Finite Group Databasebeta

← C2×#24911127 #35571830

Subgroups — C2×#24911127 #35571830

Order 21248.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581772C211yesmaximal, characteristic, complemented
2C22×#14581769C211yesmaximal, characteristic, complemented
3C23×(C2×D83)⋊C4C211yesmaximal, characteristic
4C22×C22⋊C4×D83C211yesmaximal, characteristic
5#24911127C2116yesmaximal, direct product factor
6C2×#19127638C211yesmaximal, characteristic, complemented
7C2×#19127623C211yesmaximal, characteristic, complemented
8C2×#19127623C211yesmaximal, characteristic, complemented
9C2×#19127614C211yesmaximal, characteristic, complemented
10C2×#19127576C211yesmaximal, characteristic, complemented
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127575C211yesmaximal, characteristic, complemented
13C2×#19127561C211yesmaximal, characteristic, complemented
14C2×#19127558C211yesmaximal, characteristic, complemented
15C2×#19127556C211yesmaximal, characteristic
16C2×#385×C83C211yesmaximal, characteristic, complemented
17C25×D83C2211yescharacteristic
18C23×Dic166C2211yescharacteristic, complemented
19C24×Dic83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C2×#14581772—28no—
23C2×#14581772C2218yescomplemented
24C2×#14581769—28no—
25C2×#14581769C2218yescomplemented
26C22×C4⋊Dic83C2211yescharacteristic, complemented
27C22×C4⋊Dic83C2211yescharacteristic, complemented
28C22×C4⋊Dic83C2211yescharacteristic, complemented
29C22×C4⋊Dic83C2211yescharacteristic, complemented
30C22×C4⋊Dic83C2211yescharacteristic, complemented
31C22×Dic83⋊C4C2211yescharacteristic, complemented
32C22×Dic83⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×(C2×D83)⋊C4—28no—
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2218yes—
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×(C2×D83)⋊C4C2211yescharacteristic
45C22×(C2×D83)⋊C4C2211yescharacteristic
46C22×(C2×D83)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D83—28no—
48C2×C22⋊C4×D83C2218yes—
49#19127638C2218yescomplemented
50#19127623C2218yescomplemented
51#19127623C2218yescomplemented
52#19127614C2218yescomplemented
53#19127576C2218yescomplemented
54#19127575C2218yescomplemented
55#19127575C2218yescomplemented
56#19127561C2218yescomplemented
57#19127558C2218yescomplemented
58#19127556C2218yes—
59C2×C83⋊#95C2211yescharacteristic, complemented
60C2×C83⋊#95C2211yescharacteristic, complemented
61C2×C83⋊#95C2211yescharacteristic, complemented
62C2×C83⋊#95C2211yescharacteristic, complemented
63C24×C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic, complemented
65C22×C4⋊C4×C83C2211yescharacteristic, complemented
66C22×C22⋊C4×C83C2211yescharacteristic
67C22×C22⋊C4×C83C2211yescharacteristic
68#385×C83C2218yescomplemented
69C2×#95×C83C2211yescharacteristic, complemented
