Finite Group Databasebeta

← C2×#24910172 #35563189

Subgroups — C2×#24910172 #35563189

Order 21248.

3566 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×(C22⋊D83)⋊C4C211yesmaximal, characteristic
4#24910172C2116yesmaximal, direct product factor
5C2×#19127605C211yesmaximal, characteristic, complemented
6C2×#19127601C211yesmaximal, characteristic
7C2×#19127593C211yesmaximal, characteristic, complemented
8C2×#19127592C211yesmaximal, characteristic, complemented
9C2×#19127589C211yesmaximal, characteristic, complemented
10C2×#19127576C211yesmaximal, characteristic, complemented
11C2×#19127575C211yesmaximal, characteristic, complemented
12C2×#19127573C211yesmaximal, characteristic, complemented
13C2×#19127572C211yesmaximal, characteristic, complemented
14C2×#19127570C211yesmaximal, characteristic, complemented
15C2×#19127546C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C24×Dic83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C2×#14581778C4116yescomplemented
22C2×#14581778C2218yes—
23C2×C4×Dic166—28no—
24C2×C4×Dic166C2218yescomplemented
25C2×(C22⋊D83)⋊C4—28no—
26C2×(C22⋊D83)⋊C4C2218yes—
27C22×C4⋊Dic83C2211yescharacteristic
28C22×C4⋊Dic83C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×C22⋊Dic83C2211yescharacteristic
35C22×C22⋊Dic83C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×C4×Dic83C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic
44C22×C4×Dic83C2211yescharacteristic
45#19127605C2218yescomplemented
46#19127601C2218yes—
47#19127593C2218yescomplemented
48#19127592C2218yescomplemented
49#19127589C2218yescomplemented
50#19127576C2218yescomplemented
51#19127575C2218yescomplemented
52#19127573C2218yescomplemented
53#19127572C2218yescomplemented
54#19127570C2218yescomplemented
55#19127546C2218yescomplemented
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C42×C83C2211yescharacteristic
67#388×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×Dic83—24no—
80C23×Dic83—42no—
81C23×Dic83—42no—
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2314yes—
89C23×Dic83C2311yescharacteristic
90C22×C4×D83—24no—
91C22×C4×D83—42no—
92C22×C4×D83—42no—
93C22×C4×D83C2314yes—
94#14581778C2×C4164yescomplemented
95C4×Dic166—232no—
96(C22⋊D83)⋊C4—232no—
97C2×C4⋊Dic83—24no—
98C2×C4⋊Dic83—42no—
99C2×C4⋊Dic83C2314yes—
100C2×C4⋊Dic83C2314yes—
101C2×Dic83⋊C4—24no—
102C2×Dic83⋊C4—24no—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4—42no—
105C2×Dic83⋊C4—42no—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×C22⋊Dic83—42no—
112C2×C22⋊Dic83C2×C418yescomplemented
113C2×C22⋊Dic83C2314yes—
114C2×C22⋊Dic83C2314yes—
115C2×(C2×D83)⋊C4—24no—
116C2×(C2×D83)⋊C4—42no—
117C2×(C2×D83)⋊C4—42no—
118C2×(C2×D83)⋊C4C2×C418yescomplemented
119C2×(C2×D83)⋊C4C2×C418yescomplemented
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×C4×Dic83—24no—
126C2×C4×Dic83—24no—
127C2×C4×Dic83C2×C418yescomplemented
128C2×C4×Dic83D418yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C25×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C2×C4⋊C4×C83—42no—
147C2×C4⋊C4×C83C2314yes—
148C2×C22⋊C4×C83—24no—
149C2×C22⋊C4×C83—42no—
150C2×C22⋊C4×C83C2×C418yescomplemented
151C2×C22⋊C4×C83C2314yes—
152C2×C22⋊C4×C83C2314yes—
153C2×C22⋊C4×C83C2314yes—
154C2×C42×C83—24no—
