Finite Group Databasebeta

← #6562237

Subgroups — #6562237

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36372C211yesmaximal, characteristic, complemented
2#34240C211yesmaximal, characteristic, complemented
3#30083C211yesmaximal, characteristic, complemented
4#30081C211yesmaximal, characteristic, complemented
5#29940C211yesmaximal, characteristic, complemented
6#29373C211yesmaximal, characteristic, complemented
7#29372C211yesmaximal, characteristic, complemented
8#29125C211yesmaximal, characteristic, complemented
9#29122C211yesmaximal, characteristic, complemented
10#27524C211yesmaximal, characteristic, complemented
11#27523C211yesmaximal, characteristic, complemented
12#27520C211yesmaximal, characteristic, complemented
13#27519C211yesmaximal, characteristic, complemented
14#26537C211yesmaximal, characteristic, complemented
15#26536C211yesmaximal, characteristic, complemented
16#25859C211yesmaximal, characteristic, complemented
17#25327C211yesmaximal, characteristic, complemented
18#25326C211yesmaximal, characteristic, complemented
19#24898C211yesmaximal, characteristic, complemented
20#24897C211yesmaximal, characteristic
21#24894C211yesmaximal, characteristic, complemented
22#24893C211yesmaximal, characteristic
23#24215C211yesmaximal, characteristic
24#23758C211yesmaximal, characteristic, complemented
25#23680C211yesmaximal, characteristic, complemented
26#23680C211yesmaximal, characteristic, complemented
27#23219C211yesmaximal, characteristic, complemented
28#23218C211yesmaximal, characteristic, complemented
29#22999C211yesmaximal, characteristic, complemented
30#22999C211yesmaximal, characteristic, complemented
31#22639C211yesmaximal, characteristic, complemented
32C22×#124C2211yescharacteristic
33C2×#488C2211yescharacteristic
34C2×#488C2211yescharacteristic
35C2×#463C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#448C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic, complemented
40C2×C4×SD16C2211yescharacteristic, complemented
41C2×C4×D8C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43#2864C2211yescharacteristic, complemented
44#2859C2211yescharacteristic, complemented
45#2851C2211yescharacteristic
46#2609—21no—
47#2573—21no—
48#2570C2211yescharacteristic, complemented
49#2566C2211yescharacteristic, complemented
50#2530—21no—
51#2497C2211yescharacteristic
52#2495C2211yescharacteristic
53#2475—21no—
54#2470—21no—
55#2460—21no—
56#2422C2211yescharacteristic
57#2420C2211yescharacteristic
58#2372—21no—
59#2372—21no—
60#2370C2211yescharacteristic, complemented
61#2367C2211yescharacteristic
62#2367C2211yescharacteristic
63#2367C2211yescharacteristic
64#2367C2211yescharacteristic
65#2359—21no—
66#2349C2211yescharacteristic, complemented
67#2343—21no—
68#2342—21no—
69#2342—21no—
70Q8×C22⋊C4C2211yescharacteristic
71Q8×C22⋊C4C2211yescharacteristic
72D4×C22⋊C4C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2337—21no—
75#2337—21no—
76#2312—21no—
77C4×#124C2211yescharacteristic
78C4×#124C2211yescharacteristic
79C4×#124C2211yescharacteristic
80C4×#124C2211yescharacteristic
81C4×#121C2211yescharacteristic
82#2293C2211yescharacteristic, complemented
83#2293C2211yescharacteristic, complemented
84#2283C2211yescharacteristic
85#2273—21no—
86C4×#117C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2096C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic, complemented
107#2072C2211yescharacteristic, complemented
108#2071C2211yescharacteristic
109#2068C2211yescharacteristic, complemented
110#2068C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2055C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#1989C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1958C2211yescharacteristic
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1939C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1880C2211yescharacteristic, complemented
154#1880C2211yescharacteristic, complemented
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1877C2211yescharacteristic, complemented
161#1865C2211yescharacteristic, complemented
162#1865C2211yescharacteristic, complemented
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1863C2211yescharacteristic, complemented
168#1863C2211yescharacteristic, complemented
169#1863C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1839C2211yescharacteristic, complemented
174#1839C2211yescharacteristic, complemented
175#1805C2211yescharacteristic, complemented
176#1805C2211yescharacteristic, complemented
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic, complemented
180#1803C2211yescharacteristic, complemented
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1797C2211yescharacteristic
184#1787C2211yescharacteristic
185#1787C2211yescharacteristic
186#1787C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C4×C4⋊C8C2211yescharacteristic, complemented
195C4×C4⋊C8C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#124—24no—
212C2×#124—24no—
213C2×#124—21no—
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#121C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C2×#117D411yescharacteristic
236C2×#117D411yescharacteristic
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42C2311yescharacteristic
242#488—24no—
243#488—24no—
244#463—24no—
245#463—24no—
246#448—42no—
247#447—42no—
248C4×SD16—42no—
249C4×SD16—42no—
250C4×D8—42no—
251C4×D8—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#400—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#394—21no—
319#394—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391—21no—
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#389—21no—
336#389—21no—
337#389—21no—
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
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#388—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#383—21no—
402#382—21no—
403#382C2311yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381—21no—
409#381—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#379—21no—
419#379—21no—
420C4×C4⋊C4—21no—
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×C22⋊C4—21no—
431C4×C22⋊C4—21no—
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
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⋊C4D411yescharacteristic
