Finite Group Databasebeta

← #35568398

Subgroups — #35568398

Order 21248.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910620C212yesmaximal, complemented
2#24910604C212yesmaximal, complemented
3#24910538C211yesmaximal, characteristic, complemented
4#24910538C211yesmaximal, characteristic, complemented
5#24910528C211yesmaximal, characteristic, complemented
6#24910528C211yesmaximal, characteristic, complemented
7#24910515C212yesmaximal, complemented
8#24910447C212yesmaximal, complemented
9#24910304C211yesmaximal, characteristic, complemented
10#24910293C211yesmaximal, characteristic, complemented
11D4×C22⋊Dic83C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic83C211yesmaximal, characteristic, complemented
13#24910230C212yesmaximal, complemented
14#24910189C211yesmaximal, characteristic, complemented
15#24910176C211yesmaximal, characteristic, complemented
16#24910168C212yesmaximal, complemented
17#24910124C212yesmaximal, complemented
18#24910124C212yesmaximal, complemented
19#24910072C211yesmaximal, characteristic, complemented
20#127×Dic83C211yesmaximal, characteristic, complemented
21#124×Dic83C211yesmaximal, characteristic, complemented
22#24909961C211yesmaximal, characteristic, complemented
23C2×#535×C83C211yesmaximal, characteristic
24C2×Q8×Dic83C2211yescharacteristic, complemented
25C2×Q8×Dic83C2211yescharacteristic, complemented
26C2×D4×Dic83C2211yescharacteristic
27C2×D4×Dic83C2211yescharacteristic
28C2×D4×Dic83C2211yescharacteristic
29C2×D4×Dic83C2211yescharacteristic
30C2×D4×Dic83C2212yescomplemented
31C2×D4×Dic83C2212yescomplemented
32C2×D4×Dic83C2212yescomplemented
33C2×D4×Dic83C2211yescharacteristic, complemented
34C2×D4×Dic83C2212yescomplemented
35C2×D4×Dic83C2211yescharacteristic, complemented
36C22×C22⋊Dic83C2212yes—
37C22×C22⋊Dic83C2212yes—
38#19127608C2211yescharacteristic, complemented
39#19127608C2211yescharacteristic, complemented
40#19127604C2212yes—
41#19127604C2212yes—
42#19127604C2211yescharacteristic
43#19127604C2211yescharacteristic
44#19127604C2211yescharacteristic
45#19127604C2211yescharacteristic
46#19127604C2212yescomplemented
47#19127604C2212yescomplemented
48#19127604C2212yescomplemented
49#19127604C2212yescomplemented
50#19127604C2211yescharacteristic, complemented
51#19127604C2211yescharacteristic, complemented
52#19127594C2211yescharacteristic
53#19127594C2212yes—
54#19127594C2211yescharacteristic
55#19127594C2211yescharacteristic
56#19127594C2212yes—
57#19127594C2211yescharacteristic
58#19127594C2212yescomplemented
59#19127594C2212yescomplemented
60#19127594C2212yescomplemented
61#19127594C2212yescomplemented
62#19127594C2212yescomplemented
63#19127594C2212yescomplemented
64#19127594C2212yescomplemented
65#19127594C2212yescomplemented
66#19127587C2211yescharacteristic, complemented
67#19127587C2212yescomplemented
68#19127587C2211yescharacteristic, complemented
69#19127587C2212yescomplemented
70#19127587C2211yescharacteristic, complemented
71#19127587C2211yescharacteristic, complemented
72#19127581C2212yes—
73#19127581C2212yes—
74#19127581C2212yes—
75#19127581C2212yes—
76#19127581C2212yes—
77#19127581C2212yes—
78#19127581C2212yescomplemented
79#19127581C2212yescomplemented
80#19127581C2212yescomplemented
81#19127581C2212yescomplemented
82#19127581C2212yescomplemented
83#19127581C2212yescomplemented
84#19127581C2212yescomplemented
85#19127581C2212yescomplemented
86#19127576C2212yescomplemented
87#19127576C2212yescomplemented
88#19127576C2212yescomplemented
89#19127576C2212yescomplemented
90#19127571C2211yescharacteristic, complemented
