Finite Group Databasebeta

← #35325972

Subgroups — #35325972

Order 21248.

2666 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581754C211yesmaximal, characteristic
2C2×#19127603C211yesmaximal, characteristic
3C2×#19127602C211yesmaximal, characteristic
4C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D83)⋊C4C212yesmaximal, complemented
6#24905701C212yesmaximal, complemented
7#24905699C212yesmaximal, complemented
8#24905692C211yesmaximal, characteristic, complemented
9(C2×D83)⋊#95C212yesmaximal, complemented
10C4×C83⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×D332C2211yescharacteristic
13C23×C4×D83C2212yes—
14C2×#14581754—24no—
15C2×#14581754—24no—
16C2×#14581754C418yescomplemented
17C22×C4⋊Dic83C2211yescharacteristic
18C22×(C2×D83)⋊C4C2212yes—
19C22×(C2×D83)⋊C4C2212yes—
20C22×(C2×D83)⋊C4C2212yes—
21C22×(C2×D83)⋊C4C2212yes—
22C22×(C2×D83)⋊C4C2212yes—
23C22×C4×Dic83C2212yes—
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127603C418yescomplemented
27#19127602C418yescomplemented
28C4⋊C4×Dic83—24no—
29C4×(C2×D83)⋊C4—28no—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C2×C83⋊#95C2211yescharacteristic
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C4⋊C4×C83C2211yescharacteristic
39C22×C42×C83C2212yes—
40C22×C42×C83C2211yescharacteristic
41C4×C4⋊C4×C83—24no—
42C2×#95×C83C2212yes—
43C24×D83C2312yes—
44C22×D332—22no—
45C22×D332—22no—
46C22×D332—22no—
47C22×D332—22no—
48C22×D332C2×C414yes—
49C22×D332C2×C414yes—
50C22×D332C2×C414yes—
51C23×Dic83C2312yes—
52C23×Dic83C2311yescharacteristic
53C23×Dic83C2311yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C22×C4×D83—24no—
57C22×C4×D83—24no—
58C22×C4×D83—24no—
59C22×C4×D83—24no—
60C22×C4×D83—42no—
61C22×C4×D83—42no—
62C22×C4×D83C2×C418yes—
63#14581754—232no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83C2×C414yescomplemented
67C2×(C2×D83)⋊C4—24no—
68C2×(C2×D83)⋊C4—24no—
69C2×(C2×D83)⋊C4—24no—
70C2×(C2×D83)⋊C4—24no—
71C2×(C2×D83)⋊C4—24no—
72C2×(C2×D83)⋊C4—24no—
73C2×(C2×D83)⋊C4—42no—
74C2×(C2×D83)⋊C4—42no—
75C2×(C2×D83)⋊C4—42no—
76C2×(C2×D83)⋊C4—42no—
77C2×(C2×D83)⋊C4C2×C418yes—
78C2×(C2×D83)⋊C4C2×C418yescomplemented
79C2×(C2×D83)⋊C4C2×C418yescomplemented
80C2×(C2×D83)⋊C4C2×C418yescomplemented
81C2×(C2×D83)⋊C4C2×C418yescomplemented
82C2×C4×Dic83—24no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—24no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—42no—
89C2×C4×Dic83C2×C414yes—
90C2×C4×Dic83C2×C414yescomplemented
91C83⋊#95—24no—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—24no—
95C83⋊#95—22no—
96C83⋊#95—42no—
97C83⋊#95D414yescomplemented
98C23×C4×C83C2312yes—
99C23×C4×C83C2311yescharacteristic
100C23×C4×C83C2312yes—
101C23×C4×C83C2311yescharacteristic
102C23×C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83—22no—
104C2×C4⋊C4×C83—22no—
105C2×C4⋊C4×C83C2×C414yes—
106C2×C4⋊C4×C83C2×C414yescomplemented
107C2×C4⋊C4×C83D414yes—
108C2×C4⋊C4×C83D414yes—
109C2×C42×C83—22no—
110C2×C42×C83—22no—
111C2×C42×C83—24no—
112C2×C42×C83—24no—
113C2×C42×C83—42no—
114C2×C42×C83C2×C414yescomplemented
115#95×C83—24no—
116C23×D83—22no—
117C23×D83—22no—
