Finite Group Databasebeta

← #2395×D83 #35570642

Subgroups — #2395×D83 #35570642

Order 21248.

3182 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D83C211yesmaximal, characteristic
2C2×#117×D83C211yesmaximal, characteristic, complemented
3#24910729C211yesmaximal, characteristic, complemented
4#24910728C211yesmaximal, characteristic, complemented
5#24910727C211yesmaximal, characteristic, complemented
6#24910726C212yesmaximal, complemented
7#24910725C211yesmaximal, characteristic, complemented
8#24910724C212yesmaximal, complemented
9#24910723C211yesmaximal, characteristic, complemented
10#24910722C211yesmaximal, characteristic, complemented
11#24910721C212yesmaximal, complemented
12#24910720C211yesmaximal, characteristic, complemented
13#24910719C212yesmaximal, complemented
14#400×D83C211yesmaximal, characteristic, complemented
15#399×D83C211yesmaximal, characteristic, complemented
16#398×D83C211yesmaximal, characteristic, complemented
17#397×D83C212yesmaximal, complemented
18#397×D83C211yesmaximal, characteristic, complemented
19#394×D83C212yesmaximal
20C4×C4⋊C4×D83C212yesmaximal, complemented
21C4×C22⋊C4×D83C212yesmaximal, complemented
22C4×C22⋊C4×D83C211yesmaximal, characteristic, complemented
23C83×#2395C211yesmaximal, characteristic, complemented
24C22×D4×D83C2211yescharacteristic
25C23×C4×D83C2211yescharacteristic
26C23×C4×D83C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×D4×Dic83C2211yescharacteristic
29C2×#14581754C2211yescharacteristic
30C2×C4×C22⋊D83C2211yescharacteristic
31C2×C4×C22⋊D83C2211yescharacteristic
32C2×(C22⋊D83)⋊C4C2211yescharacteristic
33C2×(C22⋊D83)⋊C4C2211yescharacteristic
34C4×D4×D83—28no—
35C2×#14581751C2211yescharacteristic, complemented
36C2×#14581750C2211yescharacteristic, complemented
37C2×#14581750C2211yescharacteristic, complemented
38C2×#14581749C2212yescomplemented
39C2×#14581748C2212yescomplemented
40#117×D83—28no—
41C2×C4⋊C4×D83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43C2×C4⋊C4×D83C2211yescharacteristic
44C2×C4⋊C4×D83C2212yes—
45C2×C4⋊C4×D83C2212yes—
46C2×C22⋊C4×D83C2212yes—
47C2×C22⋊C4×D83C2211yescharacteristic
48C2×C22⋊C4×D83C2211yescharacteristic
49C2×C22⋊C4×D83C2212yes—
50C2×C22⋊C4×D83C2212yes—
51C2×C22⋊C4×D83C2212yes—
52C2×C42×D83C2212yes—
53C2×C42×D83C2211yescharacteristic
54C2×C42×D83C2212yes—
55#19127643C2212yescomplemented
56#19127642C2212yescomplemented
57#19127641C2211yescharacteristic, complemented
58#19127640C2211yescharacteristic, complemented
59#19127639C2211yescharacteristic, complemented
60#19127638C2211yescharacteristic, complemented
61#19127637C2212yescomplemented
62#19127637C2211yescharacteristic, complemented
63#19127636C2211yescharacteristic, complemented
64#19127636C2212yescomplemented
65#19127635C2212yescomplemented
66#19127634C2212yescomplemented
67#19127633C2211yescharacteristic, complemented
68#19127632C2211yescharacteristic, complemented
69#19127631C2211yescharacteristic, complemented
70#19127630C2212yescomplemented
71#19127630C2212yescomplemented
72#19127630C2212yescomplemented
73#19127629C2212yescomplemented
74#19127629C2212yescomplemented
75#19127629C2212yescomplemented
76#19127628C2211yescharacteristic, complemented
77#19127628C2212yescomplemented
78#19127627C2211yescharacteristic, complemented
79#19127627C2212yescomplemented
80#19127626C2212yescomplemented
81#19127626C2211yescharacteristic, complemented
82#19127619C2212yes—
83#19127618C2212yes—
84#19127617C2212yes—