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×Dic83—28no—
190C22×Dic83—44no—
191C22×Dic83—44no—
192C22×Dic83—416no—
193C22×Dic83C22×C414yes—
194C22×Dic83C22×C414yes—
195C22×Dic83C22×C414yes—
196C22×Dic83C2×D414yes—
197C22×Dic83C2×D414yes—
198C22×Dic83#4114yes—
199C22×Dic83C2412yes—
200C22×Dic83C2412yes—
201C22×Dic83C2412yes—
202C22×Dic83C2412yes—
203C22×Dic83C2412yes—
204C22×Dic83C2412yes—
205C22×Dic83C2412yes—
206C2×C4×D83—28no—
207C2×C4×D83—44no—
208C2×C4×D83—44no—
209C2×C4×D83—416no—
210C4⋊Dic83—28no—
211C4⋊Dic83—44no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—44no—
216Dic83⋊C4—44no—
217C22⋊Dic83—44no—
218C22⋊Dic83C22×C4116yescomplemented
219(C2×D83)⋊C4—28no—
220(C2×D83)⋊C4—44no—
221(C2×D83)⋊C4—44no—
222(C2×D83)⋊C4C22×C4116yescomplemented
223(C2×D83)⋊C4C22×C4116yescomplemented
224C4×Dic83—28no—
225C4×Dic83—28no—
226C4×Dic83C22×C4116yescomplemented
227C4×Dic83C2×D4116yes—
228C24×C83—22no—
229C24×C83—22no—
230C24×C83—22no—
231C24×C83—22no—
232C24×C83—22no—
233C24×C83—22no—
234C24×C83C22×C414yes—
235C24×C83C2412yes—
236C24×C83C2411yescharacteristic
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×C83—22no—
252C22×C4×C83C22×C414yes—
253C22×C4×C83C22×C414yes—
254C22×C4×C83C2×D414yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2412yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C4⋊C4×C83—44no—
262C22⋊C4×C83—28no—
263C22⋊C4×C83—44no—
264C22⋊C4×C83C22×C4116yescomplemented
265C42×C83—28no—
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×C83H(5,𝔽2)12yes—
284C23×C83H(5,𝔽2)12yes—
285C23×C832−1+412yes—
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—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—44no—
321C2×C4×C83—44no—
322C2×C4×C83—44no—
323C2×C4×C83C23×C414yes—
324C2×C4×C83C23×C414yes—
325C2×C4×C83C22×D414yes—
326C22⋊D83—232no—
327C2×Dic83—28no—
328C2×Dic83—28no—
329C2×Dic83—28no—
330C2×Dic83—22no—
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—416no—
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×C83#52014yes—
368C22×C83#52014yes—
369C22×C83#53514yes—
370C22×C83#53614yes—
371C22×C83#54214yes—
372C22×C83#54214yes—
373C22×C83C24×C411yescharacteristic
374C22×C83C23×D411yescharacteristic
375C22×C83C22×#4111yescharacteristic
376C22×C83C2×H(5,𝔽2)11yescharacteristic
377C22×C83C2×H(5,𝔽2)11yescharacteristic
378C22×C83C2×2−1+411yescharacteristic
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—42no—
392C4×C83—42no—
393C4×C83—42no—
394Dic83—24no—
395Dic83—24no—
396Dic83—24no—
397Dic83—42no—
398Dic83—42no—
399Dic83—42no—
400Dic83C2×C4×D418yes—
401C2×#2326—831nomaximal, Sylow
402C2×C83—44no—
403C2×C83#232618yescomplemented
404C2×C83C22×C4×D411yescharacteristic
405C2×C83C2×#52011yescharacteristic
406C2×C83C2×#52011yescharacteristic
407C2×C83C2×#53511yescharacteristic
408C2×C83C2×#53611yescharacteristic
409C2×C83C2×#54211yescharacteristic
410C2×C83C2×#54211yescharacteristic
411D83—44no—
412C22×#124—831no—
413C22×C4×Q8—831no—
414C22×C4×D4—831no—
415#2326—8316no—
416C2×#391—831no—
417C2×#390—831no—
418C2×#388—831no—
419C2×#388—831no—
420C2×#388—831no—
421C2×#388D8311yescharacteristic, complemented
422C2×#385—831no—
423C2×#385—831no—
424C2×#385—831no—
425C2×#385—831no—
426C2×#384—831no—
427C2×#376—831no—