91#19127567C2211yescharacteristic, complemented
92#19127564C2212yescomplemented
93#19127561C2211yescharacteristic
94#19127561C2211yescharacteristic
95#19127561C2212yescomplemented
96#19127557C2212yes—
97#19127557C2212yes—
98C4×C4⋊Dic83C2211yescharacteristic, complemented
99C4×C4⋊Dic83C2211yescharacteristic, complemented
100C4×C4⋊Dic83C2211yescharacteristic, complemented
101C4×C4⋊Dic83C2211yescharacteristic, complemented
102C22⋊C4×Dic83C2212yescomplemented
103C22⋊C4×Dic83C2212yescomplemented
104C22⋊C4×Dic83C2212yescomplemented
105C22⋊C4×Dic83C2212yescomplemented
106C4×C22⋊Dic83C2211yescharacteristic
107C4×C22⋊Dic83C2211yescharacteristic
108C4×C22⋊Dic83C2212yescomplemented
109#19127547C2211yescharacteristic, complemented
110C2×C83⋊#95C2212yescomplemented
111C42×Dic83C2211yescharacteristic, complemented
112C22×#41×C83C2211yescharacteristic
113C23×D4×C83C2211yescharacteristic
114#535×C83C4116yescomplemented
115C2×#127×C83C2211yescharacteristic
116C2×#127×C83C2211yescharacteristic
117C2×#124×C83C2211yescharacteristic
118C2×#124×C83C2211yescharacteristic
119C2×#121×C83C2212yes—
120C2×#121×C83C2212yes—
121C2×#120×C83C2212yes—
122C2×#120×C83C2212yes—
123C2×#117×C83C2211yescharacteristic
124C23×Dic83C2312yes—
125C23×Dic83C2312yes—
126C23×Dic83C2312yes—
127C23×Dic83C2312yes—
128C23×Dic83C2312yes—
129C23×Dic83C2312yes—
130Q8×Dic83—42no—
131Q8×Dic83—42no—
132D4×Dic83—42no—
133D4×Dic83—42no—
134D4×Dic83—42no—
135D4×Dic83—42no—
136D4×Dic83—42no—
137D4×Dic83—42no—
138D4×Dic83—44no—
139D4×Dic83—44no—
140D4×Dic83—44no—
141D4×Dic83—44no—
142C2×C4⋊Dic83C2311yescharacteristic
143C2×C4⋊Dic83C2311yescharacteristic
144C2×C4⋊Dic83C2311yescharacteristic
145C2×C4⋊Dic83C2311yescharacteristic
146C2×C4⋊Dic83C2311yescharacteristic
147C2×C4⋊Dic83C2311yescharacteristic
148C2×C4⋊Dic83C2311yescharacteristic
149C2×C4⋊Dic83C2311yescharacteristic
150C2×C4⋊Dic83C2312yes—
151C2×C4⋊Dic83C2312yes—
152C2×C4⋊Dic83C2312yes—
153C2×C4⋊Dic83C2312yes—
154C2×C22⋊Dic83—44no—
155C2×C22⋊Dic83—44no—
156C2×C22⋊Dic83C2311yescharacteristic
157C2×C22⋊Dic83C2312yes—
158C2×C22⋊Dic83C2312yes—
159C2×C22⋊Dic83C2312yes—
160C2×C22⋊Dic83C2311yescharacteristic
161C2×C22⋊Dic83C2311yescharacteristic
162C2×C22⋊Dic83C2311yescharacteristic
163C2×C22⋊Dic83C2312yes—
164C2×C22⋊Dic83C2312yes—
165C2×C22⋊Dic83C2312yes—
166C2×C22⋊Dic83C2312yes—
167C2×C22⋊Dic83C2312yes—
168C2×C22⋊Dic83C2312yes—
169C2×C22⋊Dic83C2312yes—
170C2×C22⋊Dic83C2312yes—
171C2×C22⋊Dic83C2312yes—
172C2×C22⋊Dic83C2312yes—
173C2×C22⋊Dic83C2312yes—
174C2×C22⋊Dic83C2312yes—
175C2×C22⋊Dic83C2312yes—
176C2×C22⋊Dic83C2312yes—
177C2×C22⋊Dic83C2312yes—
178C2×C22⋊Dic83C2312yes—
179C2×C22⋊Dic83C2312yes—
180C2×C4×Dic83C2311yescharacteristic
181C2×C4×Dic83C2311yescharacteristic
182C2×C4×Dic83C2311yescharacteristic
183C2×C4×Dic83C2311yescharacteristic
184C2×C4×Dic83C2311yescharacteristic
185C2×C4×Dic83C2311yescharacteristic
186C2×C4×Dic83C2312yes—
187C2×C4×Dic83C2312yes—
188C2×C4×Dic83C2311yescharacteristic
189C2×C4×Dic83C2311yescharacteristic
190C2×C4×Dic83C2312yes—
191C2×C4×Dic83C2312yes—
192C83⋊#95C2312yes—
193C83⋊#95C2312yes—
194C83⋊#95C2311yescharacteristic
195C83⋊#95C2311yescharacteristic
196C83⋊#95C2311yescharacteristic
197C83⋊#95C2311yescharacteristic
198C83⋊#95C2312yes—
199C83⋊#95C2312yes—
200C83⋊#95C2311yescharacteristic
201C83⋊#95C2311yescharacteristic
202C83⋊#95C2312yes—
203C83⋊#95C2312yes—
204C83⋊#95C2312yes—
205C83⋊#95C2312yes—
206C83⋊#95C2311yescharacteristic
207C83⋊#95C2311yescharacteristic
208C83⋊#95C2312yes—
209C83⋊#95C2312yes—
210C83⋊#95C2311yescharacteristic
