Finite Group Databasebeta

← #6673625

Subgroups — #6673625

Order 512.

1712 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3349C211yesmaximal, characteristic
2C2×#3082C211yesmaximal, characteristic, complemented
3#42644C211yesmaximal, characteristic
4#36007C211yesmaximal, characteristic
5#33019C211yesmaximal, characteristic, complemented
6#31253C211yesmaximal, characteristic, complemented
7#31239C211yesmaximal, characteristic, complemented
8#31143C211yesmaximal, characteristic, complemented
9#31119C211yesmaximal, characteristic, complemented
10#30977C211yesmaximal, characteristic, complemented
11#30968C211yesmaximal, characteristic, complemented
12#30917C211yesmaximal, characteristic, complemented
13#30912C211yesmaximal, characteristic, complemented
14#29786C211yesmaximal, characteristic, complemented
15#29649C211yesmaximal, characteristic, complemented
16#28355C211yesmaximal, characteristic, complemented
17#28102C211yesmaximal, characteristic
18#26911C211yesmaximal, characteristic, complemented
19#26910C211yesmaximal, characteristic, complemented
20#26809C211yesmaximal, characteristic, complemented
21#26795C211yesmaximal, characteristic, complemented
22#26473C211yesmaximal, characteristic, complemented
23#26465C211yesmaximal, characteristic, complemented
24#26351C211yesmaximal, characteristic, complemented
25#26337C211yesmaximal, characteristic, complemented
26#24586C211yesmaximal, characteristic, complemented
27#24482C211yesmaximal, characteristic, complemented
28#24096C211yesmaximal, characteristic
29#23967C211yesmaximal, characteristic
30#22621C211yesmaximal, characteristic, complemented
31#22072C211yesmaximal, characteristic
32C2×#556C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#519C2211yescharacteristic
36#3349—28no—
37C2×#501C2211yescharacteristic
38C2×#484C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#485C2211yescharacteristic
41C2×#485C2211yescharacteristic
42C2×#485C2211yescharacteristic
43#3082—28no—
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#477C2211yescharacteristic
51C2×#477C2211yescharacteristic
52C2×#475C2211yescharacteristic
53C2×#475C2211yescharacteristic
54C2×#470C2211yescharacteristic
55C2×#467C2211yescharacteristic
56C2×#451C2211yescharacteristic
57C2×#441C2211yescharacteristic
58C2×#435C2211yescharacteristic
59C2×#428C2211yescharacteristic
60C2×#427C2211yescharacteristic
61C2×#427C2211yescharacteristic
62C2×#424C2211yescharacteristic
63C2×#419C2211yescharacteristic
64C22×#103C2211yescharacteristic
65#2814—21no—
66#2721—21no—
67#2719—21no—
68#2716—21no—
69#2713—21no—
70#2663—21no—
71#2637—21no—
72#2625—21no—
73#2625C2211yescharacteristic
74#2625C2211yescharacteristic
75#2604—21no—
76#2581—21no—
77#2552C2211yescharacteristic
78#2550C2211yescharacteristic
79#2499—21no—
80#2499C2211yescharacteristic
81#2492C2211yescharacteristic
82#2489C2211yescharacteristic
83#2485C2211yescharacteristic
84#2478—21no—
85#2478—21no—
86#2474—21no—
87#2474—21no—
88#2453C2211yescharacteristic
89#2451C2211yescharacteristic
90#2451C2211yescharacteristic
91#2451C2211yescharacteristic
92#2441C2211yescharacteristic
93#2439C2211yescharacteristic
94#2434C2211yescharacteristic
95#2429C2211yescharacteristic
96#2429C2211yescharacteristic
97#2409C2211yescharacteristic
98#2399—21no—
99#2395C2211yescharacteristic
100#2365C2211yescharacteristic
101#2365C2211yescharacteristic
102#2362C2211yescharacteristic
103#2362C2211yescharacteristic
104#2346C2211yescharacteristic
105#2345C2211yescharacteristic
106#2097C2211yescharacteristic
107#2096C2211yescharacteristic
108#2088C2211yescharacteristic
109#2088C2211yescharacteristic
110#2085C2211yescharacteristic
111#2084C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2058C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2056C2211yescharacteristic
129#2056C2211yescharacteristic
130#2043C2211yescharacteristic
131#2043C2211yescharacteristic
132#2036C2211yescharacteristic
133#2036C2211yescharacteristic
134#2035C2211yescharacteristic
135#2035C2211yescharacteristic
136#2026C2211yescharacteristic
137#2026C2211yescharacteristic
138#2026C2211yescharacteristic
139#2026C2211yescharacteristic
140#2024C2211yescharacteristic
141#2024C2211yescharacteristic
142#2016C2211yescharacteristic
143#2016C2211yescharacteristic
144#2001C2211yescharacteristic
145#2001C2211yescharacteristic
