Finite Group Databasebeta

← #6684220

Subgroups — #6684220

Order 512.

1745 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3389C211yesmaximal, characteristic
2C2×#3376C211yesmaximal, characteristic
3#39490C211yesmaximal, characteristic, complemented
4#36261C211yesmaximal, characteristic, complemented
5#33032C211yesmaximal, characteristic, complemented
6#30972C211yesmaximal, characteristic, complemented
7#30965C211yesmaximal, characteristic, complemented
8#30960C211yesmaximal, characteristic, complemented
9#30953C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic, complemented
11#30821C211yesmaximal, characteristic, complemented
12#30819C211yesmaximal, characteristic, complemented
13#30809C211yesmaximal, characteristic, complemented
14#30284C211yesmaximal, characteristic, complemented
15#29870C211yesmaximal, characteristic, complemented
16#28686C211yesmaximal, characteristic, complemented
17#28652C211yesmaximal, characteristic, complemented
18#26398C211yesmaximal, characteristic, complemented
19#26386C211yesmaximal, characteristic, complemented
20#26378C211yesmaximal, characteristic, complemented
21#26374C211yesmaximal, characteristic, complemented
22#26180C211yesmaximal, characteristic
23#26176C211yesmaximal, characteristic
24#26164C211yesmaximal, characteristic
25#26160C211yesmaximal, characteristic
26#25945C211yesmaximal, characteristic, complemented
27#25850C211yesmaximal, characteristic, complemented
28#25845C211yesmaximal, characteristic, complemented
29#25656C211yesmaximal, characteristic, complemented
30#22244C211yesmaximal, characteristic, complemented
31#21122C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×#554C2211yescharacteristic
36#3389—28no—
37#3376—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#491C2211yescharacteristic
43C2×#491C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#488C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#475C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#463C2211yescharacteristic
56C2×#463C2211yescharacteristic
57C2×#461C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#442C2211yescharacteristic
61C2×#442C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×C4×D8C2211yescharacteristic
65#2862C2211yescharacteristic
66#2859C2211yescharacteristic
67#2857—21no—
68#2689—21no—
69#2689—21no—
70#2689—21no—
71#2689—21no—
72#2621—21no—
73#2584C2211yescharacteristic
74#2584C2211yescharacteristic
75#2583—21no—
76#2583—21no—
77#2568C2211yescharacteristic
78#2567C2211yescharacteristic
79#2552C2211yescharacteristic
80#2551C2211yescharacteristic
81#2550C2211yescharacteristic
82#2550C2211yescharacteristic
83#2549—21no—
84#2549—21no—
85#2503—21no—
86#2499—21no—
87#2453C2211yescharacteristic
88#2453C2211yescharacteristic
89#2453C2211yescharacteristic
90#2453C2211yescharacteristic
91#2447C2211yescharacteristic
92#2447C2211yescharacteristic
93#2447C2211yescharacteristic
94#2447C2211yescharacteristic
95#2440—21no—
96#2440—21no—
97#2349C2211yescharacteristic
98#2349C2211yescharacteristic
99D4×C4⋊C4C2211yescharacteristic
100D4×C4⋊C4C2211yescharacteristic
101#2317—21no—
102C4×C4⋊Q8C2211yescharacteristic
103#2293C2211yescharacteristic
104C2×#389—21no—
105C42×D4C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2097C2211yescharacteristic
109#2097C2211yescharacteristic
110#2096C2211yescharacteristic
111#2096C2211yescharacteristic
112#2095C2211yescharacteristic
113#2095C2211yescharacteristic
114#2088C2211yescharacteristic
115#2088C2211yescharacteristic
116#2087C2211yescharacteristic
117#2086C2211yescharacteristic
118#2085C2211yescharacteristic
119#2085C2211yescharacteristic
120#2084C2211yescharacteristic
121#2083C2211yescharacteristic
122#2073C2211yescharacteristic
123#2073C2211yescharacteristic
124#2071C2211yescharacteristic
125#2071C2211yescharacteristic
126#2068C2211yescharacteristic
127#2068C2211yescharacteristic
128#2066C2211yescharacteristic
129#2066C2211yescharacteristic
130#2059C2211yescharacteristic
131#2059C2211yescharacteristic
132#2059C2211yescharacteristic
133#2059C2211yescharacteristic
134#2059C2211yescharacteristic
135#2059C2211yescharacteristic
136#2057C2211yescharacteristic
137#2057C2211yescharacteristic
138#2042C2211yescharacteristic
139#2042C2211yescharacteristic
140#2042C2211yescharacteristic
141#2042C2211yescharacteristic
142#2026C2211yescharacteristic
143#2026C2211yescharacteristic
144#2024C2211yescharacteristic
145#2024C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1988C2211yescharacteristic
149#1985C2211yescharacteristic
150#1985C2211yescharacteristic
151#1981C2211yescharacteristic
152#1944C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1928C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1920C2211yescharacteristic
167#1919C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic
185#1877C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1864C2211yescharacteristic
189#1864C2211yescharacteristic
190#1864C2211yescharacteristic
191#1864C2211yescharacteristic
192#1864C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1862C2211yescharacteristic
196#1862C2211yescharacteristic
197#1862C2211yescharacteristic
198#1862C2211yescharacteristic
199#1862C2211yescharacteristic
200#1831C2211yescharacteristic
201#1776C2211yescharacteristic
202#1762C2211yescharacteristic
203#1762C2211yescharacteristic
204#1745C2211yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208#556—24no—
209#556—42no—
210#554—24no—
211#554—24no—
212#554—24no—
213#554—42no—
214#554—42no—
215#554—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8D411yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117—21no—
258C22×C4⋊C4—21no—
259C22×C4⋊C4—21no—
260C22×C4⋊C4—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4—21no—
263C22×C42—21no—
264#501—24no—
265#501—24no—
266#501—42no—
267#499—24no—
268#491—24no—
269#491—42no—
270#489—24no—
271#488—24no—
272#479—24no—
273#478—24no—
