Finite Group Databasebeta

← #6809623

Subgroups — #6809623

Order 512.

1649 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3243C211yesmaximal, characteristic
2C2×#3242C211yesmaximal, characteristic, complemented
3#39347C211yesmaximal, characteristic
4#35330C211yesmaximal, characteristic, complemented
5#33112C211yesmaximal, characteristic
6#30969C211yesmaximal, characteristic, complemented
7#30963C211yesmaximal, characteristic, complemented
8#30950C211yesmaximal, characteristic, complemented
9#30948C211yesmaximal, characteristic, complemented
10#30836C211yesmaximal, characteristic, complemented
11#30830C211yesmaximal, characteristic, complemented
12#30820C211yesmaximal, characteristic, complemented
13#30814C211yesmaximal, characteristic, complemented
14#29648C211yesmaximal, characteristic, complemented
15#29647C211yesmaximal, characteristic
16#28815C211yesmaximal, characteristic, complemented
17#28812C211yesmaximal, characteristic, complemented
18#27912C211yesmaximal, characteristic
19#27774C211yesmaximal, characteristic, complemented
20#27772C211yesmaximal, characteristic, complemented
21#27653C211yesmaximal, characteristic, complemented
22#26471C211yesmaximal, characteristic, complemented
23#26470C211yesmaximal, characteristic, complemented
24#26050C211yesmaximal, characteristic, complemented
25#26050C211yesmaximal, characteristic, complemented
26#24614C211yesmaximal, characteristic, complemented
27#24612C211yesmaximal, characteristic
28#24074C211yesmaximal, characteristic
29#24071C211yesmaximal, characteristic, complemented
30#22600C211yesmaximal, characteristic, complemented
31C4×#485C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#541C2211yescharacteristic
36#3243—28no—
37#3242—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#500C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#491C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#487C2211yescharacteristic
46C2×#484C2211yescharacteristic
47C2×#484C2211yescharacteristic
48C2×#481C2211yescharacteristic
49C2×#485C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#483C2211yescharacteristic
53C2×#483C2211yescharacteristic
54C2×#480C2211yescharacteristic
55C2×#479C2211yescharacteristic
56C2×#479C2211yescharacteristic
57C2×#479C2211yescharacteristic
58C2×#477C2211yescharacteristic
59C2×#477C2211yescharacteristic
60C2×#475C2211yescharacteristic
61C2×#478C2211yescharacteristic
62C2×#474C2211yescharacteristic
63C2×#433C2211yescharacteristic
64C2×#433C2211yescharacteristic
65#2862—21no—
66#2859—21no—
67#2850C2211yescharacteristic
68#2721—21no—
69#2720—21no—
70#2715—21no—
71#2695—21no—
72#2660—21no—
73#2660—21no—
74#2625C2211yescharacteristic
75#2624C2211yescharacteristic
76#2553—21no—
77#2550C2211yescharacteristic
78#2550C2211yescharacteristic
79#2550C2211yescharacteristic
80#2550C2211yescharacteristic
81#2550C2211yescharacteristic
82#2550C2211yescharacteristic
83#2550C2211yescharacteristic
84#2550C2211yescharacteristic
85#2550C2211yescharacteristic
86#2549—21no—
87#2549—21no—
88#2549—21no—
89#2549—21no—
90#2545C2211yescharacteristic
91#2521—21no—
92#2519—21no—
93#2489—21no—
94#2454C2211yescharacteristic
95#2451C2211yescharacteristic
96#2448C2211yescharacteristic
97#2446C2211yescharacteristic
98#2367C2211yescharacteristic
99#2351C2211yescharacteristic
100#2317C2211yescharacteristic
101#2317C2211yescharacteristic
102C4×C22⋊Q8C2211yescharacteristic
103#2285C2211yescharacteristic
104C2×#382C2211yescharacteristic
105C4×#117C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2092C2211yescharacteristic
109#2092C2211yescharacteristic
110#2087C2211yescharacteristic
111#2087C2211yescharacteristic
112#2086C2211yescharacteristic
113#2086C2211yescharacteristic
114#2085C2211yescharacteristic
115#2085C2211yescharacteristic
116#2074C2211yescharacteristic
117#2074C2211yescharacteristic
118#2068C2211yescharacteristic
119#2067C2211yescharacteristic
120#2066C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2058C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2058C2211yescharacteristic
132#2058C2211yescharacteristic
133#2058C2211yescharacteristic
134#2043C2211yescharacteristic
135#2043C2211yescharacteristic
136#2042C2211yescharacteristic
137#2042C2211yescharacteristic
138#2026C2211yescharacteristic
139#2026C2211yescharacteristic
140#2025C2211yescharacteristic
141#2025C2211yescharacteristic
142#2024C2211yescharacteristic
143#2024C2211yescharacteristic
144#2023C2211yescharacteristic
145#2023C2211yescharacteristic
146#1983C2211yescharacteristic
147#1983C2211yescharacteristic
