Finite Group Databasebeta

← C2×#24910535 #35564012

Subgroups — C2×#24910535 #35564012

Order 21248.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581778C211yesmaximal, characteristic
2C22×C4×Dic166C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D83C211yesmaximal, characteristic
4#24910535C2116yesmaximal, direct product factor
5C2×#19127605C211yesmaximal, characteristic, complemented
6C2×#19127601C211yesmaximal, characteristic
7C2×#19127595C211yesmaximal, characteristic, complemented
8C2×#19127594C211yesmaximal, characteristic, complemented
9C2×#19127592C211yesmaximal, characteristic, complemented
10C2×#19127592C211yesmaximal, characteristic, complemented
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127574C211yesmaximal, characteristic, complemented
13C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
14C2×#19127552C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581778C4116yescomplemented
21C2×#14581778C2218yes—
22C2×C4×Dic166—28no—
23C2×C4×Dic166C2218yescomplemented
24C2×C4×C22⋊D83—28no—
25C2×C4×C22⋊D83C2218yes—
26C22×C4⋊Dic83C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41C22×C4×Dic83C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic
44C22×C4×Dic83C2211yescharacteristic
45#19127605C2218yescomplemented
46#19127601C2218yes—
47#19127595C2218yescomplemented
48#19127594C2218yescomplemented
49#19127592C2218yescomplemented
50#19127592C2218yescomplemented
51#19127575C2218yescomplemented
52#19127574C2218yescomplemented
53C4×Dic83⋊C4C2218yescomplemented
54#19127552C2218yescomplemented
55#19127548C2218yescomplemented
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C24×C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66C22×C42×C83C2211yescharacteristic
67C4×C22⋊C4×C83C2218yescomplemented
68C2×#95×C83C2211yescharacteristic
69C2×#95×C83C2211yescharacteristic
70C24×D83C2311yescharacteristic
71C22×Dic166—24no—
72C22×Dic166—24no—
73C22×Dic166C2×C418yescomplemented
74C22×Dic166C2314yes—
75C22×C22⋊D83—24no—
76C22×C22⋊D83—24no—
77C22×C22⋊D83C2×C418yes—
78C22×C22⋊D83C2314yes—
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C22×C4×D83—24no—
87C22×C4×D83—24no—
88C22×C4×D83—42no—
89C22×C4×D83C2314yes—
90#14581778C2×C4164yescomplemented
91C4×Dic166—232no—
92C4×C22⋊D83—232no—
93C2×C4⋊Dic83—24no—
94C2×C4⋊Dic83C2314yes—
95C2×Dic83⋊C4—24no—
96C2×Dic83⋊C4—24no—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4D418yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×C22⋊Dic83—24no—
106C2×C22⋊Dic83—42no—
107C2×C22⋊Dic83C2×C418yescomplemented
108C2×C22⋊Dic83C2314yes—
109C2×C22⋊Dic83C2314yes—
110C2×C22⋊Dic83C2314yes—
111C2×(C2×D83)⋊C4—24no—
112C2×(C2×D83)⋊C4—24no—
113C2×(C2×D83)⋊C4—42no—
114C2×(C2×D83)⋊C4C2×C418yescomplemented
115C2×(C2×D83)⋊C4C2×C418yescomplemented
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×C4×Dic83—24no—
122C2×C4×Dic83—24no—
123C2×C4×Dic83—24no—
124C2×C4×Dic83—42no—
125C2×C4×Dic83C2×C418yescomplemented
126C2×C4×Dic83C2314yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2314yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C25×C83C2311yescharacteristic
138C23×C4×C83—24no—
139C23×C4×C83—24no—
140C23×C4×C83—42no—
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2314yes—
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148C2×C22⋊C4×C83—24no—
