Finite Group Databasebeta

← #6675131

Subgroups — #6675131

Order 512.

1876 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3222C211yesmaximal, characteristic
2C2×#3107C211yesmaximal, characteristic, complemented
3#37793C211yesmaximal, characteristic, complemented
4#35254C211yesmaximal, characteristic
5#33011C211yesmaximal, characteristic, complemented
6#31226C211yesmaximal, characteristic, complemented
7#31214C211yesmaximal, characteristic, complemented
8#31166C211yesmaximal, characteristic, complemented
9#31163C211yesmaximal, characteristic, complemented
10#30825C211yesmaximal, characteristic, complemented
11#30812C211yesmaximal, characteristic, complemented
12#30760C211yesmaximal, characteristic, complemented
13#30741C211yesmaximal, characteristic, complemented
14#29726C211yesmaximal, characteristic, complemented
15#29632C211yesmaximal, characteristic
16#28320C211yesmaximal, characteristic, complemented
17#28130C211yesmaximal, characteristic, complemented
18#26825C211yesmaximal, characteristic, complemented
19#26823C211yesmaximal, characteristic, complemented
20#26591C211yesmaximal, characteristic, complemented
21#26588C211yesmaximal, characteristic, complemented
22#26259C211yesmaximal, characteristic, complemented
23#26250C211yesmaximal, characteristic, complemented
24#26173C211yesmaximal, characteristic, complemented
25#26159C211yesmaximal, characteristic, complemented
26#24619C211yesmaximal, characteristic, complemented
27#24501C211yesmaximal, characteristic, complemented
28#24072C211yesmaximal, characteristic, complemented
29#23933C211yesmaximal, characteristic, complemented
30#22604C211yesmaximal, characteristic, complemented
31#22059C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36#3222—28no—
37C2×#497C2211yescharacteristic
38C2×#492C2211yescharacteristic
39C2×#490C2211yescharacteristic
40C2×#488C2211yescharacteristic
41#3107—28no—
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#485C2211yescharacteristic
45C2×#475C2211yescharacteristic, complemented
46C2×#474C2211yescharacteristic, complemented
47C2×#464C2211yescharacteristic
48C2×#464C2211yescharacteristic
49C2×#462C2211yescharacteristic, complemented
50C2×#460C2211yescharacteristic
51C2×#460C2211yescharacteristic
52C2×#461C2211yescharacteristic, complemented
53C2×#452C2211yescharacteristic
54C2×#452C2211yescharacteristic
55C2×#452C2211yescharacteristic
56C2×#450C2211yescharacteristic
57C2×#450C2211yescharacteristic
58C2×#450C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic, complemented
60C2×C4×Q16C2211yescharacteristic, complemented
61C2×C4×SD16C2211yescharacteristic, complemented
62C2×C4×SD16C2211yescharacteristic, complemented
63C2×#433C2211yescharacteristic
64C2×#431C2211yescharacteristic
65#2855C2211yescharacteristic
66#2854—21no—
67#2854—21no—
68#2726—21no—
69#2719—21no—
70#2698—21no—
71#2689—21no—
72#2625C2211yescharacteristic
73#2624—21no—
74#2624—21no—
75#2621C2211yescharacteristic
76#2550C2211yescharacteristic, complemented
77#2546C2211yescharacteristic, complemented
78#2478—21no—
79#2478—21no—
80#2462—21no—
81#2453—21no—
82#2453C2211yescharacteristic, complemented
83#2451C2211yescharacteristic, complemented
84#2448C2211yescharacteristic
85#2448C2211yescharacteristic
86#2448C2211yescharacteristic
87#2448C2211yescharacteristic
88#2446C2211yescharacteristic, complemented
89#2446C2211yescharacteristic, complemented
90#2445C2211yescharacteristic
91#2445C2211yescharacteristic
92#2445C2211yescharacteristic
93#2445C2211yescharacteristic
94#2418—21no—
95#2418—21no—
96#2418—21no—
97#2418—21no—
98#2365C2211yescharacteristic, complemented
99#2351C2211yescharacteristic, complemented
100#2323C2211yescharacteristic
101#2316C2211yescharacteristic
102#2311C2211yescharacteristic
103#2309C2211yescharacteristic
104#2296C2211yescharacteristic
105C2×#390C2211yescharacteristic
106#2092C2211yescharacteristic
107#2092C2211yescharacteristic
108#2088C2211yescharacteristic, complemented
109#2087C2211yescharacteristic, complemented
110#2074C2211yescharacteristic, complemented
111#2073C2211yescharacteristic, complemented
112#2067C2211yescharacteristic
113#2066C2211yescharacteristic, complemented
114#2066C2211yescharacteristic, complemented
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2056C2211yescharacteristic, complemented
121#2056C2211yescharacteristic, complemented
122#2055C2211yescharacteristic
123#2055C2211yescharacteristic
124#2055C2211yescharacteristic
125#2055C2211yescharacteristic
126#2055C2211yescharacteristic, complemented
