Finite Group Databasebeta

← #6373423

Subgroups — #6373423

Order 512.

2227 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3126C211yesmaximal, characteristic
2#34280C211yesmaximal, characteristic
3C4×#519C211yesmaximal, characteristic, complemented
4#21622C211yesmaximal, characteristic, complemented
5#21621C211yesmaximal, characteristic, complemented
6#21618C211yesmaximal, characteristic, complemented
7C4×#479C211yesmaximal, characteristic, complemented
8#21590C211yesmaximal, characteristic, complemented
9#21588C211yesmaximal, characteristic, complemented
10#21582C211yesmaximal, characteristic, complemented
11C4×#482C211yesmaximal, characteristic, complemented
12#21515C211yesmaximal, characteristic, complemented
13#21515C211yesmaximal, characteristic, complemented
14#21505C211yesmaximal, characteristic, complemented
15C4×#460C211yesmaximal, characteristic, complemented
16#21462C211yesmaximal, characteristic, complemented
17#21462C211yesmaximal, characteristic, complemented
18#21454C211yesmaximal, characteristic, complemented
19C4×#448C211yesmaximal, characteristic, complemented
20#21399C211yesmaximal, characteristic
21#21367C211yesmaximal, characteristic, complemented
22#21124C211yesmaximal, characteristic, complemented
23#21124C211yesmaximal, characteristic, complemented
24#21120C211yesmaximal, characteristic, complemented
25#21115C211yesmaximal, characteristic, complemented
26#20745C211yesmaximal, characteristic, complemented
27#20506C211yesmaximal, characteristic, complemented
28#20504C211yesmaximal, characteristic, complemented
29#20504C211yesmaximal, characteristic, complemented
30#20504C211yesmaximal, characteristic, complemented
31#20468C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#3126C4116yescomplemented
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#448C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic
49C2×#440C2211yescharacteristic
50C2×#440C2211yescharacteristic
51C2×C4×SD16C2211yescharacteristic
52C2×C4×SD16C2211yescharacteristic
53C2×C4×SD16C2211yescharacteristic
54C2×C4×SD16C2211yescharacteristic
55C2×C4×SD16C2211yescharacteristic
56C2×C4×SD16C2211yescharacteristic
57C2×#433C2211yescharacteristic
58C2×#433C2211yescharacteristic
59#2374—21no—
60#2374—21no—
61#2364—21no—
62#2364—21no—
63#2363—21no—
64#2363—21no—
65#2359—21no—
66#2359—21no—
67#2330C2211yescharacteristic
68#2328C2211yescharacteristic
69#2324C2211yescharacteristic
70#2324C2211yescharacteristic
71#2314C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C4×#125C2211yescharacteristic
74C4×#121C2211yescharacteristic
75C4×#121C2211yescharacteristic
76#2293C2211yescharacteristic
77#2293C2211yescharacteristic
78#2276—21no—
79#2276—21no—
80#2276C2211yescharacteristic
81#2276C2211yescharacteristic
82#2276C2211yescharacteristic
83#2276C2211yescharacteristic
84#2275C2211yescharacteristic
85#2275C2211yescharacteristic
86#2274—21no—
87#2274—21no—
88#2274C2211yescharacteristic
89#2274C2211yescharacteristic
90C42×Q8—21no—
91C42×Q8—21no—
92C42×Q8C2211yescharacteristic
93C42×Q8C2211yescharacteristic
94C42×Q8C2211yescharacteristic
95C42×Q8C2211yescharacteristic
96C4×#117—21no—
97C4×#117—21no—
98C4×#117C2211yescharacteristic
99C4×#117C2211yescharacteristic
100#1989C2211yescharacteristic
101#1989C2211yescharacteristic
102#1982C2211yescharacteristic
103#1982C2211yescharacteristic
104#1949C2211yescharacteristic
105#1949C2211yescharacteristic
106#1948C2211yescharacteristic
107#1947C2211yescharacteristic
108#1926C2211yescharacteristic
109#1926C2211yescharacteristic
110#1926C2211yescharacteristic
111#1926C2211yescharacteristic
112#1925C2211yescharacteristic
113#1925C2211yescharacteristic
114#1925C2211yescharacteristic
115#1925C2211yescharacteristic
116#1921C2211yescharacteristic
117#1921C2211yescharacteristic
118#1920C2211yescharacteristic
119#1920C2211yescharacteristic
120#1919C2211yescharacteristic
121#1919C2211yescharacteristic
122#1918C2211yescharacteristic
123#1918C2211yescharacteristic
124#1880C2211yescharacteristic
125#1880C2211yescharacteristic
126#1880C2211yescharacteristic
127#1880C2211yescharacteristic
128#1880C2211yescharacteristic