118C23×D83—22no—
119C23×D83—22no—
120C23×D83—22no—
121C23×D83—22no—
122C23×D83—22no—
123C23×D83—22no—
124C23×D83—22no—
125C23×D83—22no—
126C23×D83—22no—
127C23×D83—22no—
128C23×D83C22×C414yes—
129C23×D83C22×C414yes—
130C23×D83C22×C414yes—
131C2×D332—28no—
132C2×D332—28no—
133C2×D332—28no—
134C2×D332—28no—
135C2×D332—28no—
136C2×D332—28no—
137C2×D332C42116yescomplemented
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—21no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83C22×C412yes—
165C22×Dic83C22×C412yes—
166C22×Dic83C22×C414yes—
167C22×Dic83C22×C412yes—
168C22×Dic83C22×C412yes—
169C22×Dic83C2×D412yes—
170C22×Dic83C2×D412yes—
171C22×Dic83#4112yes—
172C22×Dic83#4112yes—
173C2×C4×D83—216no—
174C2×C4×D83—216no—
175C2×C4×D83—48no—
176C2×C4×D83—48no—
177C2×C4×D83—48no—
178C2×C4×D83—48no—
179C2×C4×D83—48no—
180C4⋊Dic83—28no—
181(C2×D83)⋊C4—216no—
182(C2×D83)⋊C4—216no—
183(C2×D83)⋊C4—216no—
184(C2×D83)⋊C4—48no—
185(C2×D83)⋊C4—48no—
186C4×Dic83—28no—
187C4×Dic83—28no—
188C4×Dic83—48no—
189C24×C83C2411yescharacteristic
190C22×C4×C83—22no—
191C22×C4×C83—21no—
192C22×C4×C83—22no—
193C22×C4×C83—21no—
194C22×C4×C83—22no—
195C22×C4×C83—22no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—22no—
200C22×C4×C83—22no—
201C22×C4×C83—21no—
202C22×C4×C83—22no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83C22×C412yes—
211C22×C4×C83C22×C414yes—
212C22×C4×C83C22×C414yes—
213C22×C4×C83C22×C412yes—
214C22×C4×C83C22×C412yes—
215C22×C4×C83C22×C412yes—
216C22×C4×C83C22×C412yes—
217C22×C4×C83C2×D412yes—
218C22×C4×C83C2×D414yes—
219C22×C4×C83C2×D412yes—
220C22×C4×C83C2×D414yes—
221C22×C4×C83C2×D412yes—
222C22×C4×C83#4112yes—
223C22×C4×C83#4112yes—
224C22×C4×C83#4112yes—
225C4⋊C4×C83—28no—
226C4⋊C4×C83C22⋊C4116yescomplemented
227C42×C83—28no—
228C42×C83—48no—
229C23×C83C23×C411yescharacteristic
230C23×C83C23×C411yescharacteristic
231C23×C83C23×C411yescharacteristic
232C23×C83C22×D411yescharacteristic
233C23×C83C22×D411yescharacteristic
234C23×C83C22×D411yescharacteristic
235C23×C83C2×#4111yescharacteristic
236C23×C83C2×#4111yescharacteristic
237C23×C83C2×#4111yescharacteristic
238C23×C83C2×#4111yescharacteristic
239C23×C83C2×#4111yescharacteristic
240C23×C83H(5,𝔽2)11yescharacteristic
241C23×C83H(5,𝔽2)11yescharacteristic
242C23×C83H(5,𝔽2)11yescharacteristic
243C23×C832−1+411yescharacteristic
244C22×D83—24no—
245C22×D83—24no—
246C22×D83—24no—
247C22×D83—24no—
248C22×D83—24no—
249C22×D83—24no—
250C22×D83—24no—
251C22×D83—24no—
252C22×D83—24no—
253C22×D83—24no—
254C22×D83—24no—
255C22×D83—24no—
256C22×D83—24no—
257C22×D83—24no—
258C22×D83—24no—
259C22×D83—24no—
260C22×D83—24no—
261C22×D83—24no—
262C22×D83—42no—
263C22×D83—42no—
264C22×D83—42no—
265C22×D83—42no—
266C22×D83—42no—
267C22×D83—42no—
268C22×D83—42no—
269C22×D83—42no—
270C22×D83—42no—
271C22×D83—42no—
272C22×D83—42no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277C22×D83—42no—
278C22×D83C2×C4218yes—
279C2×C4×C83—22no—
280C2×C4×C83—24no—
281C2×C4×C83—24no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—24no—
286C2×C4×C83—24no—
287C2×C4×C83—24no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—24no—
