Finite Group Databasebeta

← (C22⋊D83)⋊#95 #35325871

Subgroups — (C22⋊D83)⋊#95 #35325871

Order 21248.

3562 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D83C211yesmaximal, characteristic
2C22×(C22⋊D83)⋊C4C212yesmaximal
3C22×C83⋊#95C211yesmaximal, characteristic, complemented
4C2×#95×D83C211yesmaximal, characteristic, complemented
5Dic83⋊#95C212yesmaximal, complemented
6Dic83⋊#95C211yesmaximal, characteristic, complemented
7#24905685C212yesmaximal, complemented
8(C2×D83)⋊#95C211yesmaximal, characteristic, complemented
9(C2×D83)⋊#95C212yesmaximal, complemented
10#95×Dic83C211yesmaximal, characteristic, complemented
11C83×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D83C2211yescharacteristic
13C24×Dic83C2212yes—
14C23×C4×D83C2212yes—
15C23×C4×D83C2211yescharacteristic
16C2×C4×C22⋊D83—28no—
17C2×C4×C22⋊D83C418yescomplemented
18C2×(C22⋊D83)⋊C4—28no—
19C2×(C22⋊D83)⋊C4—28no—
20C2×(C22⋊D83)⋊C4C4116yescomplemented
21C22×Dic83⋊C4C2212yes—
22C22×Dic83⋊C4C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×(C2×D83)⋊C4C2212yes—
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×C4×Dic83C2212yes—
27C22×C4×Dic83C2211yescharacteristic
28C2×C83⋊#95—24no—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2211yescharacteristic
36#95×D83—24no—
37C24×C4×C83C2211yescharacteristic
38C22×C22⋊C4×C83C2212yes—
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C2×#95×C83C2212yes—
42C24×D83C2311yescharacteristic
43C22×C22⋊D83C2×C418yes—
44C22×C22⋊D83C2×C414yes—
45C22×C22⋊D83D414yes—
46C22×C22⋊D83D418yes—
47C22×C22⋊D83Q814yes—
48C23×Dic83—24no—
49C23×Dic83—24no—
50C23×Dic83—24no—
51C23×Dic83—24no—
52C23×Dic83—42no—
53C23×Dic83—42no—
54C23×Dic83C2×C418yescomplemented
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2312yes—
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2312yes—
59C23×Dic83C2311yescharacteristic
60C22×C4×D83—24no—
61C22×C4×D83—24no—
62C22×C4×D83—24no—
63C22×C4×D83—24no—
64C22×C4×D83—24no—
65C22×C4×D83—22no—
66C22×C4×D83—22no—
67C22×C4×D83—42no—
68C22×C4×D83—42no—
69C22×C4×D83—42no—
70C22×C4×D83C2×C418yescomplemented
71C22×C4×D83C2×C414yescomplemented
72C4×C22⋊D83—232no—
73(C22⋊D83)⋊C4—264no—
74C2×Dic83⋊C4—24no—
75C2×Dic83⋊C4—24no—
76C2×Dic83⋊C4—24no—
77C2×Dic83⋊C4C2×C418yescomplemented
78C2×Dic83⋊C4C2×C414yescomplemented
79C2×C22⋊Dic83—24no—
80C2×C22⋊Dic83C2×C414yescomplemented
81C2×(C2×D83)⋊C4—24no—
82C2×(C2×D83)⋊C4—24no—
83C2×(C2×D83)⋊C4—24no—
84C2×(C2×D83)⋊C4C2×C418yescomplemented
85C2×(C2×D83)⋊C4C2×C414yescomplemented
86C2×C4×Dic83—24no—
87C2×C4×Dic83—24no—
88C2×C4×Dic83—24no—
89C2×C4×Dic83C2×C418yescomplemented
90C2×C4×Dic83C2×C414yescomplemented
91C83⋊#95—24no—
92C83⋊#95—24no—
93C83⋊#95—24no—
94C83⋊#95—22no—
95C83⋊#95—42no—
96C83⋊#95—42no—
97C83⋊#95D414yescomplemented
98C25×C83C2311yescharacteristic
99C23×C4×C83—24no—
100C23×C4×C83—22no—
101C23×C4×C83—22no—
102C23×C4×C83—42no—
