Finite Group Databasebeta

← #7183874

Subgroups — #7183874

Order 512.

1931 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3386C211yesmaximal, characteristic, complemented
2C2×#3239C211yesmaximal, characteristic, complemented
3#59127C211yesmaximal, characteristic, complemented
4#59085C211yesmaximal, characteristic, complemented
5#31244C211yesmaximal, characteristic, complemented
6#31234C211yesmaximal, characteristic, complemented
7#31134C211yesmaximal, characteristic, complemented
8#31122C211yesmaximal, characteristic, complemented
9#30965C211yesmaximal, characteristic, complemented
10#30946C211yesmaximal, characteristic, complemented
11#30799C211yesmaximal, characteristic, complemented
12#30779C211yesmaximal, characteristic, complemented
13#28649C211yesmaximal, characteristic, complemented
14#28426C211yesmaximal, characteristic, complemented
15#26916C211yesmaximal, characteristic, complemented
16#26902C211yesmaximal, characteristic, complemented
17#26803C211yesmaximal, characteristic, complemented
18#26787C211yesmaximal, characteristic
19#26641C211yesmaximal, characteristic, complemented
20#26625C211yesmaximal, characteristic
21#26478C211yesmaximal, characteristic, complemented
22#26462C211yesmaximal, characteristic, complemented
23#25939C211yesmaximal, characteristic, complemented
24#25849C211yesmaximal, characteristic, complemented
25#25465C211yesmaximal, characteristic, complemented
26#25286C211yesmaximal, characteristic, complemented
27#24302C211yesmaximal, characteristic, complemented
28#24158C211yesmaximal, characteristic
29#23711C211yesmaximal, characteristic, complemented
30#23168C211yesmaximal, characteristic, complemented
31#22106C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8—21no—
34C2×D4×Q8C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×#529C2211yescharacteristic
37#3386—28no—
38#3239—28no—
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#501C2211yescharacteristic
42C2×#500C2211yescharacteristic
43C2×#489C2211yescharacteristic
44C2×#489C2211yescharacteristic
45C2×#484C2211yescharacteristic
46C2×#484C2211yescharacteristic
47C2×#481C2211yescharacteristic
48C2×#481C2211yescharacteristic
49C2×#477C2211yescharacteristic
50C2×#477C2211yescharacteristic
51C2×#477C2211yescharacteristic
52C2×#475C2211yescharacteristic
53C2×#475C2211yescharacteristic
54C2×#475C2211yescharacteristic
55C2×#478C2211yescharacteristic
56C2×#478C2211yescharacteristic
57C2×#474C2211yescharacteristic
58C2×#474C2211yescharacteristic
59C2×#474C2211yescharacteristic
60C2×#463C2211yescharacteristic
61C2×#446C2211yescharacteristic
62C2×#440C2211yescharacteristic
63C2×#440C2211yescharacteristic
64C2×C4×SD16C2211yescharacteristic
65C2×#432C2211yescharacteristic
66#2725—21no—
67#2716—21no—
68#2677—21no—
69#2677—21no—
70#2592C2211yescharacteristic
71#2558—21no—
72#2551C2211yescharacteristic
73#2551C2211yescharacteristic
74#2546C2211yescharacteristic
75#2545C2211yescharacteristic
76#2542C2211yescharacteristic
77#2492C2211yescharacteristic
78#2490C2211yescharacteristic
79#2475—21no—
80#2460—21no—
81#2458—21no—
82#2453C2211yescharacteristic
83#2452—21no—
84#2452C2211yescharacteristic
85#2452C2211yescharacteristic
86#2452C2211yescharacteristic
87#2449—21no—
88#2449—21no—
89#2440C2211yescharacteristic
90#2440C2211yescharacteristic
91#2434—21no—
92#2429—21no—
93#2429C2211yescharacteristic
94#2426C2211yescharacteristic
95#2409—21no—
96#2370C2211yescharacteristic
97#2367C2211yescharacteristic
98#2365C2211yescharacteristic
99#2365C2211yescharacteristic
100#2362—21no—
101#2361C2211yescharacteristic
102#2361C2211yescharacteristic
103C4×C22⋊Q8C2211yescharacteristic
104C4×C22⋊Q8C2211yescharacteristic
105C4×#121C2211yescharacteristic
106#2095C2211yescharacteristic
107#2093C2211yescharacteristic
108#2086C2211yescharacteristic
109#2084C2211yescharacteristic
110#2083C2211yescharacteristic
111#2076C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2065C2211yescharacteristic