70C2×#95×C83C2211yescharacteristic, complemented
71C24×D83—24no—
72C24×D83—24no—
73C24×D83—24no—
74C24×D83—24no—
75C24×D83—42no—
76C24×D83—42no—
77C24×D83Q818yescomplemented
78C24×D83C2311yescharacteristic
79C24×D83C2314yes—
80C24×D83C2311yescharacteristic
81C22×Dic166—24no—
82C22×Dic166—24no—
83C22×Dic166—42no—
84C22×Dic166C2314yescomplemented
85C23×Dic83—24no—
86C23×Dic83—24no—
87C23×Dic83—42no—
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91C23×Dic83C2311yescharacteristic
92C23×Dic83C2311yescharacteristic
93C23×Dic83C2314yes—
94C23×Dic83C2311yescharacteristic
95C22×C4×D83—24no—
96C22×C4×D83—24no—
97C22×C4×D83—24no—
98C22×C4×D83—24no—
99C22×C4×D83—42no—
100C22×C4×D83—42no—
101C22×C4×D83C2314yes—
102C22×C4×D83C2314yes—
103#14581772—232no—
104#14581769—232no—
105C2×C4⋊Dic83—24no—
106C2×C4⋊Dic83—24no—
107C2×C4⋊Dic83—24no—
108C2×C4⋊Dic83—42no—
109C2×C4⋊Dic83—42no—
110C2×C4⋊Dic83C2314yescomplemented
111C2×C4⋊Dic83C2314yescomplemented
112C2×C4⋊Dic83C2314yescomplemented
113C2×C4⋊Dic83C2314yescomplemented
114C2×C4⋊Dic83C2314yescomplemented
115C2×Dic83⋊C4—24no—
116C2×Dic83⋊C4—24no—
117C2×Dic83⋊C4C2314yescomplemented
118C2×Dic83⋊C4C2314yescomplemented
119C2×C22⋊Dic83—24no—
120C2×C22⋊Dic83—24no—
121C2×C22⋊Dic83C2314yes—
122C2×C22⋊Dic83C2314yes—
123C2×(C2×D83)⋊C4—24no—
124C2×(C2×D83)⋊C4—24no—
125C2×(C2×D83)⋊C4—24no—
126C2×(C2×D83)⋊C4—24no—
127C2×(C2×D83)⋊C4—232no—
128C2×(C2×D83)⋊C4—24no—
129C2×(C2×D83)⋊C4—24no—
130C2×(C2×D83)⋊C4—24no—
131C2×(C2×D83)⋊C4—42no—
132C2×(C2×D83)⋊C4—42no—
133C2×(C2×D83)⋊C4D418yes—
134C2×(C2×D83)⋊C4C2314yes—
135C2×(C2×D83)⋊C4C2314yes—
136C2×(C2×D83)⋊C4C2314yes—
137C2×(C2×D83)⋊C4C2314yes—
138C2×(C2×D83)⋊C4C2314yes—
139C2×(C2×D83)⋊C4C2314yes—
140C2×(C2×D83)⋊C4C2314yes—
141C2×(C2×D83)⋊C4C2314yes—
142C2×(C2×D83)⋊C4C2314yes—
143C2×(C2×D83)⋊C4C2314yes—
144C22⋊C4×D83—232no—
145C83⋊#95C2314yescomplemented
146C83⋊#95C2314yescomplemented
147C83⋊#95C2314yescomplemented
148C83⋊#95C2314yescomplemented
149C25×C83C2311yescharacteristic
150C23×C4×C83—24no—
151C23×C4×C83—24no—
152C23×C4×C83—42no—
153C23×C4×C83C2311yescharacteristic
154C23×C4×C83C2311yescharacteristic
155C23×C4×C83C2311yescharacteristic
156C23×C4×C83C2314yes—
157C23×C4×C83C2311yescharacteristic
158C23×C4×C83C2311yescharacteristic
159C23×C4×C83C2311yescharacteristic
160C2×C4⋊C4×C83—24no—
161C2×C4⋊C4×C83—42no—
162C2×C4⋊C4×C83C2314yescomplemented
163C2×C4⋊C4×C83C2314yescomplemented
164C2×C22⋊C4×C83—24no—
165C2×C22⋊C4×C83D418yes—
166C2×C22⋊C4×C83C2314yes—
167C2×C22⋊C4×C83C2314yes—
168#95×C83C2314yescomplemented
169#95×C83C2314yescomplemented
170C23×D83—22no—
171C23×D83—22no—
172C23×D83—22no—
173C23×D83—22no—
174C23×D83—232no—
175C23×D83—28no—
176C23×D83—22no—
177C23×D83—22no—
178C23×D83—22no—
179C23×D83—28no—
