Finite Group Databasebeta

← #6684175

Subgroups — #6684175

Order 512.

1759 conjugacy classes of subgroups.

The subgroup lattice has 1283 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3386C211yesmaximal, characteristic, complemented
2C2×#3375C211yesmaximal, characteristic
3#42481C211yesmaximal, characteristic
4#35937C211yesmaximal, characteristic, complemented
5#33035C211yesmaximal, characteristic, complemented
6#30977C211yesmaximal, characteristic, complemented
7#30966C211yesmaximal, characteristic, complemented
8#30957C211yesmaximal, characteristic, complemented
9#30946C211yesmaximal, characteristic, complemented
10#30831C211yesmaximal, characteristic, complemented
11#30821C211yesmaximal, characteristic, complemented
12#30815C211yesmaximal, characteristic
13#30805C211yesmaximal, characteristic
14#30289C211yesmaximal, characteristic, complemented
15#29872C211yesmaximal, characteristic, complemented
16#28686C211yesmaximal, characteristic, complemented
17#28649C211yesmaximal, characteristic, complemented
18#26397C211yesmaximal, characteristic, complemented
19#26385C211yesmaximal, characteristic, complemented
20#26381C211yesmaximal, characteristic, complemented
21#26369C211yesmaximal, characteristic, complemented
22#26179C211yesmaximal, characteristic
23#26177C211yesmaximal, characteristic, complemented
24#26165C211yesmaximal, characteristic, complemented
25#26159C211yesmaximal, characteristic
26#25937C211yesmaximal, characteristic, complemented
27#25841C211yesmaximal, characteristic, complemented
28#25838C211yesmaximal, characteristic, complemented
29#25653C211yesmaximal, characteristic
30#22245C211yesmaximal, characteristic, complemented
31#21128C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36#3386—28no—
37#3375—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#500C2211yescharacteristic
41C2×#500C2211yescharacteristic
42C2×#489C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#488C2211yescharacteristic
45C2×#486C2211yescharacteristic
46C2×#477C2211yescharacteristic
47C2×#477C2211yescharacteristic
48C2×#477C2211yescharacteristic
49C2×#475C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#474C2211yescharacteristic
53C2×#474C2211yescharacteristic
54C2×#474C2211yescharacteristic
55C2×#464C2211yescharacteristic
56C2×#464C2211yescharacteristic
57C2×#460C2211yescharacteristic
58C2×#446C2211yescharacteristic
59C2×#446C2211yescharacteristic
60C2×#440C2211yescharacteristic
61C2×#440C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic
64C2×C4×SD16C2211yescharacteristic
65#2814—21no—
66#2700—21no—
67#2700—21no—
68#2680—21no—
69#2680—21no—
70#2660—21no—
71#2660C2211yescharacteristic
72#2640C2211yescharacteristic
73#2638—21no—
74#2614—21no—
75#2592C2211yescharacteristic
76#2584—21no—
77#2584C2211yescharacteristic
78#2567C2211yescharacteristic
79#2551—21no—
80#2551—21no—
81#2551C2211yescharacteristic
82#2551C2211yescharacteristic
83#2550—21no—
84#2550—21no—
85#2550C2211yescharacteristic
86#2550C2211yescharacteristic
87#2546—21no—
88#2546C2211yescharacteristic
89#2452C2211yescharacteristic
90#2452C2211yescharacteristic
91#2451C2211yescharacteristic
92#2451C2211yescharacteristic
93#2447C2211yescharacteristic
94#2447C2211yescharacteristic
95#2445C2211yescharacteristic
96#2445C2211yescharacteristic
97#2409—21no—
98#2399—21no—
99#2399C2211yescharacteristic
100#2351C2211yescharacteristic
101#2351C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2319C2211yescharacteristic
105#2276C2211yescharacteristic
106#2097C2211yescharacteristic
107#2097C2211yescharacteristic
108#2095C2211yescharacteristic
109#2095C2211yescharacteristic
110#2093C2211yescharacteristic
111#2093C2211yescharacteristic
112#2092C2211yescharacteristic
113#2092C2211yescharacteristic
114#2088C2211yescharacteristic
115#2088C2211yescharacteristic
116#2087C2211yescharacteristic
117#2086C2211yescharacteristic
118#2085C2211yescharacteristic
119#2085C2211yescharacteristic
120#2083C2211yescharacteristic
121#2083C2211yescharacteristic
122#2073C2211yescharacteristic
123#2073C2211yescharacteristic
124#2071C2211yescharacteristic
125#2071C2211yescharacteristic
126#2068C2211yescharacteristic
127#2067C2211yescharacteristic
128#2066C2211yescharacteristic
129#2065C2211yescharacteristic
130#2057C2211yescharacteristic
131#2057C2211yescharacteristic
132#2057C2211yescharacteristic
133#2057C2211yescharacteristic
134#2057C2211yescharacteristic
135#2057C2211yescharacteristic
136#2057C2211yescharacteristic
137#2057C2211yescharacteristic
138#2042C2211yescharacteristic
139#2042C2211yescharacteristic
140#2041C2211yescharacteristic
141#2041C2211yescharacteristic
142#2026C2211yescharacteristic
143#2025C2211yescharacteristic