121#2065C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2057C2211yescharacteristic
125#2057C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2055C2211yescharacteristic
129#2043C2211yescharacteristic
130#2042C2211yescharacteristic
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2034C2211yescharacteristic
134#2034C2211yescharacteristic
135#2024C2211yescharacteristic
136#2024C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#2013C2211yescharacteristic
142#2012C2211yescharacteristic
143#2000C2211yescharacteristic
144#2000C2211yescharacteristic
145#1999C2211yescharacteristic
146#1989C2211yescharacteristic
147#1987C2211yescharacteristic
148#1987C2211yescharacteristic
149#1985C2211yescharacteristic
150#1983C2211yescharacteristic
151#1983C2211yescharacteristic
152#1981C2211yescharacteristic
153#1973C2211yescharacteristic
154#1970C2211yescharacteristic
155#1959C2211yescharacteristic
156#1956C2211yescharacteristic
157#1948C2211yescharacteristic
158#1947C2211yescharacteristic
159#1944C2211yescharacteristic
160#1942C2211yescharacteristic
161#1940C2211yescharacteristic
162#1940C2211yescharacteristic
163#1939C2211yescharacteristic
164#1936C2211yescharacteristic
165#1935C2211yescharacteristic
166#1934C2211yescharacteristic
167#1933C2211yescharacteristic
168#1928C2211yescharacteristic
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#1880C2211yescharacteristic
183#1879C2211yescharacteristic
184#1879C2211yescharacteristic
185#1879C2211yescharacteristic
186#1877C2211yescharacteristic
187#1877C2211yescharacteristic
188#1872C2211yescharacteristic
189#1872C2211yescharacteristic
190#1865C2211yescharacteristic
191#1865C2211yescharacteristic
192#1865C2211yescharacteristic
193#1863C2211yescharacteristic
194#1863C2211yescharacteristic
195#1862C2211yescharacteristic
196#1852C2211yescharacteristic
197#1852C2211yescharacteristic
198#1797C2211yescharacteristic
199#1776C2211yescharacteristic
200#1776C2211yescharacteristic
201C4×#106C2211yescharacteristic
202#1771C2211yescharacteristic
203#1763C2211yescharacteristic
204#1762C2211yescharacteristic
205C23×Q8—21no—
206C23×Q8—21no—
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#557—24no—
211#557—42no—
212D4×Q8—24no—
213D4×Q8—42no—
214D4×Q8—48no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—24no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231#529—24no—
232#529—42no—
233C2×#126—21no—
234C2×#125—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#123—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⋊Q8—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—21no—
251C2×C22⋊Q8D411yescharacteristic
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2311yescharacteristic
256C2×C4×Q8—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
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×#117—21no—
272C22×C4⋊C4—21no—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#501—24no—
277#501—24no—
278#501D418yescomplemented
279#500—24no—
280#489—24no—
281#489—24no—
282#484—24no—
283#484—24no—
284#481—24no—
285#481—24no—
286#478—24no—
287#478—24no—
288#477—24no—
289#477—24no—
290#477—42no—
291#475—24no—
292#475—24no—
293#475—24no—
294#474—24no—
295#474—24no—
296#474—24no—
297#463—42no—
298#446—24no—
299#440—24no—
300#440—24no—
301C4×SD16—24no—
302#432—24no—
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#107C2311yescharacteristic
308C2×#107C2311yescharacteristic
309C2×#107C2311yescharacteristic
310C2×#107C2311yescharacteristic
311C2×#107C2311yescharacteristic
312C2×#107C2311yescharacteristic
313C2×#107C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×#106C2311yescharacteristic
318C2×#106C2311yescharacteristic
319C2×#106C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323C2×C4⋊C8C2311yescharacteristic
324C2×C4⋊C8C2311yescharacteristic
325C2×C4⋊C8C2311yescharacteristic
326C2×C4⋊C8C2311yescharacteristic
327C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
355C2×C22⋊C8C2311yescharacteristic
356C2×C22⋊C8C2311yescharacteristic
357C2×C22⋊C8C2311yescharacteristic
