Finite Group Databasebeta

← C2×#24912811 #35574609

Subgroups — C2×#24912811 #35574609

Order 21248.

3374 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×#14581754C211yesmaximal, characteristic
2C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
3#24912811C2116yesmaximal, direct product factor
4C2×#19127634C211yesmaximal, characteristic, complemented
5C2×#19127623C211yesmaximal, characteristic, complemented
6C2×#19127623C211yesmaximal, characteristic, complemented
7C2×#19127588C211yesmaximal, characteristic, complemented
8C2×#19127584C211yesmaximal, characteristic, complemented
9C2×#19127579C211yesmaximal, characteristic
10C2×#19127579C211yesmaximal, characteristic
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127575C211yesmaximal, characteristic, complemented
13C2×#19127572C211yesmaximal, characteristic, complemented
14C2×#19127572C211yesmaximal, characteristic, complemented
15C2×#19127558C211yesmaximal, characteristic, complemented
16C2×#398×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C2×#14581754—28no—
23C2×#14581754C2218yes—
24C22×C4⋊Dic83C2211yescharacteristic
25C22×C4⋊Dic83C2211yescharacteristic
26C22×C4⋊Dic83C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C2×C4⋊C4×D83—28no—
32C2×C4⋊C4×D83C2218yescomplemented
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×C4×Dic83C2211yescharacteristic
42#19127634C2218yescomplemented
43#19127623C2218yescomplemented
44#19127623C2218yescomplemented
45#19127588C2218yescomplemented
46#19127584C2218yescomplemented
47#19127579C2218yes—
48#19127579C2218yes—
49#19127575C2218yescomplemented
50#19127575C2218yescomplemented
51#19127572C2218yescomplemented
52#19127572C2218yescomplemented
53#19127558C2218yescomplemented
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65#398×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C24×D83C2311yescharacteristic
71C22×D332—24no—
72C22×D332—24no—
73C22×D332Q818yes—
74C22×D332C2314yes—
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C22×C4×D83—24no—
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83—24no—
85C22×C4×D83—24no—
86C22×C4×D83—42no—
87C22×C4×D83—42no—
88C22×C4×D83—42no—
89C22×C4×D83—42no—
90C22×C4×D83—42no—
91C22×C4×D83—42no—
92C22×C4×D83D418yes—
93C22×C4×D83C2314yes—
94C22×C4×D83C2314yes—
95C22×C4×D83C2314yes—
96C22×C4×D83C2314yes—
97#14581754—232no—
98C2×C4⋊Dic83—24no—
99C2×C4⋊Dic83—24no—
100C2×C4⋊Dic83—42no—
101C2×C4⋊Dic83C2314yes—
102C2×C4⋊Dic83C2314yes—
103C2×C4⋊Dic83C2314yes—
104C2×Dic83⋊C4—24no—
105C2×Dic83⋊C4—24no—
106C2×Dic83⋊C4—24no—
107C2×Dic83⋊C4—42no—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C4⋊C4×D83—232no—
113C2×(C2×D83)⋊C4—24no—
114C2×(C2×D83)⋊C4—24no—
115C2×(C2×D83)⋊C4—24no—
116C2×(C2×D83)⋊C4—24no—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4—24no—
119C2×(C2×D83)⋊C4—42no—
120C2×(C2×D83)⋊C4—42no—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2314yes—
129C2×C4×Dic83—24no—
130C2×C4×Dic83C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C2×C4⋊C4×C83—24no—
146C2×C4⋊C4×C83—24no—
147C2×C4⋊C4×C83—42no—
148C2×C4⋊C4×C83—42no—
149C2×C4⋊C4×C83C2314yes—
