Finite Group Databasebeta

← C2×#24921551 #36312619

Subgroups — C2×#24921551 #36312619

Order 21248.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921551C2132yesmaximal, direct product factor
2C2×#19128427C212yesmaximal, complemented
3C2×#19128426C211yesmaximal, characteristic, complemented
4C2×#19128426C211yesmaximal, characteristic, complemented
5C2×#19128425C211yesmaximal, characteristic, complemented
6C2×#19128423C212yesmaximal, complemented
7C2×#19128393C212yesmaximal, complemented
8C2×#19128384C214yesmaximal, complemented
9C2×#19128366C211yesmaximal, characteristic, complemented
10C2×#19128364C212yesmaximal, complemented
11C2×#19128310C214yesmaximal, complemented
12C2×#19128309C212yesmaximal, complemented
13C2×#19128253C212yesmaximal, complemented
14C2×#19128237C212yesmaximal
15C2×#19128235C211yesmaximal, characteristic
16C2×#19128177C212yesmaximal, complemented
17C22×C4×Dic166C211yesmaximal, characteristic, complemented
18C2×#533×C83C211yesmaximal, characteristic, complemented
19C23×Dic166C2211yescharacteristic
20C22×Q8×D83C2212yes—
21#19128427C22132yescomplemented
22#19128426C22116yescomplemented
23#19128426C22116yescomplemented
24#19128425C22116yescomplemented
25#19128423C22132yescomplemented
26#19128393C22132yescomplemented
27#19128384C22164yescomplemented
28#19128366C22116yescomplemented
29#19128364C22132yescomplemented
30#19128310C22164yescomplemented
31#19128309C22132yescomplemented
32#19128253C22132yescomplemented
33C2×#14581791C2214yes—
34C2×#14581791C2212yes—
35C2×#14581790C2212yes—
36C2×#14581790C2212yes—
37#19128237C22132yes—
38#19128235C22116yes—
39C2×#14581787C2214yes—
40C2×#14581787C2214yes—
41C2×#14581787C2214yes—
42C2×#14581786C2214yes—
43C2×#14581786C2212yes—
44C2×#14581784C2214yes—
45C2×#14581784C2211yescharacteristic
46C2×#14581783C2212yes—
47C2×#14581783C2214yes—
48C2×#14581783C2212yes—
49C2×#14581782C2214yes—
50C2×#14581782C2214yes—
51C2×#14581782C2214yes—
52C2×#14581781C2212yes—
53C2×#14581780C2211yescharacteristic
54C2×#14581776C2214yes—
55C2×#14581775C2212yes—
56C2×#14581772C2212yes—
57C2×#14581771C2211yescharacteristic
58C2×#14581770C2214yes—
59C2×#14581770C2214yes—
60C2×#14581769C2214yes—
61C2×#14581768C2212yes—
62C2×#14581766C2211yescharacteristic
63#19128177C22132yescomplemented
64C2×Q8×Dic83C2212yes—
65C2×Q8×Dic83C2212yes—
66C2×Q8×Dic83C2212yes—
67C2×C4×Dic166C2211yescharacteristic
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2211yescharacteristic
71C2×C4×Dic166C2211yescharacteristic
72C2×C4×Dic166C2212yes—
73C2×C4×Dic166C2214yes—
74C2×C4×Dic166C2211yescharacteristic
75C2×C4×Dic166C22116yescomplemented
76C2×#14581757C2212yes—
77C2×#14581757C2214yes—
78C2×#14581757C2212yes—
79C2×C4×D332C2211yescharacteristic
80C2×#14581754C2212yes—
81C2×C4×C22⋊D83C2212yes—
82C2×(C22⋊D83)⋊C4C2214yes—
83C2×#14581750C2212yes—