180C23×D83—22no—
181C23×D83—22no—
182C23×D83—22no—
183C23×D83—232no—
184C23×D83—28no—
185C23×D83—28no—
186C23×D83—416no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—416no—
190C23×D83—416no—
191C23×D83—416no—
192C23×D83—416no—
193C23×D83C2×D414yes—
194C23×D83C2×Q814yes—
195C23×D83C2×Q814yes—
196C23×D83C2×Q8116yescomplemented
197C23×D83#4114yes—
198C23×D83C2412yes—
199C23×D83C2412yes—
200C2×Dic166—28no—
201C2×Dic166—28no—
202C2×Dic166—44no—
203C2×Dic166—416no—
204C22×Dic83—22no—
205C22×Dic83—22no—
206C22×Dic83—28no—
207C22×Dic83—22no—
208C22×Dic83—22no—
209C22×Dic83—22no—
210C22×Dic83—22no—
211C22×Dic83—22no—
212C22×Dic83—22no—
213C22×Dic83—22no—
214C22×Dic83—22no—
215C22×Dic83—22no—
216C22×Dic83—22no—
217C22×Dic83—22no—
218C22×Dic83—22no—
219C22×Dic83—22no—
220C22×Dic83—22no—
221C22×Dic83—22no—
222C22×Dic83—28no—
223C22×Dic83—44no—
224C22×Dic83—416no—
225C22×Dic83C2×D414yes—
226C22×Dic83C2412yes—
227C22×Dic83C2412yes—
228C22×Dic83C2412yes—
229C22×Dic83C2412yes—
230C22×Dic83C2412yes—
231C22×Dic83C2412yes—
232C2×C4×D83—28no—
233C2×C4×D83—28no—
234C2×C4×D83—28no—
235C2×C4×D83—28no—
236C2×C4×D83—44no—
237C2×C4×D83—44no—
238C2×C4×D83—416no—
239C2×C4×D83—416no—
240C4⋊Dic83—28no—
241C4⋊Dic83—28no—
242C4⋊Dic83—28no—
243C4⋊Dic83—44no—
244C4⋊Dic83—44no—
245Dic83⋊C4—28no—
246Dic83⋊C4—28no—
247C22⋊Dic83—28no—
248C22⋊Dic83—28no—
249(C2×D83)⋊C4—28no—
250(C2×D83)⋊C4—28no—
251(C2×D83)⋊C4—28no—
252(C2×D83)⋊C4—28no—
253(C2×D83)⋊C4—28no—
254(C2×D83)⋊C4—28no—
255(C2×D83)⋊C4—28no—
256(C2×D83)⋊C4—44no—
257(C2×D83)⋊C4—44no—
258(C2×D83)⋊C4C2×D4116yes—
259C24×C83—22no—
260C24×C83—22no—
261C24×C83—22no—
262C24×C83—22no—
263C24×C83C2×D414yes—
264C24×C83C2×Q814yes—
265C24×C83#4114yes—
266C24×C83C2412yes—
267C24×C83C2411yescharacteristic
268C22×C4×C83—22no—
269C22×C4×C83—22no—
270C22×C4×C83—22no—
271C22×C4×C83—22no—
272C22×C4×C83—22no—
273C22×C4×C83—22no—
274C22×C4×C83—22no—
275C22×C4×C83—22no—
276C22×C4×C83—22no—
277C22×C4×C83—22no—
278C22×C4×C83—28no—
279C22×C4×C83—22no—
280C22×C4×C83—22no—
281C22×C4×C83—22no—
282C22×C4×C83—22no—
283C22×C4×C83—22no—
284C22×C4×C83—28no—
285C22×C4×C83—44no—
286C22×C4×C83—416no—
287C22×C4×C83C2×D414yes—
288C22×C4×C83C2×D414yes—
289C22×C4×C83C2×D414yes—
290C22×C4×C83C2412yes—
291C22×C4×C83C2412yes—
292C22×C4×C83C2412yes—
293C22×C4×C83C2412yes—
294C22×C4×C83C2412yes—
295C22×C4×C83C2412yes—
296C4⋊C4×C83—28no—
297C4⋊C4×C83—44no—
298C22⋊C4×C83—28no—
299C22⋊C4×C83C2×D4116yes—
300C23×C83—28no—
301C23×C83—28no—
302C23×C83—28no—
303C23×C83—28no—
304C23×C83—28no—
305C23×C83—28no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83C22⋊Q8116yescomplemented
311C23×C83C22×D412yes—
312C23×C83C22×D414yes—
313C23×C83C22×D412yes—
314C23×C83C22×Q814yes—
315C23×C83C22×Q812yes—
316C23×C83C2×#4112yes—