211C83⋊#95C2311yescharacteristic
212C83⋊#95C2311yescharacteristic
213C83⋊#95C2311yescharacteristic
214C25×C83C2312yes—
215C2×#41×C83—42no—
216C2×#41×C83—42no—
217C2×#41×C83C2×C418yescomplemented
218C22×Q8×C83C2311yescharacteristic
219C22×D4×C83—42no—
220C22×D4×C83—42no—
221C22×D4×C83C2×C418yescomplemented
222C22×D4×C83C2311yescharacteristic
223C22×D4×C83C2311yescharacteristic
224C22×D4×C83C2311yescharacteristic
225C22×D4×C83C2312yes—
226C22×D4×C83C2312yes—
227C22×D4×C83C2312yes—
228C22×D4×C83C2312yes—
229C22×D4×C83C2312yes—
230C22×D4×C83C2312yes—
231C23×C4×C83C2311yescharacteristic
232C23×C4×C83C2312yes—
233#127×C83C2×C418yescomplemented
234#127×C83C2×C418yescomplemented
235#124×C83C2×C418yescomplemented
236#124×C83C2×C418yescomplemented
237#121×C83C2×C4116yescomplemented
238#121×C83C2×C4116yescomplemented
239#120×C83C2×C4116yescomplemented
240#120×C83C2×C4116yescomplemented
241#117×C83C2×C418yescomplemented
242C2×C4⋊C4×C83C2311yescharacteristic
243C2×C4⋊C4×C83C2311yescharacteristic
244C2×C22⋊C4×C83C2312yes—
245C2×C22⋊C4×C83C2312yes—
246C2×C22⋊C4×C83C2312yes—
247C2×C22⋊C4×C83C2312yes—
248C2×C22⋊C4×C83C2311yescharacteristic
249C2×C22⋊C4×C83C2311yescharacteristic
250C2×C42×C83C2311yescharacteristic
251C2×C42×C83C2311yescharacteristic
252C22×Dic83—24no—
253C22×Dic83—24no—
254C22×Dic83—24no—
255C22×Dic83—42no—
256C22×Dic83—42no—
257C22×Dic83—42no—
258C22×Dic83—42no—
259C22×Dic83—42no—
260C22×Dic83—42no—
261C22×Dic83—42no—
262C22×Dic83—42no—
263C22×Dic83—42no—
264C22×Dic83—42no—
265C22×Dic83—42no—
266C22×Dic83—42no—
267C22×Dic83—42no—
268C22×Dic83—42no—
269C22×Dic83—42no—
270C22×Dic83C2411yescharacteristic
271C22×Dic83C2411yescharacteristic
272C22×Dic83C2412yes—
273C22×Dic83C2411yescharacteristic
274C22×Dic83C2412yes—
275C22×Dic83C2412yes—
276C22×Dic83C2412yes—
277C22×Dic83C2411yescharacteristic
278C22×Dic83C2411yescharacteristic
279C22×Dic83C2411yescharacteristic
280C22×Dic83C2411yescharacteristic
281C22×Dic83C2411yescharacteristic
282C4⋊Dic83—22no—
283C4⋊Dic83—22no—
284C4⋊Dic83—22no—
285C4⋊Dic83—22no—
286C4⋊Dic83—22no—
287C4⋊Dic83—22no—
288C4⋊Dic83—41no—
289C4⋊Dic83—41no—
290C4⋊Dic83—42no—
291C4⋊Dic83—42no—
292C4⋊Dic83—42no—
293C4⋊Dic83—42no—
294C22⋊Dic83—22no—
295C22⋊Dic83—22no—
296C22⋊Dic83—24no—
297C22⋊Dic83—24no—
298C22⋊Dic83—24no—
299C22⋊Dic83—42no—
300C22⋊Dic83—42no—
301C22⋊Dic83—42no—
302C22⋊Dic83—42no—
303C22⋊Dic83—42no—
304C22⋊Dic83—41no—
305C22⋊Dic83—41no—
306C22⋊Dic83—42no—
307C22⋊Dic83—42no—
308C22⋊Dic83—42no—
309C22⋊Dic83—42no—
310C22⋊Dic83—42no—
311C22⋊Dic83—42no—
312C22⋊Dic83—42no—
313C22⋊Dic83—42no—
314C22⋊Dic83—42no—
315C22⋊Dic83—42no—
316C22⋊Dic83—42no—
317C22⋊Dic83—42no—
318C4×Dic83—22no—
319C4×Dic83—22no—
320C4×Dic83—22no—
321C4×Dic83—22no—
322C4×Dic83—22no—
323C4×Dic83—22no—
324C4×Dic83—41no—
325C4×Dic83—41no—
326C4×Dic83—42no—
327C4×Dic83—42no—
328C4×Dic83—42no—
329C4×Dic83—42no—
330C24×C83—42no—
331C24×C83—42no—
332C24×C83—42no—
333C24×C83—42no—
334C24×C83—42no—
335C24×C83—42no—
336C24×C83C22×C418yes—
337C24×C83C2412yes—
338C24×C83C2412yes—
339C24×C83C2412yes—
340C24×C83C2411yescharacteristic
341#41×C83—416no—
342C2×Q8×C83—22no—
343C2×Q8×C83—22no—
344C2×Q8×C83C22×C414yes—
345C2×D4×C83—22no—
346C2×D4×C83—22no—
347C2×D4×C83—22no—
348C2×D4×C83—22no—
349C2×D4×C83—22no—
350C2×D4×C83—22no—
351C2×D4×C83—416no—
352C2×D4×C83—42no—
353C2×D4×C83—42no—
354C2×D4×C83—42no—
355C2×D4×C83—42no—
356C2×D4×C83—42no—
357C2×D4×C83—42no—
358C2×D4×C83—42no—
359C2×D4×C83—42no—
360C2×D4×C83—42no—
361C2×D4×C83—42no—
362C2×D4×C83—42no—
363C2×D4×C83—42no—
364C2×D4×C83C22×C414yes—
365C2×D4×C83C22×C414yes—