144#2024C2211yescharacteristic
145#2023C2211yescharacteristic
146#1989C2211yescharacteristic
147#1988C2211yescharacteristic
148#1987C2211yescharacteristic
149#1984C2211yescharacteristic
150#1984C2211yescharacteristic
151#1983C2211yescharacteristic
152#1944C2211yescharacteristic
153#1943C2211yescharacteristic
154#1942C2211yescharacteristic
155#1941C2211yescharacteristic
156#1936C2211yescharacteristic
157#1935C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic
160#1928C2211yescharacteristic
161#1928C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
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#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1880C2211yescharacteristic
181#1880C2211yescharacteristic
182#1878C2211yescharacteristic
183#1878C2211yescharacteristic
184#1878C2211yescharacteristic
185#1878C2211yescharacteristic
186#1865C2211yescharacteristic
187#1865C2211yescharacteristic
188#1864C2211yescharacteristic
189#1863C2211yescharacteristic
190#1863C2211yescharacteristic
191#1863C2211yescharacteristic
192#1863C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1862C2211yescharacteristic
196#1862C2211yescharacteristic
197#1862C2211yescharacteristic
198#1862C2211yescharacteristic
199#1862C2211yescharacteristic
200#1832C2211yescharacteristic
201#1776C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C4×#102C2211yescharacteristic
204#1746C2211yescharacteristic
205C23×Q8—21no—
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#559—24no—
210#559—42no—
211Q82—24no—
212Q82—42no—
213#557—24no—
214#557—42no—
215D4×Q8—24no—
216D4×Q8—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#125—21no—
233C2×#125—21no—
234C2×#125C2311yescharacteristic
235C2×#125C2311yescharacteristic
236C2×#124—21no—
237C2×#124C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#123—21no—
240C2×#123—21no—
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265#501—24no—
266#501—24no—
267#500—24no—
268#500—42no—
269#489—24no—
270#489—24no—
271#488—42no—
272#486—24no—
273#478—24no—
274#478—24no—
275#477—24no—
276#477—24no—
277#477—24no—
278#475—24no—
279#474—24no—
280#474—24no—
281#474—24no—
282#464—24no—
283#464—24no—
284#460—24no—
285#446—24no—
286#446—24no—
287#440—24no—
288#440—24no—
289#440D418yes—
290C4×Q16—24no—
291C4×SD16—24no—
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347#398—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#398D411yescharacteristic
357#398D411yescharacteristic
358#398D411yescharacteristic
359#398D411yescharacteristic
360#397—21no—
361#397—21no—
362#397—21no—
363#397—21no—
364#397—21no—
365#397—21no—
366#397—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#395D411yescharacteristic
383#395D411yescharacteristic
384#395D411yescharacteristic
385#395D411yescharacteristic
386#394—21no—
387#394—21no—
388#394—21no—
389#394—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#393—21no—
394#393—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#390C2311yescharacteristic
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
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#389—21no—
423#389—21no—
424#389—21no—
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#384—21no—
452#384—21no—
453#384—21no—
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#382—21no—
457#382—21no—
458#382C2311yescharacteristic
459#382C2311yescharacteristic
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×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—44no—
523C22×Q8—82no—
524C22×Q8—82no—
525C22×Q8C2×D411yescharacteristic
526C22×Q8C2×D411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2411yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16C2×D414yes—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570C4⋊Q8—44no—
571C4⋊Q8—44no—
572C4⋊Q8—82no—
573C4⋊Q8—82no—
574C4⋊Q8—82no—
575#127—22no—
576#127—41no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125—41no—
581#125—44no—
582#125—44no—
583#124—22no—
584#124—22no—
585#124—22no—
586#124—41no—
587#124—44no—
588#123—44no—
589#123—44no—
590#123—82no—
591#123—82no—
592C22⋊Q8—44no—
593C22⋊Q8—44no—
594C22⋊Q8—44no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—44no—
617C4×Q8—44no—
618C4×Q8C2×D414yes—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4C2×D414yes—
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—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⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×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×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
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—22no—
736#107—22no—
737#107—22no—
738#107—41no—
739#107—41no—
740#107—41no—
741#107—41no—
