Finite Group Databasebeta

← #7183885

Subgroups — #7183885

Order 512.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3384C211yesmaximal, characteristic, complemented
2C2×#3235C211yesmaximal, characteristic, complemented
3#59153C211yesmaximal, characteristic, complemented
4#59080C211yesmaximal, characteristic, complemented
5#31247C211yesmaximal, characteristic, complemented
6#31234C211yesmaximal, characteristic, complemented
7#31147C211yesmaximal, characteristic, complemented
8#31121C211yesmaximal, characteristic, complemented
9#30966C211yesmaximal, characteristic, complemented
10#30954C211yesmaximal, characteristic, complemented
11#30794C211yesmaximal, characteristic, complemented
12#30780C211yesmaximal, characteristic, complemented
13#28650C211yesmaximal, characteristic, complemented
14#28421C211yesmaximal, characteristic, complemented
15#26904C211yesmaximal, characteristic, complemented
16#26889C211yesmaximal, characteristic, complemented
17#26812C211yesmaximal, characteristic, complemented
18#26797C211yesmaximal, characteristic, complemented
19#26634C211yesmaximal, characteristic, complemented
20#26619C211yesmaximal, characteristic, complemented
21#26475C211yesmaximal, characteristic, complemented
22#26464C211yesmaximal, characteristic, complemented
23#25946C211yesmaximal, characteristic, complemented
24#25844C211yesmaximal, characteristic, complemented
25#25461C211yesmaximal, characteristic, complemented
26#25288C211yesmaximal, characteristic, complemented
27#24304C211yesmaximal, characteristic, complemented
28#24152C211yesmaximal, characteristic, complemented
29#23708C211yesmaximal, characteristic, complemented
30#23168C211yesmaximal, characteristic, complemented
31#22106C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548—21no—
35C2×#533C2211yescharacteristic
36C2×#532C2211yescharacteristic
37#3384—28no—
38#3235—28no—
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#501C2211yescharacteristic
42C2×#498C2211yescharacteristic
43C2×#490C2211yescharacteristic
44C2×#490C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#482C2211yescharacteristic
49C2×#478C2211yescharacteristic
50C2×#478C2211yescharacteristic
51C2×#478C2211yescharacteristic
52C2×#476C2211yescharacteristic
53C2×#476C2211yescharacteristic
54C2×#476C2211yescharacteristic
55C2×#476C2211yescharacteristic
56C2×#476C2211yescharacteristic
57C2×#474C2211yescharacteristic
58C2×#474C2211yescharacteristic
59C2×#474C2211yescharacteristic
60C2×#459C2211yescharacteristic
61C2×#446C2211yescharacteristic
62C2×#442C2211yescharacteristic
63C2×#442C2211yescharacteristic
64C2×C4×D8C2211yescharacteristic
65C2×#432C2211yescharacteristic
66#2692—21no—
67#2683—21no—
68#2676—21no—
69#2676—21no—
70#2584C2211yescharacteristic
71#2566C2211yescharacteristic
72#2551C2211yescharacteristic
73#2550C2211yescharacteristic
74#2548C2211yescharacteristic
75#2541C2211yescharacteristic
76#2491C2211yescharacteristic
77#2491C2211yescharacteristic
78#2465—21no—
79#2465—21no—
80#2463—21no—
81#2463—21no—
82#2452—21no—
83#2452C2211yescharacteristic
84#2452C2211yescharacteristic
85#2452C2211yescharacteristic
86#2452C2211yescharacteristic
87#2449—21no—
88#2441C2211yescharacteristic
89#2439C2211yescharacteristic
90#2436—21no—
91#2429—21no—
92#2428C2211yescharacteristic
93#2428C2211yescharacteristic
94#2426—21no—
95#2407—21no—
96#2370C2211yescharacteristic
97#2366C2211yescharacteristic
98#2366C2211yescharacteristic
99#2365C2211yescharacteristic
100#2363C2211yescharacteristic
101#2363C2211yescharacteristic
102#2360—21no—
103C4×C22⋊Q8C2211yescharacteristic
104C4×#121C2211yescharacteristic
105C4×#121C2211yescharacteristic
106#2094C2211yescharacteristic
107#2092C2211yescharacteristic
108#2088C2211yescharacteristic
109#2085C2211yescharacteristic
110#2084C2211yescharacteristic
111#2077C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2058C2211yescharacteristic
123#2058C2211yescharacteristic