149C2×C22⋊C4×C83C2×C418yescomplemented
150C2×C22⋊C4×C83C2314yes—
151C2×C22⋊C4×C83C2314yes—
152C2×C42×C83—24no—
153C2×C42×C83—42no—
154C2×C42×C83C2314yes—
155C2×C42×C83C2314yes—
156#95×C83C2314yes—
157#95×C83C2314yes—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83C22×C414yes—
165C23×D83C2412yes—
166C2×Dic166—232no—
167C2×Dic166—28no—
168C2×Dic166—28no—
169C2×Dic166C22×C4116yescomplemented
170C2×C22⋊D83—232no—
171C2×C22⋊D83—28no—
172C2×C22⋊D83—28no—
173C2×C22⋊D83C22×C4116yes—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83—22no—
188C22×Dic83—22no—
189C22×Dic83C22×C414yes—
190C22×Dic83C22×C414yes—
191C22×Dic83C22×C414yes—
192C22×Dic83C2×D414yes—
193C22×Dic83C2×D414yes—
194C22×Dic83#4114yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2412yes—
199C22×Dic83C2412yes—
200C22×Dic83C2412yes—
201C22×Dic83C2412yes—
202C2×C4×D83—28no—
203C2×C4×D83—28no—
204C2×C4×D83—44no—
205C2×C4×D83—416no—
206C4⋊Dic83—28no—
207Dic83⋊C4—28no—
208Dic83⋊C4—28no—
209Dic83⋊C4—28no—
210Dic83⋊C4—28no—
211Dic83⋊C4C2×D4116yes—
212C22⋊Dic83—28no—
213C22⋊Dic83—44no—
214C22⋊Dic83C22×C4116yescomplemented
215(C2×D83)⋊C4—28no—
216(C2×D83)⋊C4—28no—
217(C2×D83)⋊C4—44no—
218(C2×D83)⋊C4C22×C4116yescomplemented
219(C2×D83)⋊C4C22×C4116yescomplemented
220C4×Dic83—28no—
221C4×Dic83—28no—
222C4×Dic83—28no—
223C4×Dic83—44no—
224C4×Dic83C22×C4116yescomplemented
225C24×C83—22no—
226C24×C83—22no—
227C24×C83—22no—
228C24×C83—22no—
229C24×C83—22no—
230C24×C83—22no—
231C24×C83C22×C414yes—
232C24×C83C2412yes—
233C24×C83C2411yescharacteristic
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—28no—
248C22×C4×C83—28no—
249C22×C4×C83—44no—
250C22×C4×C83—416no—
251C22×C4×C83C22×C414yes—
252C22×C4×C83C22×C414yes—
253C22×C4×C83C2×D414yes—
254C22×C4×C83#4114yes—
255C22×C4×C83#4114yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C22×C4×C83C2412yes—
262C22⋊C4×C83—28no—
263C22⋊C4×C83C22×C4116yescomplemented
264C42×C83—28no—
265C42×C83—44no—
266C23×C83—28no—
267C23×C83—28no—
268C23×C83—28no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—44no—
276C23×C83—44no—
277C23×C83—44no—
278C23×C83—44no—
279C23×C83C23×C414yes—
280C23×C83C23×C412yes—
281C23×C83C22×D412yes—
282C23×C83C2×#4112yes—
283C23×C83C2×#4112yes—
284C23×C83C2×#4112yes—
285C23×C83H(5,𝔽2)12yes—
286C23×C832−1+412yes—
287C23×C83C2511yescharacteristic
288C22×D83—28no—
289C22×D83—28no—
290C22×D83—28no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—44no—
298C22×D83—44no—
299C22×D83—44no—
300C22×D83—44no—
301C22×D83C23×C414yes—
302C2×C4×C83—28no—
303C2×C4×C83—28no—
304C2×C4×C83—28no—
305C2×C4×C83—28no—
306C2×C4×C83—28no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—416no—
321C2×C4×C83—44no—
322C2×C4×C83C23×C414yes—
323C2×C4×C83C23×C414yes—
324C2×C4×C83C22×D414yes—
325C2×C4×C83C2×#4114yes—
326C2×C4×C83C2×#4114yes—
327C22⋊D83—232no—
328C2×Dic83—28no—
329C2×Dic83—28no—
330C2×Dic83—28no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—44no—
347C2×Dic83—44no—
348C2×Dic83—44no—
349C2×Dic83C4×D4116yes—
350C2×Dic83C23×C414yes—
351C2×Dic83C23×C414yes—
352C2×Dic83C23×C414yes—
353C2×Dic83C22×D414yes—
354C2×Dic83C22×D414yes—
355C2×Dic83C2×#4114yes—
356C4×D83—416no—
357Dic166—232no—
358C22×C83—24no—
359C22×C83—24no—
360C22×C83—24no—
361C22×C83—416no—