317C23×C83C2×#4114yes—
318C23×C83C2×#4112yes—
319C23×C83H(5,𝔽2)12yes—
320C23×C83H(5,𝔽2)12yes—
321C23×C83C2511yescharacteristic
322C22×D83—28no—
323C22×D83—28no—
324C22×D83—28no—
325C22×D83—28no—
326C22×D83—28no—
327C22×D83—28no—
328C22×D83—22no—
329C22×D83—22no—
330C22×D83—22no—
331C22×D83—22no—
332C22×D83—28no—
333C22×D83—28no—
334C22×D83—232no—
335C22×D83—28no—
336C22×D83—22no—
337C22×D83—22no—
338C22×D83—22no—
339C22×D83—22no—
340C22×D83—22no—
341C22×D83—22no—
342C22×D83—232no—
343C22×D83—416no—
344C22×D83—4128no—
345C22×D83—416no—
346C22×D83—416no—
347C22×D83—416no—
348C22×D83—416no—
349C22×D83—44no—
350C22×D83—44no—
351C22×D83—44no—
352C22×D83—44no—
353C22×D83C22⋊Q8116yescomplemented
354C22×D83C22×D414yes—
355C22×D83C22×Q814yes—
356C22×D83C22×Q814yes—
357C22×D83C2×#4114yes—
358C2×C4×C83—28no—
359C2×C4×C83—28no—
360C2×C4×C83—28no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—22no—
374C2×C4×C83—22no—
375C2×C4×C83—22no—
376C2×C4×C83—416no—
377C2×C4×C83—44no—
378C2×C4×C83—44no—
379C2×C4×C83—44no—
380C2×C4×C83C22×D414yes—
381C2×C4×C83C22×D414yes—
382C2×C4×C83C22×D414yes—
383C2×Dic83—28no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—22no—
400C2×Dic83—22no—
401C2×Dic83—416no—
402C2×Dic83—44no—
403C2×Dic83—44no—
404C2×Dic83—44no—
405C2×Dic83—44no—
406C2×Dic83—44no—
407C2×Dic83C22×D414yes—
408C4×D83—416no—
409C4×D83—416no—
410Dic166—416no—
411C22×C83—24no—
412C22×C83—24no—
413C22×C83—232no—
414C22×C83—24no—
415C22×C83—24no—
416C22×C83—24no—
417C22×C83—24no—
418C22×C83C2×C22⋊Q814yes—
419C22×C83C2×C22⋊Q814yes—
420C22×C83C2×C22⋊Q818yescomplemented
421C22×C83#54314yes—
422C22×C83D4214yes—
423C22×C83#54614yes—
424C22×C83#54614yes—
425C22×C83#55114yes—
426C22×C83C23×D411yescharacteristic
427C22×C83C23×D411yescharacteristic
428C22×C83C23×Q811yescharacteristic
429C22×C83C22×#4111yescharacteristic
430C22×C83C22×#4111yescharacteristic
431C22×C83C2×H(5,𝔽2)11yescharacteristic
432C22×C83C2×H(5,𝔽2)11yescharacteristic
433C2×D83—24no—
434C2×D83—24no—
435C2×D83—232no—
436C2×D83—24no—
437C2×D83—24no—
438C2×D83—24no—
439C2×D83—24no—
440C2×D83—24no—
441C2×D83—24no—
442C2×D83—24no—
443C2×D83—464no—
444C2×D83—416no—
445C2×D83—42no—
446C2×D83—42no—
447C2×D83—42no—
448C2×D83—42no—
449C2×D83C2×C22⋊Q818yescomplemented
450C4×C83—24no—
451C4×C83—24no—
452C4×C83—24no—
453C4×C83—42no—
454C4×C83—42no—
455C4×C83—42no—
456Dic83—24no—
457Dic83—42no—
458Dic83—42no—
459Dic83—42no—
460Dic83—42no—
461Dic83—42no—
462C2×#2437—831nomaximal, Sylow
463C2×C83—28no—
464C2×C83#243718yescomplemented
465C2×C83C22×C22⋊Q811yescharacteristic
466C2×C83C22×C22⋊Q811yescharacteristic
467C2×C83C2×#54311yescharacteristic
468C2×C83C2×D4211yescharacteristic
469C2×C83C2×#54611yescharacteristic
470C2×C83C2×#54611yescharacteristic