85#19127617C2212yes—
86#19127616C2212yes—
87#19127616C2212yes—
88#19127615C2212yes—
89C4⋊C4×Dic83C2212yescomplemented
90C4⋊C4×Dic83C2212yescomplemented
91C4×Dic83⋊C4C2212yescomplemented
92C4×Dic83⋊C4C2212yescomplemented
93C4×C4⋊Dic83C2212yescomplemented
94#19127552C2212yescomplemented
95#19127552C2212yescomplemented
96C22⋊C4×Dic83C2212yescomplemented
97C22⋊C4×Dic83C2212yescomplemented
98C22⋊C4×Dic83C2212yescomplemented
99C4×(C2×D83)⋊C4C2212yescomplemented
100C4×(C2×D83)⋊C4C2212yescomplemented
101C4×(C2×D83)⋊C4C2212yescomplemented
102C4×C22⋊Dic83C2211yescharacteristic, complemented
103C4×C22⋊Dic83C2212yescomplemented
104#19127548C2212yescomplemented
105#19127548C2212yescomplemented
106#19127548C2211yescharacteristic, complemented
107#19127548C2211yescharacteristic, complemented
108#95×D83C2212yes—
109#95×D83C2212yes—
110#95×D83C2212yes—
111#95×D83C2212yes—
112#95×D83C2211yescharacteristic
113#95×D83C2211yescharacteristic
114C2×C4×D4×C83C2211yescharacteristic
115C2×#117×C83C2211yescharacteristic, complemented
116#400×C83C2211yescharacteristic, complemented
117#399×C83C2211yescharacteristic, complemented
118#398×C83C2211yescharacteristic, complemented
119#397×C83C2212yescomplemented
120#397×C83C2211yescharacteristic, complemented
121#394×C83C2212yes—
122C4×C4⋊C4×C83C2212yescomplemented
123C4×C22⋊C4×C83C2211yescharacteristic, complemented
124C4×C22⋊C4×C83C2212yescomplemented
125C24×D83C2311yescharacteristic
126C24×D83C2311yescharacteristic
127C22×D332C2311yescharacteristic
128C22×C22⋊D83C2311yescharacteristic
129C22×C22⋊D83C2311yescharacteristic
130C2×D4×D83—24no—
131C2×D4×D83—24no—
132C2×D4×D83—24no—
133C23×Dic83C2311yescharacteristic
134C23×Dic83C2311yescharacteristic
135C22×C4×D83—28no—
136C22×C4×D83—24no—
137C22×C4×D83—28no—
138C22×C4×D83D418yes—
139C22×C4×D83C2311yescharacteristic
140C22×C4×D83C2312yes—
141C22×C4×D83C2312yes—
142C22×C4×D83C2312yes—
143C22×C4×D83C2311yescharacteristic
144C22×C4×D83C2311yescharacteristic
145C22×C4×D83C2311yescharacteristic
146C22×C4×D83C2311yescharacteristic
147C22×C4×D83C2311yescharacteristic
148C22×C4×D83C2311yescharacteristic
149C22×C4×D83C2312yes—
150C22×C4×D83C2311yescharacteristic
151C22×C4×D83C2311yescharacteristic
152C4×D332—24no—
153D4×Dic83—24no—
154#14581754—24no—
155C4×C22⋊D83—24no—
156C4×C22⋊D83—24no—
157(C22⋊D83)⋊C4—24no—
158(C22⋊D83)⋊C4—24no—
159#14581751—24no—
160#14581750—24no—
161#14581750—24no—
162#14581749—28no—
163#14581748—28no—
164C2×C4⋊Dic83C2312yes—
165C2×C4⋊Dic83C2312yes—
166C2×C4⋊Dic83C2311yescharacteristic
167C2×C4⋊Dic83C2311yescharacteristic
168C2×C4⋊Dic83C2311yescharacteristic
169C2×Dic83⋊C4C2312yes—
170C2×Dic83⋊C4C2312yes—
171C2×Dic83⋊C4C2312yes—
172C2×Dic83⋊C4C2312yes—
173C2×Dic83⋊C4C2312yes—
174C2×Dic83⋊C4C2311yescharacteristic
175C2×Dic83⋊C4C2311yescharacteristic
176C2×Dic83⋊C4C2312yes—
177C4⋊C4×D83—24no—
178C4⋊C4×D83—24no—
179C4⋊C4×D83—24no—
180C4⋊C4×D83—28no—
181C4⋊C4×D83—28no—
182C2×C22⋊Dic83C2312yes—
183C2×C22⋊Dic83C2312yes—
184C2×C22⋊Dic83C2312yes—
185C2×C22⋊Dic83C2312yes—
186C2×C22⋊Dic83C2311yescharacteristic
187C2×C22⋊Dic83C2311yescharacteristic
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2311yescharacteristic
197C2×(C2×D83)⋊C4C2311yescharacteristic
198C2×(C2×D83)⋊C4C2311yescharacteristic
199C2×(C2×D83)⋊C4C2311yescharacteristic
200C22⋊C4×D83—28no—
201C22⋊C4×D83—24no—
202C22⋊C4×D83—28no—
203C22⋊C4×D83—24no—
204C22⋊C4×D83—28no—
205C22⋊C4×D83—28no—
