Finite Group Databasebeta

← C4⋊C4×(C2×D83)⋊C4 #35325817

Subgroups — C4⋊C4×(C2×D83)⋊C4 #35325817

Order 21248.

2574 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D83C211yesmaximal, characteristic
2C2×#19127558C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D83)⋊C4C212yesmaximal
5C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
6#24905698C212yesmaximal, complemented
7#24905696C212yesmaximal, complemented
8#24905693C211yesmaximal, characteristic, complemented
9#24905692C211yesmaximal, characteristic, complemented
10(C2×D83)⋊#95C212yesmaximal
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2212yes—
13C23×C4×D83C2211yescharacteristic
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4⋊Dic83C2211yescharacteristic
16C22×Dic83⋊C4C2212yes—
17C2×C4⋊C4×D83—24no—
18C2×C4⋊C4×D83—24no—
19C2×C4⋊C4×D83C418yescomplemented
20C22×(C2×D83)⋊C4C2212yes—
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×C4×Dic83C2212yes—
24C22×C4×Dic83C2211yescharacteristic
25#19127558C418yescomplemented
26C4⋊C4×Dic83—24no—
27C4×(C2×D83)⋊C4—28no—
28C4×(C2×D83)⋊C4C418yescomplemented
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2211yescharacteristic
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×D83C2311yescharacteristic
44C23×Dic83C2312yes—
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2312yes—
47C23×Dic83C2311yescharacteristic
48C23×Dic83C2311yescharacteristic
49C22×C4×D83—24no—
50C22×C4×D83—24no—
51C22×C4×D83—22no—
52C22×C4×D83—22no—
53C22×C4×D83—24no—
54C22×C4×D83—24no—
55C22×C4×D83—22no—
56C22×C4×D83—22no—
57C22×C4×D83—42no—
58C22×C4×D83—42no—
59C22×C4×D83C2×C418yes—
60C22×C4×D83C2×C414yes—
61C22×C4×D83C2×C414yes—
62C22×C4×D83C2×C414yes—
63C2×C4⋊Dic83—22no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—22no—
67C2×C4⋊Dic83C2×C414yes—
68C2×C4⋊Dic83C2×C414yescomplemented
69C2×Dic83⋊C4—24no—
70C2×Dic83⋊C4—24no—
71C2×Dic83⋊C4C2×C418yes—
72C4⋊C4×D83—232no—
73C2×(C2×D83)⋊C4—24no—
74C2×(C2×D83)⋊C4—22no—
75C2×(C2×D83)⋊C4—22no—
76C2×(C2×D83)⋊C4—24no—
77C2×(C2×D83)⋊C4C2×C418yes—
78C2×(C2×D83)⋊C4C2×C414yes—
79C2×(C2×D83)⋊C4C2×C414yes—
80C2×(C2×D83)⋊C4D414yes—
81C2×(C2×D83)⋊C4Q814yes—
82C2×C4×Dic83—24no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—24no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—42no—
87C2×C4×Dic83C2×C414yescomplemented
88C83⋊#95—24no—
89C83⋊#95—24no—
90C83⋊#95—24no—
91C83⋊#95—42no—
92C83⋊#95—42no—
93C83⋊#95C2×C418yescomplemented
94C83⋊#95C2×C414yescomplemented
95C83⋊#95C2×C414yescomplemented
96C23×C4×C83C2312yes—
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2312yes—
99C23×C4×C83C2311yescharacteristic
100C23×C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83—22no—
102C2×C4⋊C4×C83—22no—
103C2×C4⋊C4×C83C2×C414yes—
104C2×C4⋊C4×C83C2×C414yescomplemented
105C2×C4⋊C4×C83D414yes—
106C2×C4⋊C4×C83D414yes—
107C2×C42×C83—22no—
108C2×C42×C83—22no—
109C2×C42×C83—24no—
110C2×C42×C83—24no—
111C2×C42×C83—42no—
112C2×C42×C83C2×C414yescomplemented
113#95×C83—24no—
114C23×D83—21no—
115C23×D83—21no—
116C23×D83—21no—
117C23×D83—21no—
118C23×D83—21no—
119C23×D83—21no—
120C23×D83—21no—