129#1880C2211yescharacteristic
130#1880C2211yescharacteristic
131#1880C2211yescharacteristic
132#1875C2211yescharacteristic
133#1875C2211yescharacteristic
134#1874C2211yescharacteristic
135#1874C2211yescharacteristic
136#1865C2211yescharacteristic
137#1865C2211yescharacteristic
138#1865C2211yescharacteristic
139#1865C2211yescharacteristic
140#1863C2211yescharacteristic
141#1863C2211yescharacteristic
142#1863C2211yescharacteristic
143#1863C2211yescharacteristic
144#1854C2211yescharacteristic
145#1854C2211yescharacteristic
146#1853C2211yescharacteristic
147#1852C2211yescharacteristic
148#1825C2211yescharacteristic
149#1825C2211yescharacteristic
150#1805C2211yescharacteristic
151#1805C2211yescharacteristic
152#1803C2211yescharacteristic
153#1803C2211yescharacteristic
154#1787C2211yescharacteristic
155#1787C2211yescharacteristic
156#1776C2211yescharacteristic
157#1776C2211yescharacteristic
158#1776C2211yescharacteristic
159#1776C2211yescharacteristic
160#1776C2211yescharacteristic
161#1776C2211yescharacteristic
162C4×#107C2211yescharacteristic
163C4×#107C2211yescharacteristic
164C4×#107C2211yescharacteristic
165C4×#106C2211yescharacteristic
166C4×#106C2211yescharacteristic
167C4×#106C2211yescharacteristic
168#1768C2211yescharacteristic
169#1768C2211yescharacteristic
170#1767C2211yescharacteristic
171C4×C4⋊C8C2211yescharacteristic
172#1763C2211yescharacteristic
173#1763C2211yescharacteristic
174#1763C2211yescharacteristic
175#1763C2211yescharacteristic
176#1763C2211yescharacteristic
177#1763C2211yescharacteristic
178#1762C2211yescharacteristic
179#1762C2211yescharacteristic
180#1762C2211yescharacteristic
181#1762C2211yescharacteristic
182#1762C2211yescharacteristic
183#1762C2211yescharacteristic
184C4×#103C2211yescharacteristic
185C4×#103C2211yescharacteristic
186C4×#103C2211yescharacteristic
187C4×#103C2211yescharacteristic
188C4×#103C2211yescharacteristic
189C4×#103C2211yescharacteristic
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1750C2211yescharacteristic
197#1750C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200#1745C2211yescharacteristic
201#1744C2211yescharacteristic
202#1726C2211yescharacteristic
203#1726C2211yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#540—24no—
210#540C2×C418yes—
211C2×#127C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#121—21no—
216C2×#121—21no—
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219#519—24no—
220#519—24no—
221#519—24no—
222#519C2×C418yescomplemented
223C2×C4×Q8—24no—
224C2×C4×Q8—24no—
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117—21no—
255C2×#117—21no—
256C2×#117—21no—
257C2×#117—21no—
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C22×C4⋊C4—21no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C42—21no—
266C22×C42C2311yescharacteristic
267#482C2×C418yescomplemented
268#482C2×C418yescomplemented
269#479C2×C418yescomplemented
270#479C2×C418yescomplemented
271#460C2×C418yescomplemented
272#460C2×C418yescomplemented
273#448C2×C418yescomplemented
274#448C2×C418yescomplemented
275#440—24no—
276#440—24no—
277#440—24no—
278#440—24no—
279#440C2×C418yescomplemented
280#440C2×C418yescomplemented
281C4×SD16—24no—
282C4×SD16—24no—
283C4×SD16—24no—
284C4×SD16—24no—
285C4×SD16C2×C418yescomplemented
286C4×SD16C2×C418yescomplemented
287#433—24no—
288#433C2×C418yescomplemented
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×C4⋊C8C2311yescharacteristic
303C2×C4⋊C8C2311yescharacteristic
304C2×C4⋊C8C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×C4×C8C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342C2×C4×C8C2311yescharacteristic
343C2×C4×C8C2311yescharacteristic
344C2×C4×C8C2311yescharacteristic
345#390—21no—
346#390—21no—
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#385—21no—
384#385—21no—
385#384C2311yescharacteristic
386#382C2311yescharacteristic
387#380C2311yescharacteristic
388#380C2311yescharacteristic
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4D411yescharacteristic
420C4×C4⋊C4D411yescharacteristic
421C4×C4⋊C4D411yescharacteristic
422C4×C4⋊C4D411yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4D411yescharacteristic