206C2×C4×Dic83C2311yescharacteristic
207C2×C4×Dic83C2311yescharacteristic
208C2×C4×Dic83C2312yes—
209C2×C4×Dic83C2312yes—
210C2×C4×Dic83C2312yes—
211C2×C4×Dic83C2311yescharacteristic
212C2×C4×Dic83C2312yes—
213C2×C4×Dic83C2312yes—
214C2×C4×Dic83C2312yes—
215C42×D83—28no—
216C42×D83—24no—
217C42×D83—28no—
218C83⋊#95C2312yes—
219C83⋊#95C2312yes—
220C83⋊#95C2312yes—
221C83⋊#95C2312yes—
222C83⋊#95C2312yes—
223C83⋊#95C2312yes—
224C83⋊#95C2312yes—
225C83⋊#95C2311yescharacteristic
226C83⋊#95C2312yes—
227C83⋊#95C2312yes—
228C83⋊#95C2312yes—
229C83⋊#95C2312yes—
230C83⋊#95C2312yes—
231C83⋊#95C2312yes—
232C83⋊#95C2311yescharacteristic
233C83⋊#95C2312yes—
234C22×D4×C83C2311yescharacteristic
235C23×C4×C83C2311yescharacteristic
236C23×C4×C83C2311yescharacteristic
237C4×D4×C83—24no—
238#117×C83—24no—
239C2×C4⋊C4×C83C2312yes—
240C2×C4⋊C4×C83C2312yes—
241C2×C4⋊C4×C83C2311yescharacteristic
242C2×C4⋊C4×C83C2311yescharacteristic
243C2×C4⋊C4×C83C2311yescharacteristic
244C2×C22⋊C4×C83C2312yes—
245C2×C22⋊C4×C83C2311yescharacteristic
246C2×C22⋊C4×C83C2311yescharacteristic
247C2×C22⋊C4×C83C2312yes—
248C2×C22⋊C4×C83C2312yes—
249C2×C22⋊C4×C83C2312yes—
250C2×C42×C83C2312yes—
251C2×C42×C83C2311yescharacteristic
252C2×C42×C83C2312yes—
253#95×C83C2312yes—
254#95×C83C2312yes—
255#95×C83C2312yes—
256#95×C83C2311yescharacteristic
257#95×C83C2312yes—
258#95×C83C2311yescharacteristic
259C23×D83—22no—
260C23×D83—24no—
261C23×D83—24no—
262C23×D83—22no—
263C23×D83—22no—
264C23×D83—22no—
265C23×D83—24no—
266C23×D83—24no—
267C23×D83C2×D414yes—
268C23×D83#4114yes—
269C23×D83C2411yescharacteristic
270C23×D83C2411yescharacteristic
271C23×D83C2411yescharacteristic
272C2×D332—22no—
273C2×D332—22no—
274C2×D332—22no—
275C2×C22⋊D83—22no—
276C2×C22⋊D83—22no—
277C2×C22⋊D83—22no—
278C2×C22⋊D83—22no—
279C2×C22⋊D83—22no—
280C2×C22⋊D83—22no—
281D4×D83—232no—
282C22×Dic83—24no—
283C22×Dic83—22no—
284C22×Dic83—24no—
285C22×Dic83C2×D414yes—
286C22×Dic83C2411yescharacteristic
287C22×Dic83C2412yes—
288C22×Dic83C2411yescharacteristic
289C22×Dic83C2412yes—
290C22×Dic83C2412yes—
291C22×Dic83C2411yescharacteristic
292C22×Dic83C2411yescharacteristic
293C22×Dic83C2412yes—
294C22×Dic83C2411yescharacteristic
295C2×C4×D83—22no—
296C2×C4×D83—24no—
297C2×C4×D83—22no—
298C2×C4×D83—24no—
299C2×C4×D83—24no—
300C2×C4×D83—24no—
301C2×C4×D83—24no—
302C2×C4×D83—232no—
303C2×C4×D83—22no—
304C2×C4×D83—22no—
305C2×C4×D83—24no—
306C2×C4×D83—24no—
307C2×C4×D83—24no—
308C2×C4×D83—24no—
309C2×C4×D83—24no—
310C2×C4×D83—24no—
311C2×C4×D83—24no—
312C2×C4×D83—24no—
313C2×C4×D83—24no—
314C2×C4×D83—24no—
315C2×C4×D83—24no—
316C2×C4×D83—22no—
317C2×C4×D83—24no—
318C2×C4×D83—22no—
319C2×C4×D83—24no—
320C2×C4×D83—416no—
321C2×C4×D83C2×D414yes—
322C2×C4×D83C2×D414yes—
323C2×C4×D83C2×D414yes—
324C2×C4×D83C2×D414yes—
325C2×C4×D83#4114yes—
326C2×C4×D83#4118yes—
327C2×C4×D83#4118yes—
328C4⋊Dic83—22no—
329C4⋊Dic83—22no—
330C4⋊Dic83—24no—
331C4⋊Dic83—22no—
332C4⋊Dic83—24no—
333Dic83⋊C4—22no—
334Dic83⋊C4—24no—
335Dic83⋊C4—24no—
336Dic83⋊C4—24no—
337Dic83⋊C4—22no—
338Dic83⋊C4—24no—
339Dic83⋊C4—24no—
340Dic83⋊C4—24no—
341C22⋊Dic83—24no—
342C22⋊Dic83—22no—
343C22⋊Dic83—24no—
344C22⋊Dic83—22no—
345C22⋊Dic83—24no—
346C22⋊Dic83—24no—
347(C2×D83)⋊C4—24no—
348(C2×D83)⋊C4—24no—
349(C2×D83)⋊C4—22no—
350(C2×D83)⋊C4—22no—
351(C2×D83)⋊C4—24no—
352(C2×D83)⋊C4—24no—
353(C2×D83)⋊C4—22no—
354(C2×D83)⋊C4—24no—
355(C2×D83)⋊C4—24no—
356(C2×D83)⋊C4—22no—
357(C2×D83)⋊C4—24no—