428C83C2×#232611yescharacteristic, complemented, Sylow
429C23×Q8—831no—
430C23×D4—831no—
431C24×C4—831no—
432C24×C4—831no—
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×C4⋊C4—831no—
446C22×C4⋊C4C2×D8311yescharacteristic
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⋊C4—831no—
454C22×C22⋊C4C2×D8311yescharacteristic
455C22×C22⋊C4C2×D8311yescharacteristic
456C22×C22⋊C4C2×D8311yescharacteristic
457C22×C42—831no—
458C22×C42—831no—
459C22×C42—831no—
460C22×C42—831no—
461C22×C42C2×D8311yescharacteristic
462#391—838no—
463#390—838no—
464#388—838no—
465#388—838no—
466#388—838no—
467#388C2×D8318yescomplemented
468#385—838no—
469#385—838no—
470#385—838no—
471#385—838no—
472#384—838no—
473#376—838no—
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—3322no—
493C23×C4—3322no—
494C23×C4—3322no—
495C23×C4—3322no—
496C23×C4—834no—
497C23×C4—834no—
498C23×C4—831no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—831no—
504C23×C4—831no—
505C23×C4—1664no—
506C23×C4—1664no—
507C23×C4C22×D8311yescharacteristic
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—42no—
517C2×C4⋊C4—3322no—
518C2×C4⋊C4—3322no—
519C2×C4⋊C4—3322no—
520C2×C4⋊C4—834no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—1664no—
528C2×C4⋊C4—1664no—
529C2×C4⋊C4—1664no—
530C2×C4⋊C4—1664no—
531C2×C4⋊C4C22×D8314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—3322no—
535C2×C22⋊C4—3322no—
536C2×C22⋊C4—3322no—
537C2×C22⋊C4—834no—
538C2×C22⋊C4—834no—
539C2×C22⋊C4—834no—
540C2×C22⋊C4—838no—
541C2×C22⋊C4—834no—
542C2×C22⋊C4—838no—
543C2×C22⋊C4—838no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—1664no—
548C2×C22⋊C4C4×D8318yescomplemented
549C2×C22⋊C4C22×D8314yes—
550C2×C22⋊C4C22×D8314yes—
551C2×C22⋊C4C22×D8314yes—
552C2×C42—24no—
553C2×C42—838no—
554C2×C42—838no—
555C2×C42—834no—
556C2×C42—834no—
557C2×C42—834no—
558C2×C42—834no—
559C2×C42—1664no—
560C2×C42—1664no—
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—22no—
609C22×C4—22no—
610C22×C4—3324no—
611C22×C4—3324no—
612C22×C4—33216no—
613C22×C4—33216no—
614C22×C4—3324no—
615C22×C4—3324no—
616C22×C4—834no—
617C22×C4—834no—
618C22×C4—834no—
619C22×C4—832no—
620C22×C4—834no—
621C22×C4—834no—
622C22×C4—834no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—1668no—
630C22×C4—1668no—
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×C4C2×C4×D8314yes—
647C22×C4C2×C4×D8314yes—
648C22×C4D4×D8314yes—
649C22×C4C23×D8312yes—
650C22×C4C23×D8312yes—
651C22×C4C23×D8312yes—
652C22×C4C23×D8312yes—
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C4⋊C4—44no—
656C4⋊C4—3324no—
657C4⋊C4—3324no—
658C4⋊C4—3324no—
659C4⋊C4—1668no—
660C4⋊C4—1668no—
661C4⋊C4—1668no—
662C4⋊C4—1668no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—3324no—
666C22⋊C4—3324no—
667C22⋊C4—3324no—
668C22⋊C4—8316no—
669C22⋊C4—8316no—
670C22⋊C4—8316no—
671C22⋊C4—1668no—
672C22⋊C4C2×C4×D83116yescomplemented
673C42—28no—
674C42—8316no—
675C42—8316no—
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—
709C23#1458183712yes—
710C23#1458183812yes—
711C23#1458183912yes—
712C23#1458183912yes—
713C23C24×D8311yescharacteristic
714Q8—16632no—
715D4—16632no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
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—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—33216no—