293C2×C4×C83—24no—
294C2×C4×C83—22no—
295C2×C4×C83—24no—
296C2×C4×C83—22no—
297C2×C4×C83—42no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—42no—
301C2×C4×C83—42no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—42no—
305C2×C4×C83C2×C4214yes—
306C2×C4×C83C2×C22⋊C418yes—
307C2×C4×C83C2×C22⋊C414yes—
308C2×C4×C83#11714yes—
309C2×C4×C83C4×D414yes—
310C2×C4×C83C4×D414yes—
311C2×C4×C83C4×D414yes—
312C2×C4×C83C4×D414yes—
313C2×C4×C83C4×D414yescomplemented
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—24no—
329C2×Dic83—24no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—24no—
334C2×Dic83—22no—
335C2×Dic83—42no—
336C2×Dic83—41no—
337C2×Dic83—41no—
338C2×Dic83—41no—
339C2×Dic83—41no—
340C2×Dic83—42no—
341C2×Dic83—41no—
342C2×Dic83—41no—
343C2×Dic83—42no—
344C2×Dic83—41no—
345C2×Dic83—41no—
346C2×Dic83—42no—
347C2×Dic83C4×D414yes—
348C2×Dic83C4×D414yescomplemented
349D332—232no—
350C4×D83—432no—
351C22×C83C22×C4211yescharacteristic
352C22×C83C22×C22⋊C411yescharacteristic
353C22×C83C2×#11711yescharacteristic
354C22×C83C2×C4×D411yescharacteristic
355C22×C83C2×C4×D411yescharacteristic
356C22×C83C2×C4×D411yescharacteristic
357C22×C83C2×C4×D411yescharacteristic
358C22×C83C2×C4×D411yescharacteristic
359C22×C83C2×C4×D411yescharacteristic
360C22×C83C2×C4×D411yescharacteristic
361C22×C83C4×#4111yescharacteristic
362C22×C83C4×#4111yescharacteristic
363C22×C83C4×#4111yescharacteristic
364C22×C83#51811yescharacteristic
365C22×C83#51811yescharacteristic
366C22×C83#51811yescharacteristic
367C22×C83#52011yescharacteristic
368C22×C83#52011yescharacteristic
369C22×C83#52011yescharacteristic
370C22×C83D4211yescharacteristic
371C22×C83D4211yescharacteristic
372C22×C83#54611yescharacteristic
373C22×C83#54611yescharacteristic
374C22×C83#54711yescharacteristic
375C22×C83#54811yescharacteristic
376C22×C83#54811yescharacteristic
377C22×C83#55011yescharacteristic
378C22×C83#55011yescharacteristic
379C22×C83#55011yescharacteristic
380C22×C83#55311yescharacteristic
381C22×C83#55311yescharacteristic
382C22×C83#55511yescharacteristic
383C22×C83#55611yescharacteristic
384C22×C83#55911yescharacteristic
385C22×C83#55911yescharacteristic
386C2×D83—28no—
387C2×D83—28no—
388C2×D83—28no—
389C2×D83—44no—
390C2×D83—44no—
391C2×D83—44no—
392C2×D83—44no—
393C2×D83—44no—
394C2×D83—44no—
395C2×D83—44no—
396C2×D83—44no—
397C2×D83—44no—
398C2×D83—44no—
399C2×D83—44no—
400C2×D83—44no—
401C4×C83—28no—
402C4×C83—24no—
403C4×C83—42no—
404C4×C83—44no—
405C4×C83C4×C22⋊C418yescomplemented
406Dic83—24no—
407Dic83—24no—
408Dic83—42no—
409Dic83—42no—
410Dic83—44no—
411#13820—831nomaximal, Sylow
412C2×C83C2×C4×C22⋊C411yescharacteristic
413C2×C83C42×D411yescharacteristic
414C2×C83#227511yescharacteristic
415C2×C83D4×C22⋊C411yescharacteristic
416C2×C83#234111yescharacteristic
417C2×C83#235411yescharacteristic
418C2×C83#235711yescharacteristic
419C2×C83#236111yescharacteristic
420C2×C83#236111yescharacteristic
421C2×C83#236311yescharacteristic
422C2×C83#236311yescharacteristic
423C2×C83#236611yescharacteristic
424C2×C83#236611yescharacteristic