121C23×D83—21no—
122C23×D83C22×C412yes—
123C23×D83C22×C412yes—
124C23×D83C22×C412yes—
125C23×D83C2×D412yes—
126C23×D83C2×Q812yes—
127C23×D83#4112yes—
128C23×D83#4112yes—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—21no—
141C22×Dic83—22no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—21no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—21no—
155C22×Dic83C22×C414yes—
156C22×Dic83C22×C412yes—
157C22×Dic83C22×C414yes—
158C22×Dic83C22×C412yes—
159C22×Dic83C22×C412yes—
160C22×Dic83C22×C412yes—
161C22×Dic83C22×C412yes—
162C22×Dic83C2×D412yes—
163C22×Dic83C2×Q812yes—
164C2×C4×D83—28no—
165C2×C4×D83—28no—
166C2×C4×D83—28no—
167C2×C4×D83—28no—
168C2×C4×D83—28no—
169C2×C4×D83—28no—
170C2×C4×D83—216no—
171C2×C4×D83—216no—
172C2×C4×D83—48no—
173C2×C4×D83—48no—
174C2×C4×D83—48no—
175C2×C4×D83—48no—
176C2×C4×D83—48no—
177C2×C4×D83C42116yescomplemented
178C4⋊Dic83—28no—
179C4⋊Dic83—28no—
180Dic83⋊C4—216no—
181(C2×D83)⋊C4—28no—
182(C2×D83)⋊C4—216no—
183(C2×D83)⋊C4C4⋊C4116yesdirect product factor
184C4×Dic83—28no—
185C4×Dic83—48no—
186C24×C83C2411yescharacteristic
187C22×C4×C83—22no—
188C22×C4×C83—21no—
189C22×C4×C83—22no—
190C22×C4×C83—21no—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—21no—
199C22×C4×C83—22no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—21no—
205C22×C4×C83—22no—
206C22×C4×C83—21no—
207C22×C4×C83C22×C412yes—
208C22×C4×C83C22×C414yes—
209C22×C4×C83C22×C414yes—
210C22×C4×C83C22×C412yes—
211C22×C4×C83C22×C412yes—
212C22×C4×C83C22×C412yes—
213C22×C4×C83C22×C412yes—
214C22×C4×C83C2×D412yes—
215C22×C4×C83C2×D414yes—
216C22×C4×C83C2×D412yes—
217C22×C4×C83C2×D414yes—
218C22×C4×C83C2×D412yes—
219C22×C4×C83C2×Q812yes—
220C22×C4×C83#4112yes—
221C22×C4×C83#4112yes—
222C4⋊C4×C83—28no—
223C4⋊C4×C83C22⋊C4116yescomplemented
224C42×C83—28no—
225C42×C83—48no—
226C23×C83C23×C411yescharacteristic
227C23×C83C23×C411yescharacteristic
228C23×C83C23×C411yescharacteristic
229C23×C83C22×D411yescharacteristic
230C23×C83C22×D411yescharacteristic
231C23×C83C22×D411yescharacteristic
232C23×C83C22×Q811yescharacteristic
233C23×C83C2×#4111yescharacteristic
234C23×C83C2×#4111yescharacteristic
235C23×C83C2×#4111yescharacteristic
236C23×C83C2×#4111yescharacteristic
237C23×C83H(5,𝔽2)11yescharacteristic
238C23×C83H(5,𝔽2)11yescharacteristic
239C23×C832−1+411yescharacteristic
240C23×C832−1+411yescharacteristic
241C22×D83—22no—
242C22×D83—22no—
243C22×D83—22no—
244C22×D83—22no—
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—22no—
252C22×D83—22no—
253C22×D83—22no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83C2×C4214yes—
270C22×D83C2×C4⋊C414yes—
271C22×D83#11714yes—
272C22×D83C4×D414yes—
273C22×D83C4×D414yes—
274C22×D83C4×Q814yes—
275C22×D83C4×Q814yes—
276C2×C4×C83—22no—
277C2×C4×C83—24no—
278C2×C4×C83—24no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—24no—
282C2×C4×C83—24no—
283C2×C4×C83—24no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—24no—
291C2×C4×C83—24no—
292C2×C4×C83—24no—
293C2×C4×C83—22no—
294C2×C4×C83—42no—
295C2×C4×C83—41no—
296C2×C4×C83—42no—
297C2×C4×C83—41no—