127#2055C2211yescharacteristic, complemented
128#2043C2211yescharacteristic, complemented
129#2043C2211yescharacteristic, complemented
130#2042C2211yescharacteristic
131#2042C2211yescharacteristic
132#2041C2211yescharacteristic
133#2041C2211yescharacteristic
134#2023C2211yescharacteristic
135#2023C2211yescharacteristic
136#2016C2211yescharacteristic, complemented
137#2015C2211yescharacteristic
138#2015C2211yescharacteristic
139#2014C2211yescharacteristic
140#2014C2211yescharacteristic
141#2013C2211yescharacteristic
142#2013C2211yescharacteristic
143#2013C2211yescharacteristic
144#2013C2211yescharacteristic
145#2013C2211yescharacteristic, complemented
146#1973C2211yescharacteristic
147#1973C2211yescharacteristic
148#1971C2211yescharacteristic, complemented
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic
151#1968C2211yescharacteristic
152#1968C2211yescharacteristic
153#1968C2211yescharacteristic, complemented
154#1944C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1940C2211yescharacteristic, complemented
157#1939C2211yescharacteristic, complemented
158#1936C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1933C2211yescharacteristic, complemented
163#1933C2211yescharacteristic, complemented
164#1927C2211yescharacteristic, complemented
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic, complemented
167#1925C2211yescharacteristic
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic, complemented
179#1878C2211yescharacteristic, complemented
180#1878C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1877C2211yescharacteristic, complemented
183#1877C2211yescharacteristic, complemented
184#1872C2211yescharacteristic
185#1872C2211yescharacteristic
186#1872C2211yescharacteristic
187#1865C2211yescharacteristic, complemented
188#1865C2211yescharacteristic, complemented
189#1865C2211yescharacteristic, complemented
190#1864C2211yescharacteristic, complemented
191#1863C2211yescharacteristic, complemented
192#1863C2211yescharacteristic, complemented
193#1863C2211yescharacteristic, complemented
194#1862C2211yescharacteristic, complemented
195#1853C2211yescharacteristic
196#1825C2211yescharacteristic
197#1818C2211yescharacteristic
198#1817C2211yescharacteristic
199#1798C2211yescharacteristic
200#1788C2211yescharacteristic
201#1786C2211yescharacteristic
202#1771C2211yescharacteristic, complemented
203C8×C4⋊C4C2211yescharacteristic, complemented
204#1750C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219#541—24no—
220#541—42no—
221#535—24no—
222#535—42no—
223#533—24no—
224#533—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#126—21no—
232C2×#126—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×#121—21no—
248C2×#121—21no—
249C2×#120—21no—
250C2×#120—21no—
251C4×#41—24no—
252C4×#41—42no—
253C2×C4×Q8—21no—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C2×#117—21no—
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C22⋊C4—21no—
272C22×C22⋊C4—21no—
273C22×C42—21no—
274C22×C42C2311yescharacteristic
275#497—24no—
276#492—24no—
277#490—24no—
278#488—24no—
279#485—24no—
280#485—24no—
281#485—42no—
282#475—24no—
283#474—24no—
284#464—24no—
285#464—24no—
286#462—24no—
287#461—24no—
288#460—24no—
289#460—24no—
290#452—24no—
291#452—24no—
292#452D418yes—
293#450—24no—
294#450—24no—
295#450—42no—
296C4×Q16—24no—
297C4×Q16—24no—
298C4×SD16—24no—
299C4×SD16—24no—
300#433—24no—
301#431—24no—
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×C22⋊C8C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351C2×C22⋊C8C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358#400—21no—
359#400—21no—
360#400—21no—
361#400—21no—
362#399—21no—
363#399—21no—
364#399—21no—
365#399—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398—21no—
376#397—21no—
377#397—21no—
378#397—21no—
379#397—21no—
380#397—21no—
381#397—21no—
382#397—21no—
383#397—21no—
384#395—21no—
385#395—21no—
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#394—21no—
391#394—21no—
392#394—21no—
393#394—21no—
394#391—21no—
395#391—21no—
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#390—21no—
406#390—21no—
407#390—21no—
408#390—21no—
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389D411yescharacteristic
430#389D411yescharacteristic
431#389D411yescharacteristic
432#389D411yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#389C2311yescharacteristic
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#388—21no—
443#388—21no—
444#388—21no—
445#388—21no—
446#388—21no—
447#388—21no—
448#388—21no—
449#388—21no—
450#388—21no—