459C4×C22⋊C4D411yescharacteristic
460C4×C22⋊C4D411yescharacteristic
461#376—21no—
462#376—21no—
463#376—21no—
464#376—21no—
465#376—21no—
466#376C2311yescharacteristic
467#376C2311yescharacteristic
468C2×#95—21no—
469C2×#95—21no—
470C43—21no—
471C43—21no—
472C43—21no—
473C43—21no—
474C43—21no—
475C43C2311yescharacteristic
476C43C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
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#340C2311yescharacteristic
500#340C2311yescharacteristic
501#336C2311yescharacteristic
502#336C2311yescharacteristic
503#336C2311yescharacteristic
504#336C2311yescharacteristic
505#336C2311yescharacteristic
506#336C2311yescharacteristic
507#336C2311yescharacteristic
508#336C2311yescharacteristic
509C22×Q8—22no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—21no—
514C22×Q8—22no—
515C22×Q8C22×C414yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16C22×C414yes—
544C2×SD16C22×C414yes—
545C2×SD16C22×C414yes—
546C2×SD16C22×C414yes—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#127—22no—
556#127C22×C414yes—
557#125—22no—
558#125C22×C414yes—
559#123—28no—
560#123—28no—
561#121—22no—
562#121—22no—
563#121—28no—
564#121—28no—
565#121C22×C414yes—
566#121C22×C414yes—
567C4×Q8—28no—
568C4×Q8—28no—
569C4×Q8—28no—
570C4×Q8—28no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—22no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8C22×C414yes—
590C4×Q8C22×C414yes—
591C4×Q8C22×C414yes—
592C4×Q8C22×C414yes—
593C4×Q8#4114yes—
594C4×Q8#4114yes—
595C4×Q8#4114yes—
596C4×Q8#4114yes—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—82no—
608C4×D4—82no—
609C4×D4—82no—
610C4×D4—82no—
611C4×D4C22×C414yes—
612C4×D4C22×C414yes—
613#117—28no—
614#117—28no—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—28no—
619#117—28no—
620#117—22no—
621#117—22no—
622#117—82no—
623#117—82no—
624#117C22×C414yes—
625#117C22×C414yes—
626#117#4114yes—
627C2×C4⋊C4—28no—
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—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⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C42—28no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—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×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#107—22no—
743#107—22no—
744#107—22no—
745#107—22no—
746#107C22×C414yes—
747#107C22×C414yes—
748#106—22no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106C22×C414yes—
753#106C22×C414yes—
754C4⋊C8—22no—
755C4⋊C8—22no—
756C4⋊C8C22×C414yes—
757C4⋊C8C22×C414yes—
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#103C22×C414yes—
767#103C22×C414yes—
768#103C22×C414yes—
769#103C22×C414yes—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102C22×C414yes—
779#102C22×C414yes—
780#102C22×C414yes—
781#102C22×C414yes—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8C22×C414yes—
785C22⋊C8C22×C414yes—
786#97—22no—
787#97—22no—
788#97—22no—
789#97—22no—
790#97—22no—
791#97C22×C414yes—
792C4×C8—22no—
793C4×C8—22no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—22no—
797C4×C8C22×C414yes—
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#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832C24—21no—
833C24—21no—
834C24C22×D411yescharacteristic
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—28no—
838C2×Q8—28no—
839C2×Q8—28no—
840C2×Q8—28no—
841C2×Q8—24no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8C23×C412yes—
849C2×Q8C23×C412yes—
850C2×Q8C2×#4112yes—
851C2×Q8C2×#4112yes—
852C2×Q8C2×#4112yes—
853C2×Q8C2×#4112yes—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4C23×C412yes—
877C2×D4C23×C412yes—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—21no—
882C22×C4—21no—
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—21no—
894C22×C4—21no—
895C22×C4—24no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4C23×C412yes—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2×#4112yes—
941C22×C4C2511yescharacteristic
942SD16—28no—
943SD16—28no—
944SD16—28no—
945SD16—28no—
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—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8C23×C412yes—