362C22×C83—42no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83C2×C4×D414yes—
367C22×C83C4×#4114yes—
368C22×C83#52014yes—
369C22×C83#54614yes—
370C22×C83#54814yes—
371C22×C83#55614yes—
372C22×C83#55914yes—
373C22×C83C24×C411yescharacteristic
374C22×C83C23×D411yescharacteristic
375C22×C83C22×#4111yescharacteristic
376C22×C83C22×#4111yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C2×H(5,𝔽2)11yescharacteristic
379C22×C83C2×2−1+411yescharacteristic
380C2×D83—24no—
381C2×D83—24no—
382C2×D83—24no—
383C2×D83—416no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C4×C83—24no—
389C4×C83—24no—
390C4×C83—24no—
391C4×C83—24no—
392C4×C83—24no—
393C4×C83—42no—
394Dic83—24no—
395Dic83—24no—
396Dic83—24no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83C2×C4×D418yes—
401C2×#2367—831nomaximal, Sylow
402C2×C83—44no—
403C2×C83#236718yescomplemented
404C2×C83C22×C4×D411yescharacteristic
405C2×C83C2×C4×#4111yescharacteristic
406C2×C83C2×#52011yescharacteristic
407C2×C83C2×#54611yescharacteristic
408C2×C83C2×#54811yescharacteristic
409C2×C83C2×#55611yescharacteristic
410C2×C83C2×#55911yescharacteristic
411D83—44no—
412C22×#124—831no—
413C22×C4×Q8—831no—
414C22×C4×D4—831no—
415#2367—8316no—
416C2×#391—831no—
417C2×#390—831no—
418C2×#388—831no—
419C2×#388—831no—
420C2×#388—831no—
421C2×#388—831no—
422C2×#385—831no—
423C2×#385—831no—
424C2×C4×C4⋊C4—831no—
425C2×C4×C4⋊C4—831no—
426C2×C4×C22⋊C4—831no—
427C2×C4×C22⋊C4D8311yescharacteristic, complemented
428C83C2×#236711yescharacteristic, complemented, Sylow
429C23×Q8—831no—
430C23×D4—831no—
431C24×C4—831no—
432C24×C4C2×D8311yescharacteristic
433C2×#124—8316no—
434C2×#124—838no—
435C2×C4×Q8—838no—
436C2×C4×Q8—1668no—
437C2×C4×D4—838no—
438C2×C4×D4—1668no—
439C22×C4⋊C4—831no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4—831no—
442C22×C4⋊C4—831no—
443C22×C4⋊C4—831no—
444C22×C4⋊C4—831no—
445C22×C22⋊C4—831no—
446C22×C22⋊C4—831no—
447C22×C22⋊C4—831no—
448C22×C22⋊C4—831no—
449C22×C22⋊C4—831no—
450C22×C22⋊C4—831no—
451C22×C22⋊C4—831no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4C2×D8311yescharacteristic
454C22×C22⋊C4C2×D8311yescharacteristic
455C22×C42—831no—
456C22×C42—831no—
457C22×C42—831no—
458C22×C42—831no—
459C22×C42—831no—
460C22×C42C2×D8311yescharacteristic
461C22×C42C2×D8311yescharacteristic
462#391—838no—
463#390—838no—
464#388—838no—
465#388—838no—
466#388—838no—
467#388—838no—
468#385—838no—
469#385—838no—
470C4×C4⋊C4—838no—
471C4×C4⋊C4—838no—
472C4×C22⋊C4—838no—
473C4×C22⋊C4C2×D8318yescomplemented
474C2×#95—831no—
475C2×#95—831no—
476C2×#95—831no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95—831no—
480C2×#95C2×D8311yescharacteristic
481C2×#95C2×D8311yescharacteristic
482C25—831no—
483C25C22×D8311yescharacteristic
484C22×Q8—838no—
485C22×Q8—834no—
486C22×Q8—1664no—
487C22×Q8—1664no—
488C22×D4—838no—
489C22×D4—834no—
490C22×D4—1664no—
491C22×D4—1664no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—3322no—
496C23×C4—834no—
497C23×C4—831no—
498C23×C4—831no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4—1664no—
505C23×C4—1664no—
506C23×C4C22×D8311yescharacteristic
507C23×C4C22×D8314yes—
508C23×C4C22×D8311yescharacteristic
509C23×C4C22×D8311yescharacteristic
510C23×C4C22×D8311yescharacteristic
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8311yescharacteristic
