Finite Group Databasebeta

← C2×#24911272 #35571886

Subgroups — C2×#24911272 #35571886

Order 21248.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581771C211yesmaximal, characteristic, complemented
2C22×#14581770C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D83C211yesmaximal, characteristic
4#24911272C2116yesmaximal, direct product factor
5C2×#19127636C211yesmaximal, characteristic, complemented
6C2×#19127632C211yesmaximal, characteristic, complemented
7C2×#19127623C211yesmaximal, characteristic, complemented
8C2×#19127621C211yesmaximal, characteristic, complemented
9C2×#19127596C211yesmaximal, characteristic, complemented
10C2×#19127587C211yesmaximal, characteristic, complemented
11C2×#19127580C211yesmaximal, characteristic
12C2×#19127580C211yesmaximal, characteristic
13C2×#19127574C211yesmaximal, characteristic, complemented
14C2×#19127574C211yesmaximal, characteristic, complemented
15C2×#19127572C211yesmaximal, characteristic, complemented
16C23×C4⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581771—28no—
21C2×#14581771C2218yescomplemented
22C2×#14581770—28no—
23C2×#14581770C2218yescomplemented
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×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×C22⋊Dic83C2211yescharacteristic
36C22×C22⋊Dic83C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43#19127636C2218yescomplemented
44#19127632C2218yescomplemented
45#19127623C2218yescomplemented
46#19127621C2218yescomplemented
47#19127596C2218yescomplemented
48#19127587C2218yescomplemented
49#19127580C2218yes—
50#19127580C2218yes—
51#19127574C2218yescomplemented
52#19127574C2218yescomplemented
53#19127572C2218yescomplemented
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C24×C4×C83C2211yescharacteristic
63C24×C4×C83C2211yescharacteristic
64C24×C4×C83C2211yescharacteristic
65C22×C4⋊C4×C83—28no—
66C22×C4⋊C4×C83C2211yescharacteristic
67C22×C4⋊C4×C83C2211yescharacteristic
68C22×C4⋊C4×C83C2211yescharacteristic
69C22×C4⋊C4×C83C2211yescharacteristic
70C22×C4⋊C4×C83C2218yescomplemented
71C24×D83C2311yescharacteristic
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166—42no—
75C22×Dic166C2314yes—
76C22×C22⋊D83—24no—
77C22×C22⋊D83—24no—
78C22×C22⋊D83Q818yescomplemented
79C22×C22⋊D83C2314yes—
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83—42no—
90C22×C4×D83C2314yes—
91#14581771—232no—
92#14581770—232no—
93C4×C22⋊D83—232no—
94C2×C4⋊Dic83—24no—
95C2×C4⋊Dic83C2314yes—
96C2×Dic83⋊C4—24no—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4—24no—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—42no—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×C22⋊Dic83—24no—
111C2×C22⋊Dic83—24no—
112C2×C22⋊Dic83D418yes—
113C2×C22⋊Dic83C2314yes—
114C2×C22⋊Dic83C2314yes—
115C2×C22⋊Dic83C2314yes—
116C2×(C2×D83)⋊C4—24no—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4—24no—
119C2×(C2×D83)⋊C4—24no—