84C2×#14581750C2214yes—
85C2×#14581749C2214yes—
86C2×#14581749C2212yes—
87C2×#14581748C2214yes—
88C22×C4⋊Dic83C2211yescharacteristic
89C22×Dic83⋊C4C2212yes—
90C22×C4×Dic83C2212yes—
91#533×C83C22116yescomplemented
92C2×C4⋊Q8×C83C2211yescharacteristic
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#125×C83C2212yes—
95C2×C22⋊Q8×C83C2212yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2212yes—
98C2×C4×Q8×C83C2212yes—
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C22×Dic166—28no—
102C22×Dic166C2318yes—
103C22×Dic166C2311yescharacteristic
104C22×Dic166C2314yes—
105C22×Dic166C2312yes—
106C22×Dic166C2311yescharacteristic
107C22×Dic166C2311yescharacteristic
108C2×Q8×D83—216no—
109C2×Q8×D83C23116yes—
110C22×D332C2311yescharacteristic
111C22×C22⋊D83C2312yes—
112C23×Dic83C2312yes—
113C23×Dic83C2312yes—
114C22×C4×D83C2314yes—
115C22×C4×D83C2312yes—
116#14581791C23132yes—
117#14581791C23116yes—
118#14581790C23116yes—
119#14581790C23116yes—
120#14581787C23132yes—
121#14581787C23132yes—
122#14581787C23132yes—
123#14581786C23132yes—
124#14581786C23116yes—
125#14581784C23132yes—
126#14581784C2318yes—
127#14581783C23116yes—
128#14581783C23132yes—
129#14581783C23116yes—
130#14581782C23132yes—
131#14581782C23132yes—
132#14581782C23132yes—
133#14581781C23116yes—
134#14581780C2318yes—
135#14581776C23132yes—
136#14581775C23116yes—
137#14581772C23116yes—
138#14581771C2318yes—
139#14581770C23132yes—
140#14581770C23132yes—
141#14581769C23132yes—
142#14581768C23116yes—
143#14581766C2318yes—
144Q8×Dic83C23116yes—
145Q8×Dic83C23116yes—
146Q8×Dic83C23116yes—
147C4×Dic166C2318yes—
148C4×Dic166C23132yes—
149C4×Dic166C23116yes—
150C4×Dic166C2318yes—
151C4×Dic166C2318yes—
152C4×Dic166C2318yes—
153C4×Dic166C23116yes—
154C4×Dic166C2318yes—
155#14581757C23116yes—
156#14581757C23116yes—
157#14581757C23132yes—
158C4×D332C2318yes—
159#14581754C23116yes—
160C4×C22⋊D83C23116yes—
161(C22⋊D83)⋊C4C23132yes—
162#14581750C23116yes—
163#14581750C23132yes—
164#14581749C23132yes—
165#14581749C23116yes—
166#14581748C23132yes—
167C2×C4⋊Dic83C2318yes—
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2311yescharacteristic
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2314yes—
172C2×C4⋊Dic83C2311yescharacteristic
173C2×C4⋊Dic83C2311yescharacteristic
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2314yes—
176C2×Dic83⋊C4C23116yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2312yes—
188C2×Dic83⋊C4C2314yes—
189C2×Dic83⋊C4C2312yes—
190C2×C22⋊Dic83C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×C4×Dic83C2312yes—
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2312yes—
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C23116yes—
203C2×C4×Dic83C2314yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2312yes—
206C2×C4×Dic83C2314yes—
207C22×Q8×C83C2312yes—
208C22×Q8×C83C2312yes—