146#1981C2211yescharacteristic
147#1981C2211yescharacteristic
148#1971C2211yescharacteristic
149#1969C2211yescharacteristic
150#1960C2211yescharacteristic
151#1956C2211yescharacteristic
152#1949C2211yescharacteristic
153#1947C2211yescharacteristic
154#1943C2211yescharacteristic
155#1942C2211yescharacteristic
156#1940C2211yescharacteristic
157#1939C2211yescharacteristic
158#1935C2211yescharacteristic
159#1935C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1928C2211yescharacteristic
163#1927C2211yescharacteristic
164#1924C2211yescharacteristic
165#1923C2211yescharacteristic
166#1921C2211yescharacteristic
167#1920C2211yescharacteristic
168#1919C2211yescharacteristic
169#1918C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic
174#1892C2211yescharacteristic
175#1892C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1878C2211yescharacteristic
182#1873C2211yescharacteristic
183#1873C2211yescharacteristic
184#1869C2211yescharacteristic
185#1865C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1863C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1854C2211yescharacteristic
192#1854C2211yescharacteristic
193#1850C2211yescharacteristic
194#1850C2211yescharacteristic
195#1850C2211yescharacteristic
196#1825C2211yescharacteristic
197#1825C2211yescharacteristic
198#1823C2211yescharacteristic
199#1818C2211yescharacteristic
200#1809C2211yescharacteristic
201#1787C2211yescharacteristic
202#1776C2211yescharacteristic
203C4×#106C2211yescharacteristic
204#1753C2211yescharacteristic
205C23×Q8C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—24no—
213#556—42no—
214#552—24no—
215#552—42no—
216#544—24no—
217#544—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242#519—24no—
243#519—42no—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117—21no—
255C2×#117—21no—
256C2×#117—21no—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263#501—24no—
264#485—24no—
265#485—24no—
266#485—24no—
267#485—42no—
268#484—24no—
269#479—24no—
270#479—24no—
271#479—24no—
272#479—24no—
273#479—24no—
274#477—24no—
275#477—24no—
276#477—24no—
277#475—24no—
278#475—24no—
279#470—24no—
280#467—24no—
281#451—42no—
282#441—24no—
283#435—24no—
284#428D418yes—
285#427—24no—
286#427—24no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304#424—24no—
305C2×C4⋊C8C2311yescharacteristic
306C2×C4⋊C8C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312#419—24no—
313C2×#103—24no—
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×C22⋊C8C2311yescharacteristic
341C2×C22⋊C8C2311yescharacteristic
342C2×C22⋊C8C2311yescharacteristic
343C2×C22⋊C8C2311yescharacteristic
344C2×C22⋊C8C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×#97C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348#400—21no—
349#400—21no—
350#400—21no—
351#400—21no—
352#400—21no—
353#400D411yescharacteristic
354#399—21no—
355#399D411yescharacteristic
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#398—21no—
366#398—21no—
367#398D411yescharacteristic
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397—21no—
374#397—21no—
375#397—21no—
376#397D411yescharacteristic
377#397D411yescharacteristic
378#397D411yescharacteristic
379#396—21no—
380#396—21no—
381#396—21no—
382#396—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#395—21no—
388#395—21no—
389#395—21no—
390#394—21no—
391#394D411yescharacteristic
392#394D411yescharacteristic
393#393—21no—
394#393—21no—
395#393—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
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#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#388—21no—
431#388—21no—
432#388—21no—
433#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#384—21no—
463#384C2311yescharacteristic
464#382—21no—
465#382—21no—
466#382C2311yescharacteristic
467#380—21no—
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
474C4×C4⋊C4—21no—
475C4×C4⋊C4—21no—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C22⋊C4—21no—
483C4×C22⋊C4C2311yescharacteristic
484C4×C22⋊C4C2311yescharacteristic
485C4×C22⋊C4C2311yescharacteristic
486#376—21no—
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#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—22no—
520C22×Q8—22no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—41no—
524C22×Q8—41no—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16C2×D414yes—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—44no—