124#2058C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2054C2211yescharacteristic
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic
133#2034C2211yescharacteristic
134#2033C2211yescharacteristic
135#2025C2211yescharacteristic
136#2025C2211yescharacteristic
137#2023C2211yescharacteristic
138#2023C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#2011C2211yescharacteristic
142#2011C2211yescharacteristic
143#1999C2211yescharacteristic
144#1999C2211yescharacteristic
145#1999C2211yescharacteristic
146#1989C2211yescharacteristic
147#1989C2211yescharacteristic
148#1987C2211yescharacteristic
149#1985C2211yescharacteristic
150#1982C2211yescharacteristic
151#1982C2211yescharacteristic
152#1982C2211yescharacteristic
153#1972C2211yescharacteristic
154#1970C2211yescharacteristic
155#1961C2211yescharacteristic
156#1957C2211yescharacteristic
157#1949C2211yescharacteristic
158#1948C2211yescharacteristic
159#1944C2211yescharacteristic
160#1942C2211yescharacteristic
161#1940C2211yescharacteristic
162#1940C2211yescharacteristic
163#1939C2211yescharacteristic
164#1936C2211yescharacteristic
165#1936C2211yescharacteristic
166#1934C2211yescharacteristic
167#1934C2211yescharacteristic
168#1926C2211yescharacteristic
169#1926C2211yescharacteristic
170#1925C2211yescharacteristic
171#1925C2211yescharacteristic
172#1924C2211yescharacteristic
173#1924C2211yescharacteristic
174#1923C2211yescharacteristic
175#1923C2211yescharacteristic
176#1921C2211yescharacteristic
177#1919C2211yescharacteristic
178#1919C2211yescharacteristic
179#1918C2211yescharacteristic
180#1917C2211yescharacteristic
181#1916C2211yescharacteristic
182#1879C2211yescharacteristic
183#1879C2211yescharacteristic
184#1879C2211yescharacteristic
185#1879C2211yescharacteristic
186#1879C2211yescharacteristic
187#1879C2211yescharacteristic
188#1875C2211yescharacteristic
189#1875C2211yescharacteristic
190#1864C2211yescharacteristic
191#1864C2211yescharacteristic
192#1864C2211yescharacteristic
193#1864C2211yescharacteristic
194#1862C2211yescharacteristic
195#1862C2211yescharacteristic
196#1854C2211yescharacteristic
197#1854C2211yescharacteristic
198#1797C2211yescharacteristic
199#1776C2211yescharacteristic
200#1776C2211yescharacteristic
201C4×#106C2211yescharacteristic
202#1771C2211yescharacteristic
203#1762C2211yescharacteristic
204#1762C2211yescharacteristic
205C22×#41—21no—
206C23×Q8—21no—
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#554—24no—
211#554—42no—
212D4×Q8—24no—
213D4×Q8—42no—
214#548—48no—
215#533—24no—
216#533—42no—
217#532—24no—
218#532—42no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#124—21no—
234C2×#124—21no—
235C2×#124—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8D411yescharacteristic
249C2×#121—21no—
250C2×#121—21no—
251C2×#121—21no—
252C2×#121—21no—
253C2×#121—21no—
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×#121C2311yescharacteristic
257C2×#121C2311yescharacteristic
258C2×C4×Q8—21no—
259C2×C4×Q8—21no—
260C2×C4×Q8—21no—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—21no—
265C2×C4×D4—21no—
266C2×C4×D4—21no—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C22×C4⋊C4—21no—
278C22×C42C2311yescharacteristic
279#501—24no—
280#501—24no—
281#501D418yescomplemented
282#498—24no—
283#490—24no—
284#490—24no—
285#482—24no—
286#482—24no—
287#482—24no—
288#482—24no—
289#478—24no—
290#478—24no—
291#478—42no—
292#476—24no—
293#476—24no—
294#476—24no—
295#476—24no—
296#476—24no—
297#474—24no—
298#474—24no—
299#474—24no—
300#459—42no—
301#446—24no—
302#442—24no—
303#442—24no—
304C4×D8—24no—
305#432—24no—
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#107C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×#106C2311yescharacteristic
321C2×#106C2311yescharacteristic
322C2×#106C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2311yescharacteristic
329C2×C4⋊C8C2311yescharacteristic
330C2×C4⋊C8C2311yescharacteristic
331C2×#102C2311yescharacteristic
332C2×#102C2311yescharacteristic