209C23×C4×C83C2311yescharacteristic
210C23×C4×C83C2311yescharacteristic
211C23×C4×C83C2311yescharacteristic
212C4⋊Q8×C83C2318yes—
213C4⋊Q8×C83C2318yes—
214#125×C83C23116yes—
215C22⋊Q8×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C4×Q8×C83C23116yes—
218C4×Q8×C83C23116yes—
219#117×C83C23116yes—
220C2×C4⋊C4×C83C2312yes—
221C2×C4⋊C4×C83C2312yes—
222C2×C4⋊C4×C83C2314yes—
223C2×C4⋊C4×C83C2314yes—
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2314yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2318yes—
232C2×C42×C83C2314yes—
233C23×D83C2412yes—
234C2×Dic166—24no—
235C2×Dic166—24no—
236C2×Dic166—216no—
237C2×Dic166—28no—
238C2×Dic166—232no—
239C2×Dic166#4118yes—
240C2×Dic166C24116yes—
241C2×Dic166C2418yes—
242C2×Dic166C2414yes—
243C2×Dic166C2414yes—
244C2×Dic166C2414yes—
245Q8×D83—264no—
246C2×D332—24no—
247C2×D332C2414yes—
248C2×C22⋊D83—28no—
249C2×C22⋊D83C2418yes—
250C22×Dic83—28no—
251C22×Dic83—28no—
252C22×Dic83C2418yes—
253C22×Dic83C2418yes—
254C22×Dic83C2412yes—
255C22×Dic83C2412yes—
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C22×Dic83C2412yes—
259C22×Dic83C2412yes—
260C22×Dic83C2412yes—
261C2×C4×D83—28no—
262C2×C4×D83—216no—
263C2×C4×D83C2418yes—
264C2×C4×D83C24116yes—
265C4⋊Dic83C2414yes—
266C4⋊Dic83C2414yes—
267C4⋊Dic83C24116yes—
268C4⋊Dic83C2414yes—
269C4⋊Dic83C24116yes—
270C4⋊Dic83C24116yes—
271C4⋊Dic83C2418yes—
272C4⋊Dic83C2414yes—
273Dic83⋊C4C24116yes—
274Dic83⋊C4C24116yes—
275Dic83⋊C4C24116yes—
276Dic83⋊C4C2418yes—
277Dic83⋊C4C2418yes—
278Dic83⋊C4C2418yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C2418yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C2418yes—
286C22⋊Dic83C2418yes—
287(C2×D83)⋊C4C2418yes—
288(C2×D83)⋊C4C24116yes—
289(C2×D83)⋊C4C2418yes—
290(C2×D83)⋊C4C2418yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C24116yes—
294C4×Dic83C2418yes—
295C4×Dic83C2418yes—
296C4×Dic83C24116yes—
297C4×Dic83C24116yes—
298C4×Dic83C24116yes—
299C4×Dic83C2418yes—
300C4×Dic83C2418yes—
301C4×Dic83C2418yes—
302C24×C83C2411yescharacteristic
303C2×Q8×C83—28no—
304C2×Q8×C83—28no—
305C2×Q8×C83C2418yes—
306C2×Q8×C83C2418yes—
307C22×C4×C83—24no—
308C22×C4×C83—24no—
309C22×C4×C83—24no—
310C22×C4×C83C2414yes—
311C22×C4×C83C2414yes—
312C22×C4×C83C2414yes—
313C22×C4×C83C2411yescharacteristic
314C22×C4×C83C2414yes—
315C22×C4×C83C2411yescharacteristic
316C22×C4×C83C2411yescharacteristic
317C22×C4×C83C2411yescharacteristic
318C22×C4×C83C2414yes—
319C22×C4×C83C2411yescharacteristic
320C22×C4×C83C2411yescharacteristic
321C4⋊C4×C83C2418yes—
322C4⋊C4×C83C24116yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2418yes—
325C4⋊C4×C83C24116yes—
326C4⋊C4×C83C2418yes—
327C22⋊C4×C83C24116yes—
328C42×C83C2414yes—
329C42×C83C24116yes—
330C42×C83C2414yes—
331C42×C83C2414yes—
332C42×C83C2414yes—
333C23×C83—22no—
334C23×C83—22no—