358C2×#97C2311yescharacteristic
359C2×#97C2311yescharacteristic
360C2×#97C2311yescharacteristic
361C2×#97C2311yescharacteristic
362C2×C4×C8C2311yescharacteristic
363C2×C4×C8C2311yescharacteristic
364#400—21no—
365#400—21no—
366#399—21no—
367#399—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#397—21no—
375#397—21no—
376#396—21no—
377#396—21no—
378#396—21no—
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#394—21no—
390#394—21no—
391#393—21no—
392#393—21no—
393#393—21no—
394#393—21no—
395#393—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391D411yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#390—21no—
405#390—21no—
406#390C2311yescharacteristic
407#390C2311yescharacteristic
408#390C2311yescharacteristic
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389—21no—
417#389—21no—
418#389D411yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#388—21no—
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#388—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#387D411yescharacteristic
451#387D411yescharacteristic
452#386—21no—
453#386—21no—
454#386—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#385—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#385—21no—
463#385—21no—
464#385D411yescharacteristic
465#385D411yescharacteristic
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#380D411yescharacteristic
469#380C2311yescharacteristic
470#380C2311yescharacteristic
471C4×C4⋊C4—21no—
472C4×C4⋊C4—21no—
473C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
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
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8—44no—
524C22×Q8—44no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8—82no—
528C22×Q8—82no—
529C22×Q8C2×D411yescharacteristic
530C22×Q8C2411yescharacteristic
531C22×Q8C2411yescharacteristic
532C22×D4—21no—
533C22×D4—21no—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D411yescharacteristic
543C23×C4C2×D411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—22no—
566C4⋊Q8—22no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—44no—
577C4⋊Q8—41no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583C4⋊Q8C2×D414yes—
584#126—44no—
585#125—22no—
586#125—22no—
587#125—41no—
588#125—44no—
589#125—44no—
590#125C2×D414yes—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—41no—
595#123—44no—
596C22⋊Q8—24no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—44no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—44no—
609C22⋊Q8—44no—
610C22⋊Q8—82no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—41no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—22no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—44no—
626C4×Q8—44no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—22no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—44no—
636C4×D4—44no—
637C4×D4—44no—
638C4×D4—44no—
639#117—44no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
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⋊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—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—44no—
680C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
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×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×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⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—22no—
752#107—22no—
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#107—41no—
758#107—41no—
759#107—41no—
760#107C2×D414yes—
761#107C2×D414yes—
762#106—22no—
763#106—22no—
764#106—22no—
765#106—22no—
766#106C2×D414yes—
767#106C2×D414yes—
768C4⋊C8—22no—
769C4⋊C8—22no—
770C4⋊C8—22no—
771C4⋊C8—22no—
772C4⋊C8—22no—
773C4⋊C8—22no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
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—41no—
800#102—41no—
801#102—41no—
802C22⋊C8—22no—
803C22⋊C8—22no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806#97—22no—
807#97—22no—