150C2×C4⋊C4×C83C2314yes—
151C2×C4⋊C4×C83C2314yes—
152C2×C4⋊C4×C83C2314yes—
153#95×C83C2314yes—
154#95×C83C2314yes—
155#95×C83C2314yes—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83—22no—
159C23×D83—22no—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83C2×D414yes—
167C23×D83C2×Q814yes—
168C23×D83C2×Q814yes—
169C23×D83#4114yes—
170C23×D83C2412yes—
171C23×D83C2412yes—
172C2×D332—232no—
173C2×D332—28no—
174C2×D332—28no—
175C2×D332C2×Q8116yes—
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×Dic83—22no—
190C22×Dic83—22no—
191C22×Dic83—22no—
192C22×Dic83C2×D414yes—
193C22×Dic83#4114yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2412yes—
199C22×Dic83C2412yes—
200C2×C4×D83—232no—
201C2×C4×D83—28no—
202C2×C4×D83—28no—
203C2×C4×D83—28no—
204C2×C4×D83—28no—
205C2×C4×D83—28no—
206C2×C4×D83—416no—
207C2×C4×D83—44no—
208C2×C4×D83—44no—
209C2×C4×D83—44no—
210C2×C4×D83—44no—
211C2×C4×D83—44no—
212C2×C4×D83—44no—
213C2×C4×D83—416no—
214C2×C4×D83—416no—
215C2×C4×D83C2×D4116yes—
216C4⋊Dic83—28no—
217C4⋊Dic83—28no—
218C4⋊Dic83—44no—
219Dic83⋊C4—28no—
220Dic83⋊C4—28no—
221Dic83⋊C4—28no—
222Dic83⋊C4—44no—
223(C2×D83)⋊C4—28no—
224(C2×D83)⋊C4—28no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4—28no—
227(C2×D83)⋊C4—28no—
228(C2×D83)⋊C4—28no—
229(C2×D83)⋊C4—44no—
230(C2×D83)⋊C4—44no—
231C4×Dic83—28no—
232C24×C83C2411yescharacteristic
233C22×C4×C83—22no—
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—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83C2×D414yes—
252C22×C4×C83C2×Q814yes—
253C22×C4×C83#4114yes—
254C22×C4×C83C2412yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C4⋊C4×C83—28no—
262C4⋊C4×C83—28no—
263C4⋊C4×C83—44no—
264C4⋊C4×C83—44no—
265C23×C83C22×D412yes—
266C23×C83C22×Q812yes—
267C23×C83C2×#4112yes—
268C23×C83C2×#4112yes—
269C23×C83C2×#4112yes—
270C23×C83H(5,𝔽2)12yes—
271C23×C83H(5,𝔽2)12yes—
272C23×C83C2511yescharacteristic
273C22×D83—28no—
274C22×D83—28no—
275C22×D83—28no—
276C22×D83—28no—
277C22×D83—28no—
278C22×D83—28no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—28no—
284C22×D83—28no—
285C22×D83—28no—
286C22×D83—22no—
287C22×D83—22no—
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—44no—
293C22×D83—44no—
294C22×D83—44no—
295C22×D83—44no—
296C22×D83C22⋊Q8116yes—
297C22×D83C22×D414yes—
298C22×D83C22×Q814yes—
299C22×D83C22×Q814yes—
300C22×D83C2×#4114yes—
301C2×C4×C83—28no—
302C2×C4×C83—28no—
303C2×C4×C83—28no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
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—22no—
321C2×C4×C83—22no—
322C2×C4×C83—44no—
323C2×C4×C83—44no—
324C2×C4×C83—44no—
325C2×C4×C83—44no—
326C2×C4×C83C22×D414yes—
327C2×C4×C83C22×Q814yes—
328C2×C4×C83C2×#4114yes—
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—22no—
347C2×Dic83—44no—
348C2×Dic83—44no—
349C2×Dic83—44no—
350C2×Dic83—44no—
351C2×Dic83C22×D414yes—
352C2×Dic83C2×#4114yes—
353D332—232no—
354C4×D83—232no—
355C4×D83—416no—
356C4×D83—416no—
357C4×D83—416no—
358C22×C83C2×C22⋊Q814yes—
359C22×C83#52514yes—
360C22×C83#53414yes—
361C22×C83#55314yes—
362C22×C83#55314yes—
363C22×C83#55414yes—
364C22×C83#55414yes—