333C2×#102C2311yescharacteristic
334C2×#102C2311yescharacteristic
335C2×#102C2311yescharacteristic
336C2×#102C2311yescharacteristic
337C2×#102C2311yescharacteristic
338C2×#102C2311yescharacteristic
339C2×#102C2311yescharacteristic
340C2×#102C2311yescharacteristic
341C2×#102C2311yescharacteristic
342C2×#102C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×C22⋊C8C2311yescharacteristic
359C2×C22⋊C8C2311yescharacteristic
360C2×C22⋊C8C2311yescharacteristic
361C2×#97C2311yescharacteristic
362C2×#97C2311yescharacteristic
363C2×#97C2311yescharacteristic
364C2×#97C2311yescharacteristic
365C2×C4×C8C2311yescharacteristic
366C2×C4×C8C2311yescharacteristic
367#399—21no—
368#398—21no—
369#398—21no—
370#396—21no—
371#396—21no—
372#396—21no—
373#396—21no—
374#396—21no—
375#396—21no—
376#396—21no—
377#396—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#394—21no—
383#394—21no—
384#394—21no—
385#394—21no—
386#394—21no—
387#394—21no—
388#393—21no—
389#393—21no—
390#393—21no—
391#393—21no—
392#393—21no—
393#393—21no—
394#393—21no—
395#392—21no—
396#392—21no—
397#392—21no—
398#392—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391D411yescharacteristic
403#390—21no—
404#390—21no—
405#390—21no—
406#390—21no—
407#390—21no—
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389D411yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
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#387D411yescharacteristic
448#387D411yescharacteristic
449#386—21no—
450#386—21no—
451#386—21no—
452#386—21no—
453#386—21no—
454#386—21no—
455#386—21no—
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385—21no—
465#385D411yescharacteristic
466#385D411yescharacteristic
467#384C2311yescharacteristic
468#382C2311yescharacteristic
469#380D411yescharacteristic
470#380C2311yescharacteristic
471#380C2311yescharacteristic
472C4×C4⋊C4—21no—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C22⋊C4—21no—
483C4×C22⋊C4—21no—
484C4×C22⋊C4—21no—
485C4×C22⋊C4—21no—
486C4×C22⋊C4C2311yescharacteristic
487C4×C22⋊C4C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516C2×#41—44no—
517C2×#41—44no—
518C2×#41—82no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8—82no—
528C22×Q8C2×D411yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4—21no—
551C23×C4C2×D411yescharacteristic
552C23×C4C2×D411yescharacteristic
553C23×C4C2411yescharacteristic
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—82no—
583C4⋊Q8C2×D414yes—
584#127—22no—
585#127—22no—
586#127—22no—
587#127—22no—
588#127—41no—
589#127—41no—
590#125—22no—
591#125—22no—
592#125—22no—
593#125—22no—
594#125—41no—
595#125C2×D414yes—
596#124—44no—
597#124—44no—
598#124—44no—
599#124—44no—
600C22⋊Q8—24no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—44no—
609C22⋊Q8—44no—
610C22⋊Q8—44no—
611C22⋊Q8—44no—
612C22⋊Q8—82no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—44no—
619#121—44no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—44no—
624#121—44no—
625#121—82no—
626C4×Q8—22no—
627C4×Q8—22no—
628C4×Q8—44no—
629C4×Q8—44no—
630C4×Q8—44no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—44no—
648C4×D4—44no—
649C4×D4—44no—
650C4×D4—44no—
651C4×D4—82no—
652#117—22no—
653#117—22no—
654#117—41no—
655#117—41no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D411yescharacteristic
687C2×C4⋊C4C2×D411yescharacteristic
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×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×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42C2×D411yescharacteristic
753C2×C42C2×D411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760#107—22no—
761#107—22no—
762#107—22no—
763#107—41no—
764#107—41no—
765#107C2×D414yes—
766#107C2×D414yes—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—41no—
775#106C2×D414yes—
776#106C2×D414yes—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—22no—
782C4⋊C8—22no—
783C4⋊C8—41no—
784C4⋊C8—41no—
785#102—22no—
786#102—22no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810#102—41no—