358(C2×D83)⋊C4—24no—
359C4×Dic83—24no—
360C4×Dic83—22no—
361C4×Dic83—24no—
362C4×Dic83—24no—
363C4×Dic83—24no—
364C4×Dic83—22no—
365C4×Dic83—22no—
366C4×Dic83—24no—
367C4×Dic83—24no—
368C24×C83C2411yescharacteristic
369C24×C83C2411yescharacteristic
370C2×D4×C83—22no—
371C2×D4×C83—22no—
372C2×D4×C83—22no—
373C22×C4×C83—24no—
374C22×C4×C83—22no—
375C22×C4×C83—24no—
376C22×C4×C83C2×D414yes—
377C22×C4×C83C2411yescharacteristic
378C22×C4×C83C2412yes—
379C22×C4×C83C2411yescharacteristic
380C22×C4×C83C2412yes—
381C22×C4×C83C2412yes—
382C22×C4×C83C2411yescharacteristic
383C22×C4×C83C2411yescharacteristic
384C22×C4×C83C2412yes—
385C22×C4×C83C2411yescharacteristic
386C4⋊C4×C83—22no—
387C4⋊C4×C83—22no—
388C4⋊C4×C83—22no—
389C4⋊C4×C83—24no—
390C4⋊C4×C83—24no—
391C22⋊C4×C83—24no—
392C22⋊C4×C83—22no—
393C22⋊C4×C83—24no—
394C22⋊C4×C83—22no—
395C22⋊C4×C83—24no—
396C22⋊C4×C83—24no—
397C42×C83—24no—
398C42×C83—22no—
399C42×C83—24no—
400C23×C83—21no—
401C23×C83—22no—
402C23×C83—22no—
403C23×C83—22no—
404C23×C83—22no—
405C23×C83—21no—
406C23×C83—21no—
407C23×C83—21no—
408C23×C83C22×D412yes—
409C23×C83C2×#4112yes—
410C23×C83C2511yescharacteristic
411C22×D83—21no—
412C22×D83—22no—
413C22×D83—22no—
414C22×D83—22no—
415C22×D83—22no—
416C22×D83—21no—
417C22×D83—21no—
418C22×D83—21no—
419C22×D83—28no—
420C22×D83—28no—
421C22×D83—28no—
422C22×D83—216no—
423C22×D83—28no—
424C22×D83—44no—
425C22×D83—48no—
426C22×D83—48no—
427C22×D83—48no—
428C22×D83—44no—
429C22×D83C22×D412yes—
430C22×D83C22×D412yes—
431C22×D83C2×#4112yes—
432C22×D83C2×#4114yes—
433C22×D83C2×#4112yes—
434C22×D83C2×#4112yes—
435C22×D83C2×#4114yes—
436D4×C83—28no—
437C2×C4×C83—21no—
438C2×C4×C83—22no—
439C2×C4×C83—22no—
440C2×C4×C83—22no—
441C2×C4×C83—21no—
442C2×C4×C83—28no—
443C2×C4×C83—21no—
444C2×C4×C83—22no—
445C2×C4×C83—22no—
446C2×C4×C83—21no—
447C2×C4×C83—22no—
448C2×C4×C83—22no—
449C2×C4×C83—22no—
450C2×C4×C83—22no—
451C2×C4×C83—22no—
452C2×C4×C83—22no—
453C2×C4×C83—22no—
454C2×C4×C83—22no—
455C2×C4×C83—22no—
456C2×C4×C83—44no—
457C2×C4×C83C22×D412yes—
458C2×C4×C83C22×D412yes—
459C2×C4×C83C2×#4114yes—
460C2×C4×C83C2×#4112yes—
461C2×C4×C83C2×#4114yes—
462C22⋊D83—28no—
463C22⋊D83—28no—
464C2×Dic83—21no—
465C2×Dic83—22no—
466C2×Dic83—22no—
467C2×Dic83—22no—
468C2×Dic83—21no—
469C2×Dic83—28no—
470C2×Dic83—21no—
471C2×Dic83—22no—
472C2×Dic83—22no—
473C2×Dic83—21no—
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—44no—
484C2×Dic83C22×D412yes—
485C2×Dic83C22×D412yes—
486C2×Dic83C2×#4114yes—
487C2×Dic83C2×#4112yes—
488C2×Dic83C2×#4114yes—
489D332—28no—
490C4×D83—28no—
491C4×D83—28no—
492C4×D83—216no—
493C4×D83—28no—
494C4×D83—28no—
495C4×D83—44no—
496C4×D83—48no—
497C4×D83—48no—
498C4×D83—44no—
499C4×D83—48no—
500C4×D83—44no—
501C4×D83—44no—
502C4×D83#123116yes—
503C22×C83—22no—
504C22×C83—22no—
505C22×C83—22no—
506C22×C83—24no—
507C22×C83—22no—
508C22×C83—41no—
509C22×C83—42no—
510C22×C83—42no—
511C22×C83—42no—
512C22×C83—41no—
513C22×C83C23×D411yescharacteristic
514C22×C83C22×#4112yes—
515C22×C83C22×#4111yescharacteristic
516C22×C83C22×#4111yescharacteristic
517C22×C83C22×#4112yes—
518C2×D83—22no—
519C2×D83—22no—
520C2×D83—22no—
521C2×D83—24no—
522C2×D83—22no—
523C2×D83—41no—
524C2×D83—42no—
525C2×D83—42no—
526C2×D83—42no—
527C2×D83—41no—
528C2×D83—416no—
529C2×D83—416no—
530C2×D83C2×#12314yes—
531C2×D83#52514yes—
532C2×D83#52918yes—
533C2×D83#52918yes—
534C2×D83#53214yes—
535C4×C83—22no—
536C4×C83—22no—
537C4×C83—24no—