148#1958C2211yescharacteristic
149#1958C2211yescharacteristic
150#1949C2211yescharacteristic
151#1949C2211yescharacteristic
152#1949C2211yescharacteristic
153#1949C2211yescharacteristic
154#1944C2211yescharacteristic
155#1944C2211yescharacteristic
156#1942C2211yescharacteristic
157#1942C2211yescharacteristic
158#1939C2211yescharacteristic
159#1939C2211yescharacteristic
160#1936C2211yescharacteristic
161#1935C2211yescharacteristic
162#1934C2211yescharacteristic
163#1933C2211yescharacteristic
164#1928C2211yescharacteristic
165#1928C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1926C2211yescharacteristic
169#1925C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1917C2211yescharacteristic
173#1917C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1875C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1854C2211yescharacteristic
188#1846C2211yescharacteristic
189#1846C2211yescharacteristic
190#1825C2211yescharacteristic
191#1824C2211yescharacteristic
192#1823C2211yescharacteristic
193#1818C2211yescharacteristic
194#1818C2211yescharacteristic
195#1805C2211yescharacteristic
196#1805C2211yescharacteristic
197#1797C2211yescharacteristic
198C4×#107C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1770C2211yescharacteristic
201C8×C4⋊C4C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C4×#103C2211yescharacteristic
204C4×C22⋊C8C2211yescharacteristic
205#544—24no—
206#544—24no—
207#544—42no—
208#544—42no—
209#542—24no—
210#542—42no—
211#541—24no—
212#541—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
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×#124—21no—
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#501—24no—
258#501—24no—
259#500—24no—
260#499—24no—
261#491—24no—
262#489—24no—
263#488—24no—
264#487—24no—
265#485—24no—
266#485D418yes—
267#484—24no—
268#484—24no—
269#483—24no—
270#483—42no—
271#482—24no—
272#481—42no—
273#480—24no—
274#479—24no—
275#479—24no—
276#479—24no—
277#478—24no—
278#477—24no—
279#477—24no—
280#475—24no—
281#474—24no—
282#433—24no—
283#433—24no—
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×#102C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344#400—21no—
345#400—21no—
346#399—21no—
347#399—21no—
348#399—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#397—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#396—21no—
366#396—21no—
367#396—21no—
368#395—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#394—21no—
379#394—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391—21no—
387#391—21no—
388#391—21no—
389#391—21no—
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
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#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#386—21no—
434#386—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#384—21no—
443#384—21no—
444#384D411yescharacteristic
445#384D411yescharacteristic
446#382—21no—
447#382—21no—
448#382—21no—
449#382—21no—
450#382—21no—
451#382D411yescharacteristic
452#382D411yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#380—21no—
459#380D411yescharacteristic
460#380D411yescharacteristic
461#380D411yescharacteristic
462#380D411yescharacteristic
463#380C2311yescharacteristic
464C4×C4⋊C4—21no—
465C4×C4⋊C4—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×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4—21no—
478C4×C22⋊C4—21no—
479#376—21no—
480C2×#95—21no—
481C2×#95—21no—
482C43—21no—
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#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—21no—
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—41no—
552#126—44no—
553#126—44no—
554#126—44no—
555#125—22no—
556#125—22no—
557#125—22no—
558#125—22no—
559#125—22no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125—41no—
565#125—44no—
566#125—44no—
567#125—44no—
568#125—44no—
569#124—22no—
570#124—22no—
571#124—22no—
572#124—41no—
573#124—44no—
574#123—44no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—44no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8C2×D414yes—
584#121—22no—
585#121—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×D4—22no—
595C4×D4—41no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117C2×D414yes—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—22no—
695C2×C42—22no—
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×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
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—22no—
719#107—22no—
720#107—22no—
721#107—22no—
