Finite Group Databasebeta

← C2×#24921803 #36312086

Subgroups — C2×#24921803 #36312086

Order 21248.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921803C2132yesmaximal, direct product factor
2C2×#19128453C214yesmaximal, complemented
3C2×Q8×Dic166C211yesmaximal, characteristic, complemented
4C2×#19128416C211yesmaximal, characteristic, complemented
5C2×#19128411C211yesmaximal, characteristic, complemented
6C2×#19128408C211yesmaximal, characteristic, complemented
7C2×#19128393C212yesmaximal, complemented
8C2×#19128391C212yesmaximal, complemented
9C2×#19128355C212yesmaximal, complemented
10C2×#19128351C212yesmaximal, complemented
11C2×#19128331C212yesmaximal, complemented
12C2×#19128329C212yesmaximal, complemented
13C2×#19128322C212yesmaximal, complemented
14C2×#19128320C212yesmaximal, complemented
15C2×#19128273C214yesmaximal, complemented
16C22×#14581792C211yesmaximal, characteristic, complemented
17C2×#19128235C211yesmaximal, characteristic, complemented
18C2×#529×C83C211yesmaximal, characteristic, complemented
19C22×#13050589C2214yes—
20C23×Dic166C2212yes—
21#19128453C22164yescomplemented
22Q8×Dic166C22116yescomplemented
23#19128416C22116yescomplemented
24#19128411C22116yescomplemented
25#19128408C22116yescomplemented
26#19128393C22132yescomplemented
27#19128391C22132yescomplemented
28#19128355C22132yescomplemented
29#19128351C22132yescomplemented
30#19128331C22132yescomplemented
31#19128329C22132yescomplemented
32#19128322C22132yescomplemented
33#19128320C22132yescomplemented
34#19128273C22164yescomplemented
35C2×#14581792C2212yes—
36C2×#14581792C2212yes—
37C2×#14581792C2212yes—
38C2×#14581792C2211yescharacteristic
39C2×#14581792C2211yescharacteristic
40C2×#14581792C2212yes—
41C2×#14581792C22116yescomplemented
42C2×#14581791C2214yes—
43C2×#14581791C2212yes—
44C2×#14581791C2214yes—
45#19128235C22116yescomplemented
46C2×#14581787C2214yes—
47C2×#14581786C2212yes—
48C2×#14581785C2214yes—
49C2×#14581784C2211yescharacteristic
50C2×#14581784C2212yes—
51C2×#14581783C2214yes—
52C2×#14581783C2212yes—
53C2×#14581782C2214yes—
54C2×#14581780C2211yescharacteristic
55C2×#14581778C2214yes—
56C2×#14581778C2214yes—
57C2×#14581776C2214yes—
58C2×#14581776C2214yes—
59C2×#14581775C2212yes—
60C2×#14581774C2214yes—
61C2×#14581773C2214yes—
62C2×#14581772C2214yes—
63C2×#14581771C2212yes—
64C2×#14581771C2211yescharacteristic
65C2×#14581770C2214yes—
66C2×#14581770C2214yes—
67C2×#14581769C2214yes—
68C2×#14581769C2214yes—
69C2×#14581769C2214yes—
70C2×#14581768C2212yes—
71C2×#14581766C2212yes—
72C2×#14581766C2211yescharacteristic
73C2×#14581763C2212yes—
74C2×Q8×Dic83C2212yes—
75C2×C4×Dic166C2212yes—
76C2×C4×Dic166C2211yescharacteristic
77C2×C4×D332C2212yes—
78C2×C4×D332C2211yescharacteristic
79C2×D4×Dic83C2212yes—
80C2×C4×C22⋊D83C2212yes—
81C2×#14581751C2212yes—
82C2×#14581750C2212yes—
83C2×#14581749C2212yes—
84C2×#14581748C2214yes—
85C22×C4⋊Dic83C2212yes—