425C2×C83#236711yescharacteristic
426C2×C83#236711yescharacteristic
427D83—48no—
428C22×C4×D4—831no—
429C2×#390—831no—
430C2×#390—831no—
431C2×C4×C4⋊C4—831no—
432C2×C4×C4⋊C4D8311yescharacteristic, complemented
433C2×C4×C22⋊C4—832no—
434#1437—832no—
435#1437—832no—
436C4⋊#95—831no—
437C22⋊#95—832no—
438C4×#95—831no—
439C83#1382011yescharacteristic, complemented, Sylow
440C23×D4—831no—
441C24×C4—832no—
442C2×C4×D4—838no—
443C2×C4×D4—1664no—
444C2×C4×D4—1664no—
445C22×C4⋊C4—831no—
446C22×C4⋊C4C2×D8311yescharacteristic
447C22×C4⋊C4C2×D8311yescharacteristic
448C22×C22⋊C4—832no—
449C22×C22⋊C4—832no—
450C22×C22⋊C4—832no—
451C22×C22⋊C4—832no—
452C22×C22⋊C4—832no—
453C22×C42—832no—
454C22×C42—831no—
455C22×C42—831no—
456C22×C42C2×D8312yes—
457C22×C42C2×D8311yescharacteristic
458#390—838no—
459#390—838no—
460C4×C4⋊C4—24no—
461C4×C4⋊C4—1664no—
462C4×C22⋊C4—1668no—
463C2×#95—832no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95—831no—
468C2×#95—832no—
469C2×#95—832no—
470C2×#95C2×D8312yes—
471C25—832no—
472C22×D4—834no—
473C22×D4—834no—
474C22×D4—834no—
475C22×D4—1662no—
476C22×D4—1662no—
477C22×D4—1662no—
478C22×D4—1662no—
479C23×C4—3322no—
480C23×C4—3322no—
481C23×C4—838no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—832no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—1664no—
488C23×C4—1664no—
489C23×C4—1664no—
490C23×C4—1664no—
491C23×C4C22×D8312yes—
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8312yes—
495C23×C4C22×D8311yescharacteristic
496C4×D4—16632no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—834no—
500C2×C4⋊C4—1662no—
501C2×C4⋊C4—1662no—
502C2×C4⋊C4C4×D8314yes—
503C2×C4⋊C4C4×D8314yescomplemented
504C2×C4⋊C4D33214yes—
505C2×C4⋊C4C22⋊D8314yes—
506C2×C22⋊C4—3322no—
507C2×C22⋊C4—3322no—
508C2×C22⋊C4—3322no—
509C2×C22⋊C4—3322no—
510C2×C22⋊C4—838no—
511C2×C22⋊C4—838no—
512C2×C22⋊C4—838no—
513C2×C22⋊C4—838no—
514C2×C22⋊C4—838no—
515C2×C22⋊C4—1664no—
516C2×C22⋊C4—1664no—
517C2×C22⋊C4—1664no—
518C2×C22⋊C4—1664no—
519C2×C22⋊C4—1664no—
520C2×C22⋊C4—1664no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—24no—
524C2×C42—24no—
525C2×C42—42no—
526C2×C42—3322no—
527C2×C42—834no—
528C2×C42—834no—
529C2×C42—1664no—
530C2×C42—1664no—
531C2×C42—1662no—
532C2×C42—1662no—
533C2×C42—1662no—
534C2×C42—1662no—
535C2×C42C4×D8314yescomplemented
536#95—24no—
537#95—3322no—
538#95—834no—
539#95—1664no—
540#95—1662no—
541#95—1662no—
542#95—1664no—
543#95—1662no—
544C24—834no—
545C24—834no—
546C24—834no—
547C24—1662no—
548C24—1662no—
549C24—1662no—
550C24—1662no—
551C24—1662no—
552C24—1662no—
553C24—1662no—
554C24—1662no—
555C24—1662no—
556C24—1662no—
557C24—1662no—
558C24—1662no—
559C24C23×D8311yescharacteristic
560C2×D4—8316no—
561C2×D4—1668no—
562C2×D4—1668no—
563C2×D4—1668no—
564C2×D4—1668no—
565C2×D4—1668no—
566C2×D4—1668no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—3328no—
588C22×C4—3328no—
589C22×C4—3328no—
590C22×C4—3328no—
591C22×C4—3328no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—832no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—834no—
601C22×C4—16616no—