366C2×D4×C83C22×C414yes—
367C2×D4×C83C22×C418yes—
368C2×D4×C83C22×C418yes—
369C2×D4×C83C22×C418yes—
370C2×D4×C83C22×C418yes—
371C2×D4×C83C22×C418yes—
372C2×D4×C83C22×C418yes—
373C22×C4×C83—22no—
374C22×C4×C83—22no—
375C22×C4×C83—42no—
376C22×C4×C83—42no—
377C22×C4×C83C22×C414yes—
378C22×C4×C83C22×C418yes—
379C22×C4×C83C2411yescharacteristic
380C22×C4×C83C2411yescharacteristic
381C22×C4×C83C2411yescharacteristic
382C22×C4×C83C2411yescharacteristic
383C22×C4×C83C2412yes—
384C22×C4×C83C2411yescharacteristic
385C22×C4×C83C2411yescharacteristic
386C4⋊C4×C83C22×C414yes—
387C4⋊C4×C83C22×C414yes—
388C22⋊C4×C83C22×C414yes—
389C22⋊C4×C83C22×C414yes—
390C22⋊C4×C83C22×C418yes—
391C22⋊C4×C83C22×C418yes—
392C22⋊C4×C83C22×C418yes—
393C22⋊C4×C83C22×C418yes—
394C42×C83C22×C414yes—
395C42×C83C22×C414yes—
396C23×C83—21no—
397C23×C83—21no—
398C23×C83—22no—
399C23×C83—22no—
400C23×C83—22no—
401C23×C83—22no—
402C23×C83—22no—
403C23×C83—22no—
404C23×C83—22no—
405C23×C83—22no—
406C23×C83—22no—
407C23×C83—22no—
408C23×C83—22no—
409C23×C83—22no—
410C23×C83—21no—
411C23×C83—21no—
412C23×C83—22no—
413C23×C83—22no—
414C23×C83—22no—
415C23×C83—22no—
416C23×C83—22no—
417C23×C83—22no—
418C23×C83—21no—
419C23×C83—21no—
420C23×C83—48no—
421C23×C83—48no—
422C23×C83—48no—
423C23×C83—84no—
424C23×C83—84no—
425C23×C83—84no—
426C23×C83—84no—
427C23×C83C23×C412yes—
428C23×C83C23×C414yes—
429C23×C83C23×C414yes—
430C23×C83C23×C414yes—
431C23×C83C2511yescharacteristic
432Q8×C83—28no—
433D4×C83—28no—
434D4×C83—28no—
435D4×C83—28no—
436D4×C83—48no—
437D4×C83—48no—
438D4×C83—48no—
439D4×C83—48no—
440D4×C83—48no—
441D4×C83—48no—
442C2×C4×C83—21no—
443C2×C4×C83—21no—
444C2×C4×C83—22no—
445C2×C4×C83—22no—
446C2×C4×C83—21no—
447C2×C4×C83—21no—
448C2×C4×C83—21no—
449C2×C4×C83—21no—
450C2×C4×C83—21no—
451C2×C4×C83—21no—
452C2×C4×C83—21no—
453C2×C4×C83—21no—
454C2×C4×C83—28no—
455C2×C4×C83—48no—
456C2×C4×C83C23×C412yes—
457C2×C4×C83C23×C412yes—
458C2×C4×C83C23×C412yes—
459C2×C4×C83C23×C412yes—
460C2×C4×C83C23×C414yes—
461C2×C4×C83C23×C412yes—
462C2×C4×C83C23×C412yes—
463C2×C4×C83H(5,𝔽2)12yes—
464C2×C4×C83H(5,𝔽2)12yes—
465C2×Dic83—21no—
466C2×Dic83—21no—
467C2×Dic83—21no—
468C2×Dic83—21no—
469C2×Dic83—21no—
470C2×Dic83—21no—
471C2×Dic83—21no—
472C2×Dic83—21no—
473C2×Dic83—21no—
474C2×Dic83—21no—
475C2×Dic83—21no—
476C2×Dic83—22no—
477C2×Dic83—22no—
478C2×Dic83—22no—
479C2×Dic83—22no—
480C2×Dic83—22no—
481C2×Dic83—22no—
482C2×Dic83—21no—
483C2×Dic83—21no—
484C2×Dic83—22no—
485C2×Dic83—22no—
486C2×Dic83—21no—
487C2×Dic83—21no—
488C2×Dic83—22no—
489C2×Dic83—22no—
490C2×Dic83—21no—
491C2×Dic83—21no—
492C2×Dic83—21no—
493C2×Dic83—21no—
494C2×Dic83—21no—
495C2×Dic83—22no—
496C2×Dic83—21no—
497C2×Dic83—22no—
498C2×Dic83—21no—
499C2×Dic83—84no—
500C2×Dic83—84no—
501C2×Dic83—84no—
502C2×Dic83—84no—
503C2×Dic83—84no—
504C2×Dic83—84no—
505C2×Dic83H(5,𝔽2)12yes—
506C2×Dic83H(5,𝔽2)12yes—
507C22×C83—22no—
508C22×C83—24no—
509C22×C83—24no—
510C22×C83—24no—
511C22×C83—24no—
512C22×C83—24no—
513C22×C83—24no—
514C22×C83—24no—
515C22×C83—24no—
516C22×C83—24no—
517C22×C83—22no—
518C22×C83—22no—
519C22×C83—42no—
520C22×C83—42no—
521C22×C83—42no—
522C22×C83—41no—
523C22×C83—42no—
524C22×C83—42no—
525C22×C83—42no—
526C22×C83—41no—
527C22×C83—42no—
528C22×C83—42no—
529C22×C83—42no—
530C22×C83—41no—
531C22×C83—42no—
532C22×C83—42no—
533C22×C83—42no—
534C22×C83—41no—
535C22×C83—816no—
536C22×C83C24×C411yescharacteristic
537C22×C83C2×H(5,𝔽2)11yescharacteristic
538C22×C83C2×H(5,𝔽2)11yescharacteristic
539C22×C83C2×H(5,𝔽2)11yescharacteristic