811C22⋊C8—22no—
812C22⋊C8—22no—
813C22⋊C8—41no—
814C22⋊C8—41no—
815#97—22no—
816#97—22no—
817#97—41no—
818#97C2×D414yes—
819C4×C8—22no—
820C4×C8—41no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24C22×D411yescharacteristic
856#41—816no—
857C2×Q8—22no—
858C2×Q8—24no—
859C2×Q8—22no—
860C2×Q8—41no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—816no—
879C2×D4—24no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D42−1+412yes—
932C2×D42−1+412yes—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—22no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C2511yescharacteristic
995D8—28no—
996D8—82no—
997D8—82no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8C22×D412yes—
1021C2×C8C22×D412yes—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4AGL(1,ℤ/8)14yes—
1074C4⋊C4C22×D412yes—
1075C4⋊C4C22×D412yes—
1076C4⋊C4C22×D412yes—
1077C4⋊C4C22×D412yes—
1078C4⋊C42−1+412yes—
1079C22⋊C4—24no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C42—22no—
1120C42—22no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—81no—
1137C42—81no—
1138C42—81no—
1139C42C22×D412yes—
1140C42H(5,𝔽2)12yes—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—21no—
1147C23—22no—
1148C23—21no—
1149C23—21no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23C23×D411yescharacteristic
1177Q8—44no—
1178Q8—48no—
1179Q8—84no—
1180Q8—84no—
1181Q8—84no—
1182Q8—84no—
1183Q8—162no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—162no—
1209D4—162no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—44no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—82no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4D4212yes—
1295C2×C4D4212yes—
1296C2×C4C2×AGL(1,ℤ/8)12yes—
1297C2×C4C2×AGL(1,ℤ/8)12yes—
1298C2×C4C2×AGL(1,ℤ/8)12yes—
1299C2×C4C23×D411yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×2−1+411yescharacteristic
1302C2×C4C2×2−1+411yescharacteristic
1303C2×C4C2×2−1+411yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—22no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—41no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22C2×D4211yescharacteristic
1349C22#348611yescharacteristic
1350C22#348911yescharacteristic
1351C22C22×AGL(1,ℤ/8)11yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C22#358511yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—41no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—42no—
1368C4—41no—
1369C4—42no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4#348611yescharacteristic
1381C4#349711yescharacteristic
1382C4#355211yescharacteristic
1383C4#356111yescharacteristic
1384C2—81no—
1385C2—82no—
1386C2—82no—
1387C2—161no—
1388C2—161no—
1389C2#4524811yescharacteristic
1390C2D4×AGL(1,ℤ/8)11yescharacteristic
1391C2#6107711yescharacteristic
1392C2#6184011yescharacteristic
1393C2#6187211yescharacteristic
1394C2#6211011yescharacteristic
1395C2#6215911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3384C2semidirect
2. C2×#3235C2semidirect
3. #59153C2semidirect
4. #59080C2semidirect
5. #31247C2semidirect
6. #31234C2semidirect
7. #31147C2semidirect
8. #31121C2semidirect
9. #30966C2semidirect
10. #30954C2semidirect
11. #30794C2semidirect
12. #30780C2semidirect
13. #28650C2semidirect
14. #28421C2semidirect
15. #26904C2semidirect
16. #26889C2semidirect
17. #26812C2semidirect
18. #26797C2semidirect
19. #26634C2semidirect
20. #26619C2semidirect
21. #26475C2semidirect
22. #26464C2semidirect
23. #25946C2semidirect
24. #25844C2semidirect
25. #25461C2semidirect
26. #25288C2semidirect
27. #24304C2semidirect
28. #24152C2semidirect
29. #23708C2semidirect
30. #23168C2semidirect
31. #22106C2semidirect
281. #501D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33842
C2×#32352
#591532
#590802
#312472
#312342
#311472
#311212
#309662
#309542
#307942
#307802
#286502
#284212
#269042
#268892
#268122
#267972
#266342
#266192
#264752
#264642
#259462
#258442
#254612
#252882
#243042
#241522
#237082
#231682
#221062