86C22×C4⋊Dic83C2212yes—
87C22×C4⋊Dic83C2212yes—
88C2×C4⋊C4×D83C2212yes—
89#529×C83C22116yescomplemented
90C2×#126×C83C2212yes—
91C2×#125×C83C2211yescharacteristic
92C2×#124×C83C2211yescharacteristic
93C2×#123×C83C2212yes—
94C2×C22⋊Q8×C83C2211yescharacteristic
95C2×#121×C83C2211yescharacteristic
96C2×C4×Q8×C83C2211yescharacteristic
97C2×C4×D4×C83C2212yes—
98C2×C4×D4×C83C2211yescharacteristic
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050589—416no—
102C2×#13050589C23132yes—
103C22×Dic166—48no—
104C22×Dic166C2311yescharacteristic
105C22×Dic166C2312yes—
106C22×Dic166C2314yes—
107C22×Dic166C2314yes—
108C22×Dic166C2312yes—
109C22×Dic166C23116yes—
110C22×D332C2311yescharacteristic
111C22×C22⋊D83C2312yes—
112C22×C22⋊D83C2314yes—
113C23×Dic83C2314yes—
114C23×Dic83C2314yes—
115C22×C4×D83C2312yes—
116C22×C4×D83C2314yes—
117#14581792C23116yes—
118#14581792C23116yes—
119#14581792C23116yes—
120#14581792C2318yes—
121#14581792C2318yes—
122#14581792C23116yes—
123#14581791C23132yes—
124#14581791C23116yes—
125#14581791C23132yes—
126#14581787C23132yes—
127#14581786C23116yes—
128#14581785C23132yes—
129#14581784C2318yes—
130#14581784C23116yes—
131#14581783C23132yes—
132#14581783C23116yes—
133#14581782C23132yes—
134#14581780C2318yes—
135#14581778C23132yes—
136#14581778C23132yes—
137#14581776C23132yes—
138#14581776C23132yes—
139#14581775C23116yes—
140#14581774C23132yes—
141#14581773C23132yes—
142#14581772C23132yes—
143#14581771C23116yes—
144#14581771C2318yes—
145#14581770C23132yes—
146#14581770C23132yes—
147#14581769C23132yes—
148#14581769C23132yes—
149#14581769C23132yes—
150#14581768C23116yes—
151#14581766C23116yes—
152#14581766C2318yes—
153#14581763C23116yes—
154Q8×Dic83C23116yes—
155C4×Dic166C23116yes—
156C4×Dic166C2318yes—
157C4×D332C23116yes—
158C4×D332C2318yes—
159D4×Dic83C23116yes—
160C4×C22⋊D83C23116yes—
161#14581751C23116yes—
162#14581750C23116yes—
163#14581749C23116yes—
164#14581748C23132yes—
165C2×C4⋊Dic83C23116yes—
166C2×C4⋊Dic83C23116yes—
167C2×C4⋊Dic83C23116yes—
168C2×C4⋊Dic83C2312yes—
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2314yes—
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2314yes—
176C2×C4⋊Dic83C2311yescharacteristic
177C2×C4⋊Dic83C2314yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2314yes—
186C4⋊C4×D83C23116yes—
187C2×C22⋊Dic83C2312yes—
188C2×C22⋊Dic83C2314yes—
189C2×C22⋊Dic83C2314yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2314yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×C4×Dic83C2314yes—
197C2×C4×Dic83C2314yes—
198C2×C4×Dic83C2312yes—
199C22×Q8×C83C2311yescharacteristic
200C22×D4×C83C2312yes—
201C22×D4×C83C2311yescharacteristic
202C23×C4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2312yes—
206#126×C83C23116yes—
207#125×C83C2318yes—
208#124×C83C2318yes—
209#123×C83C23116yes—
210C22⋊Q8×C83C2318yes—
211#121×C83C2318yes—
212C4×Q8×C83C2318yes—
213C4×D4×C83C23116yes—
214C4×D4×C83C2318yes—