335C23×C832−1+414yes—
336C23×C83C2512yes—
337C23×C83C2511yescharacteristic
338C22×D83—24no—
339C22×D83—24no—
340C22×D83—24no—
341C22×D83C2514yes—
342Q8×C83—216no—
343Q8×C83—216no—
344C2×C4×C83—22no—
345C2×C4×C83—28no—
346C2×C4×C83—22no—
347C2×C4×C83—28no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—28no—
351C2×C4×C83—28no—
352C2×C4×C83—28no—
353C2×C4×C83C2×#4114yes—
354C2×C4×C832−1+414yes—
355C2×C4×C83C2512yes—
356C2×C4×C83C2512yes—
357C2×C4×C83C2512yes—
358C2×C4×C83C2512yes—
359C2×C4×C83C2518yes—
360C2×C4×C83C2518yes—
361C2×C4×C83C2512yes—
362C2×C4×C83C2512yes—
363C22⋊D83—216no—
364C2×Dic83—24no—
365C2×Dic83—24no—
366C2×Dic83—216no—
367C2×Dic83—24no—
368C2×Dic83—24no—
369C2×Dic83—24no—
370C2×Dic83—24no—
371C2×Dic83—216no—
372C2×Dic83C2×#4118yes—
373C2×Dic83C2514yes—
374C2×Dic83C2514yes—
375C2×Dic83C2514yes—
376C2×Dic83C2514yes—
377C2×Dic83C2514yes—
378C2×Dic83C2514yes—
379C2×Dic83C2514yes—
380D332—28no—
381C4×D83—216no—
382C4×D83—232no—
383Dic166—28no—
384Dic166—28no—
385Dic166—232no—
386Dic166—216no—
387Dic166C2×#41116yes—
388C22×C83—22no—
389C22×C83—22no—
390C22×C83—28no—
391C22×C83C22×#4112yes—
392C22×C83C2×2−1+412yes—
393C22×C83C2×2−1+414yes—
394C22×C83C2×2−1+412yes—
395C22×C83C2611yescharacteristic
396C2×D83—24no—
397C2×D83—24no—
398C2×D83—24no—
399C2×D83—48no—
400C4×C83—22no—
401C4×C83—28no—
402C4×C83—22no—
403C4×C83—22no—
404C4×C83—22no—
405C4×C83—28no—
406C4×C83C22×#4114yes—
407C4×C83C2×2−1+414yes—
408Dic83—24no—
409Dic83—24no—
410Dic83—24no—
411Dic83—24no—
412Dic83—24no—
413Dic83—24no—
414Dic83C22×#4118yes—
415C2×#3523—831nomaximal, Sylow
416C2×C83—24no—
417C2×C83#352314yescomplemented
418C2×C83C23×#4111yescharacteristic
419C2×C83C22×2−1+411yescharacteristic
420C2×C83C22×2−1+411yescharacteristic
421D83—44no—
422#3523—8332no—
423C2×#557—831no—
424C2×#557—831no—
425C2×#557—832no—
426C2×#556—831no—
427C2×#556—832no—
428C2×#552—832no—
429C2×#552—834no—
430C2×D4×Q8—831no—
431C2×D4×Q8—832no—
432C2×#541—834no—
433C2×#541—832no—
434C2×#533—832no—
435C2×#533D8311yescharacteristic, complemented
436C2×#529—831no—
437C2×#529—832no—
438C2×#519—832no—
439C22×C4×Q8—831no—
440C83C2×#352311yescharacteristic, complemented, Sylow
441C23×Q8—832no—
442C23×Q8—831no—
443#557—8316no—
444#557—8316no—
445#557—8332no—
446#556—8316no—
447#556—8332no—
448#552—8332no—
449#552—8364no—
450D4×Q8—8316no—
451D4×Q8—8332no—
452#541—8364no—
453#541—8332no—
454#533—8332no—
455#533C2×D83116yescomplemented
456C2×C4⋊Q8—832no—
457C2×C4⋊Q8—832no—
458C2×C4⋊Q8—832no—
459C2×C4⋊Q8—834no—
460C2×C4⋊Q8C2×D8311yescharacteristic
461C2×C4⋊Q8C2×D8311yescharacteristic
462#529—8332no—
463#529—8316no—
464C2×#126—834no—
465C2×#126—834no—
466C2×#126—834no—
467C2×#126—832no—
468C2×#126—834no—
469C2×#125—832no—
470C2×#125—834no—
471C2×#125—834no—
472C2×#125—834no—
473C2×#125—834no—
474C2×#125—832no—