451#388—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#387—21no—
459#387—21no—
460#387—21no—
461#387—21no—
462#387—21no—
463#386—21no—
464#386—21no—
465#386—21no—
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#385D411yescharacteristic
471#385D411yescharacteristic
472#385D411yescharacteristic
473#385D411yescharacteristic
474#382—21no—
475#382C2311yescharacteristic
476#381—21no—
477#380—21no—
478#380—21no—
479#380—21no—
480#380—21no—
481#380C2311yescharacteristic
482#379—21no—
483#379—21no—
484C4×C4⋊C4—21no—
485C4×C4⋊C4—21no—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41C2×D414yes—
522C22×Q8—21no—
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—22no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2×D411yescharacteristic
547C23×C4C2×D411yescharacteristic
548C23×C4C2411yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16C2×D414yes—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
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×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16C2×D414yes—
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—22no—
595C4⋊Q8—22no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600C4⋊Q8—41no—
601#127—22no—
602#127—22no—
603#127—41no—
604#127—41no—
605#126—44no—
606#126—44no—
607#125—22no—
608#125—41no—
609#125—44no—
610#125—44no—
611#125—44no—
612#124—22no—
613#124—22no—
614#124—41no—
615#124—41no—
616#123—82no—
617#123—82no—
618#123—82no—
619#123—82no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—44no—
626C22⋊Q8C2×D414yes—
627#121—44no—
628#121—44no—
629#120—44no—
630#120—44no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—22no—
634C4×Q8—22no—
635C4×Q8—22no—
636C4×Q8—22no—
637C4×Q8—41no—
638C4×Q8—41no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×Q8—41no—
644C4×Q8—41no—
645C4×Q8—44no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—44no—
651C4×D4—44no—
652#117—22no—
653#117—22no—
654#117—22no—
655#117—22no—
656#117—41no—
657#117—41no—
658#117—44no—
659#117—44no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
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—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
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—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—82no—
744C2×C22⋊C4—82no—
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—22no—
750C2×C42—22no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—44no—
761C2×C42C2×D411yescharacteristic
762C2×C42C2×D411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769#107—22no—
770#107—22no—
771#107—41no—
772#106—22no—
773#106—22no—
774#106—41no—
775#106—41no—
776#106—41no—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—41no—
782C4⋊C8—41no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103C2×D414yes—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811#102—41no—
812#102—41no—
813#102—41no—
814#102C2×D414yes—
815C22⋊C8—22no—
816C22⋊C8—22no—
817C22⋊C8—22no—
818C22⋊C8C2×D414yes—
819#97—22no—
820#97—41no—
821C4×C8—22no—
822C4×C8—22no—
823C4×C8—22no—
824C4×C8—41no—
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#95—21no—
850#95—21no—
851#95—21no—
852#95—21no—
853#95—21no—
854#95—21no—
855#95—21no—
856#95C2×D411yescharacteristic
857#95C2×D411yescharacteristic
858#95C2×D411yescharacteristic
859#95C2×D411yescharacteristic
860#95C2×D411yescharacteristic
861#95C2×D411yescharacteristic
862#95C2×D411yescharacteristic
863#95C2×D411yescharacteristic
864C24—21no—
865C24—21no—
866C24—21no—
867C24—42no—
868C24—42no—
869C24—42no—
870C24—81no—
871C24—81no—
872C24—81no—
873C24—81no—
874C24C22×D411yescharacteristic
875#41—44no—
876#41—44no—
877#41—44no—
878#41—44no—
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—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—81no—
904C2×Q8C22×D412yes—
905C2×Q8C22×D412yes—
906C2×D4—24no—
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—21no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—82no—
936C2×D4—82no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4C22×D412yes—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—24no—
956C22×C4—22no—
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—41no—
969C22×C4—41no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D412yes—
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4H(5,𝔽2)12yes—
996C22×C4C2511yescharacteristic
997Q16—44no—
998Q16—44no—
999Q16—82no—
1000SD16—44no—
1001SD16—44no—
1002SD16—82no—
1003SD16—82no—
1004SD16—82no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C4⋊C4—24no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4C22×D412yes—