274#478—24no—
275#478—24no—
276#478—24no—
277#478—24no—
278#475—24no—
279#474—24no—
280#474—24no—
281#463—24no—
282#463—24no—
283#461—24no—
284#446—24no—
285#446—24no—
286#442—24no—
287#442D418yes—
288#440—24no—
289C4×SD16—24no—
290C4×D8—24no—
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#97C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346#400—21no—
347#400—21no—
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#395—21no—
371#395—21no—
372#395—21no—
373#395—21no—
374#395—21no—
375#395—21no—
376#395—21no—
377#395—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391D411yescharacteristic
385#391D411yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389D411yescharacteristic
413#389D411yescharacteristic
414#389D411yescharacteristic
415#389D411yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#384—21no—
449#384—21no—
450#384D411yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#382—21no—
454#382—21no—
455#382—21no—
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#381—21no—
459#381—21no—
460#381—21no—
461#381—21no—
462#380—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4—21no—
478C2×#95—21no—
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#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2×D411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8C2×D414yes—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—42no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—82no—
561#126—44no—
562#126—44no—
563#125—22no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—22no—
571#125—41no—
572#125—41no—
573#125—41no—
574#125—41no—
575#124—22no—
576#124—22no—
577#124—41no—
578#124—41no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4C2×D414yes—
616C4×D4C2×D414yes—
617#117—44no—
618#117—44no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4—44no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4—44no—
660C2×C4⋊C4—82no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
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×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—82no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#106—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—41no—
738#106—41no—
739#106C2×D414yes—
740C4⋊C8—22no—
741C4⋊C8—22no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102C2×D414yes—
771#102C2×D414yes—
772#97—22no—
773#97—22no—
774#97—22no—
775#97C2×D414yes—
776C4×C8—22no—
777C4×C8—22no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—41no—
841C2×Q8—41no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4C22×D412yes—
862C2×D4C22×D412yes—
863C2×D42−1+412yes—
864C2×D42−1+412yes—
865C22×C4—24no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C2511yescharacteristic
924SD16—44no—
925SD16—44no—
926D8—28no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8C22×D412yes—
950C2×C8C22×D412yes—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4C22×D412yes—
1023C4⋊C4C22×D412yes—
1024C4⋊C42−1+412yes—
1025C4⋊C42−1+412yes—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C42—22no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—41no—
1058C42—41no—
1059C42—41no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—81no—
1065C42—81no—
1066C42C22×D412yes—
1067C42H(5,𝔽2)12yes—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23C23×D411yescharacteristic
1083Q8—41no—
1084Q8—41no—
1085Q8—41no—
1086Q8—41no—
1087Q8—41no—
1088Q8—41no—
1089Q8—41no—
1090Q8—41no—
1091Q8—82no—
1092Q8—82no—
1093Q8—162no—
1094Q8—162no—
1095Q8—162no—
1096D4—22no—
1097D4—22no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—41no—
1102D4—41no—
1103D4#53614yes—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—48no—
1148C2×C4—48no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—84no—
1190C2×C4—84no—
1191C2×C4—162no—
1192C2×C4—162no—
1193C2×C4—162no—
1194C2×C4—162no—
1195C2×C4D4212yes—
1196C2×C4D4212yes—
1197C2×C4#57512yes—
1198C2×C4C23×D411yescharacteristic
1199C2×C4C2×H(5,𝔽2)11yescharacteristic
1200C2×C4C2×2−1+411yescharacteristic
1201C2×C4C2×2−1+411yescharacteristic
1202C2×C4C2×2−1+411yescharacteristic
1203C2×C4C2×2−1+411yescharacteristic
1204C8—22no—
1205C8—22no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C22—24no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C2×D4211yescharacteristic
1227C22#348611yescharacteristic
1228C22#348611yescharacteristic
1229C22C2×#57511yescharacteristic
1230C22#358411yescharacteristic
1231C22#358511yescharacteristic
1232C22#358611yescharacteristic
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—42no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—42no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4C2×#53611yescharacteristic
1262C4#349911yescharacteristic
1263C4#355211yescharacteristic
1264C4#355211yescharacteristic
1265C2—44no—
1266C2—82no—
1267C2#3767511yescharacteristic
1268C2#6106711yescharacteristic
1269C2#6109211yescharacteristic
1270C2#6183111yescharacteristic
1271C2#6184511yescharacteristic
1272C2#6186211yescharacteristic
1273C2#6187311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #39490C2semidirect
4. #36261C2semidirect
5. #33032C2semidirect
6. #30972C2semidirect
7. #30965C2semidirect
8. #30960C2semidirect
9. #30953C2semidirect
10. #30831C2semidirect
11. #30821C2semidirect
12. #30819C2semidirect
13. #30809C2semidirect
14. #30284C2semidirect
15. #29870C2semidirect
16. #28686C2semidirect
17. #28652C2semidirect
18. #26398C2semidirect
19. #26386C2semidirect
20. #26378C2semidirect
21. #26374C2semidirect
26. #25945C2semidirect
27. #25850C2semidirect
28. #25845C2semidirect
29. #25656C2semidirect
30. #22244C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33892
C2×#33762
#394902
#362612
#330322
#309722
#309652
#309602
#309532
#308312
#308212
#308192
#308092
#302842
#298702
#286862
#286522
#263982
#263862
#263782
#263742
#261802
#261762
#261642
#261602
#259452
#258502
#258452
#256562
#222442
#211222