Finite Group Databasebeta

← #7519415

Subgroups — #7519415

Order 512.

2031 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3385C211yesmaximal, characteristic, complemented
2C22×#474C211yesmaximal, characteristic
3#59151C211yesmaximal, characteristic, complemented
4#36215C211yesmaximal, characteristic
5#31252C211yesmaximal, characteristic, complemented
6#31235C211yesmaximal, characteristic, complemented
7#30962C211yesmaximal, characteristic, complemented
8#30946C211yesmaximal, characteristic, complemented
9#28543C211yesmaximal, characteristic, complemented
10#26384C211yesmaximal, characteristic, complemented
11#26372C211yesmaximal, characteristic, complemented
12#26344C211yesmaximal, characteristic, complemented
13#26342C211yesmaximal, characteristic, complemented
14#26071C211yesmaximal, characteristic, complemented
15#26065C211yesmaximal, characteristic, complemented
16#26058C211yesmaximal, characteristic, complemented
17#26040C211yesmaximal, characteristic, complemented
18#25958C211yesmaximal, characteristic
19#25950C211yesmaximal, characteristic
20#25850C211yesmaximal, characteristic, complemented
21#25816C211yesmaximal, characteristic, complemented
22#25481C211yesmaximal, characteristic, complemented
23#25462C211yesmaximal, characteristic, complemented
24#24840C211yesmaximal, characteristic, complemented
25#24833C211yesmaximal, characteristic, complemented
26#24341C211yesmaximal, characteristic, complemented
27#22979C211yesmaximal, characteristic, complemented
28#22954C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic
30#22854C211yesmaximal, characteristic
31#21453C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36#3385—28no—
37C2×#501C2211yescharacteristic, complemented
38C2×#501C2211yescharacteristic, complemented
39C2×#501C2211yescharacteristic, complemented
40C2×#500C2211yescharacteristic, complemented
41C2×#479C2211yescharacteristic, complemented
42C2×#479C2211yescharacteristic, complemented
43C2×#477C2211yescharacteristic, complemented
44C2×#476C2211yescharacteristic
45C2×#474—28no—
46C2×#474C2211yescharacteristic
47C2×#474C2211yescharacteristic
48C2×#474C2211yescharacteristic
49C2×#474C2211yescharacteristic
50C2×#474C2211yescharacteristic
51C2×#474C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#450C2211yescharacteristic
56C2×#446C2211yescharacteristic, complemented
57C2×#440C2211yescharacteristic
58C2×#440C2211yescharacteristic
59C2×#440C2211yescharacteristic
60C2×C4×SD16C2211yescharacteristic
61C22×#107C2211yescharacteristic
62C22×#107C2211yescharacteristic
63C22×C4⋊C8C2211yescharacteristic
64C22×#102C2211yescharacteristic
65C22×#102C2211yescharacteristic
66#2851C2211yescharacteristic
67#2848—21no—
68#2734—21no—
69#2734—21no—
70#2580C2211yescharacteristic
71#2579—21no—
72#2567C2211yescharacteristic, complemented
73#2567C2211yescharacteristic, complemented
74#2566C2211yescharacteristic
75#2564—21no—
76#2551—21no—
77#2551C2211yescharacteristic, complemented
78#2551C2211yescharacteristic, complemented
79#2454C2211yescharacteristic
80#2452C2211yescharacteristic
81#2451—21no—
82#2451C2211yescharacteristic, complemented
83#2451C2211yescharacteristic, complemented
84#2450—21no—
85#2449—21no—
86#2442C2211yescharacteristic
87#2440—21no—
88#2440C2211yescharacteristic
89#2440C2211yescharacteristic
90#2440C2211yescharacteristic
91#2437—21no—
92#2437—21no—
93#2434—21no—
94#2434—21no—
95#2369C2211yescharacteristic, complemented
96#2360—21no—
97#2360C2211yescharacteristic
98#2360C2211yescharacteristic
99#2349C2211yescharacteristic
100#2349C2211yescharacteristic
101D4×C4⋊C4C2211yescharacteristic
102D4×C22⋊C4C2211yescharacteristic
103D4×C22⋊C4C2211yescharacteristic
104C4×C22⋊Q8C2211yescharacteristic
105C4×C22⋊Q8C2211yescharacteristic
106C2×#385—21no—
107#2097C2211yescharacteristic, complemented
108#2095C2211yescharacteristic, complemented
109#2094C2211yescharacteristic
110#2093C2211yescharacteristic
111#2088C2211yescharacteristic, complemented
112#2087C2211yescharacteristic, complemented
113#2086C2211yescharacteristic, complemented
114#2086C2211yescharacteristic, complemented
115#2085C2211yescharacteristic, complemented
116#2083C2211yescharacteristic, complemented
117#2083C2211yescharacteristic, complemented
118#2083C2211yescharacteristic, complemented
119#2068C2211yescharacteristic, complemented
120#2068C2211yescharacteristic, complemented