538C4×C83—41no—
539C4×C83—42no—
540C4×C83—42no—
541C4×C83—41no—
542C4×C83—42no—
543C4×C83C2×#12314yes—
544Dic83—22no—
545Dic83—22no—
546Dic83—24no—
547Dic83—41no—
548Dic83—42no—
549Dic83—42no—
550Dic83—41no—
551Dic83—42no—
552Dic83C2×#12314yes—
553C2×#2395—831nomaximal, Sylow
554C2×C83—42no—
555C2×C83—42no—
556C2×C83C22×#12311yescharacteristic
557C2×C83C2×#52511yescharacteristic
558C2×C83C2×#52912yes—
559C2×C83C2×#52912yes—
560C2×C83C2×#53211yescharacteristic
561D83—42no—
562D83—42no—
563D83#239518yesdirect product factor
564C22×C4×D4—831no—
565C22×#117—831no—
566#2395—831no—
567#2395—831no—
568#2395—831no—
569#2395—832no—
570#2395—831no—
571#2395—832no—
572#2395—832no—
573#2395—831no—
574#2395—832no—
575#2395—831no—
576#2395—831no—
577#2395D8311yescharacteristic, direct product factor
578C2×#400—831no—
579C2×#399—831no—
580C2×#398—831no—
581C2×#397—832no—
582C2×#397—831no—
583C2×#394—832no—
584C2×C4×C4⋊C4—832no—
585C2×C4×C22⋊C4—831no—
586C2×C4×C22⋊C4—832no—
587C83C2×#239511yescharacteristic, complemented, Sylow
588C23×D4—831no—
589C24×C4—831no—
590C24×C4—831no—
591C2×C4×D4—831no—
592C2×C4×D4—831no—
593C2×C4×D4—831no—
594C2×C4×D4—831no—
595C2×C4×D4—831no—
596C2×C4×D4—831no—
597C2×C4×D4—831no—
598C2×C4×D4—1668no—
599C2×C4×D4C2×D8311yescharacteristic
600C2×#117—831no—
601C2×#117—831no—
602C2×#117—831no—
603C2×#117—832no—
604C2×#117—832no—
605C2×#117—1668no—
606C2×#117C2×D8311yescharacteristic, complemented
607C22×C4⋊C4—832no—
608C22×C4⋊C4—831no—
609C22×C4⋊C4—832no—
610C22×C4⋊C4—831no—
611C22×C4⋊C4—831no—
612C22×C22⋊C4—832no—
613C22×C22⋊C4—832no—
614C22×C22⋊C4—832no—
615C22×C22⋊C4—832no—
616C22×C22⋊C4—831no—
617C22×C22⋊C4—831no—
618C22×C42—832no—
619C22×C42—831no—
620C22×C42—832no—
621#400—831no—
622#400—831no—
623#400—831no—
624#400—832no—
625#400—832no—
626#400C2×D8311yescharacteristic, complemented
627#399—832no—
628#399—831no—
629#399—832no—
630#399—831no—
631#399—831no—
632#399C2×D8311yescharacteristic, complemented
633#398—831no—
634#398—831no—
635#398—832no—
636#398—831no—
637#398—832no—
638#398C2×D8311yescharacteristic, complemented
639#397—832no—
640#397—831no—
641#397—832no—
642#397—831no—
643#397—832no—
644#397—832no—
645#397—832no—
646#397—832no—
647#397—831no—
648#397—832no—
649#397—832no—
650#397—832no—
651#397C2×D8312yescomplemented
652#397C2×D8311yescharacteristic, complemented
653#394—832no—
654#394—832no—
655#394—832no—
656#394—832no—
657#394—832no—
658#394—832no—
659#394—832no—
660#394C2×D8312yes—
661C4×C4⋊C4—832no—
662C4×C4⋊C4—832no—
663C4×C4⋊C4—832no—
664C4×C4⋊C4—832no—
665C4×C4⋊C4—832no—
666C4×C4⋊C4—832no—
667C4×C4⋊C4—832no—
668C4×C4⋊C4C2×D8312yescomplemented
669C4×C22⋊C4—832no—
670C4×C22⋊C4—831no—
671C4×C22⋊C4—832no—
672C4×C22⋊C4—832no—
673C4×C22⋊C4—832no—
674C4×C22⋊C4—832no—
675C4×C22⋊C4—832no—
676C4×C22⋊C4—832no—
677C4×C22⋊C4—832no—
678C4×C22⋊C4—832no—
679C4×C22⋊C4—831no—
680C4×C22⋊C4—831no—
681C4×C22⋊C4C2×D8312yescomplemented
682C4×C22⋊C4C2×D8311yescharacteristic, complemented
683C2×#95—832no—
684C2×#95—832no—
685C2×#95—832no—
686C2×#95—831no—
687C2×#95—832no—
688C2×#95—831no—
689C25—831no—
690C25—831no—
691C22×D4—831no—
692C22×D4—831no—
693C22×D4—831no—
694C22×D4—1664no—
695C22×D4—1664no—
696C22×D4—1664no—
697C22×D4C22×D8311yescharacteristic
698C23×C4—831no—
699C23×C4—831no—
700C23×C4—838no—
701C23×C4—832no—
702C23×C4—831no—
703C23×C4—831no—
704C23×C4—831no—
705C23×C4—831no—
706C23×C4—831no—
707C23×C4—831no—
708C23×C4—832no—