103C23×C4×C83C2×C414yescomplemented
104C23×C4×C83C2312yes—
105C23×C4×C83C2312yes—
106C23×C4×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108C2×C22⋊C4×C83—24no—
109C2×C22⋊C4×C83—24no—
110C2×C22⋊C4×C83C2×C418yescomplemented
111#95×C83—22no—
112#95×C83—22no—
113#95×C83—42no—
114C23×D83—21no—
115C23×D83—22no—
116C23×D83—21no—
117C23×D83—22no—
118C23×D83—21no—
119C23×D83—21no—
120C23×D83C22×C414yes—
121C23×D83C22×C412yes—
122C23×D83C2×D412yes—
123C23×D83C2×D414yes—
124C23×D83C2×Q812yes—
125C2×C22⋊D83C42116yes—
126C2×C22⋊D83C22⋊C4132yes—
127C2×C22⋊D83C22⋊C4116yes—
128C2×C22⋊D83C4⋊C4132yes—
129C2×C22⋊D83C4⋊C4116yes—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—216no—
135C22×Dic83—21no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—21no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—21no—
148C22×Dic83—21no—
149C22×Dic83—216no—
150C22×Dic83—48no—
151C22×Dic83—48no—
152C22×Dic83—48no—
153C22×Dic83—48no—
154C22×Dic83—48no—
155C22×Dic83C22×C412yes—
156C22×Dic83C22×C414yes—
157C22×Dic83C22×C412yes—
158C22×Dic83C22×C414yes—
159C22×Dic83C22×C414yes—
160C22×Dic83C22×C412yes—
161C22×Dic83C2×D414yes—
162C22×Dic83C2×D412yes—
163C22×Dic83C2×D414yes—
164C22×Dic83C2×Q812yes—
165C22×Dic83#4114yes—
166C2×C4×D83—216no—
167C2×C4×D83—28no—
168C2×C4×D83—28no—
169C2×C4×D83—216no—
170C2×C4×D83—48no—
171C2×C4×D83—44no—
172C2×C4×D83—48no—
173C2×C4×D83—48no—
174C2×C4×D83—48no—
175C2×C4×D83—48no—
176C2×C4×D83—48no—
177C2×C4×D83—48no—
178Dic83⋊C4—216no—
179Dic83⋊C4—28no—
180C22⋊Dic83—28no—
181(C2×D83)⋊C4—216no—
182(C2×D83)⋊C4—28no—
183C4×Dic83—216no—
184C4×Dic83—28no—
185C24×C83—21no—
186C24×C83—22no—
187C24×C83—21no—
188C24×C83—21no—
189C24×C83—22no—
190C24×C83—21no—
191C24×C83C22×C414yes—
192C24×C83C22×C412yes—
193C24×C83C2×D412yes—
194C24×C83C2×D414yes—
195C24×C83C2×Q812yes—
196C24×C83C2411yescharacteristic
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—28no—
200C22×C4×C83—22no—
201C22×C4×C83—22no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—21no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—21no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—28no—
217C22×C4×C83—44no—
218C22×C4×C83—48no—
219C22×C4×C83—48no—
220C22×C4×C83C22×C414yes—
221C22×C4×C83C22×C414yes—
222C22×C4×C83C22×C412yes—
223C22×C4×C83C22×C412yes—
224C22×C4×C83C2×D412yes—
225C22×C4×C83#4112yes—
226C22⋊C4×C83—216no—
227C23×C83—22no—
228C23×C83—24no—
229C23×C83—24no—
230C23×C83—22no—
231C23×C83—22no—
232C23×C83—24no—
233C23×C83—24no—
234C23×C83—22no—
235C23×C83—24no—
236C23×C83—22no—
237C23×C83—24no—
238C23×C83—24no—
239C23×C83—24no—
240C23×C83—24no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—24no—
244C23×C83—22no—
245C23×C83C2×C4214yes—
246C23×C83C2×C22⋊C418yes—
247C23×C83C2×C22⋊C414yes—
248C23×C83C2×C4⋊C418yes—
249C23×C83C2×C4⋊C414yes—
250C23×C83C23×C412yes—
251C23×C83C23×C411yescharacteristic
252C23×C83C22×D412yes—
253C23×C83C22×D411yescharacteristic