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×C4×Dic83—24no—
127C2×C4×Dic83C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C25×C83C2311yescharacteristic
137C23×C4×C83—24no—
138C23×C4×C83—24no—
139C23×C4×C83—24no—
140C23×C4×C83—24no—
141C23×C4×C83—24no—
142C23×C4×C83—24no—
143C23×C4×C83—24no—
144C23×C4×C83—42no—
145C23×C4×C83—42no—
146C23×C4×C83C2314yes—
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149C23×C4×C83C2314yes—
150C23×C4×C83C2314yes—
151C23×C4×C83C2311yescharacteristic
152C23×C4×C83C2311yescharacteristic
153C23×C4×C83C2311yescharacteristic
154C23×C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83—24no—
156C2×C4⋊C4×C83—24no—
157C2×C4⋊C4×C83—24no—
158C2×C4⋊C4×C83—232no—
159C2×C4⋊C4×C83D418yescomplemented
160C2×C4⋊C4×C83C2314yes—
161C2×C4⋊C4×C83C2314yes—
162C2×C4⋊C4×C83C2314yes—
163C2×C4⋊C4×C83C2314yes—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83—22no—
167C23×D83—22no—
168C23×D83—22no—
169C23×D83—22no—
170C23×D83C2×Q814yes—
171C23×D83C2412yes—
172C2×Dic166—28no—
173C2×Dic166—28no—
174C2×Dic166—44no—
175C2×Dic166—416no—
176C2×C22⋊D83—232no—
177C2×C22⋊D83—28no—
178C2×C22⋊D83—28no—
179C2×C22⋊D83C2×Q8116yescomplemented
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×Dic83—22no—
193C22×Dic83—22no—
194C22×Dic83—22no—
195C22×Dic83—22no—
196C22×Dic83—22no—
197C22×Dic83—22no—
198C22×Dic83C2×D414yes—
199C22×Dic83C2×D414yes—
200C22×Dic83C2×Q814yes—
201C22×Dic83C2412yes—
202C22×Dic83C2412yes—
203C22×Dic83C2412yes—
204C22×Dic83C2412yes—
205C22×Dic83C2412yes—
206C22×Dic83C2412yes—
207C22×Dic83C2412yes—
208C2×C4×D83—28no—
209C2×C4×D83—28no—
210C2×C4×D83—44no—
211C2×C4×D83—416no—
212C4⋊Dic83—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—28no—
216Dic83⋊C4—28no—
217Dic83⋊C4—28no—
218Dic83⋊C4—28no—
219Dic83⋊C4—44no—
220C22⋊Dic83—28no—
221C22⋊Dic83—28no—
222C22⋊Dic83C2×D4116yes—
223(C2×D83)⋊C4—28no—
224(C2×D83)⋊C4—28no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4—28no—
227(C2×D83)⋊C4—44no—
228C4×Dic83—28no—
229C24×C83—22no—
230C24×C83—22no—
231C24×C83—22no—
232C24×C83—22no—
233C24×C83C2×D414yes—
234C24×C83C2×Q814yes—
235C24×C83#4114yes—
236C24×C83C2412yes—
237C24×C83C2411yescharacteristic
238C22×C4×C83—232no—
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—28no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—28no—
249C22×C4×C83—28no—
250C22×C4×C83—28no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—22no—
254C22×C4×C83—22no—
255C22×C4×C83—28no—
256C22×C4×C83—22no—
257C22×C4×C83—22no—
258C22×C4×C83—28no—
259C22×C4×C83—28no—
260C22×C4×C83—44no—
261C22×C4×C83—44no—
262C22×C4×C83—416no—
263C22×C4×C83—416no—
264C22×C4×C83C2×D414yes—
265C22×C4×C83C2×D414yes—
266C22×C4×C83C2×D414yes—
267C22×C4×C83#4114yes—
268C22×C4×C83C2412yes—
269C22×C4×C83C2412yes—
270C22×C4×C83C2412yes—
271C22×C4×C83C2412yes—
272C22×C4×C83C2412yes—
273C22×C4×C83C2412yes—
274C4⋊C4×C83—28no—
275C4⋊C4×C83—28no—
276C4⋊C4×C83—28no—