215#117×C83C23116yes—
216C2×C4⋊C4×C83C2312yes—
217C2×C4⋊C4×C83C2312yes—
218C2×C4⋊C4×C83C2311yescharacteristic
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2312yes—
222C2×C22⋊C4×C83C2312yes—
223C2×C22⋊C4×C83C2312yes—
224C2×C22⋊C4×C83C2312yes—
225C2×C22⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2312yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2318yes—
232C2×C42×C83C2312yes—
233C23×D83C2412yes—
234#13050589—464no—
235C2×Dic166—24no—
236C2×Dic166—44no—
237C2×Dic166—48no—
238C2×Dic166—44no—
239C2×Dic166—432no—
240C2×Dic166—48no—
241C2×Dic166C2414yes—
242C2×Dic166C2418yes—
243C2×Dic166C24116yes—
244C2×Dic166C24116yes—
245C2×Dic166C2418yes—
246C2×D332—24no—
247C2×D332C2414yes—
248C2×C22⋊D83—28no—
249C2×C22⋊D83—48no—
250C2×C22⋊D83C2418yes—
251C2×C22⋊D83C24116yes—
252C22×Dic83—216no—
253C22×Dic83—48no—
254C22×Dic83C24116yes—
255C22×Dic83C2414yes—
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C22×Dic83C2414yes—
259C22×Dic83C2412yes—
260C22×Dic83C24116yes—
261C2×C4×D83—28no—
262C2×C4×D83—48no—
263C2×C4×D83C2418yes—
264C2×C4×D83C24116yes—
265C4⋊Dic83C2418yes—
266C4⋊Dic83C2414yes—
267C4⋊Dic83C2418yes—
268C4⋊Dic83C2418yes—
269C4⋊Dic83C24116yes—
270C4⋊Dic83C24116yes—
271C4⋊Dic83C24116yes—
272C4⋊Dic83C2414yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C24116yes—
275Dic83⋊C4C24116yes—
276Dic83⋊C4C2418yes—
277Dic83⋊C4C2418yes—
278Dic83⋊C4C2418yes—
279Dic83⋊C4C24116yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C2418yes—
283C22⋊Dic83C24116yes—
284C22⋊Dic83C24116yes—
285C22⋊Dic83C2418yes—
286(C2×D83)⋊C4C24116yes—
287(C2×D83)⋊C4C2418yes—
288(C2×D83)⋊C4C24116yes—
289(C2×D83)⋊C4C2418yes—
290(C2×D83)⋊C4C2418yes—
291(C2×D83)⋊C4C2418yes—
292C4×Dic83C24116yes—
293C4×Dic83C24116yes—
294C4×Dic83C2418yes—
295C24×C83C2412yes—
296C24×C83C2411yescharacteristic
297C2×Q8×C83—24no—
298C2×Q8×C83C2414yes—
299C2×D4×C83—28no—
300C2×D4×C83—24no—
301C2×D4×C83C2414yes—
302C2×D4×C83C2418yes—
303C22×C4×C83—24no—
304C22×C4×C83—24no—
305C22×C4×C83—28no—
306C22×C4×C83—24no—
307C22×C4×C83C2414yes—
308C22×C4×C83C2418yes—
309C22×C4×C83C2414yes—
310C22×C4×C83C2412yes—
311C22×C4×C83C2411yescharacteristic
312C22×C4×C83C2411yescharacteristic
313C22×C4×C83C2411yescharacteristic
314C22×C4×C83C2411yescharacteristic
315C22×C4×C83C2414yes—
316C22×C4×C83C2412yes—
317C22×C4×C83C2412yes—
318C22×C4×C83C2411yescharacteristic
319C22×C4×C83C2411yescharacteristic
320C4⋊C4×C83C2418yes—
321C4⋊C4×C83C2418yes—
322C4⋊C4×C83C2418yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2414yes—
325C4⋊C4×C83C2414yes—
326C22⋊C4×C83C2418yes—
327C22⋊C4×C83C2418yes—
328C22⋊C4×C83C2418yes—
329C22⋊C4×C83C2418yes—
330C22⋊C4×C83C2418yes—
331C42×C83C2414yes—
332C42×C83C2418yes—
333C42×C83C2414yes—
334C42×C83C2414yes—
335C42×C83C2414yes—
336C23×C83—22no—
337C23×C83—22no—
338C23×C83—24no—
339C23×C83—24no—
340C23×C83—24no—
341C23×C83H(5,𝔽2)14yes—
342C23×C83C2514yes—
343C23×C83C2512yes—