254C23×C83C22×D411yescharacteristic
255C23×C83C22×Q811yescharacteristic
256C23×C83C2×#4112yes—
257C23×C83C2×#4111yescharacteristic
258C23×C83H(5,𝔽2)12yes—
259C23×C83H(5,𝔽2)11yescharacteristic
260C23×C832−1+411yescharacteristic
261C22×D83—24no—
262C22×D83—22no—
263C22×D83—24no—
264C22×D83—22no—
265C22×D83—24no—
266C22×D83—22no—
267C22×D83—24no—
268C22×D83—22no—
269C22×D83—24no—
270C22×D83—22no—
271C22×D83—24no—
272C22×D83—24no—
273C22×D83—24no—
274C22×D83—24no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—24no—
278C22×D83—22no—
279C22×D83C2×C4214yes—
280C22×D83C2×C22⋊C418yes—
281C22×D83C2×C22⋊C414yes—
282C22×D83C2×C4⋊C414yes—
283C22×D83C2×C4⋊C418yes—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—24no—
287C2×C4×C83—24no—
288C2×C4×C83—24no—
289C2×C4×C83—24no—
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—24no—
297C2×C4×C83—416no—
298C2×C4×C83—42no—
299C2×C4×C83—42no—
300C2×C4×C83—42no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83—42no—
305C2×C4×C83—42no—
306C2×C4×C83—42no—
307C2×C4×C83—42no—
308C2×C4×C83C4×D414yescomplemented
309C22⋊D83#95164yescomplemented
310C2×Dic83—24no—
311C2×Dic83—24no—
312C2×Dic83—24no—
313C2×Dic83—24no—
314C2×Dic83—24no—
315C2×Dic83—24no—
316C2×Dic83—22no—
317C2×Dic83—24no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—24no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—24no—
324C2×Dic83—22no—
325C2×Dic83—432no—
326C2×Dic83—42no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329C2×Dic83—42no—
330C2×Dic83—42no—
331C2×Dic83—42no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83C2×C4214yes—
335C2×Dic83C2×C22⋊C418yes—
336C2×Dic83C2×C22⋊C414yes—
337C2×Dic83C2×C4⋊C414yes—
338C2×Dic83C2×C4⋊C418yes—
339C2×Dic83C4×D418yescomplemented
340C4×D83—432no—
341C4×D83—416no—
342C22×C83—28no—
343C22×C83—24no—
344C22×C83—24no—
345C22×C83—28no—
346C22×C83—24no—
347C22×C83—28no—
348C22×C83—24no—
349C22×C83—28no—
350C22×C83—24no—
351C22×C83—24no—
352C22×C83C2×#9518yescomplemented
353C22×C83C22×C4211yescharacteristic
354C22×C83C22×C22⋊C411yescharacteristic
355C22×C83C22×C22⋊C412yes—
356C22×C83C22×C4⋊C411yescharacteristic
357C22×C83C22×C4⋊C412yes—
358C22×C83C2×C4×D412yes—
359C22×C83C2×C4×D411yescharacteristic
360C22×C83C4×#4112yes—
361C22×C83C4×#4111yescharacteristic
362C22×C83#51812yes—
363C22×C83#51811yescharacteristic
364C22×C83#52012yes—
365C22×C83#52011yescharacteristic
366C22×C83D4212yes—
367C22×C83D4211yescharacteristic
368C22×C83#54612yes—
369C22×C83#54612yes—
370C22×C83#54612yes—
371C22×C83#54712yes—
372C22×C83#54711yescharacteristic
373C22×C83D4×Q811yescharacteristic
374C22×C83#55412yes—
375C22×C83#55411yescharacteristic
376C2×D83—24no—
377C2×D83—28no—
378C2×D83—24no—
379C2×D83—28no—
380C2×D83—24no—
381C2×D83—28no—
382C2×D83—24no—
383C2×D83—28no—
384C2×D83—24no—
385C2×D83—24no—
386C2×D83C2×#9518yescomplemented
387C4×C83—24no—
388C4×C83—44no—
389C4×C83—42no—