365C22×C83C23×D411yescharacteristic
366C22×C83C23×Q811yescharacteristic
367C22×C83C22×#4111yescharacteristic
368C22×C83C22×#4111yescharacteristic
369C22×C83C22×#4111yescharacteristic
370C22×C83C2×H(5,𝔽2)11yescharacteristic
371C22×C83C2×H(5,𝔽2)11yescharacteristic
372C2×D83—232no—
373C2×D83—24no—
374C2×D83—24no—
375C2×D83—24no—
376C2×D83—24no—
377C2×D83—24no—
378C2×D83—24no—
379C2×D83—24no—
380C2×D83—24no—
381C2×D83—24no—
382C2×D83—416no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83C2×C22⋊Q818yes—
388C4×C83—24no—
389C4×C83—24no—
390C4×C83—24no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395Dic83—24no—
396Dic83—24no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83—42no—
401C2×#2579—831nomaximal, Sylow
402C2×C83#257918yescomplemented
403C2×C83C22×C22⋊Q811yescharacteristic
404C2×C83C2×#52511yescharacteristic
405C2×C83C2×#53411yescharacteristic
406C2×C83C2×#55311yescharacteristic
407C2×C83C2×#55311yescharacteristic
408C2×C83C2×#55411yescharacteristic
409C2×C83C2×#55411yescharacteristic
410D83—28no—
411D83—44no—
412C22×C4×D4—831no—
413C23×C4⋊C4—831no—
414#2579—8316no—
415C2×#398—831no—
416C2×#398D8311yescharacteristic, complemented
417C2×#396—831no—
418C2×#396—831no—
419C2×#387—831no—
420C2×#387—831no—
421C2×#386—831no—
422C2×#386—831no—
423C2×#385—831no—
424C2×#385—831no—
425C2×#385—831no—
426C2×#385—831no—
427C2×#380—831no—
428C83C2×#257911yescharacteristic, complemented, Sylow
429C23×D4—831no—
430C24×C4—831no—
431C24×C4—831no—
432C24×C4—831no—
433C24×C4—831no—
434C2×C4×D4—838no—
435C2×C4×D4—1668no—
436C22×C4⋊C4—831no—
437C22×C4⋊C4—831no—
438C22×C4⋊C4—831no—
439C22×C4⋊C4—831no—
440C22×C4⋊C4—831no—
441C22×C4⋊C4—831no—
442C22×C4⋊C4—831no—
443C22×C4⋊C4—838no—
444C22×C4⋊C4—1668no—
445C22×C4⋊C4C2×D8311yescharacteristic
446C22×C4⋊C4C2×D8311yescharacteristic
447C22×C4⋊C4C2×D8311yescharacteristic
448C22×C4⋊C4C2×D8311yescharacteristic
449C22×C22⋊C4—831no—
450C22×C22⋊C4—831no—
451C22×C22⋊C4—831no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4—831no—
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—831no—
457C22×C42—831no—
458#398—838no—
459#398C2×D8318yescomplemented
460#396—838no—
461#396—838no—
462#387—838no—
463#387—838no—
464#386—838no—
465#386—838no—
466#385—838no—
467#385—838no—
468#385—838no—
469#385—838no—
470#380—838no—
471C2×#95—831no—
472C2×#95—831no—
473C2×#95—831no—
474C2×#95—831no—
475C2×#95—831no—
476C2×#95—831no—
477C2×#95—831no—
478C2×#95C2×D8311yescharacteristic
479C2×#95C2×D8311yescharacteristic
480C2×#95C2×D8311yescharacteristic
481C25—831no—
482C25—831no—
483C22×D4—838no—
484C22×D4—834no—
485C22×D4—1664no—
486C22×D4—1664no—
487C23×C4—3322no—
488C23×C4—3322no—
489C23×C4—3322no—
490C23×C4—3322no—
491C23×C4—3322no—
492C23×C4—3322no—
493C23×C4—838no—
494C23×C4—834no—
495C23×C4—834no—
496C23×C4—834no—
497C23×C4—831no—
498C23×C4—831no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—834no—
504C23×C4—1664no—
505C23×C4—1664no—
506C23×C4—1664no—
507C23×C4—1664no—
508C23×C4—1664no—
509C23×C4C22×D8311yescharacteristic
510C23×C4C22×D8311yescharacteristic