344C23×C83C2511yescharacteristic
345C22×D83—24no—
346C22×D83—24no—
347C22×D83—24no—
348C22×D83C2514yes—
349Q8×C83—28no—
350D4×C83—216no—
351D4×C83—28no—
352C2×C4×C83—28no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—24no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—24no—
359C2×C4×C83—24no—
360C2×C4×C83—28no—
361C2×C4×C83—216no—
362C2×C4×C83—28no—
363C2×C4×C832−1+414yes—
364C2×C4×C832−1+414yes—
365C2×C4×C83C2512yes—
366C2×C4×C83C2512yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2512yes—
369C2×C4×C83C2514yes—
370C2×C4×C83C2514yes—
371C2×C4×C83C2514yes—
372C2×C4×C83C2512yes—
373C2×C4×C83C2512yes—
374C22⋊D83—216no—
375C22⋊D83—416no—
376C2×Dic83—28no—
377C2×Dic83—28no—
378C2×Dic83—232no—
379C2×Dic83—24no—
380C2×Dic83—24no—
381C2×Dic83—24no—
382C2×Dic83—416no—
383C2×Dic83C2514yes—
384C2×Dic83C2514yes—
385C2×Dic83C2518yes—
386C2×Dic83C2514yes—
387C2×Dic83C2518yes—
388D332—28no—
389C4×D83—216no—
390C4×D83—416no—
391Dic166—28no—
392Dic166—48no—
393Dic166—416no—
394Dic166—48no—
395Dic166—416no—
396C22×C83—22no—
397C22×C83—22no—
398C22×C83—28no—
399C22×C83—24no—
400C22×C83—24no—
401C22×C83—24no—
402C22×C83—48no—
403C22×C83C2×H(5,𝔽2)14yes—
404C22×C83C2×H(5,𝔽2)12yes—
405C22×C83C2×2−1+412yes—
406C22×C83C2×2−1+412yes—
407C22×C83C2611yescharacteristic
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—24no—
411C2×D83—48no—
412C4×C83—22no—
413C4×C83—22no—
414C4×C83—24no—
415C4×C83—22no—
416C4×C83—22no—
417C4×C83—24no—
418C4×C83—24no—
419C4×C83C2×2−1+414yes—
420C4×C83C2×2−1+414yes—
421Dic83—28no—
422Dic83—28no—
423Dic83—24no—
424Dic83—24no—
425Dic83—24no—
426C2×#3544—831nomaximal, Sylow
427C2×C83—24no—
428C2×C83—44no—
429C2×C83#354414yescomplemented
430C2×C83C22×H(5,𝔽2)11yescharacteristic
431C2×C83C22×2−1+411yescharacteristic
432C2×C83C22×2−1+411yescharacteristic
433D83—44no—
434#3544—8332no—
435C2×#563—834no—
436C2×Q82—831no—
437C2×#555—831no—
438C2×#554—831no—
439C2×#554—831no—
440C2×#552—832no—
441C2×#552—832no—
442C2×#547—832no—
443C2×#547—832no—
444C2×#544—832no—
445C2×#544—832no—
446C2×#542—832no—
447C2×#542—832no—
448C2×#536—834no—
449C22×C4⋊Q8—831no—
450C2×#529—831no—
451C2×#529D8311yescharacteristic, complemented
452C83C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—834no—
454C23×Q8—832no—
455#563—8364no—
456Q82—8316no—
457#555—8316no—
458#554—8316no—
459#554—8316no—
460#552—8332no—
461#552—8332no—
462#547—8332no—
463#547—8332no—
464#544—8332no—
465#544—8332no—
466#542—8332no—
467#542—8332no—
468#536—8364no—
469C2×C4⋊Q8—834no—
470C2×C4⋊Q8—834no—
471C2×C4⋊Q8—832no—
472C2×C4⋊Q8—832no—
473C2×C4⋊Q8—832no—
474C2×C4⋊Q8—831no—
475C2×C4⋊Q8—831no—
476C2×C4⋊Q8—832no—
477C2×C4⋊Q8—8316no—
478C2×C4⋊Q8—832no—
479#529—8316no—
480#529C2×D83116yescomplemented
481C2×#126—834no—
482C2×#126—834no—
483C2×#126—832no—
484C2×#126C2×D8312yes—
485C2×#125—832no—
486C2×#125—834no—
487C2×#125—834no—
488C2×#125—831no—
489C2×#125—832no—