298C2×C4×C83—42no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—42no—
302C2×C4×C83C2×C4214yes—
303C2×C4×C83C2×C22⋊C418yes—
304C2×C4×C83C2×C22⋊C414yes—
305C2×C4×C83C2×C4⋊C414yescomplemented
306C2×C4×C83#11714yes—
307C2×C4×C83C4×D414yes—
308C2×C4×C83C4×D414yes—
309C2×C4×C83C4×D414yes—
310C2×C4×C83C4×D414yes—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
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—24no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—24no—
327C2×Dic83—24no—
328C2×Dic83—24no—
329C2×Dic83—24no—
330C2×Dic83—22no—
331C2×Dic83—24no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83—42no—
335C2×Dic83—42no—
336C2×Dic83—42no—
337C2×Dic83—41no—
338C2×Dic83—42no—
339C2×Dic83—41no—
340C2×Dic83—42no—
341C2×Dic83—41no—
342C2×Dic83—42no—
343C2×Dic83—41no—
344C2×Dic83C2×C4214yes—
345C2×Dic83C2×C4⋊C414yescomplemented
346C4×D83—232no—
347C4×D83—432no—
348C22×C83C22×C4211yescharacteristic
349C22×C83C22×C22⋊C411yescharacteristic
350C22×C83C22×C4⋊C411yescharacteristic
351C22×C83C2×#11711yescharacteristic
352C22×C83C2×#11711yescharacteristic
353C22×C83C2×C4×D411yescharacteristic
354C22×C83C2×C4×D411yescharacteristic
355C22×C83C2×C4×D411yescharacteristic
356C22×C83C2×C4×D411yescharacteristic
357C22×C83C2×C4×D411yescharacteristic
358C22×C83C2×C4×D411yescharacteristic
359C22×C83C2×C4×Q811yescharacteristic
360C22×C83C2×C4×Q811yescharacteristic
361C22×C83#51811yescharacteristic
362C22×C83#51911yescharacteristic
363C22×C83#52011yescharacteristic
364C22×C83#52011yescharacteristic
365C22×C83#52011yescharacteristic
366C22×C83#52011yescharacteristic
367C22×C83D4211yescharacteristic
368C22×C83D4211yescharacteristic
369C22×C83#54611yescharacteristic
370C22×C83#54611yescharacteristic
371C22×C83#54711yescharacteristic
372C22×C83#54711yescharacteristic
373C22×C83#54811yescharacteristic
374C22×C83#54811yescharacteristic
375C22×C83D4×Q811yescharacteristic
376C22×C83D4×Q811yescharacteristic
377C22×C83#55211yescharacteristic
378C22×C83#55211yescharacteristic
379C22×C83#55311yescharacteristic
380C22×C83#55311yescharacteristic
381C22×C83#55411yescharacteristic
382C22×C83#55411yescharacteristic
383C2×D83—24no—
384C2×D83—24no—
385C2×D83—24no—
386C2×D83—24no—
387C2×D83—24no—
388C2×D83—24no—
389C2×D83—24no—
390C2×D83—24no—
391C2×D83—24no—
392C2×D83—24no—
393C2×D83—24no—
394C2×D83—24no—
395C2×D83—24no—
396C2×D83—24no—
397C2×D83C4×C4⋊C418yescomplemented
398C4×C83—28no—
399C4×C83—24no—
400C4×C83—42no—
401C4×C83—44no—
402C4×C83C4×C22⋊C418yescomplemented
403Dic83—24no—
404Dic83—24no—
405Dic83—44no—
406Dic83—42no—
407Dic83—44no—
408C22⋊C4×C4⋊C4—831nomaximal, Sylow
409C2×C83C2×C4×C22⋊C411yescharacteristic
410C2×C83C2×C4×C4⋊C411yescharacteristic
411C2×C83#227411yescharacteristic
412C2×C83D4×C22⋊C411yescharacteristic
413C2×C83Q8×C22⋊C411yescharacteristic
414C2×C83#234411yescharacteristic
415C2×C83#234511yescharacteristic
416C2×C83D4×C4⋊C411yescharacteristic
417C2×C83D4×C4⋊C411yescharacteristic
418C2×C83#235211yescharacteristic
419C2×C83#235211yescharacteristic
420C2×C83#236011yescharacteristic
421C2×C83#236011yescharacteristic
422C2×C83#236111yescharacteristic