742#107C2×D414yes—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747C4⋊C8—22no—
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753#103—22no—
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—41no—
763#103—41no—
764#103C2×D414yes—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—41no—
777#102—41no—
778#102C2×D414yes—
779#97—22no—
780#97—22no—
781#97C2×D414yes—
782C4×C8—22no—
783C4×C8—22no—
784C4×C8—22no—
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#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827C24—21no—
828C24—21no—
829C2×Q8—22no—
830C2×Q8—22no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8—42no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—816no—
866C2×Q8C22×D412yes—
867C2×Q82−1+412yes—
868C2×Q82−1+412yes—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4C22×D412yes—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—24no—
893C22×C4—21no—
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—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
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×D411yescharacteristic
927C22×C4C2511yescharacteristic
928Q16—44no—
929SD16—28no—
930SD16—44no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
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×C8C22×D412yes—
954C2×C8C22×D412yes—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
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—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
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—81no—
1013C4⋊C4—81no—
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⋊C4—81no—
1026C4⋊C4C22×D412yes—
1027C4⋊C4C22×D412yes—
1028C4⋊C42−1+412yes—
1029C4⋊C42−1+412yes—
1030C22⋊C4—24no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C42—24no—
1051C42—24no—
1052C42—24no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—42no—
1066C42—42no—
1067C42—42no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42C22×D412yes—
1075C42H(5,𝔽2)12yes—
1076C23—22no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23C23×D411yescharacteristic
1091Q8—22no—
1092Q8—22no—
1093Q8—22no—
1094Q8—44no—
1095Q8—44no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—84no—
1101Q8—84no—
1102Q8—84no—
1103Q8—84no—
1104Q8—162no—
1105Q8—162no—
1106Q8—162no—
1107Q8#53614yes—
1108D4—22no—
1109D4—22no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—84no—
1117D4—162no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—22no—
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—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—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—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—162no—
1202C2×C4D4212yes—
1203C2×C4D4212yes—
1204C2×C4#57612yes—
1205C2×C4#57812yes—
1206C2×C4C23×D411yescharacteristic
1207C2×C4C2×H(5,𝔽2)11yescharacteristic
1208C2×C4C2×2−1+411yescharacteristic
1209C2×C4C2×2−1+411yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4C2×2−1+411yescharacteristic
1212C8—22no—
1213C8—22no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22C2×D4211yescharacteristic
1235C22#348611yescharacteristic
1236C22#348611yescharacteristic
1237C22C2×#57611yescharacteristic
1238C22C2×#57811yescharacteristic
1239C22#358511yescharacteristic
1240C22#358611yescharacteristic
1241C4—24no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—42no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4C2×#53611yescharacteristic
1270C4#349911yescharacteristic
1271C4#355211yescharacteristic
1272C4#355211yescharacteristic
1273C2—82no—
1274C2—161no—
1275C2#3767511yescharacteristic
1276C2#6107211yescharacteristic
1277C2#6107611yescharacteristic
1278C2#6185411yescharacteristic
1279C2#6185711yescharacteristic
1280C2#6187011yescharacteristic
1281C2#6187411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
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
1. C2×#3386C2semidirect
4. #35937C2semidirect
5. #33035C2semidirect
6. #30977C2semidirect
7. #30966C2semidirect
8. #30957C2semidirect
9. #30946C2semidirect
10. #30831C2semidirect
11. #30821C2semidirect
14. #30289C2semidirect
15. #29872C2semidirect
16. #28686C2semidirect
17. #28649C2semidirect
18. #26397C2semidirect
19. #26385C2semidirect
20. #26381C2semidirect
21. #26369C2semidirect
23. #26177C2semidirect
24. #26165C2semidirect
26. #25937C2semidirect
27. #25841C2semidirect
28. #25838C2semidirect
30. #22245C2semidirect
31. #21128C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33862
C2×#33752
#424812
#359372
#330352
#309772
#309662
#309572
#309462
#308312
#308212
#308152
#308052
#302892
#298722
#286862
#286492
#263972
#263852
#263812
#263692
#261792
#261772
#261652
#261592
#259372
#258412
#258382
#256532
#222452
#211282