121#2068C2211yescharacteristic, complemented
122#2067C2211yescharacteristic
123#2067C2211yescharacteristic
124#2066C2211yescharacteristic, complemented
125#2065C2211yescharacteristic
126#2065C2211yescharacteristic
127#2059C2211yescharacteristic, complemented
128#2059C2211yescharacteristic, complemented
129#2058C2211yescharacteristic, complemented
130#2058C2211yescharacteristic, complemented
131#2057C2211yescharacteristic, complemented
132#2057C2211yescharacteristic, complemented
133#2057C2211yescharacteristic, complemented
134#2057C2211yescharacteristic, complemented
135#2057C2211yescharacteristic, complemented
136#2057C2211yescharacteristic, complemented
137#2023C2211yescharacteristic
138#2023C2211yescharacteristic
139#1993C2211yescharacteristic, complemented
140#1993C2211yescharacteristic, complemented
141#1989C2211yescharacteristic, complemented
142#1985C2211yescharacteristic, complemented
143#1973C2211yescharacteristic
144#1968C2211yescharacteristic
145#1949C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1944C2211yescharacteristic, complemented
149#1943C2211yescharacteristic, complemented
150#1942C2211yescharacteristic, complemented
151#1942C2211yescharacteristic, complemented
152#1940C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1934C2211yescharacteristic
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1921C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1872C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic
189#1847C2211yescharacteristic, complemented
190#1845C2211yescharacteristic, complemented
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic
196#1786C2211yescharacteristic
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1752C2211yescharacteristic
203C8×C22⋊C4C2211yescharacteristic
204#1749C2211yescharacteristic
205C23×Q8—21no—
206C23×D4C2311yescharacteristic
207C24×C4—21no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212Q82—24no—
213Q82—42no—
214#554—24no—
215#554—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—24no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—42no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
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⋊Q8D411yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C4×Q8—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—24no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—42no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C22×C4⋊C4—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4—21no—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C42C2311yescharacteristic
270#501—24no—
271#501—24no—
272#501—42no—
273#500—24no—
274#479—24no—
275#479—24no—
276#477—24no—
277#476—24no—
278#474—24no—
279#474—24no—
280#474—24no—
281#474—24no—
282#474—24no—
283#474—24no—
284#474—24no—
285#474—24no—
286#474D418yes—
287#450Q818yescomplemented
288#446—24no—
289#440—24no—
290#440—24no—
291#440—42no—
292C4×SD16—24no—
293C2×#107—24no—
294C2×#107—24no—
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×C4⋊C8—24no—
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#102—24no—
333C2×#102—24no—
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×#97C2311yescharacteristic
351C2×#97C2311yescharacteristic
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×C4×C8C2311yescharacteristic
355C2×C4×C8C2311yescharacteristic
356#400—21no—
357#399—21no—
358#399—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#396—21no—
369#395—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#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#393—21no—
383#393—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391D411yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#389—21no—
398#389—21no—
399#389—21no—
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389D411yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387D411yescharacteristic
426#387D411yescharacteristic
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—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#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385D411yescharacteristic
453#385D411yescharacteristic
454#384—21no—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#380—21no—
461#380—21no—
462#380—21no—
463#380—21no—
464#380—21no—
465#380D411yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#379—21no—
470#379—21no—
471C4×C4⋊C4—21no—
472C4×C4⋊C4—21no—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4—21no—