808#97—41no—
809#97C2×D414yes—
810C4×C8—22no—
811C4×C8—41no—
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#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#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848C24—21no—
849C24—21no—
850C24C22×D411yescharacteristic
851C2×Q8—22no—
852C2×Q8—24no—
853C2×Q8—22no—
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—21no—
864C2×Q8—21no—
865C2×Q8—41no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8—81no—
885C2×Q8—81no—
886C2×Q8—816no—
887C2×Q8—816no—
888C2×Q82−1+412yes—
889C2×D4—24no—
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—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—81no—
906C2×D42−1+412yes—
907C22×C4—22no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C2511yescharacteristic
965SD16—28no—
966SD16—82no—
967D8—82no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8C22×D412yes—
991C2×C8C22×D412yes—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4AGL(1,ℤ/8)14yes—
1055C4⋊C4C22×D412yes—
1056C4⋊C4C22×D412yes—
1057C4⋊C4C22×D412yes—
1058C4⋊C4C22×D412yes—
1059C4⋊C42−1+412yes—
1060C22⋊C4—24no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C42—22no—
1091C42—22no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42C22×D412yes—
1113C42H(5,𝔽2)12yes—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—22no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23#57812yes—
1135C23C23×D411yescharacteristic
1136Q8—22no—
1137Q8—22no—
1138Q8—44no—
1139Q8—48no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—84no—
1147Q8—84no—
1148Q8—84no—
1149Q8—84no—
1150Q8—84no—
1151Q8—84no—
1152D4—22no—
1153D4—22no—
1154D4—48no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—84no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—44no—
1203C2×C4—44no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4D4212yes—
1251C2×C4D4212yes—
1252C2×C4C2×AGL(1,ℤ/8)12yes—
1253C2×C4C2×AGL(1,ℤ/8)12yes—
1254C2×C4C2×AGL(1,ℤ/8)12yes—
1255C2×C4C23×D411yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×2−1+411yescharacteristic
1258C2×C4C2×2−1+411yescharacteristic
1259C2×C4C2×2−1+411yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—22no—
1262C8—22no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22C2×D4211yescharacteristic
1291C22#348611yescharacteristic
1292C22#348911yescharacteristic
1293C22C22×AGL(1,ℤ/8)11yescharacteristic
1294C22C2×#57811yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—41no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—41no—
1315C4—41no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#348611yescharacteristic
1325C4#349711yescharacteristic
1326C4#355211yescharacteristic
1327C4#356111yescharacteristic
1328C2—42no—
1329C2—82no—
1330C2—161no—
1331C2#4524811yescharacteristic
1332C2D4×AGL(1,ℤ/8)11yescharacteristic
1333C2#6107611yescharacteristic
1334C2#6183711yescharacteristic
1335C2#6187911yescharacteristic
1336C2#6211111yescharacteristic
1337C2#6215811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
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×#3386C2semidirect
2. C2×#3239C2semidirect
3. #59127C2semidirect
4. #59085C2semidirect
5. #31244C2semidirect
6. #31234C2semidirect
7. #31134C2semidirect
8. #31122C2semidirect
9. #30965C2semidirect
10. #30946C2semidirect
11. #30799C2semidirect
12. #30779C2semidirect
13. #28649C2semidirect
14. #28426C2semidirect
15. #26916C2semidirect
16. #26902C2semidirect
17. #26803C2semidirect
19. #26641C2semidirect
21. #26478C2semidirect
22. #26462C2semidirect
23. #25939C2semidirect
24. #25849C2semidirect
25. #25465C2semidirect
26. #25286C2semidirect
27. #24302C2semidirect
29. #23711C2semidirect
30. #23168C2semidirect
31. #22106C2semidirect
278. #501D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33862
C2×#32392
#591272
#590852
#312442
#312342
#311342
#311222
#309652
#309462
#307992
#307792
#286492
#284262
#269162
#269022
#268032
#267872
#266412
#266252
#264782
#264622
#259392
#258492
#254652
#252862
#243022
#241582
#237112
#231682
#221062