390C4×C83—44no—
391Dic83—28no—
392Dic83—42no—
393Dic83—44no—
394Dic83—42no—
395Dic83C2×#9518yescomplemented
396D4×#95—831nomaximal, Sylow
397C2×C83—28no—
398C2×C83C22×#9511yescharacteristic
399C2×C83C42×D411yescharacteristic
400C2×C83#227511yescharacteristic
401C2×C83D4×C22⋊C411yescharacteristic
402C2×C83D4×C22⋊C412yes—
403C2×C83#233911yescharacteristic
404C2×C83#233912yes—
405C2×C83D4×C4⋊C411yescharacteristic
406C2×C83D4×C4⋊C412yes—
407C2×C83#234911yescharacteristic
408C2×C83#234912yes—
409D83—28no—
410C22×C4×D4—831no—
411C22×C4×D4—832no—
412C22×#95—831no—
413C22×#95—831no—
414C4⋊#95—831no—
415C4⋊#95—832no—
416C22⋊#95—831no—
417C22⋊#95—832no—
418C22⋊#95—832no—
419C22⋊#95D8311yescharacteristic, complemented
420C4×#95—831no—
421C83D4×#9511yescharacteristic, complemented, Sylow
422C23×D4—831no—
423C24×C4—832no—
424C24×C4—832no—
425C24×C4—831no—
426C24×C4C2×D8311yescharacteristic
427C2×C4×D4—838no—
428C2×C4×D4—8316no—
429C2×C4×D4—1668no—
430C2×C4×D4—1668no—
431C2×C4×D4—1668no—
432C22×C4⋊C4—831no—
433C22×C4⋊C4—832no—
434C22×C22⋊C4—831no—
435C22×C22⋊C4—831no—
436C22×C22⋊C4—832no—
437C22×C22⋊C4C2×D8312yes—
438C22×C42—832no—
439C22×C42—831no—
440C2×#95—832no—
441C2×#95—832no—
442C2×#95—831no—
443C2×#95—832no—
444C2×#95—832no—
445C2×#95—832no—
446C2×#95—831no—
447C2×#95—1664no—
448C2×#95—1664no—
449C2×#95C2×D8311yescharacteristic
450C2×#95C2×D8311yescharacteristic
451C2×#95C2×D8312yes—
452C25—831no—
453C25C22×D8311yescharacteristic
454C22×D4—834no—
455C22×D4—838no—
456C22×D4—834no—
457C22×D4—838no—
458C22×D4—834no—
459C23×C4—24no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—42no—
463C23×C4—3322no—
464C23×C4—3322no—
465C23×C4—3322no—
466C23×C4—3322no—
467C23×C4—3322no—
468C23×C4—838no—
469C23×C4—838no—
470C23×C4—834no—
471C23×C4—831no—
472C23×C4—832no—
473C23×C4—831no—
474C23×C4—832no—
475C23×C4—831no—
476C23×C4—1664no—
477C23×C4—1664no—
478C23×C4—1664no—
479C23×C4—1664no—
480C23×C4—1664no—
481C23×C4—1664no—
482C23×C4—1664no—
483C23×C4—1664no—
484C23×C4—1664no—
485C23×C4—1662no—
486C23×C4—1662no—
487C23×C4C4×D8314yescomplemented
488C23×C4C22×D8312yes—
489C23×C4C22×D8311yescharacteristic
490C23×C4C22×D8312yes—
491C23×C4C22×D8311yescharacteristic
492C4×D4—16664no—
493C4×D4—16632no—
494C2×C4⋊C4—834no—
495C2×C4⋊C4—838no—
496C2×C4⋊C4—1664no—
497C2×C4⋊C4—1664no—
498C2×C4⋊C4—1664no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—838no—
504C2×C22⋊C4—1664no—
505C2×C22⋊C4—1664no—
506C2×C22⋊C4—1664no—
507C2×C22⋊C4—1664no—
508C2×C22⋊C4C4×D8318yescomplemented
509C2×C42—838no—
510C2×C42—834no—
511C2×C42—1664no—
512C2×C42—1664no—
513C2×C42—1664no—
514#95—22no—
515#95—22no—
516#95—42no—
517#95—3322no—
518#95—3322no—
519#95—834no—
520#95—1664no—
521#95—1664no—
522#95—1664no—
523#95—1662no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—834no—
531C24—832no—
532C24—834no—
533C24—832no—
534C24—832no—
535C24—1661no—
536C24—1662no—