490C2×#125C2×D8311yescharacteristic
491C2×#124—834no—
492C2×#124—834no—
493C2×#124—831no—
494C2×#124C2×D8311yescharacteristic
495C2×#123—834no—
496C2×#123—832no—
497C2×#123—834no—
498C2×#123—834no—
499C2×#123—834no—
500C2×#123C2×D8312yes—
501C2×C22⋊Q8—832no—
502C2×C22⋊Q8—831no—
503C2×C22⋊Q8—832no—
504C2×C22⋊Q8—834no—
505C2×C22⋊Q8—834no—
506C2×C22⋊Q8—834no—
507C2×C22⋊Q8—834no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8C2×D8311yescharacteristic
511C2×#121—832no—
512C2×#121—831no—
513C2×#121—832no—
514C2×#121C2×D8311yescharacteristic
515C2×C4×Q8—832no—
516C2×C4×Q8—831no—
517C2×C4×Q8—832no—
518C2×C4×Q8C2×D8311yescharacteristic
519C2×C4×D4—832no—
520C2×C4×D4—832no—
521C2×C4×D4—831no—
522C2×C4×D4—832no—
523C2×C4×D4C2×D8312yes—
524C2×C4×D4C2×D8311yescharacteristic
525C2×#117—832no—
526C2×#117—832no—
527C2×#117—834no—
528C2×#117—832no—
529C2×#117C2×D8312yes—
530C22×C4⋊C4—832no—
531C22×C4⋊C4—832no—
532C22×C4⋊C4—832no—
533C22×C4⋊C4—832no—
534C22×C42C2×D8311yescharacteristic
535C2×#41—33216no—
536C2×#41—8332no—
537C22×Q8—3328no—
538C22×Q8—832no—
539C22×Q8—834no—
540C22×Q8—834no—
541C22×Q8—832no—
542C22×Q8—8316no—
543C22×Q8—831no—
544C22×Q8C22×D8311yescharacteristic
545C22×D4—834no—
546C22×D4—832no—
547C22×D4—831no—
548C22×D4C22×D8311yescharacteristic
549C22×D4C22×D8312yes—
550C23×C4—834no—
551C23×C4—834no—
552C23×C4—834no—
553C23×C4—832no—
554C23×C4C22×D8311yescharacteristic
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8312yes—
557C23×C4C22×D8311yescharacteristic
558C4⋊Q8—8332no—
559C4⋊Q8—8332no—
560C4⋊Q8—8316no—
561C4⋊Q8—8316no—
562C4⋊Q8—8316no—
563C4⋊Q8—838no—
564C4⋊Q8—838no—
565C4⋊Q8—8316no—
566C4⋊Q8—8316no—
567#126—8332no—
568#126—8332no—
569#126—8316no—
570#126C22×D83116yes—
571#125—8332no—
572#125—8316no—
573#125—8332no—
574#125—838no—
575#125—8316no—
576#125C22×D8318yes—
577#124—8332no—
578#124—8332no—
579#124—838no—
580#124C22×D8318yes—
581#123—8332no—
582#123—8316no—
583#123—8332no—
584#123—8332no—
585#123—8332no—
586#123C22×D83116yes—
587C22⋊Q8—8316no—
588C22⋊Q8—838no—
589C22⋊Q8—8316no—
590C22⋊Q8—8332no—
591C22⋊Q8—8332no—
592C22⋊Q8—8332no—
593C22⋊Q8—8332no—
594C22⋊Q8—8332no—
595C22⋊Q8—8332no—
596C22⋊Q8C22×D8318yes—
597#121—8316no—
598#121—838no—
599#121—8316no—
600#121C22×D8318yes—
601C4×Q8—8316no—
602C4×Q8—838no—
603C4×Q8—8316no—
604C4×Q8C22×D8318yes—
605C4×D4—8316no—
606C4×D4—8316no—
607C4×D4—838no—
608C4×D4—8316no—
609C4×D4C22×D83116yes—
610C4×D4C22×D8318yes—
611#117—8316no—
612#117—8316no—
613#117—8332no—
614#117—8316no—
615#117C22×D83116yes—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—831no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—832no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—8316no—
626C2×C4⋊C4—8316no—
627C2×C4⋊C4—8316no—
628C2×C4⋊C4—831no—
629C2×C4⋊C4—834no—
630C2×C4⋊C4—834no—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—832no—
633C2×C4⋊C4—832no—
634C2×C4⋊C4—832no—