423C2×C83#236111yescharacteristic
424D83—28no—
425C23×C4⋊C4—831no—
426C2×#380—831no—
427C2×C4×C4⋊C4—831no—
428C2×C4×C4⋊C4D8311yescharacteristic, complemented
429C2×C4×C22⋊C4—831no—
430C2×C4×C22⋊C4—832no—
431#1436—832no—
432#1436—832no—
433C4⋊#95—831no—
434C4⋊#95—831no—
435C22⋊#95—832no—
436C83C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
437C24×C4—832no—
438C24×C4—831no—
439C22×C4⋊C4—832no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4—831no—
442C22×C4⋊C4—838no—
443C22×C4⋊C4—1664no—
444C22×C4⋊C4—1664no—
445C22×C4⋊C4C2×D8311yescharacteristic
446C22×C4⋊C4C2×D8311yescharacteristic
447C22×C22⋊C4—831no—
448C22×C22⋊C4—831no—
449C22×C22⋊C4—832no—
450C22×C42—832no—
451C22×C42—831no—
452C22×C42C2×D8312yes—
453C22×C42C2×D8311yescharacteristic
454#380—838no—
455C4×C4⋊C4—24no—
456C4×C4⋊C4—1664no—
457C4×C22⋊C4—838no—
458C4×C22⋊C4—1668no—
459C2×#95—832no—
460C2×#95—832no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—832no—
464C2×#95—832no—
465C2×#95—832no—
466C2×#95—832no—
467C2×#95C2×D8312yes—
468C25—831no—
469C23×C4—3322no—
470C23×C4—3322no—
471C23×C4—838no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—834no—
475C23×C4—834no—
476C23×C4—834no—
477C23×C4—832no—
478C23×C4—831no—
479C23×C4—832no—
480C23×C4—1664no—
481C23×C4—1664no—
482C23×C4—1664no—
483C23×C4—1664no—
484C23×C4—1662no—
485C23×C4—1662no—
486C23×C4—1662no—
487C23×C4—1662no—
488C23×C4C22×D8312yes—
489C23×C4C22×D8311yescharacteristic
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8312yes—
492C23×C4C22×D8311yescharacteristic
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—838no—
496C2×C4⋊C4—834no—
497C2×C4⋊C4—834no—
498C2×C4⋊C4—1664no—
499C2×C4⋊C4—1662no—
500C2×C4⋊C4—1664no—
501C2×C4⋊C4—1662no—
502C2×C4⋊C4—1662no—
503C2×C4⋊C4—1662no—
504C2×C4⋊C4—16632no—
505C2×C4⋊C4C4×D8314yes—
506C2×C4⋊C4C4×D8314yescomplemented
507C2×C4⋊C4D33214yes—
508C2×C4⋊C4C22⋊D8314yes—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4—834no—
512C2×C22⋊C4—834no—
513C2×C22⋊C4—838no—
514C2×C22⋊C4—1664no—
515C2×C22⋊C4—1662no—
516C2×C22⋊C4—1664no—
517C2×C22⋊C4—1662no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—24no—
521C2×C42—24no—
522C2×C42—42no—
523C2×C42—3322no—
524C2×C42—834no—
525C2×C42—1664no—
526C2×C42—1664no—
527C2×C42—1662no—
528C2×C42—1662no—
529C2×C42C4×D8314yescomplemented
530#95—24no—
531#95—3322no—
532#95—3322no—
533#95—834no—
534#95—834no—
535#95—838no—
536#95—1664no—
537#95—1664no—
538#95—1664no—
539C24—832no—
540C24—832no—
541C24—832no—
542C24—832no—
543C24—832no—
544C24—832no—
545C24—832no—
546C24—1661no—
547C24—1661no—
548C24—1661no—
549C24—1661no—
550C24—1661no—
551C24—1661no—
552C24—1661no—
553C24—1661no—
554C24C23×D8311yescharacteristic
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—3328no—
576C22×C4—3328no—
577C22×C4—3328no—
578C22×C4—3328no—
579C22×C4—3328no—
580C22×C4—832no—
581C22×C4—832no—
582C22×C4—832no—
583C22×C4—832no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—8316no—
587C22×C4—832no—
588C22×C4—834no—
589C22×C4—834no—
590C22×C4—16616no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1661no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1661no—