967C2×C8C23×C412yes—
968C2×C8C23×C412yes—
969C2×C8C23×C412yes—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4C4×D414yes—
1010C4⋊C4C4×D414yes—
1011C4⋊C4C23×C412yes—
1012C4⋊C4C23×C412yes—
1013C4⋊C4C23×C412yes—
1014C4⋊C4C23×C412yes—
1015C4⋊C4C2×#4112yes—
1016C4⋊C4C2×#4112yes—
1017C4⋊C4C2×#4112yes—
1018C4⋊C4C2×#4112yes—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4C4×D414yes—
1042C22⋊C4C4×D414yes—
1043C42—24no—
1044C42—24no—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—24no—
1049C42—24no—
1050C42—24no—
1051C42—24no—
1052C42—24no—
1053C42—24no—
1054C42—24no—
1055C42—22no—
1056C42—22no—
1057C42—24no—
1058C42—24no—
1059C42—22no—
1060C42—22no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—41no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42C23×C412yes—
1090C42C23×C412yes—
1091C42C2×#4112yes—
1092C42C2×#4112yes—
1093C42C2×#4112yes—
1094C42C2×#4112yes—
1095C42C2×#4112yes—
1096C42C2×#4112yes—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—22no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C2×C4×D412yes—
1118C23C23×D411yescharacteristic
1119Q8—216no—
1120Q8—22no—
1121Q8—22no—
1122Q8—22no—
1123Q8—22no—
1124Q8—22no—
1125Q8—22no—
1126Q8C4×#4114yes—
1127Q8C4×#4114yes—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—84no—
1138D4—84no—
1139D4—84no—
1140C2×C4—216no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—44no—
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—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—82no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4C2×C4×D412yes—
1226C2×C4C2×C4×D412yes—
1227C2×C4C2×C4×D412yes—
1228C2×C4C2×C4×D412yes—
1229C2×C4C2×C4×D412yes—
1230C2×C4#52512yes—
1231C2×C4#52512yes—
1232C2×C4#52512yes—
1233C2×C4#52512yes—
1234C2×C4#57712yes—
1235C2×C4C24×C411yescharacteristic
1236C2×C4C22×#4111yescharacteristic
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C22×C4×D411yescharacteristic
1271C22C2×#52511yescharacteristic
1272C22C2×#52511yescharacteristic
1273C22C2×#57711yescharacteristic
1274C22#358411yescharacteristic
1275C22#358511yescharacteristic
1276C22#358611yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—24no—
1287C4—24no—
1288C4—22no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—41no—
1294C4—42no—
1295C4—42no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—42no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4C2×C4×#4111yescharacteristic
1305C4C2×C4×#4111yescharacteristic
1306C4#344411yescharacteristic
1307C4#344411yescharacteristic
1308C2—42no—
1309C2—82no—
1310C2—82no—
1311C2C4×#52511yescharacteristic
1312C2C4×#57711yescharacteristic
1313C2#6017411yescharacteristic
1314C2#6058211yescharacteristic
1315C2#6058711yescharacteristic
1316C2#6059311yescharacteristic
1317C2#6059811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#540C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C4×#519C2semidirect
4. #21622C2semidirect
5. #21621C2semidirect
6. #21618C2semidirect
7. C4×#479C2semidirect
8. #21590C2semidirect
9. #21588C2semidirect
10. #21582C2semidirect
11. C4×#482C2semidirect
12. #21515C2semidirect
13. #21515C2semidirect
14. #21505C2semidirect
15. C4×#460C2semidirect
16. #21462C2semidirect
17. #21462C2semidirect
18. #21454C2semidirect
19. C4×#448C2semidirect
21. #21367C2semidirect
22. #21124C2semidirect
23. #21124C2semidirect
24. #21120C2semidirect
25. #21115C2semidirect
26. #20745C2semidirect
27. #20506C2semidirect
28. #20504C2semidirect
29. #20504C2semidirect
30. #20504C2semidirect
31. #20468C2semidirect
36. #3126C4semidirect
222. #519C2×C4semidirect
267. #482C2×C4semidirect
268. #482C2×C4semidirect
269. #479C2×C4semidirect
270. #479C2×C4semidirect
271. #460C2×C4semidirect
272. #460C2×C4semidirect
273. #448C2×C4semidirect
274. #448C2×C4semidirect
279. #440C2×C4semidirect
280. #440C2×C4semidirect
285. C4×SD16C2×C4semidirect
286. C4×SD16C2×C4semidirect
288. #433C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#31262
#342802
C4×#5192
#216222
#216212
#216182
C4×#4792
#215902
#215882
#215822
C4×#4822
#215152
#215052
C4×#4602
#214622
#214542
C4×#4482
#213992
#213672
#211242
#211202
#211152
#207452
#205062
#205042
#204682