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8311yescharacteristic
513C23×C4C22×D8311yescharacteristic
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8311yescharacteristic
516C4×D4—16632no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—42no—
521C2×C4⋊C4—3322no—
522C2×C4⋊C4—3322no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—16632no—
531C2×C4⋊C4—1664no—
532C2×C4⋊C4—1664no—
533C2×C4⋊C4—1664no—
534C2×C4⋊C4—1664no—
535C2×C4⋊C4—1664no—
536C2×C4⋊C4C22×D8314yes—
537C2×C4⋊C4C22×D8314yes—
538C2×C4⋊C4C22×D8314yes—
539C2×C4⋊C4C22×D8314yes—
540C2×C22⋊C4—3322no—
541C2×C22⋊C4—3322no—
542C2×C22⋊C4—834no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—834no—
550C2×C22⋊C4—1664no—
551C2×C22⋊C4—1664no—
552C2×C22⋊C4—1664no—
553C2×C22⋊C4—1664no—
554C2×C22⋊C4—1664no—
555C2×C22⋊C4—1664no—
556C2×C42—834no—
557C2×C42—1664no—
558#95—834no—
559#95—834no—
560#95—834no—
561#95—834no—
562#95—834no—
563#95—834no—
564#95—834no—
565#95C22×D8314yes—
566#95C22×D8314yes—
567#95C22×D8314yes—
568C24—834no—
569C24—834no—
570C24—834no—
571C24—832no—
572C24—834no—
573C24—832no—
574C24—1662no—
575C24—1662no—
576C24—1662no—
577C24—1662no—
578C24—1662no—
579C24—1662no—
580C24—1662no—
581C24—1662no—
582C24—1662no—
583C24—1662no—
584C24C23×D8311yescharacteristic
585C2×D4—8316no—
586C2×D4—1668no—
587C2×D4—16632no—
588C2×D4—1668no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
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—33216no—
608C22×C4—3324no—
609C22×C4—3324no—
610C22×C4—3324no—
611C22×C4—3324no—
612C22×C4—3324no—
613C22×C4—3324no—
614C22×C4—33216no—
615C22×C4—33216no—
616C22×C4—8316no—
617C22×C4—834no—
618C22×C4—834no—
619C22×C4—832no—
620C22×C4—832no—
621C22×C4—832no—
622C22×C4—832no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—1668no—
626C22×C4—1668no—
627C22×C4—1668no—
628C22×C4—1668no—
629C22×C4—16632no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4—1662no—
633C22×C4—1662no—
634C22×C4—1662no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1662no—
638C22×C4—1662no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1662no—
642C22×C4—1662no—
643C22×C4—1662no—
644C22×C4—1662no—
645C22×C4—1662no—
646C22×C4—1668no—
647C22×C4D4×D8314yes—
648C22×C4Q8×D8314yes—
649C22×C4#1305059114yes—
650C22×C4C23×D8312yes—
651C22×C4C23×D8312yes—
652C22×C4C23×D8312yes—
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8312yes—
656C22×C4C23×D8312yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—3324no—
662C4⋊C4—3324no—
663C4⋊C4—1668no—
664C4⋊C4—1668no—
665C4⋊C4—1668no—
666C4⋊C4—1668no—
667C4⋊C4—1668no—
668C22⋊C4—3324no—
669C22⋊C4—3324no—
670C22⋊C4—1668no—
671C22⋊C4—1668no—
672C22⋊C4—1668no—
673C22⋊C4—1668no—
674C22⋊C4—1668no—
675C22⋊C4—1668no—
676C42—1668no—
677C23—3324no—
678C23—3324no—
679C23—3324no—
680C23—3324no—
681C23—8316no—
682C23—834no—
683C23—834no—
684C23—834no—
685C23—834no—
686C23—1668no—
687C23—1668no—
688C23—1668no—
689C23—1662no—
690C23—1662no—
691C23—1662no—
692C23—1662no—
693C23—1662no—
694C23—1662no—
695C23—1668no—
696C23—1668no—
697C23—1668no—
698C23—1668no—
699C23—1668no—
700C23—1668no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23C2×D4×D8312yes—