540C22×C83C2×H(5,𝔽2)11yescharacteristic
541C22×C83#58511yescharacteristic
542C22×C83#58511yescharacteristic
543C4×C83—22no—
544C4×C83—24no—
545C4×C83—22no—
546C4×C83—22no—
547C4×C83—22no—
548C4×C83—22no—
549C4×C83#51814yes—
550Dic83—22no—
551Dic83—22no—
552Dic83—42no—
553Dic83—41no—
554Dic83—42no—
555Dic83—41no—
556Dic83—42no—
557Dic83—41no—
558Dic83—41no—
559Dic83—42no—
560Dic83—41no—
561Dic83—41no—
562#34438—831nomaximal, Sylow
563C2×C83—44no—
564C2×C83—44no—
565C2×C83—44no—
566C2×C83—42no—
567C2×C83C2×#51811yescharacteristic
568C2×C83C4×H(5,𝔽2)11yescharacteristic
569C2×C83C4×H(5,𝔽2)11yescharacteristic
570C2×C83#354311yescharacteristic
571C2×C83#354611yescharacteristic
572C2×C83#355811yescharacteristic
573C2×C83#356211yescharacteristic
574C2×#535D8311yescharacteristic
575#2377—832no—
576#2375—832no—
577#2367—831no—
578#2367—831no—
579#2366—831no—
580#2366—831no—
581#2364—832no—
582#2358—832no—
583#2341—831no—
584#2339—831no—
585D4×C22⋊C4—831no—
586D4×C22⋊C4—831no—
587#2333—832no—
588#2328—831no—
589#2326—831no—
590#2325—832no—
591#2321—832no—
592#2321—832no—
593#2314—831no—
594C4×#127—831no—
595C4×#124—831no—
596#2298—831no—
597C83#3443811yescharacteristic, complemented, Sylow
598C22×#41C2×D8311yescharacteristic
599C23×D4C2×D8311yescharacteristic
600#535Dic83116yescomplemented
601C2×#127C2×D8311yescharacteristic
602C2×#127C2×D8311yescharacteristic
603C2×#124C2×D8311yescharacteristic
604C2×#124C2×D8311yescharacteristic
605C2×#121C2×D8312yes—
606C2×#121C2×D8312yes—
607C2×#120C2×D8312yes—
608C2×#120C2×D8312yes—
609C2×C4×Q8—831no—
610C2×C4×Q8—831no—
611C2×C4×D4—832no—
612C2×C4×D4—831no—
613C2×C4×D4—831no—
614C2×C4×D4—832no—
615C2×C4×D4—832no—
616C2×C4×D4—832no—
617C2×C4×D4—831no—
618C2×C4×D4—831no—
619C2×C4×D4—831no—
620C2×C4×D4—831no—
621C2×#117C2×D8311yescharacteristic
622C22×C22⋊C4—832no—
623C22×C22⋊C4—832no—
624#391—831no—
625#391—831no—
626#390—832no—
627#390—831no—
628#390—831no—
629#390—832no—
630#390—832no—
631#390—832no—
632#390—832no—
633#390—831no—
634#390—831no—
635#390—831no—
636#390—832no—
637#390—831no—
638#388—832no—
639#388—832no—
640#388—831no—
641#388—831no—
642#388—832no—
643#388—832no—
644#388—832no—
645#388—832no—
646#388—832no—
647#388—832no—
648#388—832no—
649#388—831no—
650#388—831no—
651#388—832no—
652#387—832no—
653#387—832no—
654#387—831no—
655#387—831no—
656#387—831no—
657#387—831no—
658#386—832no—
659#386—832no—
660#386—832no—
661#386—832no—
662#386—832no—
663#386—832no—
664#386—832no—
665#386—832no—
666#386—832no—
667#386—832no—
668#386—832no—
669#386—832no—
670#386—832no—
671#386—832no—
672#385—832no—
673#385—832no—
674#385—832no—
675#385—832no—
676#384—831no—
677#382—831no—
678#381—832no—
679#380—831no—
680#380—831no—
681#380—832no—
682#379—832no—
683#379—832no—
684C4×C4⋊C4—831no—
685C4×C4⋊C4—831no—
686C4×C4⋊C4—831no—
687C4×C4⋊C4—831no—
688C4×C22⋊C4—832no—
689C4×C22⋊C4—831no—
690C4×C22⋊C4—831no—
691C4×C22⋊C4—832no—
692C4×C22⋊C4—832no—
693C4×C22⋊C4—832no—
694C4×C22⋊C4—832no—
695#376—831no—
696C2×#95—832no—
697C43—831no—
698C25C22×D8312yes—
699C2×#41—42no—
700C2×#41—42no—
701C2×#41C2×Dic8318yescomplemented
702C22×Q8C22×D8311yescharacteristic
703C22×D4—42no—
704C22×D4—42no—
705C22×D4C2×Dic8318yescomplemented
706C22×D4C22×D8311yescharacteristic
707C22×D4C22×D8311yescharacteristic
708C22×D4C22×D8311yescharacteristic
709C22×D4C22×D8312yes—
710C22×D4C22×D8312yes—
711C22×D4C22×D8312yes—
712C22×D4C22×D8312yes—
713C22×D4C22×D8312yes—
714C22×D4C22×D8312yes—
715C23×C4—832no—
716C23×C4—832no—
717C23×C4—832no—
718C23×C4—832no—
719C23×C4—832no—
720C23×C4—832no—