1092C22⋊C4—24no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C42—22no—
1128C42—22no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—81no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—22no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—84no—
1178C23—84no—
1179C23—84no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23—162no—
1184C23D4212yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—22no—
1189Q8—22no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—84no—
1203D4—22no—
1204D4—22no—
1205D4—48no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—84no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
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—44no—
1265C2×C4—44no—
1266C2×C4—48no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
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—84no—
1304C2×C4—84no—
1305C2×C4—162no—
1306C2×C4D4212yes—
1307C2×C4#57712yes—
1308C2×C4#57712yes—
1309C2×C4C23×D411yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4#58511yescharacteristic
1312C2×C4#58511yescharacteristic
1313C2×C4#58511yescharacteristic
1314C2×C4#58511yescharacteristic
1315C8—22no—
1316C8—22no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—168no—
1352C22#344911yescharacteristic
1353C22C2×D4211yescharacteristic
1354C22#348711yescharacteristic
1355C22C2×#57711yescharacteristic
1356C22C2×#57711yescharacteristic
1357C22#358411yescharacteristic
1358C22#358611yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—42no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—42no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4#348511yescharacteristic
1386C4#348511yescharacteristic
1387C4#353311yescharacteristic
1388C4#353311yescharacteristic
1389C2—42no—
1390C2—82no—
1391C2—161no—
1392C2—161no—
1393C2#3765511yescharacteristic
1394C2#6095611yescharacteristic
1395C2#6099111yescharacteristic
1396C2#6105511yescharacteristic
1397C2#6107511yescharacteristic
1398C2#6192511yescharacteristic
1399C2#6193311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3107C2semidirect
3. #37793C2semidirect
5. #33011C2semidirect
6. #31226C2semidirect
7. #31214C2semidirect
8. #31166C2semidirect
9. #31163C2semidirect
10. #30825C2semidirect
11. #30812C2semidirect
12. #30760C2semidirect
13. #30741C2semidirect
14. #29726C2semidirect
16. #28320C2semidirect
17. #28130C2semidirect
18. #26825C2semidirect
19. #26823C2semidirect
20. #26591C2semidirect
21. #26588C2semidirect
22. #26259C2semidirect
23. #26250C2semidirect
24. #26173C2semidirect
25. #26159C2semidirect
26. #24619C2semidirect
27. #24501C2semidirect
28. #24072C2semidirect
29. #23933C2semidirect
30. #22604C2semidirect
31. #22059C2semidirect
45. C2×#475C22semidirect
46. C2×#474C22semidirect
49. C2×#462C22semidirect
52. C2×#461C22semidirect
59. C2×C4×Q16C22semidirect
60. C2×C4×Q16C22semidirect
61. C2×C4×SD16C22semidirect
62. C2×C4×SD16C22semidirect
76. #2550C22semidirect
77. #2546C22semidirect
82. #2453C22semidirect
83. #2451C22semidirect
88. #2446C22semidirect
89. #2446C22semidirect
98. #2365C22semidirect
99. #2351C22semidirect
108. #2088C22semidirect
109. #2087C22semidirect
110. #2074C22semidirect
111. #2073C22semidirect
113. #2066C22semidirect
114. #2066C22semidirect
118. #2059C22semidirect
119. #2059C22semidirect
120. #2056C22semidirect
121. #2056C22semidirect
126. #2055C22semidirect
127. #2055C22semidirect
128. #2043C22semidirect
129. #2043C22semidirect
136. #2016C22semidirect
145. #2013C22semidirect
148. #1971C22semidirect
153. #1968C22semidirect
154. #1944C22semidirect
155. #1941C22semidirect
156. #1940C22semidirect
157. #1939C22semidirect
158. #1936C22semidirect
159. #1935C22semidirect
162. #1933C22semidirect
163. #1933C22semidirect
164. #1927C22semidirect
166. #1926C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
178. #1880C22semidirect
179. #1878C22semidirect
180. #1878C22semidirect
181. #1878C22semidirect
182. #1877C22semidirect
183. #1877C22semidirect
187. #1865C22semidirect
188. #1865C22semidirect
189. #1865C22semidirect
190. #1864C22semidirect
191. #1863C22semidirect
192. #1863C22semidirect
193. #1863C22semidirect
194. #1862C22semidirect
202. #1771C22semidirect
203. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32222
C2×#31072
#377932
#352542
#330112
#312262
#312142
#311662
#311632
#308252
#308122
#307602
#307412
#297262
#296322
#283202
#281302
#268252
#268232
#265912
#265882
#262592
#262502
#261732
#261592
#246192
#245012
#240722
#239332
#226042
#220592