Finite Group Databasebeta

← #35569476

Subgroups — #35569476

Order 21248.

2608 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128347C211yesmaximal, characteristic
2#24910619C212yesmaximal, complemented
3#24910601C212yesmaximal, complemented
4#24910595C212yesmaximal, complemented
5#24910532C211yesmaximal, characteristic, complemented
6#24910499C211yesmaximal, characteristic, complemented
7#24910488C211yesmaximal, characteristic, complemented
8#24910412C211yesmaximal, characteristic, complemented
9#24910410C211yesmaximal, characteristic, complemented
10#24910311C212yesmaximal, complemented
11#24910303C211yesmaximal, characteristic, complemented
12C22⋊C4×D332C211yesmaximal, characteristic, complemented
13#24910259C212yesmaximal, complemented
14#24910174C211yesmaximal, characteristic, complemented
15#24910155C212yesmaximal, complemented
16#24910145C211yesmaximal, characteristic, complemented
17#24910119C212yesmaximal, complemented
18#24910107C211yesmaximal, characteristic, complemented
19#24910057C212yesmaximal, complemented
20#24910043C211yesmaximal, characteristic, complemented
21C4×#14581766C211yesmaximal, characteristic, complemented
22#24909953C211yesmaximal, characteristic, complemented
23C83×#2290C211yesmaximal, characteristic, complemented
24C22×#13050590C2211yescharacteristic
25C23×D332C2211yescharacteristic
26#19128347C4116yescomplemented
27C2×#14581780C2211yescharacteristic
28C2×#14581777C2212yes—
29C2×#14581771C2211yescharacteristic
30C2×#14581766C2211yescharacteristic
31C2×#14581765C2212yes—
32C2×#14581760C2212yes—
33C2×C4×Dic166C2211yescharacteristic, complemented
34C2×C4×Dic166C2211yescharacteristic, complemented
35C2×C4×D332C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×C4×D332C2211yescharacteristic
38C2×C4×C22⋊D83C2212yescomplemented
39C2×#14581751C2211yescharacteristic
40C2×#14581751C2211yescharacteristic, complemented
41C2×#14581750C2212yescomplemented
42C2×C22⋊C4×D83C2212yes—
43C2×C22⋊C4×D83C2212yes—
44#19127607C2211yescharacteristic, complemented
45#19127607C2211yescharacteristic, complemented
46#19127604C2212yes—
47#19127603C2211yescharacteristic
48#19127603C2211yescharacteristic
49#19127603C2211yescharacteristic
50#19127603C2211yescharacteristic
51#19127603C2211yescharacteristic
52#19127603C2211yescharacteristic
53#19127602C2212yes—
54#19127602C2212yes—
55#19127601C2212yescomplemented
56#19127601C2212yescomplemented
57#19127601C2212yescomplemented
58#19127599C2211yescharacteristic, complemented
59#19127599C2211yescharacteristic, complemented
60#19127596C2212yescomplemented
61#19127595C2212yes—
62#19127595C2212yes—
63#19127594C2212yes—
64#19127594C2212yescomplemented
65#19127593C2212yescomplemented
66#19127593C2212yescomplemented
67#19127593C2212yescomplemented
68#19127593C2212yescomplemented
69#19127592C2212yescomplemented
70#19127591C2212yescomplemented
71#19127590C2212yescomplemented
72#19127590C2212yescomplemented
73#19127590C2212yescomplemented
74#19127590C2212yescomplemented
75#19127589C2212yes—
76#19127589C2212yes—
77#19127583C2212yescomplemented
78#19127582C2212yescomplemented
79#19127580C2212yescomplemented
80#19127580C2212yescomplemented
81#19127580C2212yescomplemented
82#19127579C2212yes—
83#19127579C2212yes—
84#19127577C2212yescomplemented
85#19127575C2212yescomplemented
86#19127575C2212yescomplemented
87#19127572C2212yescomplemented
88#19127571C2211yescharacteristic, complemented
89#19127563C2212yescomplemented
90#19127561C2211yescharacteristic
91#19127561C2211yescharacteristic, complemented