706C23C2×Q8×D8312yes—
707C23#41×D8312yes—
708C23#41×D8312yes—
709C23C2×#1305059112yes—
710C23#1458183712yes—
711C23#1458183812yes—
712C23C24×D8311yescharacteristic
713D4—16632no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
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—22no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—33216no—
740C2×C4—33216no—
741C2×C4—33216no—
742C2×C4—3324no—
743C2×C4—3324no—
744C2×C4—3324no—
745C2×C4—3324no—
746C2×C4—834no—
747C2×C4—834no—
748C2×C4—16632no—
749C2×C4—1662no—
750C2×C4—1662no—
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—1668no—
762C2×C4—1668no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4C2×D4×D8314yes—
768C2×C4C2×Q8×D8314yes—
769C2×C4C2×#1305059114yes—
770C22—3322no—
771C22—3322no—
772C22—3322no—
773C22—33216no—
774C22—3322no—
775C22—838no—
776C22—1664no—
777C22—1664no—
778C22—1664no—
779C22—1664no—
780C22—1664no—
781C22—1664no—
782C22—1664no—
783C22—1664no—
784C22—16632no—
785C22—1664no—
786C22C22⋊Q8×D8314yes—
787C22#1912821414yes—
788C22#1912825914yes—
789C22#1912839614yes—
790C22#1912840414yes—
791C22#1912840714yes—
792C22#1912841214yes—
793C22C22×D4×D8311yescharacteristic
794C22C22×Q8×D8311yescharacteristic
795C22C2×#41×D8311yescharacteristic
796C22C2×#41×D8311yescharacteristic
797C22C22×#1305059111yescharacteristic
798C22C2×#1458183711yescharacteristic
799C22C2×#1458183811yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—3322no—
808C4—3322no—
809C4—3322no—
810C4—3322no—
811C4—1664no—
812C4—1664no—
813C2—3324no—
814C2—1668no—
815C2#2491281118yesdirect product factor
816C2C2×C22⋊Q8×D8311yescharacteristic
817C2C2×#1912821411yescharacteristic
818C2C2×#1912825911yescharacteristic
819C2C2×#1912839611yescharacteristic
820C2C2×#1912840411yescharacteristic
821C2C2×#1912840711yescharacteristic
822C2C2×#1912841211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#398×C83C2
socleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×#398D83
hypocenterC83C2×#2579
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D83C2semidirect
3. #24912811C2direct (N × H)
4. C2×#19127634C2semidirect
5. C2×#19127623C2semidirect
6. C2×#19127623C2semidirect
7. C2×#19127588C2semidirect
8. C2×#19127584C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127575C2semidirect
13. C2×#19127572C2semidirect
14. C2×#19127572C2semidirect
15. C2×#19127558C2semidirect
16. C2×#398×C83C2semidirect
32. C2×C4⋊C4×D83C22semidirect
42. #19127634C22semidirect
43. #19127623C22semidirect
44. #19127623C22semidirect
45. #19127588C22semidirect
46. #19127584C22semidirect
49. #19127575C22semidirect
50. #19127575C22semidirect
51. #19127572C22semidirect
52. #19127572C22semidirect
53. #19127558C22semidirect
65. #398×C83C22semidirect
402. C2×C83#2579semidirect
416. C2×#398D83semidirect
428. C83C2×#2579semidirect
459. #398C2×D83semidirect
815. C2#24912811direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817542
C22×C4⋊C4×D832
#249128112
C2×#191276342
C2×#191276232
C2×#191275882
C2×#191275842
C2×#191275792
C2×#191275752
C2×#191275722
C2×#191275582
C2×#398×C832
C2×#257983