537C24—1661no—
538C24—1662no—
539C24—1661no—
540C24—1661no—
541C24C2×C4×D8312yes—
542C24C2×C4×D8314yes—
543C24D4×D8312yes—
544C24D4×D8314yes—
545C24Q8×D8312yes—
546C24C23×D8311yescharacteristic
547C2×D4—8316no—
548C2×D4—8332no—
549C2×D4—8316no—
550C2×D4—8316no—
551C2×D4—8332no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—3328no—
576C22×C4—3328no—
577C22×C4—3324no—
578C22×C4—3328no—
579C22×C4—3328no—
580C22×C4—3328no—
581C22×C4—3328no—
582C22×C4—3328no—
583C22×C4—3328no—
584C22×C4—3328no—
585C22×C4—3328no—
586C22×C4—3328no—
587C22×C4—3328no—
588C22×C4—834no—
589C22×C4—832no—
590C22×C4—834no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—834no—
594C22×C4—834no—
595C22×C4—834no—
596C22×C4—832no—
597C22×C4—834no—
598C22×C4—832no—
599C22×C4—16616no—
600C22×C4—1668no—
601C22×C4—16616no—
602C22×C4—16616no—
603C22×C4—1661no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1661no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1661no—
615C22×C4—1662no—
616C22×C4—1661no—
617C22×C4—16616no—
618C22×C4—1668no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1662no—
623C22×C4C2×C4×D8314yes—
624C22×C4C2×C4×D8312yes—
625C22×C4C2×C4×D8314yes—
626C22×C4C2×C4×D8312yes—
627C22×C4D4×D8312yes—
628C22×C4#1305058912yes—
629C4⋊C4—16616no—
630C4⋊C4—1668no—
631C22⋊C4—216no—
632C22⋊C4—16616no—
633C22⋊C4—1668no—
634C22⋊C4—1668no—
635C42—1668no—
636C42—16616no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—834no—
656C23—834no—
657C23—838no—
658C23—834no—
659C23—838no—
660C23—1664no—
661C23—1662no—
662C23—1664no—
663C23—1664no—
664C23—1664no—
665C23—1664no—
666C23—1662no—
667C23—1662no—
668C23—1664no—
669C23—1662no—
670C23—1664no—
671C23—1662no—
672C23—1664no—
673C23—1662no—
674C23—1664no—
675C23—1662no—
676C23—1664no—
677C23—1662no—
678C23C42×D8314yes—
679C23C22⋊C4×D8318yes—
680C23C22⋊C4×D8314yes—
681C23C4⋊C4×D8314yes—
682C23C4⋊C4×D8318yes—
683C23C22×C4×D8312yes—
684C23C22×C4×D8311yescharacteristic
685C23C2×D4×D8311yescharacteristic
686C23C2×D4×D8312yes—
687C23C2×D4×D8311yescharacteristic
688C23C2×Q8×D8311yescharacteristic
689C23#41×D8312yes—
690C23C2×#1305058911yescharacteristic
691C23#1458183712yes—
692C23#1458183811yescharacteristic
693C23#1458183911yescharacteristic
694D4—8364no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—33216no—
720C2×C4—33232no—
721C2×C4—3322no—
722C2×C4—3322no—
723C2×C4—3322no—
724C2×C4—3322no—
725C2×C4—3322no—
726C2×C4—3322no—
727C2×C4—3322no—
728C2×C4—3322no—
729C2×C4—33232no—
730C2×C4—834no—
731C2×C4—834no—
732C2×C4—838no—
733C2×C4—834no—
734C2×C4—838no—
735C2×C4—838no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1664no—
739C2×C4—1664no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1664no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—1664no—
746C2×C4—1664no—
747C2×C4—1664no—
748C2×C4—1664no—
749C2×C4—1664no—
750C2×C4—1664no—
751C2×C4(C22⋊D83)⋊C414yescomplemented
