Finite Group Databasebeta

← #6684189

Subgroups — #6684189

Order 512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1233 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3388C211yesmaximal, characteristic
2C2×#3377C211yesmaximal, characteristic
3#42676C211yesmaximal, characteristic
4#35957C211yesmaximal, characteristic, complemented
5#33041C211yesmaximal, characteristic, complemented
6#30977C211yesmaximal, characteristic, complemented
7#30968C211yesmaximal, characteristic, complemented
8#30961C211yesmaximal, characteristic, complemented
9#30952C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic
11#30823C211yesmaximal, characteristic
12#30819C211yesmaximal, characteristic
13#30811C211yesmaximal, characteristic
14#30288C211yesmaximal, characteristic, complemented
15#29874C211yesmaximal, characteristic
16#28686C211yesmaximal, characteristic, complemented
17#28652C211yesmaximal, characteristic, complemented
18#26395C211yesmaximal, characteristic, complemented
19#26389C211yesmaximal, characteristic, complemented
20#26383C211yesmaximal, characteristic, complemented
21#26369C211yesmaximal, characteristic, complemented
22#26181C211yesmaximal, characteristic
23#26177C211yesmaximal, characteristic
24#26165C211yesmaximal, characteristic
25#26161C211yesmaximal, characteristic
26#25931C211yesmaximal, characteristic, complemented
27#25843C211yesmaximal, characteristic
28#25842C211yesmaximal, characteristic, complemented
29#25646C211yesmaximal, characteristic
30#22245C211yesmaximal, characteristic, complemented
31#21128C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#554C2211yescharacteristic
36#3388—28no—
37#3377—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#499C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#491C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#487C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#475C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#478C2211yescharacteristic
53C2×#478C2211yescharacteristic
54C2×#476C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#464C2211yescharacteristic
57C2×#462C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic
64C2×C4×SD16C2211yescharacteristic
65#2817—21no—
66#2698—21no—
67#2698—21no—
68#2689—21no—
69#2689—21no—
70#2660—21no—
71#2660C2211yescharacteristic
72#2642C2211yescharacteristic
73#2627—21no—
74#2625—21no—
75#2584—21no—
76#2584C2211yescharacteristic
77#2584C2211yescharacteristic
78#2568C2211yescharacteristic
79#2567—21no—
80#2567C2211yescharacteristic
81#2552—21no—
82#2552—21no—
83#2552C2211yescharacteristic
84#2552C2211yescharacteristic
85#2550—21no—
86#2550—21no—
87#2550C2211yescharacteristic
88#2550C2211yescharacteristic
89#2484—21no—
90#2453C2211yescharacteristic
91#2453C2211yescharacteristic
92#2451C2211yescharacteristic
93#2451C2211yescharacteristic
94#2447C2211yescharacteristic
95#2447C2211yescharacteristic
96#2447C2211yescharacteristic
97#2447C2211yescharacteristic
98#2399—21no—
99#2399C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2319C2211yescharacteristic
105#2276C2211yescharacteristic
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#2084C2211yescharacteristic
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#2058C2211yescharacteristic
135#2058C2211yescharacteristic
136#2057C2211yescharacteristic
137#2057C2211yescharacteristic
138#2042C2211yescharacteristic
139#2042C2211yescharacteristic
140#2042C2211yescharacteristic
141#2042C2211yescharacteristic
142#2026C2211yescharacteristic
143#2026C2211yescharacteristic
144#2026C2211yescharacteristic
145#2026C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1988C2211yescharacteristic
149#1984C2211yescharacteristic
150#1984C2211yescharacteristic
151#1981C2211yescharacteristic
152#1944C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1935C2211yescharacteristic
157#1935C2211yescharacteristic
158#1933C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1921C2211yescharacteristic
167#1918C2211yescharacteristic
168#1917C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1878C2211yescharacteristic
185#1878C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1865C2211yescharacteristic
189#1865C2211yescharacteristic
190#1865C2211yescharacteristic
191#1865C2211yescharacteristic
192#1865C2211yescharacteristic
193#1864C2211yescharacteristic
194#1864C2211yescharacteristic
195#1863C2211yescharacteristic
196#1863C2211yescharacteristic
197#1863C2211yescharacteristic
198#1862C2211yescharacteristic
199#1862C2211yescharacteristic
200#1832C2211yescharacteristic
201#1776C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C4×#102C2211yescharacteristic
204#1746C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208#557—24no—
209#557—24no—
210#557—42no—
211#557—42no—
212#556—24no—
213#556—42no—
214#554—24no—
215#554—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C22×C4⋊C4—21no—
258#501—24no—
259#501—24no—
260#499—24no—
261#499—42no—
262#491—24no—
263#489—24no—
264#488—24no—
265#487—42no—
266#479—24no—
267#479—24no—
268#479—24no—
269#478—24no—
270#478—24no—
271#478—24no—
272#477—24no—
273#476—24no—
274#475—24no—
275#464—24no—
276#464—24no—
277#462—24no—
278#446—24no—
279#446—24no—
280#441—24no—
281#440—24no—
282#440D418yes—
283C4×Q16—24no—
284C4×SD16—24no—
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#400—21no—
345#400—21no—
346#400—21no—
347#400—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—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#398D411yescharacteristic
363#398D411yescharacteristic
364#398D411yescharacteristic
365#398D411yescharacteristic
366#397—21no—
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—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#395—21no—
383#395—21no—
