. #1864C22semidirect
188. #1864C22semidirect
191. #1824C22semidirect
192. #1804C22semidirect
193. #1804C22semidirect
194. #1803C22semidirect
195. #1797C22semidirect
196. #1797C22semidirect
199. #1787C22semidirect
202. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#590932
#401692
#321882
#321232
#318042
#316532
#315152
#314002
#312172
#310322
#305262
#305242
#304522
#304452
#297192
#296672
#281152
#275262
#272242
#269272
#269082
#267232
#266152
#253732
#253262
#243732
#243662
#242582
#241522
#238662
#233162