635C2×C4⋊C4—834no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—8316no—
638C2×C4⋊C4C22×D8311yescharacteristic
639C2×C4⋊C4C22×D8311yescharacteristic
640C2×C4⋊C4C22×D8312yes—
641C2×C4⋊C4C22×D8312yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C4⋊C4C22×D8312yes—
644C2×C22⋊C4—832no—
645C2×C22⋊C4—834no—
646C2×C22⋊C4—834no—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—834no—
649C2×C22⋊C4—832no—
650C2×C22⋊C4—834no—
651C2×C22⋊C4—832no—
652C2×C22⋊C4—832no—
653C2×C22⋊C4C22×D8312yes—
654C2×C22⋊C4C22×D8312yes—
655C2×C22⋊C4C22×D8312yes—
656C2×C22⋊C4C22×D8312yes—
657C2×C22⋊C4C22×D8312yes—
658C2×C42—834no—
659C2×C42—832no—
660C2×C42—834no—
661C2×C42C22×D8311yescharacteristic
662C2×C42C22×D8311yescharacteristic
663C2×C42C22×D8312yes—
664C2×C42C22×D8311yescharacteristic
665C2×C42C22×D8311yescharacteristic
666C2×C42C22×D8318yes—
667C24—832no—
668C24C23×D8312yes—
669C24C23×D8311yescharacteristic
670#41—33264no—
671C2×Q8—24no—
672C2×Q8—3324no—
673C2×Q8—3328no—
674C2×Q8—3324no—
675C2×Q8—33232no—
676C2×Q8—3328no—
677C2×Q8—838no—
678C2×Q8—8316no—
679C2×Q8—8316no—
680C2×Q8—838no—
681C2×Q8—834no—
682C2×Q8—1664no—
683C2×Q8C23×D8314yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—3328no—
687C2×D4—8316no—
688C2×D4—838no—
689C2×D4—834no—
690C2×D4—1668no—
691C2×D4—1664no—
692C2×D4C23×D8314yes—
693C2×D4C23×D8318yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—3328no—
699C22×C4—3328no—
700C22×C4—8316no—
701C22×C4—8316no—
702C22×C4—8316no—
703C22×C4—832no—
704C22×C4—832no—
705C22×C4—834no—
706C22×C4—832no—
707C22×C4—834no—
708C22×C4—838no—
709C22×C4—16616no—
710C22×C4—1668no—
711C22×C4C23×D8314yes—
712C22×C4C23×D8314yes—
713C22×C4C23×D8314yes—
714C22×C4C23×D8318yes—
715C22×C4C23×D8312yes—
716C22×C4C23×D8312yes—
717C22×C4C23×D8311yescharacteristic
718C22×C4C23×D8311yescharacteristic
719C22×C4C23×D8311yescharacteristic
720C22×C4C23×D8311yescharacteristic
721C22×C4C23×D8312yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C4⋊C4—838no—
725C4⋊C4—838no—
726C4⋊C4—834no—
727C4⋊C4—838no—
728C4⋊C4—838no—
729C4⋊C4—8316no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—8316no—
733C4⋊C4—834no—
734C4⋊C4—8316no—
735C4⋊C4—8316no—
736C4⋊C4—838no—
737C4⋊C4—838no—
738C4⋊C4—838no—
739C4⋊C4—838no—
740C4⋊C4—8316no—
741C4⋊C4—8316no—
742C4⋊C4C23×D8314yes—
743C4⋊C4C23×D8314yes—
744C4⋊C4C23×D8318yes—
745C4⋊C4C23×D8318yes—
746C4⋊C4C23×D8318yes—
747C4⋊C4C23×D8318yes—
748C22⋊C4—838no—
749C22⋊C4—8316no—
750C22⋊C4—8316no—
751C22⋊C4—838no—
752C22⋊C4—8316no—
753C22⋊C4—838no—
754C22⋊C4—8316no—
755C22⋊C4—838no—
756C22⋊C4—838no—
757C22⋊C4C23×D8318yes—
758C22⋊C4C23×D8318yes—
759C22⋊C4C23×D8318yes—
760C22⋊C4C23×D8318yes—
761C22⋊C4C23×D8318yes—
762C42—8316no—
763C42—838no—
764C42—8316no—
765C42C23×D8314yes—
766C42C23×D8314yes—
767C42C23×D8314yes—
768C42C23×D8314yes—
769C42C23×D8318yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—834no—
776C23—1664no—
777C23—1664no—
778C23—1664no—
779C23#1458183814yes—