471C2×C83C2×#55111yescharacteristic
472D83—28no—
473D83—44no—
474C22×C22⋊Q8—831no—
475C22×C22⋊Q8—831no—
476C23×C22⋊C4—831no—
477C23×C22⋊C4—831no—
478#2437—8316no—
479C2×#399—831no—
480C2×#396—831no—
481C2×#396—831no—
482C2×#393—831no—
483C2×#385—831no—
484C2×#385—831no—
485C2×#385—831no—
486C2×#385D8311yescharacteristic, complemented
487C2×#380—831no—
488C2×#380—831no—
489C2×#379—831no—
490C83C2×#243711yescharacteristic, complemented, Sylow
491C26—831no—
492C23×Q8—831no—
493C24×C4—831no—
494C24×C4—831no—
495C24×C4—831no—
496C24×C4C2×D8311yescharacteristic
497C2×C22⋊Q8—838no—
498C2×C22⋊Q8—838no—
499C2×C22⋊Q8—1668no—
500C2×C22⋊Q8—1668no—
501C22×C4⋊C4—831no—
502C22×C4⋊C4—831no—
503C22×C4⋊C4—831no—
504C22×C4⋊C4—831no—
505C22×C4⋊C4—831no—
506C22×C4⋊C4—831no—
507C22×C4⋊C4—831no—
508C22×C4⋊C4C2×D8311yescharacteristic, complemented
509C22×C4⋊C4C2×D8311yescharacteristic, complemented
510C22×C22⋊C4—831no—
511C22×C22⋊C4—831no—
512C22×C22⋊C4—831no—
513C22×C22⋊C4—831no—
514C22×C22⋊C4—831no—
515C22×C22⋊C4—831no—
516C22×C22⋊C4—831no—
517C22×C22⋊C4—831no—
518C22×C22⋊C4—831no—
519C22×C22⋊C4—838no—
520C22×C22⋊C4—831no—
521C22×C22⋊C4—831no—
522C22×C22⋊C4—831no—
523C22×C22⋊C4—838no—
524C22×C22⋊C4—1668no—
525C22×C22⋊C4—1668no—
526C22×C22⋊C4C2×D8311yescharacteristic
527C22×C22⋊C4C2×D8311yescharacteristic
528#399—838no—
529#396—838no—
530#396—838no—
531#393—838no—
532#385—838no—
533#385—838no—
534#385—838no—
535#385C2×D8318yescomplemented
536#380—838no—
537#380—838no—
538#379—838no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95C2×D8311yescharacteristic, complemented
544C2×#95C2×D8311yescharacteristic, complemented
545C25—3322no—
546C25—3322no—
547C25—838no—
548C25—834no—
549C25—831no—
550C25—831no—
551C25—1664no—
552C25—1664no—
553C25—1664no—
554C25—1664no—
555C25C22×D8311yescharacteristic
556C22×Q8—3322no—
557C22×Q8—834no—
558C22×Q8—1664no—
559C22×Q8—1664no—
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—42no—
563C23×C4—3322no—
564C23×C4—3322no—
565C23×C4—3322no—
566C23×C4—834no—
567C23×C4—834no—
568C23×C4—834no—
569C23×C4—831no—
570C23×C4—831no—
571C23×C4—831no—
572C23×C4—831no—
573C23×C4—831no—
574C23×C4—831no—
575C23×C4—1664no—
576C23×C4—1664no—
577C23×C4—1664no—
578C23×C4—1664no—
579C23×C4—1664no—
580C23×C4—1664no—
581C23×C4C22×D8311yescharacteristic
582C23×C4C22×D8311yescharacteristic
583C23×C4C22×D8311yescharacteristic
584C23×C4C22×D8314yes—
585C23×C4C22×D8311yescharacteristic
586C23×C4C22×D8311yescharacteristic
587C23×C4C22×D8311yescharacteristic
588C22⋊Q8—16632no—
589C22⋊Q8—16632no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—3322no—
593C2×C4⋊C4—3322no—
594C2×C4⋊C4—834no—
595C2×C4⋊C4—834no—
596C2×C4⋊C4—834no—
597C2×C4⋊C4—834no—
598C2×C4⋊C4—834no—
599C2×C4⋊C4—834no—
600C2×C4⋊C4—834no—