598C22×C4—1662no—
599C22×C4—1661no—
600C22×C4—1662no—
601C22×C4—1661no—
602C22×C4—1662no—
603C22×C4—1661no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1661no—
609C22×C4—16616no—
610C22×C4—1661no—
611C22×C4—1661no—
612C22×C4—1661no—
613C22×C4—1661no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1661no—
617C22×C4—1661no—
618C22×C4—1668no—
619C22×C4—1668no—
620C22×C4—1668no—
621C22×C4—1668no—
622C22×C4—1668no—
623C22×C4—1668no—
624C22×C4C2×C4×D8312yes—
625C22×C4C2×C4×D8314yes—
626C22×C4C2×C4×D8314yes—
627C22×C4C2×C4×D8312yes—
628C22×C4C2×C4×D8312yes—
629C22×C4C2×C4×D8312yes—
630C22×C4C2×C4×D8312yes—
631C22×C4D4×D8312yes—
632C22×C4C2×C22⋊D8314yes—
633C22×C4C2×C22⋊D8312yes—
634C22×C4C2×D33214yes—
635C22×C4C2×D33212yes—
636C22×C4Q8×D8312yes—
637C22×C4#1305059012yes—
638C22×C4#1305059012yes—
639C4⋊C4—28no—
640C4⋊C4—16616no—
641C4⋊C4—1668no—
642C4⋊C4—1668no—
643C4⋊C4(C2×D83)⋊C4116yesdirect product factor
644C22⋊C4—8316no—
645C22⋊C4—1668no—
646C22⋊C4—16616no—
647C42—28no—
648C42—48no—
649C42—3328no—
650C42—1668no—
651C23—834no—
652C23—834no—
653C23—834no—
654C23—834no—
655C23—834no—
656C23—834no—
657C23—834no—
658C23—1662no—
659C23—1662no—
660C23—1662no—
661C23—1662no—
662C23—1662no—
663C23—1662no—
664C23—1662no—
665C23—1662no—
666C23—1662no—
667C23—1662no—
668C23—1662no—
669C23—1662no—
670C23—1662no—
671C23—1662no—
672C23—1662no—
673C23—1662no—
674C23—1662no—
675C23—1662no—
676C23—1662no—
677C23—1662no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23—1662no—
686C23C22×C4×D8311yescharacteristic
687C23C22×C4×D8311yescharacteristic
688C23C22×C4×D8311yescharacteristic
689C23C2×D4×D8311yescharacteristic
690C23C22×C22⋊D8311yescharacteristic
691C23C22×D33211yescharacteristic
692C23C2×Q8×D8311yescharacteristic
693C23#41×D8311yescharacteristic
694C23#41×D8311yescharacteristic
695C23C2×#1305059011yescharacteristic
696C23C2×#1305059011yescharacteristic
697C23#1458183711yescharacteristic
698C23#1458183811yescharacteristic
699C23#1458183911yescharacteristic
700C23#1458184011yescharacteristic
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—33232no—
728C2×C4—3322no—
729C2×C4—3322no—
730C2×C4—3322no—
731C2×C4—3322no—
732C2×C4—3322no—
733C2×C4—3321no—
734C2×C4—3322no—
735C2×C4—3321no—
736C2×C4—3322no—
737C2×C4—3321no—
738C2×C4—3322no—
739C2×C4—3321no—
740C2×C4—834no—
741C2×C4—834no—
742C2×C4—1664no—
743C2×C4—1662no—
744C2×C4—1664no—
745C2×C4—1664no—
746C2×C4—1662no—
747C2×C4—1664no—
748C2×C4—1664no—
749C2×C4—1662no—
750C2×C4—1664no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—16632no—
764C2×C4C42×D8314yes—
765C2×C4C2×(C2×D83)⋊C418yes—
766C2×C4C2×(C2×D83)⋊C414yes—
767C2×C4C4⋊C4×D8314yescomplemented
768C2×C4#1458174914yes—
769C2×C4C4×C22⋊D8314yes—
770C2×C4C4×C22⋊D8314yes—
771C2×C4C4×D33214yes—
772C2×C4C4×D33214yes—
773C22—838no—
774C22—1664no—
775C22—1664no—
776C22—1664no—
777C22—1664no—
778C22—1664no—
779C22—1664no—
780C22—1664no—
781C22—1664no—
782C22—1664no—
783C22—1664no—
784C22—1664no—
785C22—1664no—
786C22—1664no—
787C22—1664no—
788C22C2×C42×D8311yescharacteristic