449C4×C22⋊C4D411yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452#376—21no—
453#376D411yescharacteristic
454#376D411yescharacteristic
455C2×#95—21no—
456C43C2311yescharacteristic
457C43C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—21no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542#125—22no—
543#125—22no—
544#125—82no—
545#124—28no—
546#124—28no—
547#124—22no—
548#124—22no—
549#124—22no—
550#124—22no—
551#124—22no—
552#124—22no—
553#124#4114yes—
554#124#4114yes—
555#123—44no—
556#121—22no—
557#121—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—82no—
581#117—24no—
582#117—42no—
583#117—44no—
584#117—82no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C22⋊C4—28no—
620C2×C22⋊C4—28no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—44no—
657C2×C22⋊C4—44no—
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C42—22no—
663C2×C42—22no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C4×C8—22no—
740C4×C8—22no—
741C4×C8—41no—
742C4×C8—41no—
743C4×C8—41no—
744C4×C8—41no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—24no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C2×Q8—24no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—82no—
815C2×Q8—82no—
816C2×Q8—82no—
817C2×Q8—82no—
818C2×Q8C2×#4112yes—
819C2×Q8C2×#4112yes—
820C2×D4—24no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4C2×#4112yes—
846C2×D4C2×#4112yes—
847C2×D4H(5,𝔽2)12yes—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2511yescharacteristic
911SD16—44no—
912SD16—44no—
913D8—44no—
914D8—44no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—41no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—41no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4#13514yes—
1023C42—22no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—41no—
1039C42—41no—
1040C42—41no—
1041C42—41no—
1042C42—41no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C42C2×#4112yes—
1053C42C2×#4112yes—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—48no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—84no—
1083C23—84no—
1084C23—162no—
1085C23—162no—
1086C23—162no—
1087C23—162no—
1088C23C2×#13512yes—
1089C23C23×D411yescharacteristic
1090Q8—22no—
1091Q8—22no—
1092Q8—22no—
1093Q8—22no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—84no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—22no—
1103D4—22no—
1104D4—22no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—84no—
1112D4—84no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—44no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—82no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—162no—
1196C2×C4—162no—
1197C2×C4—162no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4#52512yes—
1201C2×C4#52512yes—
1202C2×C4C2×#13512yes—
1203C2×C4C2×#13512yes—
1204C2×C4#57512yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C22×#4111yescharacteristic
1207C2×C4C2×H(5,𝔽2)11yescharacteristic
1208C2×C4#58511yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C8—41no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—168no—
1248C22C2×#52511yescharacteristic
1249C22#348811yescharacteristic
1250C22#350011yescharacteristic
1251C22C22×#13511yescharacteristic
1252C22C2×#57511yescharacteristic
1253C22#358411yescharacteristic
1254C22#358511yescharacteristic
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—42no—
1269C4—41no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4#351311yescharacteristic
1282C4#351311yescharacteristic
1283C4#352111yescharacteristic
1284C4#352111yescharacteristic
1285C2—42no—
1286C2—82no—
1287C2—82no—
1288C2—82no—
1289C2#3598211yescharacteristic
1290C2#6053611yescharacteristic
1291C2#6058711yescharacteristic
1292C2#6195511yescharacteristic
1293C2#6199011yescharacteristic
1294C2#6253311yescharacteristic
1295C2#6259211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
LCSG ▷ C22×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
1. #36372C2semidirect
2. #34240C2semidirect
3. #30083C2semidirect
4. #30081C2semidirect
5. #29940C2semidirect
6. #29373C2semidirect
7. #29372C2semidirect
8. #29125C2semidirect
9. #29122C2semidirect
10. #27524C2semidirect
11. #27523C2semidirect
12. #27520C2semidirect
13. #27519C2semidirect
14. #26537C2semidirect
15. #26536C2semidirect
16. #25859C2semidirect
17. #25327C2semidirect
18. #25326C2semidirect
19. #24898C2semidirect
21. #24894C2semidirect
24. #23758C2semidirect
25. #23680C2semidirect
26. #23680C2semidirect
27. #23219C2semidirect
28. #23218C2semidirect
29. #22999C2semidirect
30. #22999C2semidirect
31. #22639C2semidirect
39. C2×C4×SD16C22semidirect
40. C2×C4×SD16C22semidirect
43. #2864C22semidirect
44. #2859C22semidirect
48. #2570C22semidirect
49. #2566C22semidirect
60. #2370C22semidirect
66. #2349C22semidirect
82. #2293C22semidirect
83. #2293C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
91. #2096C22semidirect
94. #2092C22semidirect
95. #2085C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
104. #2074C22semidirect
106. #2073C22semidirect
107. #2072C22semidirect
109. #2068C22semidirect
110. #2068C22semidirect
113. #2055C22semidirect
114. #2055C22semidirect
127. #1989C22semidirect
128. #1989C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1939C22semidirect
136. #1939C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1933C22semidirect
144. #1933C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
153. #1880C22semidirect
154. #1880C22semidirect
159. #1877C22semidirect
160. #1877C22semidirect
161. #1865C22semidirect
162. #1865C22semidirect
167. #1863C22semidirect
168. #1863C22semidirect
169. #1863C22semidirect
170. #1863C22semidirect
173. #1839C22semidirect
174. #1839C22semidirect
175. #1805C22semidirect
176. #1805C22semidirect
179. #1803C22semidirect
180. #1803C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. C8×C4⋊C4C22semidirect
193. C8×C4⋊C4C22semidirect
194. C4×C4⋊C8C22semidirect
195. C4×C4⋊C8C22semidirect
196. C4×#103C22semidirect
197. C4×#103C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#363722
#342402
#300832
#300812
#299402
#293732
#293722
#291252
#291222
#275242
#275232
#275202
#275192
#265372
#265362
#258592
#253272
#253262
#248982
#248972
#248942
#248932
#242152
#237582
#236802
#232192
#232182
#229992
#226392