601C2×C4⋊C4—1664no—
602C2×C4⋊C4—1664no—
603C2×C4⋊C4—1664no—
604C2×C4⋊C4—1664no—
605C2×C4⋊C4—1664no—
606C2×C4⋊C4C22×D8314yescomplemented
607C2×C4⋊C4C22×D8314yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—3322no—
610C2×C22⋊C4—3322no—
611C2×C22⋊C4—834no—
612C2×C22⋊C4—834no—
613C2×C22⋊C4—838no—
614C2×C22⋊C4—834no—
615C2×C22⋊C4—834no—
616C2×C22⋊C4—834no—
617C2×C22⋊C4—834no—
618C2×C22⋊C4—834no—
619C2×C22⋊C4—834no—
620C2×C22⋊C4—834no—
621C2×C22⋊C4—834no—
622C2×C22⋊C4—834no—
623C2×C22⋊C4—834no—
624C2×C22⋊C4—16632no—
625C2×C22⋊C4—1664no—
626C2×C22⋊C4—1664no—
627C2×C22⋊C4—1664no—
628C2×C22⋊C4—1664no—
629C2×C22⋊C4—1664no—
630C2×C22⋊C4—1664no—
631C2×C22⋊C4—1664no—
632C2×C22⋊C4—1664no—
633C2×C22⋊C4—1664no—
634C2×C22⋊C4—16632no—
635C2×C22⋊C4D33218yes—
636C2×C22⋊C4C22×D8314yes—
637C2×C22⋊C4C22×D8314yes—
638#95—834no—
639#95—834no—
640#95—834no—
641#95—834no—
642#95C22×D8314yescomplemented
643#95C22×D8314yescomplemented
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—33216no—
649C24—33216no—
650C24—33216no—
651C24—33216no—
652C24—33216no—
653C24—3324no—
654C24—3324no—
655C24—8316no—
656C24—834no—
657C24—834no—
658C24—834no—
659C24—832no—
660C24—834no—
661C24—832no—
662C24—1668no—
663C24—16632no—
664C24—1668no—
665C24—16632no—
666C24—1662no—
667C24—1668no—
668C24—1662no—
669C24—1662no—
670C24—1668no—
671C24—1662no—
672C24—1662no—
673C24—1662no—
674C24—1662no—
675C24—1662no—
676C24—1662no—
677C24—1662no—
678C24C2×D33214yes—
679C24Q8×D8314yes—
680C24#1305058914yes—
681C24C23×D8312yes—
682C24C23×D8311yescharacteristic
683C2×Q8—33216no—
684C2×Q8—3324no—
685C2×Q8—1668no—
686C2×Q8—1668no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—416no—
706C22×C4—33216no—
707C22×C4—33216no—
708C22×C4—3324no—
709C22×C4—3324no—
710C22×C4—33216no—
711C22×C4—3324no—
712C22×C4—834no—
713C22×C4—832no—
714C22×C4—832no—
715C22×C4—832no—
716C22×C4—832no—
717C22×C4—832no—
718C22×C4—832no—
719C22×C4—1668no—
720C22×C4—1668no—
721C22×C4—1668no—
722C22×C4—1662no—
723C22×C4—1662no—
724C22×C4—1662no—
725C22×C4—1662no—
726C22×C4—1662no—
727C22×C4—1662no—
728C22×C4—1662no—
729C22×C4—1662no—
730C22×C4—1668no—
731C22×C4—1662no—
732C22×C4—1662no—
733C22×C4—1662no—
734C22×C4—1662no—
735C22×C4—1662no—
736C22×C4—1662no—
737C22×C4—1662no—
738C22×C4—1668no—
739C22×C4—1668no—
740C22×C4—1662no—
741C22×C4—1662no—
742C22×C4D4×D8314yes—
743C22×C4C2×D33214yes—
744C22×C4C2×D33214yes—
745C22×C4C23×D8312yes—
746C22×C4C23×D8312yes—
747C22×C4C23×D8312yes—
748C22×C4C23×D8312yes—
749C22×C4C23×D8312yes—
750C22×C4C23×D8312yes—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C4⋊C4—3324no—
754C4⋊C4—3324no—
755C4⋊C4—1668no—
756C4⋊C4—1668no—
757C4⋊C4—1668no—
758C4⋊C4—1668no—
759C4⋊C4—1668no—
760C22⋊C4—28no—
761C22⋊C4—3324no—
762C22⋊C4—3324no—
763C22⋊C4—8316no—