752C22—24no—
753C22—28no—
754C22—24no—
755C22—28no—
756C22—24no—
757C22—28no—
758C22—24no—
759C22—28no—
760C22—24no—
761C22—24no—
762C22—838no—
763C22—1664no—
764C22—1668no—
765C22—1664no—
766C22—1668no—
767C22—1664no—
768C22—1668no—
769C22—1664no—
770C22—1668no—
771C22—1664no—
772C22—1664no—
773C22#95×D8318yescomplemented
774C22C2×C42×D8311yescharacteristic
775C22C2×C22⋊C4×D8311yescharacteristic
776C22C2×C22⋊C4×D8312yes—
777C22C2×C4⋊C4×D8311yescharacteristic
778C22C2×C4⋊C4×D8312yes—
779C22C4×D4×D8312yes—
780C22C2×(C22⋊D83)⋊C411yescharacteristic
781C22C4×#1305058912yes—
782C22#1912816911yescharacteristic
783C22#1912817312yes—
784C22#1912817411yescharacteristic
785C22#1912818012yes—
786C22#1912818111yescharacteristic
787C22#1912833312yes—
788C22#1912833511yescharacteristic
789C22#1912833812yes—
790C22#1912834012yes—
791C22#1912834312yes—
792C22#1912834912yes—
793C22#1912835111yescharacteristic
794C22#1912836411yescharacteristic
795C22#1912840512yes—
796C22#1912840911yescharacteristic
797C4—24no—
798C4—42no—
799C4—44no—
800C4—44no—
801C4—3322no—
802C4—3324no—
803C4—3322no—
804C4—838no—
805C4—1668no—
806C2—28no—
807C2—1668no—
808C2C2×#95×D8311yescharacteristic
809C2C4×(C22⋊D83)⋊C411yescharacteristic
810C2#2490982211yescharacteristic
811C2#2491027911yescharacteristic
812C2#2491028112yes—
813C2#2491028711yescharacteristic
814C2#2491028912yes—
815C2#2491035911yescharacteristic
816C2#2491036112yes—
817C2#2491036711yescharacteristic
818C2#2491036912yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC83×C22⋊#95C2
socle, cosocleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC22⋊#95D83
hypocenterC83D4×#95
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C22×C83⋊#95C2semidirect
4. C2×#95×D83C2semidirect
5. Dic83⋊#95C2semidirect
6. Dic83⋊#95C2semidirect
7. #24905685C2semidirect
8. (C2×D83)⋊#95C2semidirect
9. (C2×D83)⋊#95C2semidirect
10. #95×Dic83C2semidirect
11. C83×C22⋊#95C2semidirect
17. C2×C4×C22⋊D83C4semidirect
20. C2×(C22⋊D83)⋊C4C4semidirect
54. C23×Dic83C2×C4semidirect
70. C22×C4×D83C2×C4semidirect
71. C22×C4×D83C2×C4semidirect
77. C2×Dic83⋊C4C2×C4semidirect
78. C2×Dic83⋊C4C2×C4semidirect
80. C2×C22⋊Dic83C2×C4semidirect
84. C2×(C2×D83)⋊C4C2×C4semidirect
85. C2×(C2×D83)⋊C4C2×C4semidirect
89. C2×C4×Dic83C2×C4semidirect
90. C2×C4×Dic83C2×C4semidirect
97. C83⋊#95D4semidirect
103. C23×C4×C83C2×C4semidirect
110. C2×C22⋊C4×C83C2×C4semidirect
308. C2×C4×C83C4×D4semidirect
309. C22⋊D83#95semidirect
339. C2×Dic83C4×D4semidirect
352. C22×C83C2×#95semidirect
386. C2×D83C2×#95semidirect
395. Dic83C2×#95semidirect
419. C22⋊#95D83semidirect
421. C83D4×#95semidirect
487. C23×C4C4×D83semidirect
508. C2×C22⋊C4C4×D83semidirect
751. C2×C4(C22⋊D83)⋊C4semidirect
773. C22#95×D83semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C22×(C22⋊D83)⋊C42
C22×C83⋊#952
C2×#95×D832
Dic83⋊#952
#249056852
(C2×D83)⋊#952
#95×Dic832
C83×C22⋊#952
D4×#9583