709C23×C4—832no—
710C23×C4—832no—
711C23×C4—831no—
712C23×C4—831no—
713C23×C4—831no—
714C23×C4—1664no—
715C23×C4—1668no—
716C23×C4—1668no—
717C23×C4C22×D8311yescharacteristic
718C23×C4C22×D8311yescharacteristic
719C4×D4—24no—
720C4×D4—1664no—
721C4×D4—1664no—
722C4×D4—1664no—
723C4×D4—1664no—
724C4×D4—1664no—
725C4×D4—1664no—
726C4×D4—1664no—
727#117—24no—
728#117—1668no—
729#117—1668no—
730#117—1664no—
731#117—1664no—
732#117—1664no—
733C2×C4⋊C4—832no—
734C2×C4⋊C4—831no—
735C2×C4⋊C4—832no—
736C2×C4⋊C4—831no—
737C2×C4⋊C4—831no—
738C2×C4⋊C4—831no—
739C2×C4⋊C4—831no—
740C2×C4⋊C4—832no—
741C2×C4⋊C4—832no—
742C2×C4⋊C4—832no—
743C2×C4⋊C4—832no—
744C2×C4⋊C4—832no—
745C2×C4⋊C4—832no—
746C2×C4⋊C4—1664no—
747C2×C4⋊C4—1664no—
748C2×C4⋊C4—1664no—
749C2×C4⋊C4—1668no—
750C2×C4⋊C4—1668no—
751C2×C4⋊C4C22×D8311yescharacteristic
752C2×C4⋊C4C22×D8311yescharacteristic
753C2×C4⋊C4C22×D8311yescharacteristic
754C2×C4⋊C4C22×D8312yes—
755C2×C4⋊C4C22×D8312yes—
756C2×C22⋊C4—832no—
757C2×C22⋊C4—831no—
758C2×C22⋊C4—831no—
759C2×C22⋊C4—832no—
760C2×C22⋊C4—832no—
761C2×C22⋊C4—832no—
762C2×C22⋊C4—832no—
763C2×C22⋊C4—832no—
764C2×C22⋊C4—831no—
765C2×C22⋊C4—831no—
766C2×C22⋊C4—831no—
767C2×C22⋊C4—831no—
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—1664no—
775C2×C22⋊C4—1668no—
776C2×C22⋊C4—1668no—
777C2×C22⋊C4—1668no—
778C2×C22⋊C4—1664no—
779C2×C22⋊C4—1668no—
780C2×C22⋊C4C22×D8312yes—
781C2×C22⋊C4C22×D8311yescharacteristic
782C2×C22⋊C4C22×D8311yescharacteristic
783C2×C22⋊C4C22×D8312yes—
784C2×C22⋊C4C22×D8312yes—
785C2×C22⋊C4C22×D8312yes—
786C2×C42—832no—
787C2×C42—832no—
788C2×C42—831no—
789C2×C42—831no—
790C2×C42—832no—
791C2×C42—832no—
792C2×C42—832no—
793C2×C42—831no—
794C2×C42—832no—
795C2×C42—1668no—
796C2×C42—1664no—
797C2×C42—1668no—
798C2×C42C22×D8312yes—
799C2×C42C22×D8311yescharacteristic
800C2×C42C22×D8312yes—
801#95—832no—
802#95—832no—
803#95—832no—
804#95—832no—
805#95—831no—
806#95—832no—
807#95—832no—
808#95—832no—
809#95—831no—
810#95—832no—
811#95—832no—
812#95—832no—
813#95—832no—
814#95—832no—
815#95—832no—
816#95—832no—
817#95C22×D8312yes—
818#95C22×D8311yescharacteristic
819#95C22×D8312yes—
820#95C22×D8311yescharacteristic
821#95C22×D8312yes—
822#95C22×D8312yes—
823C24—831no—
824C24—834no—
825C24—834no—
826C24—831no—
827C24—831no—
828C24—1662no—
829C24—1664no—
830C24—1664no—
831C24—1664no—
832C24—1664no—
833C24—1662no—
834C24—1662no—
835C24—1662no—
836C24C23×D8311yescharacteristic
837C24C23×D8311yescharacteristic
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—1662no—
842C2×D4—1662no—
843C2×D4—1662no—
844C2×D4—1662no—
845C2×D4—16632no—
846C2×D4—1662no—
847C2×D4—1662no—
848C2×D4—1662no—
849C2×D4—1662no—
850C2×D4—1662no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—33216no—
855C22×C4—831no—
856C22×C4—834no—
857C22×C4—838no—
858C22×C4—834no—
859C22×C4—832no—
860C22×C4—831no—
861C22×C4—831no—
862C22×C4—834no—
863C22×C4—834no—
864C22×C4—834no—
865C22×C4—838no—
866C22×C4—834no—
867C22×C4—832no—
868C22×C4—831no—
869C22×C4—831no—
870C22×C4—832no—
871C22×C4—832no—
872C22×C4—1662no—
873C22×C4—1664no—
874C22×C4—1662no—
875C22×C4—1664no—
876C22×C4—1664no—
877C22×C4—1664no—
878C22×C4—1662no—
879C22×C4—1664no—
880C22×C4—1664no—
881C22×C4—1664no—
882C22×C4—1664no—
883C22×C4—1664no—
884C22×C4—1664no—
885C22×C4—1664no—
886C22×C4—1664no—
887C22×C4—1664no—
888C22×C4—16632no—
889C22×C4—1662no—
890C22×C4—1664no—
891C22×C4—1664no—
892C22×C4—1664no—
893C22×C4—1662no—