92#19127560C2212yescomplemented
93#19127560C2212yescomplemented
94#19127558C2212yescomplemented
95#19127556C2212yes—
96#19127556C2212yes—
97#19127556C2212yes—
98C4⋊C4×Dic83C2212yescomplemented
99C4×C4⋊Dic83C2211yescharacteristic, complemented
100C4×C4⋊Dic83C2211yescharacteristic, complemented
101C4×C4⋊Dic83C2211yescharacteristic, complemented
102#19127552C2212yescomplemented
103C4×(C2×D83)⋊C4C2212yescomplemented
104C4×(C2×D83)⋊C4C2212yescomplemented
105C4×(C2×D83)⋊C4C2212yescomplemented
106#19127548C2212yescomplemented
107#19127548C2212yescomplemented
108#19127548C2212yescomplemented
109C2×C4×D4×C83C2211yescharacteristic
110C2×#117×C83C2211yescharacteristic
111C22×C42×C83C2211yescharacteristic, complemented
112#388×C83C2211yescharacteristic
113#388×C83C2211yescharacteristic
114#387×C83C2211yescharacteristic, complemented
115#387×C83C2211yescharacteristic, complemented
116#386×C83C2211yescharacteristic
117#386×C83C2211yescharacteristic
118#385×C83C2211yescharacteristic, complemented
119#385×C83C2211yescharacteristic, complemented
120C4×C4⋊C4×C83C2211yescharacteristic, complemented
121C4×C22⋊C4×C83C2211yescharacteristic
122C4×C22⋊C4×C83C2211yescharacteristic, complemented
123#376×C83C2211yescharacteristic, complemented
124C24×D83C2312yes—
125C2×#13050590—42no—
126C2×#13050590—42no—
127C2×#13050590C2×C418yescomplemented
128C22×Dic166C2311yescharacteristic
129C22×D332—42no—
130C22×D332—42no—
131C22×D332C2×C418yescomplemented
132C22×D332C2311yescharacteristic
133C22×D332C2311yescharacteristic
134C22×D332C2312yes—
135C22×C22⋊D83C2312yes—
136C22×C22⋊D83C2312yes—
137C22×C4×D83C2312yes—
138C22×C4×D83C2312yes—
139C22×C4×D83C2312yes—
140C22×C4×D83C2312yes—
141#14581780C2×C418yescomplemented
142#14581777C2×C4116yescomplemented
143#14581771C2×C418yescomplemented
144#14581766C2×C418yes—
145#14581765C2×C4116yescomplemented
146#14581760C2×C4116yescomplemented
147C4×Dic166—42no—
148C4×Dic166—42no—
149C4×D332—42no—
150C4×D332—42no—
151C4×D332C2×C418yescomplemented
152C4×C22⋊D83—44no—
153#14581751—42no—
154#14581751—42no—
155#14581750—44no—
156C2×C4⋊Dic83C2311yescharacteristic
157C2×C4⋊Dic83C2311yescharacteristic
158C2×C4⋊Dic83C2311yescharacteristic
159C2×C4⋊Dic83C2311yescharacteristic
160C2×C4⋊Dic83C2312yes—
161C2×C4⋊Dic83C2312yes—
162C2×C4⋊Dic83C2311yescharacteristic
163C2×Dic83⋊C4C2312yes—
164C2×Dic83⋊C4C2312yes—
165C2×Dic83⋊C4C2312yes—
166C2×Dic83⋊C4C2312yes—
167C2×Dic83⋊C4C2312yes—
168C2×C22⋊Dic83C2312yes—
169C2×C22⋊Dic83C2312yes—
170C2×C22⋊Dic83C2312yes—
171C2×C22⋊Dic83C2312yes—
172C2×C22⋊Dic83C2312yes—
173C2×(C2×D83)⋊C4C2312yes—
174C2×(C2×D83)⋊C4C2312yes—
175C2×(C2×D83)⋊C4C2312yes—
176C2×(C2×D83)⋊C4C2312yes—
177C2×(C2×D83)⋊C4C2312yes—
178C2×(C2×D83)⋊C4C2312yes—
179C2×(C2×D83)⋊C4C2312yes—
180C2×(C2×D83)⋊C4C2312yes—
181C2×(C2×D83)⋊C4C2312yes—
182C2×(C2×D83)⋊C4C2312yes—
183C2×(C2×D83)⋊C4C2312yes—
184C2×(C2×D83)⋊C4C2312yes—
185C2×(C2×D83)⋊C4C2312yes—
186C2×(C2×D83)⋊C4C2312yes—
187C2×(C2×D83)⋊C4C2312yes—
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C22⋊C4×D83—44no—
192C22⋊C4×D83C2×C4116yescomplemented
193C2×C4×Dic83C2312yes—
194C2×C4×Dic83C2312yes—
195C2×C4×Dic83C2312yes—
196C2×C4×Dic83C2312yes—
197C2×C4×Dic83C2312yes—
198C2×C4×Dic83C2312yes—
199C2×C4×Dic83C2312yes—
200C83⋊#95C2312yes—
201C83⋊#95C2312yes—
202C83⋊#95C2312yes—
203C83⋊#95C2312yes—
204C83⋊#95C2312yes—
205C83⋊#95C2312yes—
206C83⋊#95C2312yes—
207C83⋊#95C2312yes—
208C83⋊#95C2312yes—
209C83⋊#95C2312yes—
210C83⋊#95C2312yes—
211C22×D4×C83C2311yescharacteristic