602C22×C4—1662no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1662no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1662no—
611C22×C4—1661no—
612C22×C4—1661no—
613C22×C4—1662no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1661no—
619C22×C4—1661no—
620C22×C4—16616no—
621C22×C4—1661no—
622C22×C4—1661no—
623C22×C4—1661no—
624C22×C4—1661no—
625C22×C4—1661no—
626C22×C4—1661no—
627C22×C4—1661no—
628C22×C4—1661no—
629C22×C4C2×C4×D8312yes—
630C22×C4C2×C4×D8314yes—
631C22×C4C2×C4×D8314yes—
632C22×C4C2×C4×D8312yes—
633C22×C4C2×C4×D8312yes—
634C22×C4C2×C4×D8312yes—
635C22×C4C2×C4×D8312yes—
636C22×C4D4×D8312yes—
637C22×C4C2×C22⋊D8314yes—
638C22×C4C2×C22⋊D8312yes—
639C22×C4C2×D33214yes—
640C22×C4C2×D33212yes—
641C22×C4#1305059012yes—
642C22×C4#1305059012yes—
643C22×C4#1305059112yes—
644C4⋊C4—28no—
645C4⋊C4—1668no—
646C4⋊C4(C2×D83)⋊C4116yescomplemented
647C22⋊C4—3328no—
648C22⋊C4—3328no—
649C22⋊C4—16616no—
650C22⋊C4—16616no—
651C22⋊C4—16616no—
652C42—28no—
653C42—48no—
654C42—3328no—
655C42—1668no—
656C42—1668no—
657C23—3322no—
658C23—3322no—
659C23—3322no—
660C23—3322no—
661C23—3322no—
662C23—3322no—
663C23—3322no—
664C23—3322no—
665C23—3322no—
666C23—3322no—
667C23—3322no—
668C23—3322no—
669C23—3322no—
670C23—3322no—
671C23—3322no—
672C23—3322no—
673C23—838no—
674C23—1664no—
675C23—1664no—
676C23—1664no—
677C23—1664no—
678C23—1664no—
679C23—1664no—
680C23—1664no—
681C23—1664no—
682C23—1664no—
683C23—1664no—
684C23—1664no—
685C23—1664no—
686C23—1664no—
687C23—1664no—
688C23—1664no—
689C23—1664no—
690C23—1664no—
691C23—1664no—
692C23C22×C4×D8311yescharacteristic
693C23C22×C4×D8311yescharacteristic
694C23C22×C4×D8311yescharacteristic
695C23C2×D4×D8311yescharacteristic
696C23C22×C22⋊D8311yescharacteristic
697C23C22×D33211yescharacteristic
698C23#41×D8311yescharacteristic
699C23#41×D8311yescharacteristic
700C23C2×#1305059011yescharacteristic
701C23C2×#1305059011yescharacteristic
702C23C2×#1305059111yescharacteristic
703C23#1458183711yescharacteristic
704C23#1458183811yescharacteristic
705C23#1458183811yescharacteristic
706C23#1458184011yescharacteristic
707D4—16632no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—33232no—
735C2×C4—3322no—
736C2×C4—3321no—
737C2×C4—3321no—
738C2×C4—3321no—
739C2×C4—3321no—
740C2×C4—3322no—
741C2×C4—3321no—
742C2×C4—3322no—
743C2×C4—3321no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—3322no—
747C2×C4—834no—
748C2×C4—834no—
749C2×C4—1662no—
750C2×C4—1664no—
751C2×C4—1662no—
752C2×C4—1664no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1664no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4C42×D8314yes—
771C2×C4C2×(C2×D83)⋊C418yes—
772C2×C4C2×(C2×D83)⋊C414yes—
773C2×C4#1458174914yes—
774C2×C4C4×C22⋊D8314yes—
775C2×C4C4×C22⋊D8314yes—
776C2×C4#1458175414yescomplemented
777C2×C4C4×D33214yes—
778C2×C4C4×D33214yes—
779C22—3324no—
780C22—3324no—
781C22—3324no—
782C22—3324no—
783C22—3324no—
784C22—3324no—
785C22—3324no—
786C22—3324no—
787C22—3324no—
788C22—3324no—
789C22—3324no—
790C22—3324no—
791C22—1668no—
792C22—1668no—
793C22—1668no—
794C22C2×C42×D8311yescharacteristic
795C22C22×(C2×D83)⋊C411yescharacteristic
796C22C2×#1458174911yescharacteristic