513#124—8364no—
514C4×Q8—16632no—
515C4×D4—16632no—
516C2×C4⋊C4—838no—
517C2×C4⋊C4—834no—
518C2×C4⋊C4—834no—
519C2×C4⋊C4—834no—
520C2×C4⋊C4—834no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—1664no—
524C2×C4⋊C4—1664no—
525C2×C4⋊C4—1664no—
526C2×C4⋊C4—1664no—
527C2×C4⋊C4—1664no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—3322no—
530C2×C22⋊C4—3322no—
531C2×C22⋊C4—834no—
532C2×C22⋊C4—834no—
533C2×C22⋊C4—838no—
534C2×C22⋊C4—834no—
535C2×C22⋊C4—838no—
536C2×C22⋊C4—838no—
537C2×C22⋊C4—834no—
538C2×C22⋊C4—834no—
539C2×C22⋊C4—834no—
540C2×C22⋊C4—834no—
541C2×C22⋊C4—834no—
542C2×C22⋊C4—1664no—
543C2×C22⋊C4—1664no—
544C2×C22⋊C4—1664no—
545C2×C22⋊C4C4×D8318yescomplemented
546C2×C22⋊C4C22×D8314yes—
547C2×C22⋊C4C22×D8314yes—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—3322no—
551C2×C42—834no—
552C2×C42—838no—
553C2×C42—834no—
554C2×C42—834no—
555C2×C42—834no—
556C2×C42—834no—
557C2×C42—1664no—
558C2×C42—1664no—
559C2×C42—1664no—
560C2×C42C22×D8314yes—
561C2×C42C22×D8314yes—
562#95—834no—
563#95—834no—
564#95—834no—
565#95—834no—
566#95—834no—
567#95—834no—
568#95C22×D8314yes—
569#95C22×D8314yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—834no—
577C24—832no—
578C24—1662no—
579C24—1662no—
580C24—1662no—
581C24—1662no—
582C24—1662no—
583C24—1662no—
584C24C2×C4×D8314yes—
585C24C23×D8312yes—
586C24C23×D8311yescharacteristic
587C2×Q8—8316no—
588C2×Q8—1668no—
589C2×Q8—16632no—
590C2×Q8—1668no—
591C2×D4—8316no—
592C2×D4—1668no—
593C2×D4—16632no—
594C2×D4—1668no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—33216no—
613C22×C4—3324no—
614C22×C4—834no—
615C22×C4—834no—
616C22×C4—834no—
617C22×C4—832no—
618C22×C4—834no—
619C22×C4—834no—
620C22×C4—834no—
621C22×C4—832no—
622C22×C4—832no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—1668no—
628C22×C4—1662no—
629C22×C4—1662no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4—1662no—
633C22×C4—1662no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1668no—
638C22×C4—1662no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1662no—
642C22×C4—1662no—
643C22×C4—1662no—
644C22×C4C2×C4×D8314yes—
645C22×C4C2×C4×D8314yes—
646C22×C4D4×D8314yes—
647C22×C4#1305059014yes—
648C22×C4#1305059014yes—
649C22×C4C23×D8312yes—
650C22×C4C23×D8312yes—
651C22×C4C23×D8312yes—
652C22×C4C23×D8312yes—
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C4⋊C4—8316no—
656C4⋊C4—1668no—
657C4⋊C4—1668no—
658C4⋊C4—1668no—
659C4⋊C4—1668no—
660C4⋊C4—1668no—
661C22⋊C4—28no—
662C22⋊C4—3324no—
663C22⋊C4—3324no—
664C22⋊C4—8316no—
665C22⋊C4—8316no—
666C22⋊C4—8316no—
667C22⋊C4—1668no—
668C22⋊C4—1668no—
669C22⋊C4—1668no—
670C22⋊C4C2×C4×D83116yescomplemented
671C42—28no—
672C42—44no—
673C42—3324no—
674C42—8316no—
675C42—1668no—
676C42—1668no—
677C42—1668no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—3324no—
692C23—3324no—
693C23—3324no—
694C23—3324no—
695C23—834no—
696C23—1668no—
697C23—1668no—
698C23—1668no—
699C23—1662no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23C22×C4×D8314yes—
706C23C22×C4×D8312yes—
707C23C2×D4×D8312yes—
708C23#41×D8312yes—
709C23C2×#1305059012yes—
710C23C2×#1305059012yes—
711C23#1458183712yes—
712C23#1458183912yes—
713C23C24×D8311yescharacteristic
714Q8—16632no—