738C2×C4—3324no—
739C2×C4—3324no—
740C2×C4—3324no—
741C2×C4—33216no—
742C2×C4—8316no—
743C2×C4—834no—
744C2×C4—834no—
745C2×C4—834no—
746C2×C4—834no—
747C2×C4—834no—
748C2×C4—834no—
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—1668no—
759C2×C4—1668no—
760C2×C4—1662no—
761C2×C4—1668no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4C22×C4×D8314yes—
768C2×C4C22×C4×D8314yes—
769C2×C4C2×D4×D8314yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—416no—
776C22—42no—
777C22—42no—
778C22—3322no—
779C22—3322no—
780C22—33216no—
781C22—3322no—
782C22—3322no—
783C22—1664no—
784C22—1664no—
785C22—1664no—
786C22C4×D4×D8314yes—
787C22#1912818014yes—
788C22#1912818114yes—
789C22#1912826714yes—
790C22#1912827314yes—
791C22#1912831514yes—
792C22#1912831714yes—
793C22C23×C4×D8311yescharacteristic
794C22C22×D4×D8311yescharacteristic
795C22C2×#41×D8311yescharacteristic
796C22C2×#1458183711yescharacteristic
797C22C2×#1458183811yescharacteristic
798C22C2×#1458183911yescharacteristic
799C22C2×#1458183911yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—3322no—
807C4—3322no—
808C4—3322no—
809C4—838no—
810C4—1664no—
811C4—1664no—
812C4—1664no—
813C2—44no—
814C2—3324no—
815C2#2491017218yesdirect product factor
816C2C2×C4×D4×D8311yescharacteristic
817C2C2×#1912818011yescharacteristic
818C2C2×#1912818111yescharacteristic
819C2C2×#1912826711yescharacteristic
820C2C2×#1912827311yescharacteristic
821C2C2×#1912831511yescharacteristic
822C2C2×#1912831711yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC2×#388D83
hypocenterC83C2×#2326
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic166C2semidirect
4. #24910172C2direct (N × H)
5. C2×#19127605C2semidirect
7. C2×#19127593C2semidirect
8. C2×#19127592C2semidirect
9. C2×#19127589C2semidirect
10. C2×#19127576C2semidirect
11. C2×#19127575C2semidirect
12. C2×#19127573C2semidirect
13. C2×#19127572C2semidirect
14. C2×#19127570C2semidirect
15. C2×#19127546C2semidirect
16. C2×#388×C83C2semidirect
21. C2×#14581778C4semidirect
24. C2×C4×Dic166C22semidirect
45. #19127605C22semidirect
47. #19127593C22semidirect
48. #19127592C22semidirect
49. #19127589C22semidirect
50. #19127576C22semidirect
51. #19127575C22semidirect
52. #19127573C22semidirect
53. #19127572C22semidirect
54. #19127570C22semidirect
55. #19127546C22semidirect
67. #388×C83C22semidirect
73. C22×Dic166C2×C4semidirect
94. #14581778C2×C4semidirect
112. C2×C22⋊Dic83C2×C4semidirect
118. C2×(C2×D83)⋊C4C2×C4semidirect
119. C2×(C2×D83)⋊C4C2×C4semidirect
127. C2×C4×Dic83C2×C4semidirect
150. C2×C22⋊C4×C83C2×C4semidirect
169. C2×Dic166C22×C4semidirect
218. C22⋊Dic83C22×C4semidirect
222. (C2×D83)⋊C4C22×C4semidirect
223. (C2×D83)⋊C4C22×C4semidirect
226. C4×Dic83C22×C4semidirect
264. C22⋊C4×C83C22×C4semidirect
403. C2×C83#2326semidirect
421. C2×#388D83semidirect
428. C83C2×#2326semidirect
467. #388C2×D83semidirect
548. C2×C22⋊C4C4×D83semidirect
672. C22⋊C4C2×C4×D83semidirect
815. C2#24910172direct (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×(C22⋊D83)⋊C42
#249101722
C2×#191276052
C2×#191276012
C2×#191275932
C2×#191275922
C2×#191275892
C2×#191275762
C2×#191275752
C2×#191275732
C2×#191275722
C2×#191275702
C2×#191275462
C2×#388×C832
C2×#232683