212C23×C4×C83C2311yescharacteristic
213C23×C4×C83C2311yescharacteristic
214C23×C4×C83C2311yescharacteristic
215C23×C4×C83C2311yescharacteristic
216C4×D4×C83C2×C418yescomplemented
217#117×C83—42no—
218C2×C4⋊C4×C83C2311yescharacteristic
219C2×C4⋊C4×C83C2311yescharacteristic
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C22⋊C4×C83C2311yescharacteristic
224C2×C22⋊C4×C83C2311yescharacteristic
225C2×C22⋊C4×C83C2311yescharacteristic
226C2×C22⋊C4×C83C2311yescharacteristic
227C2×C22⋊C4×C83C2311yescharacteristic
228C2×C22⋊C4×C83C2311yescharacteristic
229C2×C22⋊C4×C83C2311yescharacteristic
230C2×C22⋊C4×C83C2311yescharacteristic
231C2×C42×C83—42no—
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2311yescharacteristic
234C2×C42×C83C2311yescharacteristic
235C2×C42×C83C2311yescharacteristic
236C2×C42×C83C2311yescharacteristic
237C2×C42×C83C2311yescharacteristic
238C2×C42×C83C2311yescharacteristic
239#95×C83C2311yescharacteristic
240#95×C83C2311yescharacteristic
241#95×C83C2311yescharacteristic
242#95×C83C2311yescharacteristic
243#95×C83C2311yescharacteristic
244#95×C83C2311yescharacteristic
245#95×C83C2311yescharacteristic
246#95×C83C2311yescharacteristic
247#95×C83C2311yescharacteristic
248#95×C83C2311yescharacteristic
249C23×D83—42no—
250C23×D83—42no—
251C23×D83—42no—
252C23×D83—42no—
253C23×D83—42no—
254C23×D83—42no—
255C23×D83C22×C418yes—
256C23×D83C2412yes—
257C23×D83C2412yes—
258#13050590—416no—
259C2×Dic166—22no—
260C2×Dic166—22no—
261C2×Dic166C22×C414yes—
262C2×D332—22no—
263C2×D332—22no—
264C2×D332—22no—
265C2×D332—22no—
266C2×D332—416no—
267C2×D332—42no—
268C2×D332—42no—
269C2×D332C22×C414yes—
270C2×D332C22×C414yes—
271C2×D332C22×C418yes—
272C2×C22⋊D83—42no—
273C2×C22⋊D83—42no—
274C2×C22⋊D83—42no—
275C2×C22⋊D83—42no—
276C2×C22⋊D83C22×C418yes—
277C2×C22⋊D83C22×C418yes—
278C22×Dic83C2412yes—
279C22×Dic83C2412yes—
280C22×Dic83C2412yes—
281C22×Dic83C2412yes—
282C22×Dic83C2412yes—
283C22×Dic83C2412yes—
284C2×C4×D83—24no—
285C2×C4×D83—42no—
286C2×C4×D83—42no—
287C2×C4×D83—42no—
288C2×C4×D83—42no—
289C2×C4×D83—42no—
290C2×C4×D83—42no—
291C2×C4×D83—42no—
292C2×C4×D83—42no—
293C2×C4×D83—42no—
294C2×C4×D83C22×C418yes—
295C2×C4×D83C22×C418yes—
296C4⋊Dic83—22no—
297C4⋊Dic83—22no—
298C4⋊Dic83—22no—
299C4⋊Dic83—22no—
300C4⋊Dic83—42no—
301C4⋊Dic83—42no—
302C4⋊Dic83C22×C414yes—
303Dic83⋊C4—42no—
304Dic83⋊C4—42no—
305Dic83⋊C4—42no—
306Dic83⋊C4—42no—
307Dic83⋊C4C22×C418yes—
308C22⋊Dic83—42no—
309C22⋊Dic83—42no—
310C22⋊Dic83—42no—
311C22⋊Dic83—42no—
312C22⋊Dic83C22×C418yes—
313(C2×D83)⋊C4—24no—
314(C2×D83)⋊C4—42no—
315(C2×D83)⋊C4—42no—
316(C2×D83)⋊C4—42no—
317(C2×D83)⋊C4—42no—
318(C2×D83)⋊C4—42no—
319(C2×D83)⋊C4—42no—
320(C2×D83)⋊C4—42no—
321(C2×D83)⋊C4—42no—
322(C2×D83)⋊C4—42no—
323(C2×D83)⋊C4—42no—
324(C2×D83)⋊C4—42no—
325(C2×D83)⋊C4—42no—
326(C2×D83)⋊C4—42no—
327(C2×D83)⋊C4C22×C418yes—
328(C2×D83)⋊C4C22×C418yes—
329(C2×D83)⋊C4C22×C418yes—
330(C2×D83)⋊C4C22×C418yes—
331C4×Dic83—24no—
332C4×Dic83—42no—
333C4×Dic83—42no—
334C4×Dic83—42no—
335C4×Dic83—42no—
336C4×Dic83—42no—
337C4×Dic83—42no—
338C24×C83C2411yescharacteristic
339C24×C83C2411yescharacteristic
340C2×D4×C83—41no—
341C2×D4×C83—41no—
342C2×D4×C83C22×C414yes—
343C22×C4×C83—22no—
344C22×C4×C83—22no—
345C22×C4×C83—22no—
346C22×C4×C83—22no—
347C22×C4×C83—22no—
348C22×C4×C83—41no—
349C22×C4×C83—41no—
350C22×C4×C83—41no—
351C22×C4×C83—41no—
352C22×C4×C83—41no—
353C22×C4×C83C22×C414yes—
354C22×C4×C83C22×C414yes—
355C22×C4×C83C2411yescharacteristic