721C23×C4C22×D8311yescharacteristic
722C23×C4C22×D8312yes—
723#127C2×Dic8318yescomplemented
724#127C2×Dic8318yescomplemented
725#124C2×Dic8318yescomplemented
726#124C2×Dic8318yescomplemented
727#121C2×Dic83116yescomplemented
728#121C2×Dic83116yescomplemented
729#120C2×Dic83116yescomplemented
730#120C2×Dic83116yescomplemented
731C4×Q8—3322no—
732C4×Q8—3322no—
733C4×D4—3324no—
734C4×D4—3324no—
735C4×D4—3324no—
736C4×D4—3322no—
737C4×D4—3322no—
738C4×D4—3322no—
739C4×D4—3322no—
740C4×D4—3322no—
741C4×D4—3322no—
742C4×D4—3324no—
743#117C2×Dic8318yescomplemented
744C2×C4⋊C4—832no—
745C2×C4⋊C4—832no—
746C2×C4⋊C4—832no—
747C2×C4⋊C4—832no—
748C2×C4⋊C4—831no—
749C2×C4⋊C4—831no—
750C2×C4⋊C4—831no—
751C2×C4⋊C4—831no—
752C2×C4⋊C4—831no—
753C2×C4⋊C4—831no—
754C2×C4⋊C4—831no—
755C2×C4⋊C4—831no—
756C2×C4⋊C4C22×D8311yescharacteristic
757C2×C4⋊C4C22×D8311yescharacteristic
758C2×C22⋊C4—3324no—
759C2×C22⋊C4—3324no—
760C2×C22⋊C4—832no—
761C2×C22⋊C4—832no—
762C2×C22⋊C4—832no—
763C2×C22⋊C4—832no—
764C2×C22⋊C4—832no—
765C2×C22⋊C4—832no—
766C2×C22⋊C4—832no—
767C2×C22⋊C4—832no—
768C2×C22⋊C4—832no—
769C2×C22⋊C4—832no—
770C2×C22⋊C4—832no—
771C2×C22⋊C4—832no—
772C2×C22⋊C4—832no—
773C2×C22⋊C4—832no—
774C2×C22⋊C4—831no—
775C2×C22⋊C4—831no—
776C2×C22⋊C4—832no—
777C2×C22⋊C4—832no—
778C2×C22⋊C4—832no—
779C2×C22⋊C4—831no—
780C2×C22⋊C4—831no—
781C2×C22⋊C4—832no—
782C2×C22⋊C4—832no—
783C2×C22⋊C4—832no—
784C2×C22⋊C4C22×D8311yescharacteristic
785C2×C22⋊C4C22×D8311yescharacteristic
786C2×C22⋊C4C22×D8312yes—
787C2×C22⋊C4C22×D8312yes—
788C2×C22⋊C4C22×D8312yes—
789C2×C22⋊C4C22×D8312yes—
790C2×C42—832no—
791C2×C42—832no—
792C2×C42—832no—
793C2×C42—832no—
794C2×C42—831no—
795C2×C42—831no—
796C2×C42—831no—
797C2×C42—831no—
798C2×C42—831no—
799C2×C42—831no—
800C2×C42—831no—
801C2×C42—831no—
802C2×C42C22×D8311yescharacteristic
803C2×C42C22×D8311yescharacteristic
804#95—831no—
805#95—832no—
806#95—832no—
807#95—832no—
808#95—831no—
809#95—831no—
810#95—831no—
811#95—831no—
812#95—831no—
813#95—831no—
814#95—831no—
815#95—832no—
816#95—831no—
817#95—831no—
818#95—832no—
819#95—832no—
820#95—832no—
821#95—832no—
822#95—832no—
823#95—832no—
824#95—831no—
825#95—831no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24C22×Dic8318yes—
833C24C23×D8311yescharacteristic
834C24C23×D8312yes—
835C24C23×D8312yes—
836C24C23×D8312yes—
837#41—416no—
838C2×Q8—22no—
839C2×Q8—22no—
840C2×Q8C22×Dic8314yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—416no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4C22×Dic8314yes—
861C2×D4C22×Dic8314yes—
862C2×D4C22×Dic8314yes—
863C2×D4C22×Dic8318yes—
864C2×D4C22×Dic8318yes—
865C2×D4C22×Dic8318yes—
866C2×D4C22×Dic8318yes—
867C2×D4C22×Dic8318yes—
868C2×D4C22×Dic8318yes—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—3322no—
874C22×C4—3322no—
875C22×C4—3322no—
876C22×C4—3322no—
877C22×C4—3322no—
878C22×C4—3322no—
879C22×C4—3322no—
880C22×C4—3322no—
881C22×C4—3322no—
882C22×C4—3322no—
883C22×C4—3322no—
884C22×C4—3322no—
885C22×C4—3322no—
886C22×C4—3322no—
887C22×C4—3322no—
888C22×C4—831no—
889C22×C4—831no—
890C22×C4—832no—
891C22×C4—831no—
892C22×C4—831no—
893C22×C4—831no—
894C22×C4—831no—
895C22×C4—832no—
896C22×C4—832no—
897C22×C4—831no—
898C22×C4—831no—
899C22×C4—832no—
900C22×C4—1664no—
901C22×C4—1664no—
902C22×C4—1664no—
903C22×C4C22×Dic8314yes—
904C22×C4C22×Dic8318yes—
905C22×C4C23×D8311yescharacteristic
906C22×C4C23×D8311yescharacteristic
907C22×C4C23×D8311yescharacteristic
908C22×C4C23×D8311yescharacteristic
909C22×C4C23×D8311yescharacteristic
910C22×C4C23×D8312yes—
911C22×C4C23×D8311yescharacteristic