277C4⋊C4×C83C2×D4116yescomplemented
278C23×C83—28no—
279C23×C83—28no—
280C23×C83—28no—
281C23×C83—28no—
282C23×C83—28no—
283C23×C83—28no—
284C23×C83—22no—
285C23×C83—22no—
286C23×C83—22no—
287C23×C83—22no—
288C23×C83C22⋊Q8116yescomplemented
289C23×C83C22×D414yes—
290C23×C83C22×D412yes—
291C23×C83C22×D412yes—
292C23×C83C22×Q814yes—
293C23×C83C22×Q812yes—
294C23×C83C2×#4114yes—
295C23×C83C2×#4112yes—
296C23×C83C2×#4112yes—
297C23×C83H(5,𝔽2)12yes—
298C23×C832−1+412yes—
299C23×C83C2511yescharacteristic
300C22×D83—28no—
301C22×D83—28no—
302C22×D83—28no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—22no—
307C22×D83—22no—
308C22×D83—22no—
309C22×D83—44no—
310C22×D83—44no—
311C22×D83—44no—
312C22×D83—44no—
313C22×D83C22×Q814yes—
314C2×C4×C83—232no—
315C2×C4×C83—28no—
316C2×C4×C83—28no—
317C2×C4×C83—28no—
318C2×C4×C83—28no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—416no—
334C2×C4×C83—416no—
335C2×C4×C83—44no—
336C2×C4×C83—44no—
337C2×C4×C83C22×D414yes—
338C2×C4×C83C22×D414yes—
339C2×C4×C83C22×D414yes—
340C2×C4×C83C2×#4114yes—
341C22⋊D83—232no—
342C2×Dic83—28no—
343C2×Dic83—28no—
344C2×Dic83—28no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—22no—
363C2×Dic83—44no—
364C2×Dic83—44no—
365C2×Dic83—44no—
366C2×Dic83—44no—
367C2×Dic83C22×D414yes—
368C2×Dic83C22×D414yes—
369C2×Dic83C22×Q814yes—
370C4×D83—416no—
371Dic166—416no—
372C22×C83—24no—
373C22×C83—24no—
374C22×C83—24no—
375C22×C83—24no—
376C22×C83—24no—
377C22×C83—24no—
378C22×C83—232no—
379C22×C83C2×C22⋊Q814yes—
380C22×C83C2×C22⋊Q818yescomplemented
381C22×C83#52514yes—
382C22×C83#53914yes—
383C22×C83D4214yes—
384C22×C83#54714yes—
385C22×C83D4×Q814yes—
386C22×C83#55414yes—
387C22×C83C23×D411yescharacteristic
388C22×C83C23×D411yescharacteristic
389C22×C83C23×Q811yescharacteristic
390C22×C83C22×#4111yescharacteristic
391C22×C83C22×#4111yescharacteristic
392C22×C83C2×H(5,𝔽2)11yescharacteristic
393C22×C83C2×2−1+411yescharacteristic
394C2×D83—24no—
395C2×D83—24no—
396C2×D83—24no—
397C2×D83—42no—
398C2×D83—42no—
399C2×D83—42no—
400C2×D83—42no—
401C2×D83—416no—
402C4×C83—24no—
403C4×C83—24no—
404C4×C83—24no—
405C4×C83—24no—
406C4×C83—42no—
407C4×C83—42no—
408Dic83—24no—
409Dic83—24no—
410Dic83—24no—
411Dic83—42no—
412Dic83—42no—
413Dic83—42no—
414Dic83—42no—
415C2×#2449—831nomaximal, Sylow
416C2×C83—28no—
417C2×C83#244918yescomplemented
418C2×C83C22×C22⋊Q811yescharacteristic
419C2×C83C2×#52511yescharacteristic
420C2×C83C2×#53911yescharacteristic
421C2×C83C2×D4211yescharacteristic
422C2×C83C2×#54711yescharacteristic
423C2×C83C2×D4×Q811yescharacteristic
424C2×C83C2×#55411yescharacteristic
425D83—44no—
426C22×C22⋊Q8—831no—
427C22×C22⋊Q8—831no—
428C22×C4×D4—831no—
429C23×C4⋊C4D8311yescharacteristic, complemented
430#2449—8316no—
431C2×#399—831no—
432C2×#398—831no—
433C2×#396—831no—
434C2×#395—831no—
435C2×#389—831no—
436C2×#387—831no—
437C2×#386—831no—
438C2×#386—831no—
439C2×#385—831no—
440C2×#385—831no—