475C2×#125—831no—
476C2×#125—834no—
477C2×#125C2×D8312yes—
478C2×#124—832no—
479C2×#124—831no—
480C2×#123—832no—
481C2×#123—834no—
482C2×C22⋊Q8—832no—
483C2×C22⋊Q8—831no—
484C2×C22⋊Q8—834no—
485C2×C22⋊Q8—834no—
486C2×C22⋊Q8—832no—
487C2×C22⋊Q8—834no—
488C2×C22⋊Q8C2×D8312yes—
489C2×C22⋊Q8C2×D8312yes—
490C2×#121—831no—
491#519—8332no—
492C2×C4×Q8—832no—
493C2×C4×Q8—832no—
494C2×C4×Q8—832no—
495C2×C4×Q8—834no—
496C2×C4×Q8—832no—
497C2×C4×Q8—832no—
498C2×C4×Q8—831no—
499C2×C4×Q8—832no—
500C2×C4×Q8—831no—
501C2×C4×Q8—831no—
502C2×C4×Q8—832no—
503C2×C4×Q8—831no—
504C2×C4×Q8—8316no—
505C2×C4×Q8—834no—
506C2×C4×Q8—831no—
507C2×C4×Q8C2×D8312yes—
508C2×C4×Q8C2×D8312yes—
509C2×C4×D4—832no—
510C2×C4×D4—832no—
511C2×C4×D4—834no—
512C2×C4×D4—831no—
513C2×#117—834no—
514C2×#117—832no—
515C2×#117—834no—
516C2×#117—832no—
517C2×#117—834no—
518C2×#117C2×D8312yes—
519C22×C4⋊C4—832no—
520C22×C4⋊C4—831no—
521C22×C42—832no—
522C22×C42C2×D8311yescharacteristic
523C22×Q8—8316no—
524C22×Q8—831no—
525C22×Q8—831no—
526C22×Q8—834no—
527C22×Q8—832no—
528C22×Q8—831no—
529C22×Q8—838no—
530C22×Q8—1668no—
531C22×Q8—16616no—
532C22×Q8C22×D8312yes—
533C22×Q8C22×D8312yes—
534C22×D4—832no—
535C22×D4—831no—
536C23×C4—832no—
537C23×C4—832no—
538C23×C4—834no—
539C23×C4—832no—
540C23×C4C22×D8311yescharacteristic
541C23×C4C22×D8311yescharacteristic
542C23×C4C22×D8311yescharacteristic
543C4⋊Q8—8316no—
544C4⋊Q8—8316no—
545C4⋊Q8—8316no—
546C4⋊Q8—8332no—
547C4⋊Q8C22×D8318yes—
548C4⋊Q8C22×D8318yes—
549#126—8332no—
550#126—8332no—
551#126—8332no—
552#126—8316no—
553#126—8332no—
554#125—8316no—
555#125—8332no—
556#125—8332no—
557#125—8332no—
558#125—8332no—
559#125—8316no—
560#125—838no—
561#125—8332no—
562#125C22×D83116yes—
563#124—8316no—
564#124—838no—
565#123—8316no—
566#123—8332no—
567C22⋊Q8—8316no—
568C22⋊Q8—838no—
569C22⋊Q8—8332no—
570C22⋊Q8—8332no—
571C22⋊Q8—8316no—
572C22⋊Q8—8332no—
573C22⋊Q8C22×D83116yes—
574C22⋊Q8C22×D83116yes—
575#121—838no—
576C4×Q8—8316no—
577C4×Q8—8316no—
578C4×Q8—8316no—
579C4×Q8—8332no—
580C4×Q8—8316no—
581C4×Q8—8316no—
582C4×Q8—838no—
583C4×Q8—8316no—
584C4×Q8—838no—
585C4×Q8—838no—
586C4×Q8—8316no—
587C4×Q8—838no—
588C4×Q8—8332no—
589C4×Q8—838no—
590C4×Q8C22×D83116yes—
591C4×Q8C22×D83116yes—
592C4×D4—8316no—
593C4×D4—8316no—
594C4×D4—8332no—
595C4×D4—838no—
596#117—8332no—
597#117—8316no—
598#117—8332no—
599#117—8316no—
600#117—8332no—
601#117C22×D83116yes—
602C2×C4⋊C4—832no—
603C2×C4⋊C4—831no—
604C2×C4⋊C4—832no—
605C2×C4⋊C4—831no—
606C2×C4⋊C4—832no—
607C2×C4⋊C4—832no—
608C2×C4⋊C4—832no—
609C2×C4⋊C4—8316no—
610C2×C4⋊C4—838no—
611C2×C4⋊C4—834no—
612C2×C4⋊C4—832no—
613C2×C4⋊C4—832no—
614C2×C4⋊C4—834no—
615C2×C4⋊C4—834no—
616C2×C4⋊C4—834no—
617C2×C4⋊C4—831no—
618C2×C4⋊C4—834no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—831no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—832no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4C22×D8312yes—