356C22×C4×C83C2411yescharacteristic
357C22×C4×C83C2411yescharacteristic
358C22×C4×C83C2411yescharacteristic
359C22×C4×C83C2411yescharacteristic
360C22×C4×C83C2411yescharacteristic
361C22×C4×C83C2411yescharacteristic
362C22×C4×C83C2411yescharacteristic
363C22×C4×C83C2411yescharacteristic
364C22×C4×C83C2411yescharacteristic
365C22×C4×C83C2411yescharacteristic
366C22×C4×C83C2411yescharacteristic
367C22×C4×C83C2411yescharacteristic
368C4⋊C4×C83—22no—
369C4⋊C4×C83—41no—
370C4⋊C4×C83—41no—
371C4⋊C4×C83—41no—
372C4⋊C4×C83C22×C414yes—
373C22⋊C4×C83—22no—
374C22⋊C4×C83—41no—
375C22⋊C4×C83—41no—
376C22⋊C4×C83—41no—
377C22⋊C4×C83—41no—
378C22⋊C4×C83—41no—
379C22⋊C4×C83C22×C414yes—
380C22⋊C4×C83C22×C414yes—
381C42×C83—22no—
382C42×C83—22no—
383C42×C83—22no—
384C42×C83—22no—
385C42×C83—41no—
386C42×C83—41no—
387C42×C83C22×C414yes—
388C23×C83—21no—
389C23×C83—21no—
390C23×C83—21no—
391C23×C83—21no—
392C23×C83—21no—
393C23×C83—21no—
394C23×C83—21no—
395C23×C83—21no—
396C23×C83—21no—
397C23×C83—21no—
398C23×C83—21no—
399C23×C83—21no—
400C23×C83C23×C412yes—
401C23×C83C23×C412yes—
402C23×C83C2511yescharacteristic
403C22×D83—22no—
404C22×D83—22no—
405C22×D83—22no—
406C22×D83—22no—
407C22×D83—22no—
408C22×D83—22no—
409C22×D83—22no—
410C22×D83—22no—
411C22×D83—22no—
412C22×D83—22no—
413C22×D83—22no—
414C22×D83—22no—
415C22×D83—48no—
416C22×D83—48no—
417C22×D83—48no—
418C22×D83—84no—
419C22×D83—84no—
420C22×D83—84no—
421C22×D83—84no—
422C22×D83C23×C414yes—
423C22×D83C23×C414yes—
424D4×C83—44no—
425C2×C4×C83—21no—
426C2×C4×C83—21no—
427C2×C4×C83—21no—
428C2×C4×C83—21no—
429C2×C4×C83—21no—
430C2×C4×C83—21no—
431C2×C4×C83—21no—
432C2×C4×C83—21no—
433C2×C4×C83—21no—
434C2×C4×C83—21no—
435C2×C4×C83—28no—
436C2×C4×C83—28no—
437C2×C4×C83—21no—
438C2×C4×C83—21no—
439C2×C4×C83—21no—
440C2×C4×C83—21no—
441C2×C4×C83—21no—
442C2×C4×C83—21no—
443C2×C4×C83—21no—
444C2×C4×C83—21no—
445C2×C4×C83—21no—
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—21no—
455C2×C4×C83—21no—
456C2×C4×C83—21no—
457C2×C4×C83—21no—
458C2×C4×C83—44no—
459C2×C4×C83—44no—
460C2×C4×C83C23×C412yes—
461C2×C4×C83C23×C412yes—
462C2×C4×C83C23×C412yes—
463C2×C4×C83C23×C412yes—
464C2×C4×C83C23×C412yes—
465C2×C4×C83H(5,𝔽2)12yes—
466C2×C4×C83H(5,𝔽2)12yes—
467C2×C4×C83H(5,𝔽2)12yes—
468C22⋊D83—48no—
469C22⋊D83—48no—
470C2×Dic83—22no—
471C2×Dic83—22no—
472C2×Dic83—22no—
473C2×Dic83—22no—
474C2×Dic83—22no—
475C2×Dic83—22no—
476C2×Dic83—22no—
477C2×Dic83—22no—
478C2×Dic83—22no—
479C2×Dic83—22no—
480C2×Dic83—22no—
481C2×Dic83—22no—
482C2×Dic83—22no—
483C2×Dic83—22no—
484C2×Dic83—22no—
485C2×Dic83—22no—
486C2×Dic83C23×C414yes—
487C2×Dic83C23×C414yes—
488D332—28no—
489D332—28no—
490D332—48no—
491C4×D83—48no—
492C4×D83—48no—
493C4×D83—84no—
494C4×D83—84no—
495Dic166—28no—
496C22×C83—22no—
497C22×C83—22no—
498C22×C83—22no—
499C22×C83—22no—
500C22×C83—22no—
501C22×C83—22no—
502C22×C83—41no—
503C22×C83—41no—
504C22×C83—41no—
505C22×C83—41no—
506C22×C83—41no—
507C22×C83—41no—
508C22×C83—41no—
509C22×C83—41no—
510C22×C83C24×C411yescharacteristic
511C22×C83C2×H(5,𝔽2)11yescharacteristic
512C22×C83C2×H(5,𝔽2)11yescharacteristic
513C22×C83C2×H(5,𝔽2)11yescharacteristic
514C22×C83#58511yescharacteristic
515C22×C83#58511yescharacteristic
516C22×C83#58511yescharacteristic
517C2×D83—24no—
518C2×D83—24no—
519C2×D83—24no—
520C2×D83—24no—
521C2×D83—24no—
522C2×D83—24no—
523C2×D83—42no—
524C2×D83—42no—
525C2×D83—42no—
526C2×D83—42no—
527C2×D83—42no—
528C2×D83—42no—
529C2×D83—42no—
530C2×D83—42no—
531C2×D83—816no—