894C22×C4—1662no—
895C22×C4—1664no—
896C22×C4—1662no—
897C22×C4—1664no—
898C22×C4—1664no—
899C22×C4—1664no—
900C22×C4D4×D8314yes—
901C22×C4C23×D8312yes—
902C22×C4C23×D8311yescharacteristic
903C22×C4C23×D8311yescharacteristic
904C22×C4C23×D8312yes—
905C22×C4C23×D8312yes—
906C22×C4C23×D8311yescharacteristic
907C22×C4C23×D8312yes—
908C22×C4C23×D8311yescharacteristic
909C22×C4C23×D8311yescharacteristic
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—1664no—
916C4⋊C4—1664no—
917C4⋊C4—1662no—
918C4⋊C4—1662no—
919C4⋊C4—1664no—
920C4⋊C4—1664no—
921C4⋊C4—1664no—
922C4⋊C4—1664no—
923C4⋊C4—1662no—
924C4⋊C4—1662no—
925C4⋊C4—1662no—
926C4⋊C4—1664no—
927C4⋊C4—1664no—
928C22⋊C4—24no—
929C22⋊C4—22no—
930C22⋊C4—24no—
931C22⋊C4—22no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—1662no—
935C22⋊C4—1664no—
936C22⋊C4—1664no—
937C22⋊C4—1664no—
938C22⋊C4—1664no—
939C22⋊C4—1662no—
940C22⋊C4—1662no—
941C22⋊C4—1664no—
942C22⋊C4—1664no—
943C22⋊C4—1662no—
944C22⋊C4—1664no—
945C22⋊C4—1664no—
946C22⋊C4—1664no—
947C22⋊C4—1662no—
948C22⋊C4—1664no—
949C22⋊C4—1662no—
950C22⋊C4—1664no—
951C22⋊C4—1664no—
952C42—24no—
953C42—22no—
954C42—24no—
955C42—1664no—
956C42—1664no—
957C42—1662no—
958C42—1662no—
959C42—1664no—
960C42—1664no—
961C42—1664no—
962C42—1662no—
963C42—1664no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—3324no—
973C23—3328no—
974C23—3328no—
975C23—3328no—
976C23—3324no—
977C23—832no—
978C23—834no—
979C23—832no—
980C23—834no—
981C23—832no—
982C23—832no—
983C23—832no—
984C23—1668no—
985C23—1668no—
986C23—1668no—
987C23—16616no—
988C23—1668no—
989C23—1661no—
990C23—1662no—
991C23—1662no—
992C23—1662no—
993C23—1662no—
994C23—1661no—
995C23—1661no—
996C23—1661no—
997C23C2×D4×D8312yes—
998C23#41×D8312yes—
999C23C24×D8311yescharacteristic
1000D4—28no—
1001D4—1668no—
1002D4—1668no—
1003D4—1668no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—44no—
1024C2×C4—3324no—
1025C2×C4—3328no—
1026C2×C4—3328no—
1027C2×C4—3324no—
1028C2×C4—3328no—
1029C2×C4—3324no—
1030C2×C4—3324no—
1031C2×C4—3324no—
1032C2×C4—832no—
1033C2×C4—834no—
1034C2×C4—8316no—
1035C2×C4—832no—
1036C2×C4—834no—
1037C2×C4—832no—
1038C2×C4—1668no—
1039C2×C4—1668no—
1040C2×C4—1668no—
1041C2×C4—16616no—
1042C2×C4—1661no—
1043C2×C4—1662no—
1044C2×C4—1662no—
1045C2×C4—1661no—
1046C2×C4—1662no—
1047C2×C4—1662no—
1048C2×C4—1662no—
1049C2×C4—1662no—
1050C2×C4—1662no—
1051C2×C4—1662no—
1052C2×C4—1662no—
1053C2×C4—1662no—
1054C2×C4—1662no—
1055C2×C4—1668no—
1056C2×C4—1661no—
1057C2×C4—1662no—
1058C2×C4—1662no—
1059C2×C4—1662no—
1060C2×C4—1661no—
1061C2×C4—1668no—
1062C2×C4C2×D4×D8312yes—
1063C2×C4C2×D4×D8312yes—
1064C2×C4#41×D8314yes—
1065C2×C4#41×D8312yes—
1066C2×C4#41×D8314yes—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—24no—
1071C22—22no—
1072C22—41no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—41no—
1077C22—33216no—
1078C22—33216no—
1079C22—3321no—
1080C22—3322no—
1081C22—3322no—
1082C22—3322no—
1083C22—3321no—
1084C22—834no—
1085C22—834no—
1086C22—838no—
1087C22—838no—
1088C22—834no—
1089C22—1662no—
1090C22—1662no—
1091C22—1662no—
1092C22—1664no—
1093C22—1662no—
1094C22C22×D4×D8311yescharacteristic
1095C22C2×#41×D8312yes—
1096C22C2×#41×D8311yescharacteristic
1097C22C2×#41×D8311yescharacteristic
1098C22C2×#41×D8312yes—
1099C4—22no—
1100C4—22no—
1101C4—24no—
1102C4—41no—
1103C4—42no—
1104C4—42no—
1105C4—41no—
1106C4—42no—
1107C4—3321no—
1108C4—3322no—
1109C4—3322no—