715D4—16632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—33216no—
737C2×C4—3324no—
738C2×C4—3324no—
739C2×C4—3324no—
740C2×C4—8316no—
741C2×C4—834no—
742C2×C4—834no—
743C2×C4—834no—
744C2×C4—834no—
745C2×C4—834no—
746C2×C4—834no—
747C2×C4—1662no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1668no—
757C2×C4—1668no—
758C2×C4—1668no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4C22×C4×D8314yes—
766C2×C4C22×C4×D8314yes—
767C2×C4C2×D4×D8314yes—
768C2×C4C2×#1305059014yes—
769C2×C4C2×#1305059014yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—3322no—
779C22—3322no—
780C22—3322no—
781C22—33216no—
782C22—3322no—
783C22—1664no—
784C22—1664no—
785C22—1664no—
786C22C4×D4×D8314yes—
787C22C4×#1305059014yes—
788C22#1912818014yes—
789C22#1912834114yes—
790C22#1912836014yes—
791C22#1912841914yes—
792C22#1912843414yes—
793C22C23×C4×D8311yescharacteristic
794C22C22×D4×D8311yescharacteristic
795C22C2×#41×D8311yescharacteristic
796C22C22×#1305059011yescharacteristic
797C22C22×#1305059011yescharacteristic
798C22C2×#1458183711yescharacteristic
799C22C2×#1458183911yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—838no—
810C4—1664no—
811C4—1664no—
812C4—1664no—
813C2—44no—
814C2—3324no—
815C2#2491053518yesdirect product factor
816C2C2×C4×D4×D8311yescharacteristic
817C2C2×C4×#1305059011yescharacteristic
818C2C2×#1912818011yescharacteristic
819C2C2×#1912834111yescharacteristic
820C2C2×#1912836011yescharacteristic
821C2C2×#1912841911yescharacteristic
822C2C2×#1912843411yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×C4×C22⋊C4×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C2×#2367
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic166C2semidirect
4. #24910535C2direct (N × H)
5. C2×#19127605C2semidirect
7. C2×#19127595C2semidirect
8. C2×#19127594C2semidirect
9. C2×#19127592C2semidirect
10. C2×#19127592C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127574C2semidirect
13. C2×C4×Dic83⋊C4C2semidirect
14. C2×#19127552C2semidirect
15. C2×#19127548C2semidirect
16. C2×C4×C22⋊C4×C83C2semidirect
20. C2×#14581778C4semidirect
23. C2×C4×Dic166C22semidirect
45. #19127605C22semidirect
47. #19127595C22semidirect
48. #19127594C22semidirect
49. #19127592C22semidirect
50. #19127592C22semidirect
51. #19127575C22semidirect
52. #19127574C22semidirect
53. C4×Dic83⋊C4C22semidirect
54. #19127552C22semidirect
55. #19127548C22semidirect
67. C4×C22⋊C4×C83C22semidirect
73. C22×Dic166C2×C4semidirect
90. #14581778C2×C4semidirect
107. C2×C22⋊Dic83C2×C4semidirect
114. C2×(C2×D83)⋊C4C2×C4semidirect
115. C2×(C2×D83)⋊C4C2×C4semidirect
125. C2×C4×Dic83C2×C4semidirect
149. C2×C22⋊C4×C83C2×C4semidirect
169. C2×Dic166C22×C4semidirect
214. C22⋊Dic83C22×C4semidirect
218. (C2×D83)⋊C4C22×C4semidirect
219. (C2×D83)⋊C4C22×C4semidirect
224. C4×Dic83C22×C4semidirect
263. C22⋊C4×C83C22×C4semidirect
403. C2×C83#2367semidirect
427. C2×C4×C22⋊C4D83semidirect
428. C83C2×#2367semidirect
473. C4×C22⋊C4C2×D83semidirect
545. C2×C22⋊C4C4×D83semidirect
670. C22⋊C4C2×C4×D83semidirect
815. C2#24910535direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817782
C22×C4×Dic1662
C22×C4×C22⋊D832
#249105352
C2×#191276052
C2×#191276012
C2×#191275952
C2×#191275942
C2×#191275922
C2×#191275752
C2×#191275742
C2×C4×Dic83⋊C42
C2×#191275522
C2×#191275482
C2×C4×C22⋊C4×C832
C2×#236783