384#395D411yescharacteristic
385#395D411yescharacteristic
386#395D411yescharacteristic
387#395D411yescharacteristic
388#391—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
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#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389C2311yescharacteristic
423#389C2311yescharacteristic
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#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384—21no—
447#384—21no—
448#384—21no—
449#384—21no—
450#384—21no—
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#381—21no—
463#380—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4—21no—
469C4×C4⋊C4—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479#376—21no—
480#376C2311yescharacteristic
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×Q8C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16C2×D414yes—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—22no—
550C4⋊Q8—41no—
551C4⋊Q8—41no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554#126—44no—
555#126—44no—
556#125—22no—
557#125—22no—
558#125—22no—
559#125—22no—
560#125—22no—
561#125—22no—
562#125—22no—
563#125—22no—
564#125—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—44no—
569#125—44no—
570#125—44no—
571#125—44no—
572#124—22no—
573#124—22no—
574#124—41no—
575#124—41no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
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×Q8—41no—
598C4×Q8—41no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—44no—
602C4×Q8—44no—
603C4×Q8C2×D414yes—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4C2×D414yes—
610#117—44no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
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—44no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
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×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—22no—
715#107—22no—
716#107—22no—
717#107—22no—
718#107—41no—
719#107—41no—
720#107C2×D414yes—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—41no—
729#106—41no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103C2×D414yes—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102C2×D414yes—
762#97—22no—
763#97—22no—
764#97C2×D414yes—
765C4×C8—22no—
766C4×C8—22no—
767C4×C8—22no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
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#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C2×Q8—22no—
820C2×Q8—22no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
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—41no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—42no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—42no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—81no—
849C2×Q8C22×D412yes—
850C2×Q82−1+412yes—
851C2×Q82−1+412yes—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4C22×D412yes—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—24no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C2511yescharacteristic
897Q16—44no—
898Q16—44no—
899SD16—28no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8C22×D412yes—
923C2×C8C22×D412yes—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C22×D412yes—
1003C4⋊C4C22×D412yes—
1004C4⋊C42−1+412yes—
1005C4⋊C42−1+412yes—
1006C22⋊C4—24no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C42—24no—
1018C42—24no—
1019C42—24no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42C22×D412yes—
1043C42H(5,𝔽2)12yes—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23C23×D411yescharacteristic
1052Q8—22no—
1053Q8—22no—
1054Q8—22no—
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—82no—
1064Q8—82no—
1065Q8—84no—
1066Q8—84no—
1067Q8—162no—
1068Q8#53614yes—
1069D4—22no—
1070D4—22no—
1071D4—41no—
1072D4—41no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
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—84no—
1159C2×C4—84no—
1160C2×C4—162no—
1161C2×C4D4212yes—
1162C2×C4D4212yes—
1163C2×C4C23×D411yescharacteristic
1164C2×C4C2×H(5,𝔽2)11yescharacteristic
1165C2×C4C2×2−1+411yescharacteristic
1166C2×C4C2×2−1+411yescharacteristic
1167C2×C4C2×2−1+411yescharacteristic
1168C2×C4C2×2−1+411yescharacteristic
1169C8—22no—
1170C8—22no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22C2×D4211yescharacteristic
1185C22#348611yescharacteristic
1186C22#348611yescharacteristic
1187C22#358411yescharacteristic
1188C22#358411yescharacteristic
1189C22#358611yescharacteristic
1190C22#358611yescharacteristic
1191C4—24no—
1192C4—22no—
1193C4—22no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—42no—
1207C4—41no—
1208C4—42no—
1209C4—41no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4C2×#53611yescharacteristic
1221C4#349911yescharacteristic
1222C4#355211yescharacteristic
1223C4#355211yescharacteristic
1224C2—82no—
1225C2#3767511yescharacteristic
1226C2#6107311yescharacteristic
1227C2#6107811yescharacteristic
1228C2#6185611yescharacteristic
1229C2#6186211yescharacteristic
1230C2#6186711yescharacteristic
1231C2#6187511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #35957C2semidirect
5. #33041C2semidirect
6. #30977C2semidirect
7. #30968C2semidirect
8. #30961C2semidirect
9. #30952C2semidirect
14. #30288C2semidirect
16. #28686C2semidirect
17. #28652C2semidirect
18. #26395C2semidirect
19. #26389C2semidirect
20. #26383C2semidirect
21. #26369C2semidirect
26. #25931C2semidirect
28. #25842C2semidirect
30. #22245C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33882
C2×#33772
#426762
#359572
#330412
#309772
#309682
#309612
#309522
#308312
#308232
#308192
#308112
#302882
#298742
#286862
#286522
#263952
#263892
#263832
#263692
#261812
#261772
#261652
#261612
#259312
#258432
#258422
#256462
#222452
#211282