441C2×#385—831no—
442C83C2×#244911yescharacteristic, complemented, Sylow
443C23×Q8—831no—
444C23×D4—831no—
445C24×C4—831no—
446C24×C4C2×D8311yescharacteristic
447C24×C4C2×D8311yescharacteristic
448C24×C4C2×D8311yescharacteristic
449C2×C22⋊Q8—838no—
450C2×C22⋊Q8—838no—
451C2×C22⋊Q8—1668no—
452C2×C22⋊Q8—1668no—
453C2×C4×D4—838no—
454C2×C4×D4—1668no—
455C22×C4⋊C4—28no—
456C22×C4⋊C4—831no—
457C22×C4⋊C4—831no—
458C22×C4⋊C4—831no—
459C22×C4⋊C4—831no—
460C22×C4⋊C4—831no—
461C22×C4⋊C4—831no—
462C22×C4⋊C4—831no—
463C22×C4⋊C4—831no—
464C22×C4⋊C4C2×D8311yescharacteristic
465C22×C4⋊C4C2×D8311yescharacteristic
466C22×C4⋊C4C2×D8311yescharacteristic
467C22×C4⋊C4C2×D8311yescharacteristic
468C22×C4⋊C4C2×D8318yescomplemented
469C22×C22⋊C4—831no—
470C22×C22⋊C4—831no—
471C22×C22⋊C4—831no—
472C22×C22⋊C4—831no—
473C22×C22⋊C4—831no—
474C22×C22⋊C4—831no—
475C22×C22⋊C4—831no—
476C22×C22⋊C4—831no—
477C22×C42—831no—
478#399—838no—
479#398—838no—
480#396—838no—
481#395—838no—
482#389—838no—
483#387—838no—
484#386—838no—
485#386—838no—
486#385—838no—
487#385—838no—
488#385—838no—
489C2×#95—831no—
490C2×#95—831no—
491C2×#95—831no—
492C2×#95—831no—
493C2×#95—831no—
494C2×#95—831no—
495C2×#95—831no—
496C2×#95—831no—
497C25—831no—
498C25C22×D8311yescharacteristic
499C22×Q8—3322no—
500C22×Q8—834no—
501C22×Q8—1664no—
502C22×Q8—1664no—
503C22×D4—838no—
504C22×D4—834no—
505C22×D4—1664no—
506C22×D4—1664no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—24no—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—42no—
516C23×C4—3322no—
517C23×C4—834no—
518C23×C4—831no—
519C23×C4—831no—
520C23×C4—831no—
521C23×C4—831no—
522C23×C4—831no—
523C23×C4—831no—
524C23×C4—831no—
525C23×C4—1664no—
526C23×C4—1664no—
527C23×C4C22×D8314yes—
528C23×C4C22×D8311yescharacteristic
529C23×C4C22×D8311yescharacteristic
530C23×C4C22×D8314yes—
531C23×C4C22×D8314yes—
532C23×C4C22×D8311yescharacteristic
533C23×C4C22×D8311yescharacteristic
534C23×C4C22×D8311yescharacteristic
535C23×C4C22×D8311yescharacteristic
536C22⋊Q8—16632no—
537C22⋊Q8—16632no—
538C4×D4—16632no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—232no—
543C2×C4⋊C4—3322no—
544C2×C4⋊C4—834no—
545C2×C4⋊C4—834no—
546C2×C4⋊C4—834no—
547C2×C4⋊C4—834no—
548C2×C4⋊C4—834no—
549C2×C4⋊C4—834no—
550C2×C4⋊C4—834no—
551C2×C4⋊C4—834no—
552C2×C4⋊C4—1664no—
553C2×C4⋊C4—1664no—
554C2×C4⋊C4—1664no—
555C2×C4⋊C4—1664no—
556C2×C4⋊C4—1664no—
557C2×C4⋊C4—1664no—
558C2×C4⋊C4—1664no—
559C2×C4⋊C4C22⋊D8318yescomplemented
560C2×C4⋊C4C22×D8314yes—
561C2×C4⋊C4C22×D8314yes—
562C2×C4⋊C4C22×D8314yes—
563C2×C4⋊C4C22×D8314yes—
564C2×C22⋊C4—3322no—
565C2×C22⋊C4—834no—
566C2×C22⋊C4—838no—
567C2×C22⋊C4—834no—
568C2×C22⋊C4—834no—
569C2×C22⋊C4—834no—
570C2×C22⋊C4—834no—
571C2×C22⋊C4—834no—
572C2×C22⋊C4—834no—
573C2×C22⋊C4—834no—
574C2×C22⋊C4—1664no—
575C2×C22⋊C4—1664no—
576C2×C22⋊C4—1664no—
577C2×C22⋊C4—1664no—
578C2×C22⋊C4—1664no—
579C2×C22⋊C4—1664no—
580C2×C42—834no—
581C2×C42—1664no—