532C4×C83—22no—
533C4×C83—22no—
534C4×C83—22no—
535C4×C83—22no—
536C4×C83—22no—
537C4×C83—41no—
538C4×C83—41no—
539C4×C83—41no—
540C4×C83—41no—
541C4×C83—41no—
542C4×C83—41no—
543C4×C83—41no—
544C4×C83#51814yes—
545Dic83—24no—
546Dic83—24no—
547Dic83—42no—
548Dic83—42no—
549Dic83—42no—
550Dic83—42no—
551#34478—831nomaximal, Sylow
552C2×C83—42no—
553C2×C83—42no—
554C2×C83C2×#51811yescharacteristic
555C2×C83#342811yescharacteristic
556C2×C83C4×H(5,𝔽2)11yescharacteristic
557C2×C83#354011yescharacteristic
558C2×C83#354211yescharacteristic
559C2×C83#354611yescharacteristic
560C2×C83#356211yescharacteristic
561D83—44no—
562D83—44no—
563C2×#546—831no—
564#2377—832no—
565#2375—832no—
566#2374—832no—
567#2367—831no—
568#2363—831no—
569#2362—831no—
570#2354—831no—
571#2354—831no—
572#2342—832no—
573#2341—831no—
574D4×C22⋊C4—831no—
575#2335—832no—
576#2326—831no—
577#2324—832no—
578#2323—831no—
579#2321—832no—
580#2319—831no—
581#2312—832no—
582#2309—831no—
583C4×#121—831no—
584#2297—831no—
585#2290D8311yescharacteristic, complemented
586C83#3447811yescharacteristic, complemented, Sylow
587C22×#41—831no—
588C23×D4—831no—
589#546—8316no—
590C2×#124—831no—
591C2×#123—832no—
592C2×C22⋊Q8—831no—
593C2×#121—831no—
594C2×#121—832no—
595C2×#120—832no—
596C2×C4×Q8—831no—
597C2×C4×Q8—831no—
598C2×C4×D4—832no—
599C2×C4×D4—831no—
600C2×C4×D4—831no—
601C2×C4×D4—831no—
602C2×C4×D4C2×D8311yescharacteristic
603C2×#117—831no—
604C2×#117—831no—
605C2×#117—832no—
606C2×#117C2×D8311yescharacteristic
607C22×C22⋊C4—832no—
608C22×C22⋊C4—832no—
609C22×C42C2×D8311yescharacteristic, complemented
610#391—831no—
611#391—831no—
612#390—832no—
613#390—832no—
614#390—832no—
615#390—832no—
616#390—832no—
617#390—832no—
618#390—831no—
619#390—831no—
620#390—831no—
621#390—831no—
622#390—831no—
623#390—831no—
624#389—832no—
625#389—831no—
626#389—831no—
627#388—832no—
628#388—832no—
629#388—832no—
630#388—832no—
631#388—832no—
632#388—832no—
633#388—832no—
634#388—832no—
635#388—832no—
636#388—832no—
637#388—832no—
638#388—832no—
639#388—832no—
640#388—832no—
641#388—832no—
642#388—832no—
643#388C2×D8311yescharacteristic
644#388C2×D8311yescharacteristic
645#387—832no—
646#387—832no—
647#387C2×D8311yescharacteristic, complemented
648#387C2×D8311yescharacteristic, complemented
649#386—832no—
650#386—832no—
651#386—832no—
652#386—832no—
653#386—832no—
654#386—832no—
655#386C2×D8311yescharacteristic
656#386C2×D8311yescharacteristic
657#385—832no—
658#385—832no—
659#385—832no—
660#385C2×D8311yescharacteristic, complemented
661#385C2×D8311yescharacteristic, complemented
662#384—831no—
663#381—832no—
664#380—831no—
665#380—831no—
666#380—832no—
667#380—832no—
668#380—832no—
669#379—832no—
670#379—832no—
671#379—832no—
672C4×C4⋊C4—832no—
673C4×C4⋊C4—831no—
674C4×C4⋊C4—831no—
675C4×C4⋊C4—831no—
676C4×C4⋊C4—832no—
677C4×C4⋊C4C2×D8311yescharacteristic, complemented
678C4×C22⋊C4—832no—
679C4×C22⋊C4—832no—
680C4×C22⋊C4—832no—
681C4×C22⋊C4—832no—
682C4×C22⋊C4—832no—
683C4×C22⋊C4—832no—
684C4×C22⋊C4C2×D8311yescharacteristic
685C4×C22⋊C4C2×D8311yescharacteristic, complemented
686#376C2×D8311yescharacteristic, complemented
687C25—832no—
688C2×#41—3322no—
689C2×#41—3322no—
690C2×#41—838no—
691C22×Q8—831no—
692C22×D4—3322no—
693C22×D4—3322no—
694C22×D4—832no—
695C22×D4—832no—
696C22×D4—838no—
697C22×D4—832no—
698C22×D4—831no—
699C22×D4—831no—
700C22×D4C22×D8311yescharacteristic
701C23×C4—832no—
702C23×C4—832no—
703C23×C4—832no—
704C23×C4—832no—
705C23×C4C22×D8311yescharacteristic