571#126—44no—
572#126—44no—
573#126—44no—
574#125—22no—
575#125—22no—
576#125—22no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—44no—
581#125—44no—
582#124—44no—
583#123—44no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—44no—
593C22⋊Q8—44no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—44no—
611C4×Q8—44no—
612C4×Q8—44no—
613C4×D4—22no—
614C4×D4—22no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—44no—
623#117—44no—
624#117—44no—
625#117—41no—
626#117—41no—
627#117C2×D414yes—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—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⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D414yes—
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#107C2×D414yes—
738#107C2×D414yes—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—41no—
744#106—41no—
745#106C2×D414yes—
746#106C2×D414yes—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785#97—22no—
786#97—41no—
787C4×C8—41no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#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#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—28no—
843C2×Q8—21no—
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—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q82−1+412yes—
879C2×Q82−1+412yes—
880C2×D4—22no—
881C2×D4—41no—
882C2×D4—41no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—24no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
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—21no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D412yes—
927C22×C4C22×D411yescharacteristic
928C22×C4H(5,𝔽2)12yes—
929C22×C4C2511yescharacteristic
930Q16—44no—
931Q16—82no—
932Q16—82no—
933M16—44no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—44no—
957C2×C8—44no—
958C2×C8C22×D412yes—
959C2×C8C22×D412yes—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4C22×D412yes—
1026C4⋊C4C22×D412yes—
1027C4⋊C4C22×D412yes—
1028C4⋊C4C22×D412yes—
1029C22⋊C4—24no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C42—24no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—42no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—81no—
1076C42—81no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23D4212yes—
1091C23C23×D411yescharacteristic
1092Q8—22no—
1093Q8—22no—
1094Q8—22no—
1095Q8—22no—
1096Q8—48no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—84no—
1110Q8—162no—
1111Q8—162no—
1112D4—82no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—48no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
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—84no—
1205C2×C4D4212yes—
1206C2×C4#57812yes—
1207C2×C4C23×D411yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4C2×2−1+411yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22C2×D4211yescharacteristic
1236C22#348911yescharacteristic
1237C22#348911yescharacteristic
1238C22C2×#57811yescharacteristic
1239C22#358411yescharacteristic
1240C22#358611yescharacteristic
1241C22#358611yescharacteristic
1242C4—22no—
1243C4—22no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4#344911yescharacteristic
1271C4#348611yescharacteristic
1272C4#353511yescharacteristic
1273C4#353511yescharacteristic
1274C2—42no—
1275C2—81no—
1276C2#3765311yescharacteristic
1277C2#6107311yescharacteristic
1278C2#6109711yescharacteristic
1279C2#6216111yescharacteristic
1280C2#6216811yescharacteristic
1281C2#6222011yescharacteristic
1282C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3082C2semidirect
5. #33019C2semidirect
6. #31253C2semidirect
7. #31239C2semidirect
8. #31143C2semidirect
9. #31119C2semidirect
10. #30977C2semidirect
11. #30968C2semidirect
12. #30917C2semidirect
13. #30912C2semidirect
14. #29786C2semidirect
15. #29649C2semidirect
16. #28355C2semidirect
18. #26911C2semidirect
19. #26910C2semidirect
20. #26809C2semidirect
21. #26795C2semidirect
22. #26473C2semidirect
23. #26465C2semidirect
24. #26351C2semidirect
25. #26337C2semidirect
26. #24586C2semidirect
27. #24482C2semidirect
30. #22621C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33492
C2×#30822
#426442
#360072
#330192
#312532
#312392
#311432
#311192
#309772
#309682
#309172
#309122
#297862
#296492
#283552
#281022
#269112
#269102
#268092
#267952
#264732
#264652
#263512
#263372
#245862
#244822
#240962
#239672
#226212
#220722