481C4×C22⋊C4—21no—
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
484C2×#95—21no—
485C2×#95—21no—
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#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516C25—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—44no—
525C22×Q8—82no—
526C22×Q8—82no—
527C22×Q8C2×D411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—21no—
532C22×D4—22no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4C2×Q814yes—
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—44no—
550C23×C4—82no—
551C23×C4—82no—
552C23×C4C2×D411yescharacteristic
553C23×C4C2×D411yescharacteristic
554C23×C4C2411yescharacteristic
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16C2×Q814yescomplemented
560C2×SD16C2×Q814yescomplemented
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—44no—
589C4⋊Q8—44no—
590C4⋊Q8—44no—
591C4⋊Q8—44no—
592C4⋊Q8—44no—
593C4⋊Q8—82no—
594C4⋊Q8—82no—
595C4⋊Q8C2×D414yes—
596#125—22no—
597#125—22no—
598#125—22no—
599#125—41no—
600C22⋊Q8—22no—
601C22⋊Q8—24no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—44no—
605C22⋊Q8—82no—
606C22⋊Q8—82no—
607C22⋊Q8—82no—
608C22⋊Q8—82no—
609C22⋊Q8C2×Q814yes—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—44no—
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—22no—
628C4×D4—44no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—44no—
636C4×D4C2×D414yes—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
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—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—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4—44no—
682C2×C4⋊C4—82no—
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
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—44no—
726C2×C22⋊C4—44no—
727C2×C22⋊C4—82no—
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—22no—
750#107—22no—
751#107—22no—
752#107—22no—
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#107—22no—
758#107—41no—
759#107—41no—
760#107—41no—
761#107—41no—
762#107C2×D414yes—
763#107C2×D414yes—
764#106—22no—
765#106—22no—
766#106—22no—
767#106—41no—
768#106—41no—
769#106—41no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—22no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777C4⋊C8C2×D414yes—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—41no—
782#103—41no—
783#103—41no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—41no—
793#102—41no—
794#102C2×D414yes—
795#102C2×D414yes—
796#102C2×Q814yescomplemented
797#102C2×Q814yescomplemented
798C22⋊C8—22no—
799C22⋊C8C2×Q814yes—
800#97—22no—
801#97—22no—
802#97—22no—
803#97—41no—
804C4×C8—22no—
805C4×C8—41no—
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#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845C24—21no—
846C24—21no—
847C24—24no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—81no—
853C24—81no—
854C24C22×D411yescharacteristic
855C2×Q8—22no—
856C2×Q8—24no—
857C2×Q8—22no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—41no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—81no—
879C2×Q8—81no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8—816no—
885C2×Q8C22×Q812yes—
886C2×D4—28no—
887C2×D4—24no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4C22×D412yes—
902C2×D4C22×Q812yes—
903C2×D4C22×Q812yes—
904C2×D42−1+412yes—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—41no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—816no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×Q812yes—
977C22×C42−1+412yes—
978C22×C4C2511yescharacteristic
979SD16—28no—
980SD16—44no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—44no—
1002C2×C8—44no—
1003C2×C8C22×D412yes—
1004C2×C8C22×D412yes—
1005C2×C8C22×Q812yes—
1006C2×C8C22×Q812yes—
1007C4⋊C4—24no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—41no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4C22×D412yes—
1076C4⋊C4C22×D412yes—
1077C4⋊C4C22×D412yes—
1078C4⋊C4C22×Q812yes—
1079C22⋊C4—24no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—24no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4#13714yes—
1103C42—22no—
1104C42—22no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42C22×D412yes—
1122C42H(5,𝔽2)12yes—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—48no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—48no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23D4×Q812yes—