582#95—834no—
583#95—834no—
584#95—834no—
585#95—834no—
586#95—834no—
587#95—834no—
588#95—834no—
589#95—834no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—834no—
595C24—832no—
596C24—1662no—
597C24—1662no—
598C24—1662no—
599C24—1662no—
600C24—1662no—
601C24—1662no—
602C24D4×D8314yes—
603C24Q8×D8314yes—
604C24#1305059014yes—
605C24C23×D8312yes—
606C24C23×D8311yescharacteristic
607C2×Q8—33216no—
608C2×Q8—3324no—
609C2×Q8—1668no—
610C2×Q8—1668no—
611C2×D4—8316no—
612C2×D4—16632no—
613C2×D4—1668no—
614C2×D4—1668no—
615C22×C4—232no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—28no—
636C22×C4—28no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—416no—
640C22×C4—416no—
641C22×C4—33216no—
642C22×C4—3324no—
643C22×C4—834no—
644C22×C4—834no—
645C22×C4—834no—
646C22×C4—832no—
647C22×C4—832no—
648C22×C4—832no—
649C22×C4—832no—
650C22×C4—832no—
651C22×C4—832no—
652C22×C4—832no—
653C22×C4—1668no—
654C22×C4—1662no—
655C22×C4—1662no—
656C22×C4—1662no—
657C22×C4—1662no—
658C22×C4—1662no—
659C22×C4—1662no—
660C22×C4—1662no—
661C22×C4—1662no—
662C22×C4—1662no—
663C22×C4—1662no—
664C22×C4—1662no—
665C22×C4—1662no—
666C22×C4—1668no—
667C22×C4—1662no—
668C22×C4—1662no—
669C22×C4—1662no—
670C22×C4—1662no—
671C22×C4—1662no—
672C22×C4—1662no—
673C22×C4C2×C22⋊D8314yes—
674C22×C4C2×C22⋊D8314yes—
675C22×C4C2×C22⋊D8314yes—
676C22×C4#1305059014yes—
677C22×C4C23×D8312yes—
678C22×C4C23×D8312yes—
679C22×C4C23×D8312yes—
680C22×C4C23×D8312yes—
681C22×C4C23×D8312yes—
682C22×C4C23×D8312yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—3324no—
687C4⋊C4—1668no—
688C4⋊C4—1668no—
689C4⋊C4—1668no—
690C4⋊C4—1668no—
691C4⋊C4—1668no—
692C4⋊C4—1668no—
693C4⋊C4—1668no—
694C4⋊C4C2×C22⋊D83116yescomplemented
695C22⋊C4—3324no—
696C22⋊C4—8316no—
697C22⋊C4—1668no—
698C22⋊C4—1668no—
699C22⋊C4—1668no—
700C22⋊C4—1668no—
701C22⋊C4—1668no—
702C22⋊C4—1668no—
703C42—1668no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—28no—
714C23—3324no—
715C23—3324no—
716C23—3324no—
717C23—3324no—
718C23—834no—
719C23—1668no—
720C23—1668no—
721C23—1668no—
722C23—1662no—
723C23—1662no—
724C23—1662no—
725C23—1662no—
726C23—1662no—
727C23—1662no—
728C23#14581770116yescomplemented
729C23C2×D4×D8314yes—
730C23C2×D4×D8312yes—
731C23C22×C22⋊D8312yes—
732C23C2×Q8×D8314yes—
733C23C2×Q8×D8312yes—
734C23C2×#1305059014yes—
735C23C2×#1305059012yes—
736C23C2×#1305059012yes—
737C23#1458183712yes—
738C23#1458184012yes—
739C23C24×D8311yescharacteristic
740Q8—33216no—
741D4—16632no—
742C2×C4—232no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—33216no—
766C2×C4—3324no—
767C2×C4—3324no—
768C2×C4—3324no—
769C2×C4—3324no—
770C2×C4—834no—
771C2×C4—834no—
772C2×C4—834no—
773C2×C4—1662no—
774C2×C4—1662no—
775C2×C4—1662no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1662no—
780C2×C4—1662no—
781C2×C4—1662no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4—1662no—
785C2×C4—1668no—
786C2×C4—1668no—