764C22⋊C4—1668no—
765C22⋊C4—1668no—
766C22⋊C4—1668no—
767C22⋊C4—1668no—
768C22⋊C4—1668no—
769C22⋊C4—1668no—
770C22⋊C4—1668no—
771C22⋊C4—1668no—
772C22⋊C4—1668no—
773C22⋊C4C2×D332116yes—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—332128no—
785C23—33216no—
786C23—33216no—
787C23—33216no—
788C23—33216no—
789C23—33216no—
790C23—3324no—
791C23—3324no—
792C23—3324no—
793C23—3324no—
794C23—8316no—
795C23—834no—
796C23—834no—
797C23—834no—
798C23—834no—
799C23—16632no—
800C23—1668no—
801C23—1668no—
802C23—1668no—
803C23—16632no—
804C23—1662no—
805C23—1662no—
806C23—1662no—
807C23—1662no—
808C23—1662no—
809C23—1662no—
810C23—1668no—
811C23—1668no—
812C23—1668no—
813C23—1668no—
814C23—1668no—
815C23—1668no—
816C23—1662no—
817C23—1662no—
818C23—1662no—
819C23—1662no—
820C23#14581772116yescomplemented
821C23C2×D4×D8312yes—
822C23C22×D33214yes—
823C23C22×D33212yes—
824C23C2×Q8×D8314yes—
825C23C2×Q8×D8312yes—
826C23#41×D8312yes—
827C23C2×#1305058914yes—
828C23C2×#1305058912yes—
829C23#1458183712yes—
830C23#1458183812yes—
831C23C24×D8311yescharacteristic
832Q8—33216no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—33216no—
856C2×C4—33216no—
857C2×C4—3324no—
858C2×C4—3324no—
859C2×C4—3324no—
860C2×C4—3324no—
861C2×C4—3324no—
862C2×C4—33216no—
863C2×C4—834no—
864C2×C4—1662no—
865C2×C4—1662no—
866C2×C4—1662no—
867C2×C4—1662no—
868C2×C4—1662no—
869C2×C4—1662no—
870C2×C4—1662no—
871C2×C4—1662no—
872C2×C4—1662no—
873C2×C4—1662no—
874C2×C4—1662no—
875C2×C4—1662no—
876C2×C4—1662no—
877C2×C4—1662no—
878C2×C4—1662no—
879C2×C4—1668no—
880C2×C4—1662no—
881C2×C4—1662no—
882C2×C4C2×D4×D8314yes—
883C2×C4C22×D33214yes—
884C2×C4C22×D33214yes—
885C22—232no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—33264no—
893C22—33216no—
894C22—3322no—
895C22—3322no—
896C22—3322no—
897C22—3322no—
898C22—838no—
899C22—1664no—
900C22—1664no—
901C22—1664no—
902C22—16632no—
903C22—1664no—
904C22—1664no—
905C22—1664no—
906C22—1664no—
907C22—1664no—
908C22—1664no—
909C22C22⋊Q8×D8314yes—
910C22C2×#1458177214yes—
911C22C2×#1458177218yescomplemented
912C22#1912832614yes—
913C22D4×D33214yes—
914C22#1912833814yes—
915C22#1912834614yes—
916C22#1912837414yes—
917C22C22×D4×D8311yescharacteristic
918C22C23×D33211yescharacteristic
919C22C22×Q8×D8311yescharacteristic
920C22C2×#41×D8311yescharacteristic
921C22C22×#1305058911yescharacteristic
922C22C2×#1458183711yescharacteristic
923C22C2×#1458183811yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—3322no—
931C4—3322no—
932C4—3322no—
933C4—3322no—
934C4—3322no—
935C4—1664no—
936C2—28no—
937C2—3324no—
938C2—1668no—
939C2#2491112718yesdirect product factor
940C2C2×C22⋊Q8×D8311yescharacteristic
941C2C22×#1458177211yescharacteristic
942C2C2×#1912832611yescharacteristic