789C22C22×(C2×D83)⋊C411yescharacteristic
790C22C2×C4⋊C4×D8311yescharacteristic
791C22#117×D8311yescharacteristic
792C22C2×#1458174911yescharacteristic
793C22C4×D4×D8311yescharacteristic
794C22C4×D4×D8311yescharacteristic
795C22C2×C4×C22⋊D8311yescharacteristic
796C22C2×C4×C22⋊D8311yescharacteristic
797C22C2×C4×D33211yescharacteristic
798C22C2×C4×D33211yescharacteristic
799C22C4×Q8×D8311yescharacteristic
800C22C4×Q8×D8311yescharacteristic
801C22#1912817311yescharacteristic
802C22#1912817711yescharacteristic
803C22#1912818011yescharacteristic
804C22#1912818111yescharacteristic
805C22#1912818211yescharacteristic
806C22#1912818311yescharacteristic
807C22D4×C22⋊D8311yescharacteristic
808C22D4×D33211yescharacteristic
809C22#1912833911yescharacteristic
810C22#1912834611yescharacteristic
811C22#1912835211yescharacteristic
812C22#1912835611yescharacteristic
813C22#1912835811yescharacteristic
814C22#1912836311yescharacteristic
815C22Q8×C22⋊D8311yescharacteristic
816C22Q8×D33211yescharacteristic
817C22#1912839011yescharacteristic
818C22#1912839211yescharacteristic
819C22#1912839511yescharacteristic
820C22#1912840111yescharacteristic
821C22#1912840611yescharacteristic
822C22#1912841111yescharacteristic
823C4—24no—
824C4—28no—
825C4—42no—
826C4—44no—
827C4—3322no—
828C4—3324no—
829C4—3324no—
830C4—1664no—
831C4—1664no—
832C4C4×(C2×D83)⋊C418yescomplemented
833C2—1668no—
834C2C2×C4×(C2×D83)⋊C411yescharacteristic
835C2C4×C4⋊C4×D8311yescharacteristic
836C2#2490981711yescharacteristic
837C2D4×(C2×D83)⋊C411yescharacteristic
838C2Q8×(C2×D83)⋊C411yescharacteristic
839C2#2491032811yescharacteristic
840C2#2491033611yescharacteristic
841C2C4⋊C4×C22⋊D8311yescharacteristic
842C2C4⋊C4×D33211yescharacteristic
843C2#2491039311yescharacteristic
844C2#2491039511yescharacteristic
845C2#2491046411yescharacteristic
846C2#2491047011yescharacteristic
847C2#2491047511yescharacteristic
848C2#2491048111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C22⋊C4×C4⋊C4
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic83C2semidirect
6. #24905698C2semidirect
7. #24905696C2semidirect
8. #24905693C2semidirect
9. #24905692C2semidirect
11. C2×C4×C4⋊C4×C83C2semidirect
19. C2×C4⋊C4×D83C4semidirect
25. #19127558C4semidirect
28. C4×(C2×D83)⋊C4C4semidirect
68. C2×C4⋊Dic83C2×C4semidirect
87. C2×C4×Dic83C2×C4semidirect
93. C83⋊#95C2×C4semidirect
94. C83⋊#95C2×C4semidirect
95. C83⋊#95C2×C4semidirect
104. C2×C4⋊C4×C83C2×C4semidirect
112. C2×C42×C83C2×C4semidirect
177. C2×C4×D83C42semidirect
183. (C2×D83)⋊C4C4⋊C4direct (N × H)
223. C4⋊C4×C83C22⋊C4semidirect
305. C2×C4×C83C2×C4⋊C4semidirect
345. C2×Dic83C2×C4⋊C4semidirect
397. C2×D83C4×C4⋊C4semidirect
402. C4×C83C4×C22⋊C4semidirect
428. C2×C4×C4⋊C4D83semidirect
436. C83C22⋊C4×C4⋊C4semidirect
506. C2×C4⋊C4C4×D83semidirect
529. C2×C42C4×D83semidirect
643. C4⋊C4(C2×D83)⋊C4direct (N × H)
767. C2×C4C4⋊C4×D83semidirect
832. 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×C4⋊C4×D832
C2×#191275582
C2×C4⋊C4×Dic832
C2×C4×(C2×D83)⋊C42
#249056982
#249056962
#249056932
#249056922
(C2×D83)⋊#952
C2×C4×C4⋊C4×C832
C22⋊C4×C4⋊C483