787C2×C4—1668no—
788C2×C4—1662no—
789C2×C4—1662no—
790C2×C4—1662no—
791C2×C4—1662no—
792C2×C4—1662no—
793C2×C4—1662no—
794C2×C4C22×C22⋊D8314yes—
795C2×C4C22×C22⋊D8314yes—
796C2×C4C22×C22⋊D8314yes—
797C2×C4C2×#1305059014yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—232no—
804C22—24no—
805C22—3322no—
806C22—3322no—
807C22—3322no—
808C22—33216no—
809C22—3322no—
810C22—1664no—
811C22—1664no—
812C22—1664no—
813C22C2×#1458177014yes—
814C22C2×#1458177018yescomplemented
815C22#1912821214yes—
816C22#1912829814yes—
817C22D4×C22⋊D8314yes—
818C22#1912835214yes—
819C22Q8×C22⋊D8314yes—
820C22#1912840614yes—
821C22C22×D4×D8311yescharacteristic
822C22C23×C22⋊D8311yescharacteristic
823C22C22×Q8×D8311yescharacteristic
824C22C22×#1305059011yescharacteristic
825C22C22×#1305059011yescharacteristic
826C22C2×#1458183711yescharacteristic
827C22C2×#1458184011yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—3322no—
835C4—3322no—
836C4—3322no—
837C4—3322no—
838C4—1664no—
839C4—1664no—
840C4—1664no—
841C2—28no—
842C2—3324no—
843C2#2491127218yesdirect product factor
844C2C22×#1458177011yescharacteristic
845C2C2×#1912821211yescharacteristic
846C2C2×#1912829811yescharacteristic
847C2C2×D4×C22⋊D8311yescharacteristic
848C2C2×#1912835211yescharacteristic
849C2C2×Q8×C22⋊D8311yescharacteristic
850C2C2×#1912840611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC23×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC23×C4⋊C4D83
hypocenterC83C2×#2449
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14581771C2semidirect
2. C22×#14581770C2semidirect
4. #24911272C2direct (N × H)
5. C2×#19127636C2semidirect
6. C2×#19127632C2semidirect
7. C2×#19127623C2semidirect
8. C2×#19127621C2semidirect
9. C2×#19127596C2semidirect
10. C2×#19127587C2semidirect
13. C2×#19127574C2semidirect
14. C2×#19127574C2semidirect
15. C2×#19127572C2semidirect
16. C23×C4⋊C4×C83C2semidirect
21. C2×#14581771C22semidirect
23. C2×#14581770C22semidirect
43. #19127636C22semidirect
44. #19127632C22semidirect
45. #19127623C22semidirect
46. #19127621C22semidirect
47. #19127596C22semidirect
48. #19127587C22semidirect
51. #19127574C22semidirect
52. #19127574C22semidirect
53. #19127572C22semidirect
70. C22×C4⋊C4×C83C22semidirect
78. C22×C22⋊D83Q8semidirect
159. C2×C4⋊C4×C83D4semidirect
179. C2×C22⋊D83C2×Q8semidirect
277. C4⋊C4×C83C2×D4semidirect
288. C23×C83C22⋊Q8semidirect
380. C22×C83C2×C22⋊Q8semidirect
417. C2×C83#2449semidirect
429. C23×C4⋊C4D83semidirect
442. C83C2×#2449semidirect
468. C22×C4⋊C4C2×D83semidirect
559. C2×C4⋊C4C22⋊D83semidirect
694. C4⋊C4C2×C22⋊D83semidirect
728. C23#14581770semidirect
814. C22C2×#14581770semidirect
843. C2#24911272direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817712
C22×#145817702
C22×C4×C22⋊D832
#249112722
C2×#191276362
C2×#191276322
C2×#191276232
C2×#191276212
C2×#191275962
C2×#191275872
C2×#191275802
C2×#191275742
C2×#191275722
C23×C4⋊C4×C832
C2×#244983