943C2C2×D4×D33211yescharacteristic
944C2C2×#1912833811yescharacteristic
945C2C2×#1912834611yescharacteristic
946C2C2×#1912837411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC25×D83C22
hypercenterC2×#385D83
hypocenterC83C2×#2437
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14581772C2semidirect
2. C22×#14581769C2semidirect
5. #24911127C2direct (N × H)
6. C2×#19127638C2semidirect
7. C2×#19127623C2semidirect
8. C2×#19127623C2semidirect
9. C2×#19127614C2semidirect
10. C2×#19127576C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127575C2semidirect
13. C2×#19127561C2semidirect
14. C2×#19127558C2semidirect
16. C2×#385×C83C2semidirect
18. C23×Dic166C22semidirect
23. C2×#14581772C22semidirect
25. C2×#14581769C22semidirect
26. C22×C4⋊Dic83C22semidirect
27. C22×C4⋊Dic83C22semidirect
28. C22×C4⋊Dic83C22semidirect
29. C22×C4⋊Dic83C22semidirect
30. C22×C4⋊Dic83C22semidirect
31. C22×Dic83⋊C4C22semidirect
32. C22×Dic83⋊C4C22semidirect
49. #19127638C22semidirect
50. #19127623C22semidirect
51. #19127623C22semidirect
52. #19127614C22semidirect
53. #19127576C22semidirect
54. #19127575C22semidirect
55. #19127575C22semidirect
56. #19127561C22semidirect
57. #19127558C22semidirect
59. C2×C83⋊#95C22semidirect
60. C2×C83⋊#95C22semidirect
61. C2×C83⋊#95C22semidirect
62. C2×C83⋊#95C22semidirect
64. C22×C4⋊C4×C83C22semidirect
65. C22×C4⋊C4×C83C22semidirect
68. #385×C83C22semidirect
69. C2×#95×C83C22semidirect
70. C2×#95×C83C22semidirect
77. C24×D83Q8semidirect
84. C22×Dic166C23semidirect
110. C2×C4⋊Dic83C23semidirect
111. C2×C4⋊Dic83C23semidirect
112. C2×C4⋊Dic83C23semidirect
113. C2×C4⋊Dic83C23semidirect
114. C2×C4⋊Dic83C23semidirect
117. C2×Dic83⋊C4C23semidirect
118. C2×Dic83⋊C4C23semidirect
145. C83⋊#95C23semidirect
146. C83⋊#95C23semidirect
147. C83⋊#95C23semidirect
148. C83⋊#95C23semidirect
162. C2×C4⋊C4×C83C23semidirect
163. C2×C4⋊C4×C83C23semidirect
168. #95×C83C23semidirect
169. #95×C83C23semidirect
196. C23×D83C2×Q8semidirect
310. C23×C83C22⋊Q8semidirect
353. C22×D83C22⋊Q8semidirect
420. C22×C83C2×C22⋊Q8semidirect
449. C2×D83C2×C22⋊Q8semidirect
464. C2×C83#2437semidirect
486. C2×#385D83semidirect
490. C83C2×#2437semidirect
508. C22×C4⋊C4C2×D83semidirect
509. C22×C4⋊C4C2×D83semidirect
535. #385C2×D83semidirect
543. C2×#95C2×D83semidirect
544. C2×#95C2×D83semidirect
606. C2×C4⋊C4C22×D83semidirect
607. C2×C4⋊C4C22×D83semidirect
642. #95C22×D83semidirect
643. #95C22×D83semidirect
820. C23#14581772semidirect
911. C22C2×#14581772semidirect
939. C2#24911127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817722
C22×#145817692
C23×(C2×D83)⋊C42
C22×C22⋊C4×D832
#249111272
C2×#191276382
C2×#191276232
C2×#191276142
C2×#191275762
C2×#191275752
C2×#191275612
C2×#191275582
C2×#191275562
C2×#385×C832
C2×#243783