626C2×C4⋊C4C22×D8314yes—
627C2×C4⋊C4C22×D8312yes—
628C2×C4⋊C4C22×D8312yes—
629C2×C4⋊C4C22×D8312yes—
630C2×C4⋊C4C22×D8314yes—
631C2×C22⋊C4—832no—
632C2×C22⋊C4—832no—
633C2×C22⋊C4—834no—
634C2×C22⋊C4—832no—
635C2×C22⋊C4—834no—
636C2×C22⋊C4—832no—
637C2×C22⋊C4—832no—
638C2×C22⋊C4—834no—
639C2×C22⋊C4C22×D8314yes—
640C2×C42—832no—
641C2×C42—834no—
642C2×C42—834no—
643C2×C42—834no—
644C2×C42—832no—
645C2×C42—832no—
646C2×C42—832no—
647C2×C42—832no—
648C2×C42—8316no—
649C2×C42C22×D8311yescharacteristic
650C2×C42C22×D8314yes—
651C2×C42C22×D8311yescharacteristic
652C2×C42C22×D8311yescharacteristic
653C2×C42C22×D8311yescharacteristic
654C2×C42C22×D8318yes—
655C24—832no—
656C24C23×D8311yescharacteristic
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—838no—
660C2×Q8—834no—
661C2×Q8—834no—
662C2×Q8—8316no—
663C2×Q8—838no—
664C2×Q8—834no—
665C2×Q8—1668no—
666C2×Q8—16616no—
667C2×Q8—16632no—
668C2×Q8—16664no—
669C2×Q8—1664no—
670C2×Q8—1664no—
671C2×Q8C23×D8318yes—
672C2×Q8C23×D8318yes—
673C2×D4—838no—
674C2×D4—834no—
675C2×D4—1668no—
676C2×D4—1664no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—832no—
681C22×C4—838no—
682C22×C4—838no—
683C22×C4—832no—
684C22×C4—832no—
685C22×C4—832no—
686C22×C4—832no—
687C22×C4—832no—
688C22×C4—832no—
689C22×C4—8316no—
690C22×C4—838no—
691C22×C4—16616no—
692C22×C4—1668no—
693C22×C4—1668no—
694C22×C4—1668no—
695C22×C4C23×D8314yes—
696C22×C4C23×D8314yes—
697C22×C4C23×D8314yes—
698C22×C4C23×D8311yescharacteristic
699C22×C4C23×D8314yes—
700C22×C4C23×D8314yes—
701C22×C4C23×D8311yescharacteristic
702C22×C4C23×D8311yescharacteristic
703C22×C4C23×D8311yescharacteristic
704C22×C4C23×D8311yescharacteristic
705C22×C4C23×D8311yescharacteristic
706C4⋊C4—838no—
707C4⋊C4—834no—
708C4⋊C4—838no—
709C4⋊C4—834no—
710C4⋊C4—838no—
711C4⋊C4—838no—
712C4⋊C4—838no—
713C4⋊C4—8316no—
714C4⋊C4—838no—
715C4⋊C4—838no—
716C4⋊C4—8316no—
717C4⋊C4—8316no—
718C4⋊C4—8316no—
719C4⋊C4—834no—
720C4⋊C4—8316no—
721C4⋊C4—838no—
722C4⋊C4—834no—
723C4⋊C4—8316no—
724C4⋊C4—8316no—
725C4⋊C4—838no—
726C4⋊C4—8316no—
727C4⋊C4C23×D8318yes—
728C4⋊C4C23×D83116yes—
729C4⋊C4C23×D8318yes—
730C4⋊C4C23×D8318yes—
731C4⋊C4C23×D8318yes—
732C4⋊C4C23×D83116yes—
733C22⋊C4—838no—
734C22⋊C4—838no—
735C22⋊C4—8316no—
736C22⋊C4—838no—
737C22⋊C4—8316no—
738C22⋊C4—838no—
739C22⋊C4—838no—
740C22⋊C4—8316no—
741C22⋊C4C23×D83116yes—
742C42—838no—
743C42—838no—
744C42—838no—
745C42—838no—
746C42—8316no—
747C42—8316no—
748C42—8316no—
749C42—838no—
750C42C23×D8314yes—
751C42C23×D8314yes—
752C42C23×D8314yes—
753C42C23×D8314yes—
754C42C23×D83116yes—
755C23—22no—
756C23—22no—
757C23—834no—
758C23—1664no—
759C23—1664no—
760C23—1664no—
761C23#1458184014yes—
762C23C24×D8312yes—
763C23C24×D8311yescharacteristic
764Q8—216no—