797C22C4×D4×D8311yescharacteristic
798C22C4×D4×D8311yescharacteristic
799C22C2×C4×C22⋊D8311yescharacteristic
800C22C2×C4×C22⋊D8311yescharacteristic
801C22C2×#1458175411yescharacteristic
802C22C2×C4×D33211yescharacteristic
803C22C2×C4×D33211yescharacteristic
804C22#1912816911yescharacteristic
805C22C4×#1305059111yescharacteristic
806C22C4×#1305059111yescharacteristic
807C22#1912817311yescharacteristic
808C22#1912817311yescharacteristic
809C22#1912817511yescharacteristic
810C22#1912818211yescharacteristic
811C22#1912818311yescharacteristic
812C22#1912818311yescharacteristic
813C22D4×C22⋊D8311yescharacteristic
814C22D4×D33211yescharacteristic
815C22#1912833911yescharacteristic
816C22#1912834611yescharacteristic
817C22#1912835211yescharacteristic
818C22#1912836211yescharacteristic
819C22#1912836311yescharacteristic
820C22#1912837011yescharacteristic
821C22#1912837211yescharacteristic
822C22#1912837311yescharacteristic
823C22#1912839511yescharacteristic
824C22#1912839911yescharacteristic
825C22#1912841411yescharacteristic
826C22#1912842311yescharacteristic
827C22#1912843411yescharacteristic
828C22#1912843611yescharacteristic
829C4—24no—
830C4—28no—
831C4—42no—
832C4—44no—
833C4—3322no—
834C4—3324no—
835C4—3322no—
836C4—1664no—
837C4—1664no—
838C4C4×(C2×D83)⋊C418yescomplemented
839C2—3328no—
840C2C2×C4×(C2×D83)⋊C411yescharacteristic
841C2C4×#1458175411yescharacteristic
842C2#2490982311yescharacteristic
843C2D4×(C2×D83)⋊C411yescharacteristic
844C2#2491030111yescharacteristic
845C2#2491040811yescharacteristic
846C2#2491043211yescharacteristic
847C2#2491047911yescharacteristic
848C2#2491048111yescharacteristic
849C2#2491050111yescharacteristic
850C2#2491050311yescharacteristic
851C2#2491052511yescharacteristic
852C2#2491052711yescharacteristic
853C2#2491053011yescharacteristic
854C2#2491053411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×C4×C4⋊C4D83
hypocenterC83#13820
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic83C2semidirect
5. C2×C4×(C2×D83)⋊C4C2semidirect
6. #24905701C2semidirect
7. #24905699C2semidirect
8. #24905692C2semidirect
9. (C2×D83)⋊#95C2semidirect
10. C4×C83⋊#95C2semidirect
11. C2×C4×C4⋊C4×C83C2semidirect
16. C2×#14581754C4semidirect
26. #19127603C4semidirect
27. #19127602C4semidirect
66. C2×C4⋊Dic83C2×C4semidirect
78. C2×(C2×D83)⋊C4C2×C4semidirect
79. C2×(C2×D83)⋊C4C2×C4semidirect
80. C2×(C2×D83)⋊C4C2×C4semidirect
81. C2×(C2×D83)⋊C4C2×C4semidirect
90. C2×C4×Dic83C2×C4semidirect
97. C83⋊#95D4semidirect
106. C2×C4⋊C4×C83C2×C4semidirect
114. C2×C42×C83C2×C4semidirect
137. C2×D332C42semidirect
226. C4⋊C4×C83C22⋊C4semidirect
313. C2×C4×C83C4×D4semidirect
348. C2×Dic83C4×D4semidirect
405. C4×C83C4×C22⋊C4semidirect
432. C2×C4×C4⋊C4D83semidirect
439. C83#13820semidirect
503. C2×C4⋊C4C4×D83semidirect
535. C2×C42C4×D83semidirect
646. C4⋊C4(C2×D83)⋊C4semidirect
776. C2×C4#14581754semidirect
838. C4C4×(C2×D83)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#145817542
C2×#191276032
C2×#191276022
C2×C4⋊C4×Dic832
C2×C4×(C2×D83)⋊C42
#249057012
#249056992
#249056922
(C2×D83)⋊#952
C4×C83⋊#952
C2×C4×C4⋊C4×C832
#1382083