Finite Group Databasebeta

← #7183708

Subgroups — #7183708

Order 512.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3384C211yesmaximal, characteristic, complemented
2C2×#3371C211yesmaximal, characteristic, complemented
3#59413C211yesmaximal, characteristic, complemented
4#39949C211yesmaximal, characteristic, complemented
5#31243C211yesmaximal, characteristic, complemented
6#31241C211yesmaximal, characteristic, complemented
7#31156C211yesmaximal, characteristic, complemented
8#31152C211yesmaximal, characteristic, complemented
9#30963C211yesmaximal, characteristic, complemented
10#30956C211yesmaximal, characteristic, complemented
11#30825C211yesmaximal, characteristic, complemented
12#30817C211yesmaximal, characteristic, complemented
13#28659C211yesmaximal, characteristic, complemented
14#28376C211yesmaximal, characteristic, complemented
15#26908C211yesmaximal, characteristic, complemented
16#26900C211yesmaximal, characteristic, complemented
17#26843C211yesmaximal, characteristic
18#26819C211yesmaximal, characteristic, complemented
19#26609C211yesmaximal, characteristic, complemented
20#26593C211yesmaximal, characteristic
21#26497C211yesmaximal, characteristic, complemented
22#26480C211yesmaximal, characteristic, complemented
23#25939C211yesmaximal, characteristic, complemented
24#25846C211yesmaximal, characteristic, complemented
25#25486C211yesmaximal, characteristic, complemented
26#25311C211yesmaximal, characteristic, complemented
27#24349C211yesmaximal, characteristic, complemented
28#24204C211yesmaximal, characteristic
29#23686C211yesmaximal, characteristic, complemented
30#23151C211yesmaximal, characteristic, complemented
31#22111C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36#3384—28no—
37#3371—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#498C2211yescharacteristic
41C2×#490C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#488C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#478C2211yescharacteristic
47C2×#478C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#476C2211yescharacteristic
50C2×#476C2211yescharacteristic
51C2×#476C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#464C2211yescharacteristic
54C2×#464C2211yescharacteristic
55C2×#460C2211yescharacteristic
56C2×#463C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#442C2211yescharacteristic
60C2×#442C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×SD16C2211yescharacteristic
64C2×C4×D8C2211yescharacteristic
65#2861C2211yescharacteristic
66#2704—21no—
67#2704—21no—
68#2700—21no—
69#2687—21no—
70#2680—21no—
71#2674—21no—
72#2663—21no—
73#2592C2211yescharacteristic
74#2584C2211yescharacteristic
75#2582C2211yescharacteristic
76#2556—21no—
77#2556—21no—
78#2550C2211yescharacteristic
79#2550C2211yescharacteristic
80#2538C2211yescharacteristic
81#2454C2211yescharacteristic
82#2454C2211yescharacteristic
83#2454C2211yescharacteristic
84#2453C2211yescharacteristic
85#2452C2211yescharacteristic
86#2451C2211yescharacteristic
87#2451C2211yescharacteristic
88#2451C2211yescharacteristic
89#2447C2211yescharacteristic
90#2447C2211yescharacteristic
91#2445C2211yescharacteristic
92#2445C2211yescharacteristic
93#2434—21no—
94#2429—21no—
95#2423—21no—
96#2415—21no—
97#2413—21no—
98#2367C2211yescharacteristic
99#2367C2211yescharacteristic
100Q8×C22⋊C4—21no—
101#2322—21no—
102C4×C4⋊Q8C2211yescharacteristic
103C4×C4⋊Q8C2211yescharacteristic
104C4×#124C2211yescharacteristic
105#2293C2211yescharacteristic
106#2097C2211yescharacteristic
107#2092C2211yescharacteristic
108#2088C2211yescharacteristic
109#2086C2211yescharacteristic
110#2085C2211yescharacteristic
111#2073C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2067C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2057C2211yescharacteristic
128#2056C2211yescharacteristic
129#2055C2211yescharacteristic
130#2055C2211yescharacteristic
131#2054C2211yescharacteristic
132#2042C2211yescharacteristic
133#2042C2211yescharacteristic
134#2041C2211yescharacteristic
135#2026C2211yescharacteristic
136#2024C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#2015C2211yescharacteristic
142#2012C2211yescharacteristic
143#2012C2211yescharacteristic
144#2012C2211yescharacteristic
145#2011C2211yescharacteristic
146#1992C2211yescharacteristic
147#1987C2211yescharacteristic
148#1985C2211yescharacteristic
149#1985C2211yescharacteristic
150#1971C2211yescharacteristic
151#1970C2211yescharacteristic
152#1969C2211yescharacteristic
153#1968C2211yescharacteristic
154#1968C2211yescharacteristic
155#1968C2211yescharacteristic
156#1959C2211yescharacteristic
157#1948C2211yescharacteristic
158#1944C2211yescharacteristic
159#1941C2211yescharacteristic
160#1941C2211yescharacteristic
161#1941C2211yescharacteristic