706C23×C4C22×D8311yescharacteristic
707C23×C4C22×D8311yescharacteristic
708C23×C4C22×D8311yescharacteristic
709#124—838no—
710#123—8316no—
711C22⋊Q8—838no—
712#121—838no—
713#121—8316no—
714#120—8316no—
715C4×Q8—3322no—
716C4×Q8—3322no—
717C4×D4—3322no—
718C4×D4—3322no—
719C4×D4—3324no—
720C4×D4—838no—
721C4×D4C4×D8318yescomplemented
722#117—42no—
723#117—3322no—
724#117—3322no—
725#117—3324no—
726C2×C4⋊C4—832no—
727C2×C4⋊C4—832no—
728C2×C4⋊C4—832no—
729C2×C4⋊C4—832no—
730C2×C4⋊C4—832no—
731C2×C4⋊C4—832no—
732C2×C4⋊C4—831no—
733C2×C4⋊C4—832no—
734C2×C4⋊C4—831no—
735C2×C4⋊C4—831no—
736C2×C4⋊C4—831no—
737C2×C4⋊C4—831no—
738C2×C4⋊C4C22×D8311yescharacteristic
739C2×C4⋊C4C22×D8311yescharacteristic
740C2×C4⋊C4C22×D8311yescharacteristic
741C2×C4⋊C4C22×D8311yescharacteristic
742C2×C4⋊C4C22×D8311yescharacteristic
743C2×C22⋊C4—3324no—
744C2×C22⋊C4—832no—
745C2×C22⋊C4—832no—
746C2×C22⋊C4—832no—
747C2×C22⋊C4—832no—
748C2×C22⋊C4—832no—
749C2×C22⋊C4—832no—
750C2×C22⋊C4—832no—
751C2×C22⋊C4—832no—
752C2×C22⋊C4—832no—
753C2×C22⋊C4—832no—
754C2×C22⋊C4—832no—
755C2×C22⋊C4—832no—
756C2×C22⋊C4—832no—
757C2×C22⋊C4—832no—
758C2×C22⋊C4—832no—
759C2×C22⋊C4—832no—
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—8316no—
767C2×C22⋊C4—832no—
768C2×C22⋊C4C22×D8311yescharacteristic
769C2×C22⋊C4C22×D8311yescharacteristic
770C2×C22⋊C4C22×D8311yescharacteristic
771C2×C22⋊C4C22×D8311yescharacteristic
772C2×C22⋊C4C22×D8311yescharacteristic
773C2×C22⋊C4C22×D8311yescharacteristic
774C2×C22⋊C4C22×D8311yescharacteristic
775C2×C22⋊C4C22×D8311yescharacteristic
776C2×C42—42no—
777C2×C42—832no—
778C2×C42—832no—
779C2×C42—832no—
780C2×C42—832no—
781C2×C42—832no—
782C2×C42—832no—
783C2×C42—832no—
784C2×C42C22×D8311yescharacteristic
785C2×C42C22×D8311yescharacteristic
786C2×C42C22×D8311yescharacteristic
787C2×C42C22×D8311yescharacteristic
788C2×C42C22×D8311yescharacteristic
789C2×C42C22×D8311yescharacteristic
790C2×C42C22×D8311yescharacteristic
791#95—832no—
792#95—832no—
793#95—832no—
794#95—832no—
795#95—832no—
796#95—832no—
797#95—832no—
798#95—832no—
799#95—832no—
800#95—832no—
801#95—832no—
802#95C22×D8311yescharacteristic
803#95C22×D8311yescharacteristic
804#95C22×D8311yescharacteristic
805#95C22×D8311yescharacteristic
806#95C22×D8311yescharacteristic
807#95C22×D8311yescharacteristic
808#95C22×D8311yescharacteristic
809#95C22×D8311yescharacteristic
810#95C22×D8311yescharacteristic
811#95C22×D8311yescharacteristic
812C24—3322no—
813C24—3322no—
814C24—3322no—
815C24—3322no—
816C24—3322no—
817C24—3322no—
818C24—838no—
819C24—832no—
820C24—832no—
821C24C23×D8311yescharacteristic
822C24C23×D8311yescharacteristic
823#41—33216no—
824C2×Q8—834no—
825C2×Q8—1662no—
826C2×Q8—1662no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—3322no—
830C2×D4—3322no—
831C2×D4—33216no—
832C2×D4—3322no—
833C2×D4—3322no—
834C2×D4—3322no—
835C2×D4—3322no—
836C2×D4—838no—
837C2×D4—838no—
838C2×D4—838no—
839C2×D4—834no—
840C2×D4—834no—
841C2×D4—1662no—
842C2×D4—1662no—
843C2×D4—1662no—
844C2×D4—1662no—
845C2×D4C2×C4×D8314yes—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—3322no—
857C22×C4—3322no—
858C22×C4—3322no—
859C22×C4—3322no—
860C22×C4—3322no—
861C22×C4—3322no—
862C22×C4—3322no—
863C22×C4—3322no—
864C22×C4—3322no—
865C22×C4—838no—
866C22×C4—838no—
867C22×C4—832no—
868C22×C4—832no—
869C22×C4—832no—
870C22×C4—832no—
871C22×C4—832no—
872C22×C4—832no—
873C22×C4—1664no—
874C22×C4C2×C4×D8314yes—
875C22×C4C2×C4×D8314yes—
876C22×C4C23×D8311yescharacteristic