912C4⋊C4—3322no—
913C4⋊C4—3322no—
914C4⋊C4—3322no—
915C4⋊C4—3322no—
916C4⋊C4—3321no—
917C4⋊C4—3321no—
918C4⋊C4—1662no—
919C4⋊C4—1662no—
920C4⋊C4—1662no—
921C4⋊C4—1662no—
922C4⋊C4—1662no—
923C4⋊C4—1662no—
924C4⋊C4C22×Dic8314yes—
925C4⋊C4C22×Dic8314yes—
926C22⋊C4—3322no—
927C22⋊C4—3322no—
928C22⋊C4—3322no—
929C22⋊C4—3322no—
930C22⋊C4—3322no—
931C22⋊C4—3322no—
932C22⋊C4—3322no—
933C22⋊C4—3322no—
934C22⋊C4—3322no—
935C22⋊C4—3322no—
936C22⋊C4—3322no—
937C22⋊C4—3322no—
938C22⋊C4—3322no—
939C22⋊C4—3322no—
940C22⋊C4—3322no—
941C22⋊C4—3321no—
942C22⋊C4—3321no—
943C22⋊C4—3322no—
944C22⋊C4—3322no—
945C22⋊C4—1662no—
946C22⋊C4—1662no—
947C22⋊C4—1664no—
948C22⋊C4—1664no—
949C22⋊C4—1664no—
950C22⋊C4C22×Dic8314yes—
951C22⋊C4C22×Dic8314yes—
952C22⋊C4C22×Dic8318yes—
953C22⋊C4C22×Dic8318yes—
954C22⋊C4C22×Dic8318yes—
955C22⋊C4C22×Dic8318yes—
956C42—3322no—
957C42—3322no—
958C42—3322no—
959C42—3322no—
960C42—3321no—
961C42—3321no—
962C42—1662no—
963C42—1662no—
964C42—1662no—
965C42—1662no—
966C42—1662no—
967C42—1662no—
968C42C22×Dic8314yes—
969C42C22×Dic8314yes—
970C23—21no—
971C23—21no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—21no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—48no—
995C23—48no—
996C23—48no—
997C23—84no—
998C23—84no—
999C23—84no—
1000C23—84no—
1001C23C23×Dic8312yes—
1002C23C23×Dic8314yes—
1003C23C23×Dic8314yes—
1004C23C23×Dic8314yes—
1005C23C24×D8311yescharacteristic
1006Q8—28no—
1007D4—28no—
1008D4—28no—
1009D4—28no—
1010D4—48no—
1011D4—48no—
1012D4—48no—
1013D4—48no—
1014D4—48no—
1015D4—48no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—28no—
1029C2×C4—48no—
1030C2×C4—832no—
1031C2×C4—832no—
1032C2×C4—6644no—
1033C2×C4—6644no—
1034C2×C4—6644no—
1035C2×C4—6644no—
1036C2×C4—6644no—
1037C2×C4—6644no—
1038C2×C4—1662no—
1039C2×C4—1662no—
1040C2×C4—1662no—
1041C2×C4—1662no—
1042C2×C4—1661no—
1043C2×C4—1662no—
1044C2×C4—1661no—
1045C2×C4—1661no—
1046C2×C4—1661no—
1047C2×C4—1661no—
1048C2×C4—1662no—
1049C2×C4—1661no—
1050C2×C4—1662no—
1051C2×C4—1662no—
1052C2×C4—1661no—
1053C2×C4—1661no—
1054C2×C4—1661no—
1055C2×C4—1661no—
1056C2×C4—1661no—
1057C2×C4—1662no—
1058C2×C4—1662no—
1059C2×C4—1661no—
1060C2×C4—1661no—
1061C2×C4—1661no—
1062C2×C4—1661no—
1063C2×C4—1661no—
1064C2×C4—1662no—
1065C2×C4—1661no—
1066C2×C4—1662no—
1067C2×C4—1661no—
1068C2×C4—1661no—
1069C2×C4—1661no—
1070C2×C4—1661no—
1071C2×C4—1661no—
1072C2×C4C23×Dic8312yes—
1073C2×C4C23×Dic8312yes—
1074C2×C4C23×Dic8312yes—
1075C2×C4C23×Dic8312yes—
1076C2×C4C23×Dic8314yes—
1077C2×C4C23×Dic8312yes—
1078C2×C4C23×Dic8312yes—
1079C2×C4#1458183712yes—
1080C2×C4#1458183712yes—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—22no—
1092C22—22no—
1093C22—42no—
1094C22—42no—
1095C22—41no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—41no—
1101C22—41no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—41no—
1107C22—42no—
1108C22—42no—
1109C22—816no—
1110C22C24×Dic8311yescharacteristic
1111C22H(5,𝔽2)×D8311yescharacteristic
1112C22H(5,𝔽2)×D8311yescharacteristic
1113C22C2×#1458183711yescharacteristic
1114C22C2×#1458183711yescharacteristic
1115C22#1912853611yescharacteristic
1116C22#1912853611yescharacteristic
1117C4—22no—
1118C4—24no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—3321no—
1124C4—3322no—
1125C4—3321no—
1126C4—3322no—
1127C4—3322no—
1128C4—3321no—
1129C4—3321no—
1130C4—3321no—
1131C4—3322no—
1132C4—3321no—
1133C4—1662no—
1134C4—1662no—
1135C4#1912817614yes—
1136C2—42no—
1137C2—44no—
1138C2—44no—
1139C2—44no—
1140C2C2×#1912817611yescharacteristic
1141C2H(5,𝔽2)×Dic8311yescharacteristic