162#1939C2211yescharacteristic
163#1939C2211yescharacteristic
164#1936C2211yescharacteristic
165#1936C2211yescharacteristic
166#1934C2211yescharacteristic
167#1934C2211yescharacteristic
168#1934C2211yescharacteristic
169#1933C2211yescharacteristic
170#1927C2211yescharacteristic
171#1927C2211yescharacteristic
172#1926C2211yescharacteristic
173#1926C2211yescharacteristic
174#1925C2211yescharacteristic
175#1925C2211yescharacteristic
176#1919C2211yescharacteristic
177#1919C2211yescharacteristic
178#1917C2211yescharacteristic
179#1917C2211yescharacteristic
180#1916C2211yescharacteristic
181#1916C2211yescharacteristic
182#1880C2211yescharacteristic
183#1879C2211yescharacteristic
184#1879C2211yescharacteristic
185#1879C2211yescharacteristic
186#1877C2211yescharacteristic
187#1877C2211yescharacteristic
188#1877C2211yescharacteristic
189#1877C2211yescharacteristic
190#1865C2211yescharacteristic
191#1865C2211yescharacteristic
192#1865C2211yescharacteristic
193#1864C2211yescharacteristic
194#1864C2211yescharacteristic
195#1863C2211yescharacteristic
196#1863C2211yescharacteristic
197#1862C2211yescharacteristic
198#1802C2211yescharacteristic
199#1770C2211yescharacteristic
200C8×C4⋊C4C2211yescharacteristic
201#1767C2211yescharacteristic
202C4×C4⋊C8C2211yescharacteristic
203#1763C2211yescharacteristic
204#1762C2211yescharacteristic
205C23×Q8—21no—
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#559—24no—
213#559—42no—
214#557—24no—
215#557—42no—
216#554—24no—
217#554—42no—
218D4×Q8—24no—
219D4×Q8—42no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8D411yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#125—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#124—21no—
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#124C2311yescharacteristic
237C2×#123—21no—
238C2×#123—21no—
239C2×#123—21no—
240C2×#123—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C22×C4⋊C4—21no—
267#501—24no—
268#501—24no—
269#498—24no—
270#490—24no—
271#489—24no—
272#488—24no—
273#479—24no—
274#479—42no—
275#478—24no—
276#478—24no—
277#478—24no—
278#476—24no—
279#476—24no—
280#476D418yes—
281#474—24no—
282#464—24no—
283#464—24no—
284#463—42no—
285#460—24no—
286#446—24no—
287#446—24no—
288#442—24no—
289#442—24no—
290#441—24no—
291#440—24no—
292C4×SD16—24no—
293C4×D8—24no—
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#106C2311yescharacteristic
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×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×#102C2311yescharacteristic
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×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×#97C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351C2×C4×C8C2311yescharacteristic
352#400—21no—
353#399—21no—
354#399—21no—
355#399—21no—
356#398—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#397—21no—
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#395—21no—
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#393—21no—
387#393—21no—
388#391—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391D411yescharacteristic
396#391D411yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389D411yescharacteristic
421#389D411yescharacteristic
422#389D411yescharacteristic
423#389D411yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
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#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#386—21no—
455#386—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#384D411yescharacteristic
465#384C2311yescharacteristic
466#382C2311yescharacteristic
467#381—21no—
468#381—21no—
469#380—21no—
470#380—21no—
471#380—21no—
472#380—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C22⋊C4—21no—
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C43C2311yescharacteristic
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#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
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—44no—
520C22×Q8—44no—
521C22×Q8—82no—
522C22×Q8C2×D411yescharacteristic
523C22×Q8C2×D411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—41no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—22no—
565C4⋊Q8—22no—
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—42no—
572C4⋊Q8—44no—
573C4⋊Q8C2×D414yes—
574#127—22no—
575#127—41no—
576#125—22no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125—22no—
581#125—41no—
582#125—41no—
583#125—41no—
584#125—44no—
585#125—44no—
586#124—22no—
587#124—22no—
588#124—22no—
589#124—22no—
590#124—22no—
591#124—41no—
592#124—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596#123—82no—
597C22⋊Q8—44no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—82no—
604C22⋊Q8—82no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—44no—