722#107C2×D414yes—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106C2×D414yes—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—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—22no—
751#103—41no—
752#103—41no—
753#103C2×D414yes—
754#103C2×D414yes—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
762#102—41no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8C2×D414yes—
767#97—22no—
768#97—22no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—22no—
772C4×C8—22no—
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#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
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—
819C24C22×D411yescharacteristic
820C2×Q8—21no—
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—42no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8C22×D412yes—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—42no—
854C2×D4—81no—
855C2×D4—81no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D412yes—
904C22×C4H(5,𝔽2)12yes—
905C22×C4C2511yescharacteristic
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×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8C22×D412yes—
929C2×C8C22×D412yes—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—22no—
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—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
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—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
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⋊C4C22×D412yes—
1002C4⋊C4C22×D412yes—
1003C4⋊C4C22×D412yes—
1004C4⋊C42−1+412yes—
1005C4⋊C42−1+412yes—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C42—24no—
1028C42—22no—
1029C42—22no—
1030C42—24no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C422−1+412yes—
1051C422−1+412yes—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23D4212yes—
1066C23C23×D411yescharacteristic
1067Q8—22no—
1068Q8—22no—
1069Q8—41no—
1070Q8—41no—
1071Q8—41no—
1072Q8—41no—
1073Q8—41no—
1074Q8—41no—
1075Q8—162no—
1076Q8—162no—
1077Q8—162no—
1078Q8—162no—
1079Q8—162no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—162no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
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—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—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
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—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—82no—
1171C2×C4—82no—
1172C2×C4—162no—
1173C2×C4—162no—
1174C2×C4—162no—
1175C2×C4#53612yes—
1176C2×C4#53612yes—
1177C2×C4D4212yes—
1178C2×C4C23×D411yescharacteristic
1179C2×C4C2×H(5,𝔽2)11yescharacteristic
1180C2×C4C2×2−1+411yescharacteristic
1181C2×C4C2×2−1+411yescharacteristic
1182C2×C4C2×2−1+411yescharacteristic
1183C2×C4C2×2−1+411yescharacteristic
1184C8—22no—
1185C8—22no—
1186C8—41no—
1187C8—41no—
1188C8—41no—
1189C8—41no—
1190C8—41no—
1191C8—41no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22C2×#53611yescharacteristic
1207C22C2×D4211yescharacteristic
1208C22#348611yescharacteristic
1209C22#358411yescharacteristic
1210C22#358411yescharacteristic
1211C22#358411yescharacteristic
1212C22#358611yescharacteristic
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—42no—
1221C4—42no—
1222C4—42no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—42no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4#349911yescharacteristic
1242C4#349911yescharacteristic
1243C4#354411yescharacteristic
1244C4#354411yescharacteristic
1245C2—42no—
1246C2—161no—
1247C2#3933711yescharacteristic
1248C2#6085911yescharacteristic
1249C2#6087611yescharacteristic
1250C2#6109011yescharacteristic
1251C2#6109611yescharacteristic
1252C2#6186211yescharacteristic
1253C2#6186711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3242C2semidirect
4. #35330C2semidirect
6. #30969C2semidirect
7. #30963C2semidirect
8. #30950C2semidirect
9. #30948C2semidirect
10. #30836C2semidirect
11. #30830C2semidirect
12. #30820C2semidirect
13. #30814C2semidirect
14. #29648C2semidirect
16. #28815C2semidirect
17. #28812C2semidirect
19. #27774C2semidirect
20. #27772C2semidirect
21. #27653C2semidirect
22. #26471C2semidirect
23. #26470C2semidirect
24. #26050C2semidirect
25. #26050C2semidirect
26. #24614C2semidirect
29. #24071C2semidirect
30. #22600C2semidirect
31. C4×#485C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32432
C2×#32422
#393472
#353302
#331122
#309692
#309632
#309502
#309482
#308362
#308302
#308202
#308142
#296482
#296472
#288152
#288122
#279122
#277742
#277722
#276532
#264712
#264702
#260502
#246142
#246122
#240742
#240712
#226002
C4×#4852