1142C2H(5,𝔽2)×Dic8311yescharacteristic
1143C2#2492178911yescharacteristic
1144C2#2492182411yescharacteristic
1145C2#2492198111yescharacteristic
1146C2#2492204711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
Fitting, prime radicalC2×#535×C83C2
socle, cosocleC23×C83C25
hypercenterC2×#535D83
hypocenterC83#34438
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. #24910620C2semidirect
2. #24910604C2semidirect
3. #24910538C2semidirect
4. #24910538C2semidirect
5. #24910528C2semidirect
6. #24910528C2semidirect
7. #24910515C2semidirect
8. #24910447C2semidirect
9. #24910304C2semidirect
10. #24910293C2semidirect
11. D4×C22⋊Dic83C2semidirect
12. D4×C22⋊Dic83C2semidirect
13. #24910230C2semidirect
14. #24910189C2semidirect
15. #24910176C2semidirect
16. #24910168C2semidirect
17. #24910124C2semidirect
18. #24910124C2semidirect
19. #24910072C2semidirect
20. #127×Dic83C2semidirect
21. #124×Dic83C2semidirect
22. #24909961C2semidirect
24. C2×Q8×Dic83C22semidirect
25. C2×Q8×Dic83C22semidirect
30. C2×D4×Dic83C22semidirect
31. C2×D4×Dic83C22semidirect
32. C2×D4×Dic83C22semidirect
33. C2×D4×Dic83C22semidirect
34. C2×D4×Dic83C22semidirect
35. C2×D4×Dic83C22semidirect
38. #19127608C22semidirect
39. #19127608C22semidirect
46. #19127604C22semidirect
47. #19127604C22semidirect
48. #19127604C22semidirect
49. #19127604C22semidirect
50. #19127604C22semidirect
51. #19127604C22semidirect
58. #19127594C22semidirect
59. #19127594C22semidirect
60. #19127594C22semidirect
61. #19127594C22semidirect
62. #19127594C22semidirect
63. #19127594C22semidirect
64. #19127594C22semidirect
65. #19127594C22semidirect
66. #19127587C22semidirect
67. #19127587C22semidirect
68. #19127587C22semidirect
69. #19127587C22semidirect
70. #19127587C22semidirect
71. #19127587C22semidirect
78. #19127581C22semidirect
79. #19127581C22semidirect
80. #19127581C22semidirect
81. #19127581C22semidirect
82. #19127581C22semidirect
83. #19127581C22semidirect
84. #19127581C22semidirect
85. #19127581C22semidirect
86. #19127576C22semidirect
87. #19127576C22semidirect
88. #19127576C22semidirect
89. #19127576C22semidirect
90. #19127571C22semidirect
91. #19127567C22semidirect
92. #19127564C22semidirect
95. #19127561C22semidirect
98. C4×C4⋊Dic83C22semidirect
99. C4×C4⋊Dic83C22semidirect
100. C4×C4⋊Dic83C22semidirect
101. C4×C4⋊Dic83C22semidirect
102. C22⋊C4×Dic83C22semidirect
103. C22⋊C4×Dic83C22semidirect
104. C22⋊C4×Dic83C22semidirect
105. C22⋊C4×Dic83C22semidirect
108. C4×C22⋊Dic83C22semidirect
109. #19127547C22semidirect
110. C2×C83⋊#95C22semidirect
111. C42×Dic83C22semidirect
114. #535×C83C4semidirect
217. C2×#41×C83C2×C4semidirect
221. C22×D4×C83C2×C4semidirect
233. #127×C83C2×C4semidirect
234. #127×C83C2×C4semidirect
235. #124×C83C2×C4semidirect
236. #124×C83C2×C4semidirect
237. #121×C83C2×C4semidirect
238. #121×C83C2×C4semidirect
239. #120×C83C2×C4semidirect
240. #120×C83C2×C4semidirect
241. #117×C83C2×C4semidirect
597. C83#34438semidirect
600. #535Dic83semidirect
701. C2×#41C2×Dic83semidirect
705. C22×D4C2×Dic83semidirect
723. #127C2×Dic83semidirect
724. #127C2×Dic83semidirect
725. #124C2×Dic83semidirect
726. #124C2×Dic83semidirect
727. #121C2×Dic83semidirect
728. #121C2×Dic83semidirect
729. #120C2×Dic83semidirect
730. #120C2×Dic83semidirect
743. #117C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249106202
#249106042
#249105382
#249105282
#249105152
#249104472
#249103042
#249102932
D4×C22⋊Dic832
#249102302
#249101892
#249101762
#249101682
#249101242
#249100722
#127×Dic832
#124×Dic832
#249099612
C2×#535×C832
#3443883