1149C23C2×#13712yes—
1150C23#57612yes—
1151C23C23×D411yescharacteristic
1152Q8—22no—
1153Q8—22no—
1154Q8—44no—
1155Q8—41no—
1156Q8—41no—
1157Q8—84no—
1158Q8—84no—
1159Q8—84no—
1160Q8—84no—
1161Q8—162no—
1162Q8—162no—
1163Q8—162no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—48no—
1170D4—41no—
1171D4—41no—
1172D4D4×Q814yes—
1173C2×C4—28no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
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—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—44no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4D4212yes—
1266C2×C4D4212yes—
1267C2×C4D4×Q812yes—
1268C2×C4C2×#13712yes—
1269C2×C4C2×#13712yes—
1270C2×C4#57612yes—
1271C2×C4C23×D411yescharacteristic
1272C2×C4C23×Q811yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×2−1+411yescharacteristic
1275C2×C4C2×2−1+411yescharacteristic
1276C2×C4#58511yescharacteristic
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—24no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—816no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22#338514yescomplemented
1307C22C2×D4211yescharacteristic
1308C22C2×D4×Q811yescharacteristic
1309C22#348911yescharacteristic
1310C22C22×#13711yescharacteristic
1311C22C2×#57611yescharacteristic
1312C22C2×#57611yescharacteristic
1313C22#358611yescharacteristic
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4C2×D4×Q811yescharacteristic
1342C4#348911yescharacteristic
1343C4#350111yescharacteristic
1344C4#353811yescharacteristic
1345C2—24no—
1346C2—44no—
1347C2—82no—
1348C2#5899811yescharacteristic
1349C2#6104911yescharacteristic
1350C2D4×#13711yescharacteristic
1351C2C2×#338511yescharacteristic
1352C2#6138111yescharacteristic
1353C2#6212711yescharacteristic
1354C2#6215511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3385C2semidirect
3. #59151C2semidirect
5. #31252C2semidirect
6. #31235C2semidirect
7. #30962C2semidirect
8. #30946C2semidirect
9. #28543C2semidirect
10. #26384C2semidirect
11. #26372C2semidirect
12. #26344C2semidirect
13. #26342C2semidirect
14. #26071C2semidirect
15. #26065C2semidirect
16. #26058C2semidirect
17. #26040C2semidirect
20. #25850C2semidirect
21. #25816C2semidirect
22. #25481C2semidirect
23. #25462C2semidirect
24. #24840C2semidirect
25. #24833C2semidirect
26. #24341C2semidirect
27. #22979C2semidirect
28. #22954C2semidirect
32. C2×Q82C22semidirect
37. C2×#501C22semidirect
38. C2×#501C22semidirect
39. C2×#501C22semidirect
40. C2×#500C22semidirect
41. C2×#479C22semidirect
42. C2×#479C22semidirect
43. C2×#477C22semidirect
56. C2×#446C22semidirect
72. #2567C22semidirect
73. #2567C22semidirect
77. #2551C22semidirect
78. #2551C22semidirect
82. #2451C22semidirect
83. #2451C22semidirect
95. #2369C22semidirect
107. #2097C22semidirect
108. #2095C22semidirect
111. #2088C22semidirect
112. #2087C22semidirect
113. #2086C22semidirect
114. #2086C22semidirect
115. #2085C22semidirect
116. #2083C22semidirect
117. #2083C22semidirect
118. #2083C22semidirect
119. #2068C22semidirect
120. #2068C22semidirect
121. #2068C22semidirect
124. #2066C22semidirect
127. #2059C22semidirect
128. #2059C22semidirect
129. #2058C22semidirect
130. #2058C22semidirect
131. #2057C22semidirect
132. #2057C22semidirect
133. #2057C22semidirect
134. #2057C22semidirect
135. #2057C22semidirect
136. #2057C22semidirect
139. #1993C22semidirect
140. #1993C22semidirect
141. #1989C22semidirect
142. #1985C22semidirect
145. #1949C22semidirect
146. #1949C22semidirect
147. #1947C22semidirect
148. #1944C22semidirect
149. #1943C22semidirect
150. #1942C22semidirect
151. #1942C22semidirect
152. #1940C22semidirect
153. #1940C22semidirect
154. #1939C22semidirect
159. #1921C22semidirect
160. #1918C22semidirect
161. #1917C22semidirect
162. #1916C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
189. #1847C22semidirect
190. #1845C22semidirect
193. #1805C22semidirect
197. #1771C22semidirect
287. #450Q8semidirect
559. C2×SD16C2×Q8semidirect
560. C2×SD16C2×Q8semidirect
796. #102C2×Q8semidirect
797. #102C2×Q8semidirect
1306. C22#3385semidirect

Maximal subgroups

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

subgroupindex
C2×#33852
C22×#4742
#591512
#362152
#312522
#312352
#309622
#309462
#285432
#263842
#263722
#263442
#263422
#260712
#260652
#260582
#260402
#259582
#259502
#258502
#258162
#254812
#254622
#248402
#248332
#243412
#229792
#229542
#228742
#228542
#214532