877C22×C4C23×D8311yescharacteristic
878C22×C4C23×D8311yescharacteristic
879C22×C4C23×D8311yescharacteristic
880C22×C4C23×D8311yescharacteristic
881C22×C4C23×D8311yescharacteristic
882C22×C4C23×D8311yescharacteristic
883C22×C4C23×D8311yescharacteristic
884C22×C4C23×D8311yescharacteristic
885C22×C4C23×D8311yescharacteristic
886C22×C4C23×D8311yescharacteristic
887C22×C4C23×D8311yescharacteristic
888C22×C4C23×D8311yescharacteristic
889C4⋊C4—22no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—3322no—
894C4⋊C4—3322no—
895C4⋊C4—3322no—
896C4⋊C4—3322no—
897C4⋊C4—3322no—
898C4⋊C4—3322no—
899C4⋊C4—834no—
900C4⋊C4—838no—
901C4⋊C4—1662no—
902C4⋊C4—1662no—
903C4⋊C4—1662no—
904C4⋊C4—1662no—
905C4⋊C4C2×C4×D8314yes—
906C22⋊C4—22no—
907C22⋊C4—41no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—3322no—
913C22⋊C4—3322no—
914C22⋊C4—3322no—
915C22⋊C4—3322no—
916C22⋊C4—3322no—
917C22⋊C4—3322no—
918C22⋊C4—3322no—
919C22⋊C4—3322no—
920C22⋊C4—3322no—
921C22⋊C4—3322no—
922C22⋊C4—3322no—
923C22⋊C4—3322no—
924C22⋊C4—3322no—
925C22⋊C4—3322no—
926C22⋊C4—3322no—
927C22⋊C4—3322no—
928C22⋊C4—3322no—
929C22⋊C4—838no—
930C22⋊C4—838no—
931C22⋊C4—838no—
932C22⋊C4—838no—
933C22⋊C4—838no—
934C22⋊C4—1664no—
935C22⋊C4C2×C4×D8314yes—
936C22⋊C4C2×C4×D8314yes—
937C42—22no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—41no—
942C42—41no—
943C42—3322no—
944C42—3322no—
945C42—3322no—
946C42—3322no—
947C42—3322no—
948C42—3322no—
949C42—1664no—
950C42C2×C4×D8314yes—
951C23—21no—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—21no—
963C23—3328no—
964C23—3328no—
965C23—3328no—
966C23—834no—
967C23—834no—
968C23—6644no—
969C23—6644no—
970C23—6644no—
971C23—6644no—
972C23—1662no—
973C23—1662no—
974C23—1662no—
975C23—1662no—
976C23—1662no—
977C23—1662no—
978C23—1662no—
979C23—1662no—
980C23—1662no—
981C23—1662no—
982C23—1662no—
983C23—1662no—
984C23C22×C4×D8312yes—
985C23C22×C4×D8312yes—
986C23C24×D8311yescharacteristic
987Q8—1668no—
988D4—44no—
989D4—3328no—
990D4—3328no—
991D4—3328no—
992D4—1668no—
993D4—1668no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—3328no—
1030C2×C4—3328no—
1031C2×C4—834no—
1032C2×C4—834no—
1033C2×C4—6644no—
1034C2×C4—6644no—
1035C2×C4—1662no—
1036C2×C4—1662no—
1037C2×C4—1662no—
1038C2×C4—1662no—
1039C2×C4—1662no—
1040C2×C4—1662no—
1041C2×C4—1662no—
1042C2×C4—1662no—
1043C2×C4—1662no—
1044C2×C4—1662no—
1045C2×C4—1662no—
1046C2×C4—1662no—
1047C2×C4—1662no—
1048C2×C4—1662no—
1049C2×C4—1662no—
1050C2×C4—1662no—
1051C2×C4C22×C4×D8312yes—
1052C2×C4C22×C4×D8312yes—
1053C2×C4C22×C4×D8312yes—
1054C2×C4C22×C4×D8312yes—
1055C2×C4C22×C4×D8312yes—
1056C2×C4#1458183712yes—
1057C2×C4#1458183812yes—
1058C2×C4#1458183812yes—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—3322no—
1074C22—3322no—
1075C22—3322no—
1076C22—3322no—
1077C22—3322no—
1078C22—3322no—
1079C22—3322no—
1080C22—3322no—
1081C22—66416no—
1082C22—1664no—
1083C22—1664no—
1084C22—1664no—
1085C22—1664no—
1086C22—1664no—
1087C22—1664no—
1088C22C23×C4×D8311yescharacteristic
1089C22C2×#1458183711yescharacteristic
1090C22C2×#1458183811yescharacteristic
1091C22C2×#1458183811yescharacteristic
1092C22#1912853711yescharacteristic
1093C22#1912853711yescharacteristic
1094C22#1912853711yescharacteristic
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—3322no—
1108C4—3322no—
1109C4—3322no—
1110C4—3322no—
1111C4—1664no—
1112C4—1664no—
1113C4#1912817314yes—
1114C2—42no—
1115C2—42no—
1116C2—3324no—
1117C2—3324no—
1118C2C2×#1912817311yescharacteristic
1119C2#2492066411yescharacteristic