765Q8—216no—
766Q8—8316no—
767Q8—16616no—
768Q8—16632no—
769Q8—1668no—
770Q8—1668no—
771D4—16616no—
772D4—1668no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—838no—
783C2×C4—834no—
784C2×C4—834no—
785C2×C4—834no—
786C2×C4—834no—
787C2×C4—834no—
788C2×C4—834no—
789C2×C4—834no—
790C2×C4—16632no—
791C2×C4—16616no—
792C2×C4—1664no—
793C2×C4—1664no—
794C2×C4—1664no—
795C2×C4—16616no—
796C2×C4—1664no—
797C2×C4—1664no—
798C2×C4—1664no—
799C2×C4—16616no—
800C2×C4#41×D8314yes—
801C2×C4#1458183914yes—
802C2×C4C24×D8312yes—
803C2×C4C24×D8318yes—
804C2×C4C24×D8318yes—
805C2×C4C24×D8312yes—
806C2×C4C24×D8312yes—
807C2×C4C24×D8312yes—
808C2×C4C24×D8312yes—
809C2×C4C24×D8312yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—3328no—
814C22—1664no—
815C22—1664no—
816C22—1664no—
817C22C2×#41×D8312yes—
818C22C2×#1458183912yes—
819C22C2×#1458184014yes—
820C22C2×#1458184012yes—
821C22C25×D8311yescharacteristic
822C4—22no—
823C4—28no—
824C4—22no—
825C4—28no—
826C4—22no—
827C4—22no—
828C4—838no—
829C4—1664no—
830C4—1664no—
831C4—1664no—
832C4—1664no—
833C4—1664no—
834C4—1664no—
835C4C2×#41×D8314yes—
836C4C2×#1458183914yes—
837C2—24no—
838C2—3324no—
839C2#2492155114yesdirect product factor
840C2C22×#41×D8311yescharacteristic
841C2C22×#1458183911yescharacteristic
842C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#533×C83C2
socleC23×C83C25
prime radicalC2×#14581766C22
hypercenterC2×#533D83
hypocenterC83C2×#3523
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #24921551C2direct (N × H)
2. C2×#19128427C2semidirect
3. C2×#19128426C2semidirect
4. C2×#19128426C2semidirect
5. C2×#19128425C2semidirect
6. C2×#19128423C2semidirect
7. C2×#19128393C2semidirect
8. C2×#19128384C2semidirect
9. C2×#19128366C2semidirect
10. C2×#19128364C2semidirect
11. C2×#19128310C2semidirect
12. C2×#19128309C2semidirect
13. C2×#19128253C2semidirect
16. C2×#19128177C2semidirect
17. C22×C4×Dic166C2semidirect
18. C2×#533×C83C2semidirect
21. #19128427C22semidirect
22. #19128426C22semidirect
23. #19128426C22semidirect
24. #19128425C22semidirect
25. #19128423C22semidirect
26. #19128393C22semidirect
27. #19128384C22semidirect
28. #19128366C22semidirect
29. #19128364C22semidirect
30. #19128310C22semidirect
31. #19128309C22semidirect
32. #19128253C22semidirect
63. #19128177C22semidirect
75. C2×C4×Dic166C22semidirect
91. #533×C83C22semidirect
417. C2×C83#3523semidirect
435. C2×#533D83semidirect
440. C83C2×#3523semidirect
455. #533C2×D83semidirect
839. C2#24921551direct (N × H)

Maximal subgroups

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

subgroupindex
#249215512
C2×#191284272
C2×#191284262
C2×#191284252
C2×#191284232
C2×#191283932
C2×#191283842
C2×#191283662
C2×#191283642
C2×#191283102
C2×#191283092
C2×#191282532
C2×#191282372
C2×#191282352
C2×#191281772
C22×C4×Dic1662
C2×#533×C832
C2×#352383