618C4×Q8—82no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—44no—
633C4×D4C2×D414yes—
634#117—82no—
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—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—44no—
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⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
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×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×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#107—22no—
741#107—22no—
742#107—22no—
743#107—22no—
744#107—41no—
745#106—22no—
746#106—22no—
747#106—22no—
748#106—22no—
749#106—41no—
750#106—41no—
751#106—41no—
752#106C2×D414yes—
753#106C2×D414yes—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—22no—
758C4⋊C8—22no—
759C4⋊C8—22no—
760C4⋊C8—41no—
761C4⋊C8C2×D414yes—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—22no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102C2×D414yes—
789#102C2×D414yes—
790#97—22no—
791#97—22no—
792#97—22no—
793#97—22no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—41no—
797C4×C8—41no—
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#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#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—21no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×Q8—42no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—816no—
870C2×Q82−1+412yes—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4C22×D412yes—
894C2×D42−1+412yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—24no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C2511yescharacteristic
944Q16—44no—
945SD16—44no—
946SD16—44no—
947SD16—82no—
948D8—28no—
949D8—82no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8C22×D412yes—
972C2×C8C22×D412yes—
973C2×C82−1+412yes—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4C22×D412yes—
1038C4⋊C4C22×D412yes—
1039C4⋊C4C22×D412yes—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C42—22no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—41no—
1085C42—41no—
1086C42—41no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42C22×D412yes—
1095C42H(5,𝔽2)12yes—
1096C23—22no—
1097C23—22no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C23×D411yescharacteristic
1118Q8—22no—
1119Q8—22no—
1120Q8—44no—
1121Q8—48no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—82no—
1129Q8—84no—
1130Q8—84no—
1131Q8—162no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—84no—
1145D4—162no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4D4212yes—
1231C2×C4D4212yes—
1232C2×C4#57512yes—
1233C2×C4#57712yes—
1234C2×C4C23×D411yescharacteristic
1235C2×C4C2×H(5,𝔽2)11yescharacteristic
1236C2×C4C2×2−1+411yescharacteristic
1237C2×C4C2×2−1+411yescharacteristic
1238C2×C4C2×2−1+411yescharacteristic
1239C2×C4#58511yescharacteristic
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22C2×D4211yescharacteristic
1270C22#348611yescharacteristic
1271C22#349711yescharacteristic
1272C22C2×#57511yescharacteristic
1273C22C2×#57711yescharacteristic
1274C22#358411yescharacteristic
1275C22#358511yescharacteristic
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—42no—
1284C4—42no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—42no—
1291C4—41no—
1292C4—42no—
1293C4—41no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4#348611yescharacteristic
1304C4#348911yescharacteristic
1305C4#355211yescharacteristic
1306C4#356111yescharacteristic
1307C2—82no—
1308C2—82no—
1309C2—161no—
1310C2#4524811yescharacteristic
1311C2#6106611yescharacteristic
1312C2#6108511yescharacteristic
1313C2#6183911yescharacteristic
1314C2#6186011yescharacteristic
1315C2#6237011yescharacteristic
1316C2#6241111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
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
1. C2×#3384C2semidirect
2. C2×#3371C2semidirect
3. #59413C2semidirect
4. #39949C2semidirect
5. #31243C2semidirect
6. #31241C2semidirect
7. #31156C2semidirect
8. #31152C2semidirect
9. #30963C2semidirect
10. #30956C2semidirect
11. #30825C2semidirect
12. #30817C2semidirect
13. #28659C2semidirect
14. #28376C2semidirect
15. #26908C2semidirect
16. #26900C2semidirect
18. #26819C2semidirect
19. #26609C2semidirect
21. #26497C2semidirect
22. #26480C2semidirect
23. #25939C2semidirect
24. #25846C2semidirect
25. #25486C2semidirect
26. #25311C2semidirect
27. #24349C2semidirect
29. #23686C2semidirect
30. #23151C2semidirect
31. #22111C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33842
C2×#33712
#594132
#399492
#312432
#312412
#311562
#311522
#309632
#309562
#308252
#308172
#286592
#283762
#269082
#269002
#268432
#268192
#266092
#265932
#264972
#264802
#259392
#258462
#254862
#253112
#243492
#242042
#236862
#231512
#221112