1110C4—3321no—
1111C4—3322no—
1112C4—834no—
1113C4—1662no—
1114C4—1662no—
1115C4—1664no—
1116C4#123×D8314yes—
1117C2—42no—
1118C2—42no—
1119C2—3322no—
1120C2—3322no—
1121C2—838no—
1122C2C2×#123×D8311yescharacteristic
1123C2#525×D8311yescharacteristic
1124C2#529×D8312yes—
1125C2#529×D8312yes—
1126C2#532×D8311yescharacteristic
subgroupG/H
centerC22×C4C23×D83
commutator, socle, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC83×#2395C2
prime radicalC22×D4×D83C22
hypercenter#2395D83
hypocenterC83C2×#2395
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. C2×#117×D83C2semidirect
3. #24910729C2semidirect
4. #24910728C2semidirect
5. #24910727C2semidirect
6. #24910726C2semidirect
7. #24910725C2semidirect
8. #24910724C2semidirect
9. #24910723C2semidirect
10. #24910722C2semidirect
11. #24910721C2semidirect
12. #24910720C2semidirect
13. #24910719C2semidirect
14. #400×D83C2semidirect
15. #399×D83C2semidirect
16. #398×D83C2semidirect
17. #397×D83C2semidirect
18. #397×D83C2semidirect
20. C4×C4⋊C4×D83C2semidirect
21. C4×C22⋊C4×D83C2semidirect
22. C4×C22⋊C4×D83C2semidirect
23. C83×#2395C2semidirect
35. C2×#14581751C22semidirect
36. C2×#14581750C22semidirect
37. C2×#14581750C22semidirect
38. C2×#14581749C22semidirect
39. C2×#14581748C22semidirect
55. #19127643C22semidirect
56. #19127642C22semidirect
57. #19127641C22semidirect
58. #19127640C22semidirect
59. #19127639C22semidirect
60. #19127638C22semidirect
61. #19127637C22semidirect
62. #19127637C22semidirect
63. #19127636C22semidirect
64. #19127636C22semidirect
65. #19127635C22semidirect
66. #19127634C22semidirect
67. #19127633C22semidirect
68. #19127632C22semidirect
69. #19127631C22semidirect
70. #19127630C22semidirect
71. #19127630C22semidirect
72. #19127630C22semidirect
73. #19127629C22semidirect
74. #19127629C22semidirect
75. #19127629C22semidirect
76. #19127628C22semidirect
77. #19127628C22semidirect
78. #19127627C22semidirect
79. #19127627C22semidirect
80. #19127626C22semidirect
81. #19127626C22semidirect
89. C4⋊C4×Dic83C22semidirect
90. C4⋊C4×Dic83C22semidirect
91. C4×Dic83⋊C4C22semidirect
92. C4×Dic83⋊C4C22semidirect
93. C4×C4⋊Dic83C22semidirect
94. #19127552C22semidirect
95. #19127552C22semidirect
96. C22⋊C4×Dic83C22semidirect
97. C22⋊C4×Dic83C22semidirect
98. C22⋊C4×Dic83C22semidirect
99. C4×(C2×D83)⋊C4C22semidirect
100. C4×(C2×D83)⋊C4C22semidirect
101. C4×(C2×D83)⋊C4C22semidirect
102. C4×C22⋊Dic83C22semidirect
103. C4×C22⋊Dic83C22semidirect
104. #19127548C22semidirect
105. #19127548C22semidirect
106. #19127548C22semidirect
107. #19127548C22semidirect
115. C2×#117×C83C22semidirect
116. #400×C83C22semidirect
117. #399×C83C22semidirect
118. #398×C83C22semidirect
119. #397×C83C22semidirect
120. #397×C83C22semidirect
122. C4×C4⋊C4×C83C22semidirect
123. C4×C22⋊C4×C83C22semidirect
124. C4×C22⋊C4×C83C22semidirect
563. D83#2395direct (N × H)
577. #2395D83direct (N × H)
587. C83C2×#2395semidirect
606. C2×#117C2×D83semidirect
626. #400C2×D83semidirect
632. #399C2×D83semidirect
638. #398C2×D83semidirect
651. #397C2×D83semidirect
652. #397C2×D83semidirect
668. C4×C4⋊C4C2×D83semidirect
681. C4×C22⋊C4C2×D83semidirect
682. C4×C22⋊C4C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D832
C2×#117×D832
#249107292
#249107282
#249107272
#249107262
#249107252
#249107242
#249107232
#249107222
#249107212
#249107202
#249107192
#400×D832
#399×D832
#398×D832
#397×D832
#394×D832
C4×C4⋊C4×D832
C4×C22⋊C4×D832
C83×#23952
C2×#239583