780C23C24×D8314yes—
781C23C24×D8312yes—
782C23C24×D8311yescharacteristic
783Q8—28no—
784Q8—3328no—
785Q8—33216no—
786Q8—3328no—
787Q8—33216no—
788Q8—1668no—
789D4—216no—
790D4—28no—
791D4—33216no—
792D4—16616no—
793D4—1668no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—33216no—
806C2×C4—33216no—
807C2×C4—834no—
808C2×C4—834no—
809C2×C4—838no—
810C2×C4—834no—
811C2×C4—838no—
812C2×C4—1668no—
813C2×C4—1664no—
814C2×C4—1668no—
815C2×C4—16632no—
816C2×C4—1664no—
817C2×C4—1664no—
818C2×C4—16616no—
819C2×C4#1458183914yes—
820C2×C4#1458183914yes—
821C2×C4C24×D8314yes—
822C2×C4C24×D8314yes—
823C2×C4C24×D8312yes—
824C2×C4C24×D8312yes—
825C2×C4C24×D8312yes—
826C2×C4C24×D8312yes—
827C2×C4C24×D8314yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—3328no—
838C22—1664no—
839C22—1664no—
840C22—1664no—
841C22C2×#1458183814yes—
842C22C2×#1458183812yes—
843C22C2×#1458183912yes—
844C22C2×#1458183912yes—
845C22C25×D8311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1668no—
854C4—1664no—
855C4—1668no—
856C4—1664no—
857C4—1664no—
858C4C2×#1458183914yes—
859C4C2×#1458183914yes—
860C2—24no—
861C2—44no—
862C2—3324no—
863C2#2492180314yesdirect product factor
864C2C22×#1458183811yescharacteristic
865C2C22×#1458183911yescharacteristic
866C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#529×C83C2
socleC23×C83C25
hypercenterC2×#529D83
hypocenterC83C2×#3544
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #24921803C2direct (N × H)
2. C2×#19128453C2semidirect
3. C2×Q8×Dic166C2semidirect
4. C2×#19128416C2semidirect
5. C2×#19128411C2semidirect
6. C2×#19128408C2semidirect
7. C2×#19128393C2semidirect
8. C2×#19128391C2semidirect
9. C2×#19128355C2semidirect
10. C2×#19128351C2semidirect
11. C2×#19128331C2semidirect
12. C2×#19128329C2semidirect
13. C2×#19128322C2semidirect
14. C2×#19128320C2semidirect
15. C2×#19128273C2semidirect
16. C22×#14581792C2semidirect
17. C2×#19128235C2semidirect
18. C2×#529×C83C2semidirect
21. #19128453C22semidirect
22. Q8×Dic166C22semidirect
23. #19128416C22semidirect
24. #19128411C22semidirect
25. #19128408C22semidirect
26. #19128393C22semidirect
27. #19128391C22semidirect
28. #19128355C22semidirect
29. #19128351C22semidirect
30. #19128331C22semidirect
31. #19128329C22semidirect
32. #19128322C22semidirect
33. #19128320C22semidirect
34. #19128273C22semidirect
41. C2×#14581792C22semidirect
45. #19128235C22semidirect
89. #529×C83C22semidirect
429. C2×C83#3544semidirect
451. C2×#529D83semidirect
452. C83C2×#3544semidirect
480. #529C2×D83semidirect
863. C2#24921803direct (N × H)

Maximal subgroups

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

subgroupindex
#249218032
C2×#191284532
C2×Q8×Dic1662
C2×#191284162
C2×#191284112
C2×#191284082
C2×#191283932
C2×#191283912
C2×#191283552
C2×#191283512
C2×#191283312
C2×#191283292
C2×#191283222
C2×#191283202
C2×#191282732
C22×#145817922
C2×#191282352
C2×#529×C832
C2×#354483