1120C2C4×#1458183811yescharacteristic
1121C2#2492173811yescharacteristic
1122C2#2492177911yescharacteristic
1123C2#2492183711yescharacteristic
1124C2#2492205111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2290C2
socle, cosocleC23×C83C25
prime radicalC2×#19128347C2
hypercenter#2290D83
hypocenterC83#34478
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #24910619C2semidirect
3. #24910601C2semidirect
4. #24910595C2semidirect
5. #24910532C2semidirect
6. #24910499C2semidirect
7. #24910488C2semidirect
8. #24910412C2semidirect
9. #24910410C2semidirect
10. #24910311C2semidirect
11. #24910303C2semidirect
12. C22⋊C4×D332C2semidirect
13. #24910259C2semidirect
14. #24910174C2semidirect
15. #24910155C2semidirect
16. #24910145C2semidirect
17. #24910119C2semidirect
18. #24910107C2semidirect
19. #24910057C2semidirect
20. #24910043C2semidirect
21. C4×#14581766C2semidirect
22. #24909953C2semidirect
23. C83×#2290C2semidirect
26. #19128347C4semidirect
33. C2×C4×Dic166C22semidirect
34. C2×C4×Dic166C22semidirect
38. C2×C4×C22⋊D83C22semidirect
40. C2×#14581751C22semidirect
41. C2×#14581750C22semidirect
44. #19127607C22semidirect
45. #19127607C22semidirect
55. #19127601C22semidirect
56. #19127601C22semidirect
57. #19127601C22semidirect
58. #19127599C22semidirect
59. #19127599C22semidirect
60. #19127596C22semidirect
64. #19127594C22semidirect
65. #19127593C22semidirect
66. #19127593C22semidirect
67. #19127593C22semidirect
68. #19127593C22semidirect
69. #19127592C22semidirect
70. #19127591C22semidirect
71. #19127590C22semidirect
72. #19127590C22semidirect
73. #19127590C22semidirect
74. #19127590C22semidirect
77. #19127583C22semidirect
78. #19127582C22semidirect
79. #19127580C22semidirect
80. #19127580C22semidirect
81. #19127580C22semidirect
84. #19127577C22semidirect
85. #19127575C22semidirect
86. #19127575C22semidirect
87. #19127572C22semidirect
88. #19127571C22semidirect
89. #19127563C22semidirect
91. #19127561C22semidirect
92. #19127560C22semidirect
93. #19127560C22semidirect
94. #19127558C22semidirect
98. C4⋊C4×Dic83C22semidirect
99. C4×C4⋊Dic83C22semidirect
100. C4×C4⋊Dic83C22semidirect
101. C4×C4⋊Dic83C22semidirect
102. #19127552C22semidirect
103. C4×(C2×D83)⋊C4C22semidirect
104. C4×(C2×D83)⋊C4C22semidirect
105. C4×(C2×D83)⋊C4C22semidirect
106. #19127548C22semidirect
107. #19127548C22semidirect
108. #19127548C22semidirect
111. C22×C42×C83C22semidirect
114. #387×C83C22semidirect
115. #387×C83C22semidirect
118. #385×C83C22semidirect
119. #385×C83C22semidirect
120. C4×C4⋊C4×C83C22semidirect
122. C4×C22⋊C4×C83C22semidirect
123. #376×C83C22semidirect
127. C2×#13050590C2×C4semidirect
131. C22×D332C2×C4semidirect
141. #14581780C2×C4semidirect
142. #14581777C2×C4semidirect
143. #14581771C2×C4semidirect
145. #14581765C2×C4semidirect
146. #14581760C2×C4semidirect
151. C4×D332C2×C4semidirect
192. C22⋊C4×D83C2×C4semidirect
216. C4×D4×C83C2×C4semidirect
585. #2290D83semidirect
586. C83#34478semidirect
609. C22×C42C2×D83semidirect
647. #387C2×D83semidirect
648. #387C2×D83semidirect
660. #385C2×D83semidirect
661. #385C2×D83semidirect
677. C4×C4⋊C4C2×D83semidirect
685. C4×C22⋊C4C2×D83semidirect
686. #376C2×D83semidirect
721. C4×D4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283472
#249106192
#249106012
#249105952
#249105322
#249104992
#249104882
#249104122
#249104102
#249103112
#249103032
C22⋊C4×D3322
#249102592
#249101742
#249101552
#249101452
#249101192
#249101072
#249100572
#249100432
C4×#145817662
#249099532
C83×#22902
#3447883