Finite Group Databasebeta

← C2×#24921558 #36312620

Subgroups — C2×#24921558 #36312620

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#24921558C2132yesmaximal, direct product factor
2C2×#19128429C211yesmaximal, characteristic, complemented
3C2×#19128427C212yesmaximal, complemented
4C2×#19128426C211yesmaximal, characteristic, complemented
5C2×#19128420C212yesmaximal, complemented
6C2×#19128390C212yesmaximal, complemented
7C2×#19128387C214yesmaximal, complemented
8C2×D4×Dic166C211yesmaximal, characteristic, complemented
9C2×#19128364C212yesmaximal, complemented
10C2×#19128311C212yesmaximal, complemented
11C2×#19128308C214yesmaximal, complemented
12C2×#19128256C211yesmaximal, characteristic, complemented
13C2×#19128255C212yesmaximal, complemented
14C2×#19128233C211yesmaximal, characteristic
15C2×#19128230C212yesmaximal
16C2×#19128178C212yesmaximal, complemented
17C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
18C2×#556×C83C211yesmaximal, characteristic, complemented
19C23×Dic166C2212yes—
20C22×Q8×D83C2211yescharacteristic
21#19128429C22116yescomplemented
22#19128427C22132yescomplemented
23#19128426C22116yescomplemented
24#19128420C22132yescomplemented
25#19128390C22132yescomplemented
26#19128387C22164yescomplemented
27D4×Dic166C22116yescomplemented
28#19128364C22132yescomplemented
29#19128311C22132yescomplemented
30#19128308C22164yescomplemented
31#19128256C22116yescomplemented
32#19128255C22132yescomplemented
33C2×#14581792C2211yescharacteristic
34C2×#14581791C2214yes—
35C2×#14581791C2212yes—
36C2×#14581790C2212yes—
37C2×#14581790C2212yes—
38#19128233C22116yes—
39#19128230C22132yes—
40C2×#14581785C2214yes—
41C2×#14581785C2214yes—
42C2×#14581785C2214yes—
43C2×#14581785C2212yes—
44C2×#14581784C2214yes—
45C2×#14581784C2212yes—
46C2×#14581783C2214yes—
47C2×#14581783C2212yes—
48C2×#14581783C2211yescharacteristic
49C2×#14581783C2212yes—
50C2×#14581782C2214yes—
51C2×#14581782C2214yes—
52C2×#14581782C2214yes—
53C2×#14581779C2211yescharacteristic
54C2×#14581774C2212yes—
55C2×#14581774C2214yes—
56C2×#14581772C2212yes—
57C2×#14581772C2211yescharacteristic
58C2×#14581771C2212yes—
59C2×#14581770C2214yes—
60C2×#14581769C2214yes—
61C2×#14581769C2214yes—
62C2×#14581768C2212yes—
63C2×#14581763C2211yescharacteristic
64#19128178C22132yescomplemented
65C2×Q8×Dic83C2211yescharacteristic
66C2×Q8×Dic83C2212yes—
67C2×Q8×Dic83C2212yes—
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2214yes—
71C2×C4×Dic166C2214yes—
72C2×C4×Dic166C2211yescharacteristic
73C2×C4×Dic166C2212yes—
74C2×#14581757C2211yescharacteristic
75C2×#14581757C2212yes—
76C2×#14581757C2212yes—
77C2×#14581757C2212yes—
78C2×#14581757C2212yes—
79C4×Q8×D83C22116yescomplemented
80C2×D4×Dic83C2212yes—
81C2×C4×C22⋊D83C2212yes—
82C2×(C22⋊D83)⋊C4C2214yes—
83C2×#14581751C2212yes—
84C2×#14581750C2212yes—
85C2×#14581749C2214yes—
86C2×#14581748C2214yes—
87C2×#14581748C2214yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2211yescharacteristic
90C2×C42×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#556×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#126×C83C2214yes—
95C2×#124×C83C2212yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×Q8×C83C2212yes—
99C2×C4×D4×C83C2211yescharacteristic
100C2×#117×C83C2212yes—
101C22×Dic166—216no—
102C22×Dic166C23116yes—
103C22×Dic166C2312yes—
104C22×Dic166C2312yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2314yes—
107C22×Dic166C2311yescharacteristic
108C2×Q8×D83—28no—
109C2×Q8×D83C2318yes—
110C22×C22⋊D83C2312yes—
111C23×Dic83C2314yes—
112C22×C4×D83C2311yescharacteristic
113C22×C4×D83C2312yes—
114C22×C4×D83C2311yescharacteristic
115C22×C4×D83C2312yes—
116C22×C4×D83C2311yescharacteristic
117#14581792C2318yes—
118#14581791C23132yes—
119#14581791C23116yes—
120#14581790C23116yes—
121#14581790C23116yes—
122#14581785C23132yes—
123#14581785C23132yes—
124#14581785C23132yes—
125#14581785C23116yes—
126#14581784C23132yes—
127#14581784C23116yes—
128#14581783C23132yes—
129#14581783C23116yes—
130#14581783C2318yes—
131#14581783C23116yes—
132#14581782C23132yes—
133#14581782C23132yes—
134#14581782C23132yes—
135#14581779C2318yes—
136#14581774C23116yes—
137#14581774C23132yes—
138#14581772C23116yes—
139#14581772C2318yes—
140#14581771C23116yes—
141#14581770C23132yes—
142#14581769C23132yes—
143#14581769C23132yes—
144#14581768C23116yes—
145#14581763C2318yes—
146Q8×Dic83C2318yes—
147Q8×Dic83C23116yes—
148Q8×Dic83C23116yes—
149C4×Dic166C2318yes—
150C4×Dic166C23132yes—
151C4×Dic166C23116yes—
152C4×Dic166C23116yes—
153C4×Dic166C2318yes—
154C4×Dic166C23132yes—
155#14581757C23116yes—
156#14581757C23116yes—
157#14581757C2318yes—
158#14581757C23116yes—
159#14581757C23116yes—
160D4×Dic83C23116yes—
161C4×C22⋊D83C23116yes—
162(C22⋊D83)⋊C4C23132yes—
163#14581751C23116yes—
164#14581750C23116yes—
165#14581749C23132yes—
166#14581748C23132yes—
167#14581748C23132yes—
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2314yes—
176C2×C4⋊Dic83C2314yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2314yes—
188C2×Dic83⋊C4C2312yes—
189C4⋊C4×D83C23116yes—
190C4⋊C4×D83C2318yes—
191C2×C22⋊Dic83C2312yes—
192C2×C22⋊Dic83C2312yes—
193C2×C22⋊Dic83C2312yes—
194C2×C22⋊Dic83C2314yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×C4×Dic83C2312yes—
198C2×C4×Dic83C2311yescharacteristic
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2314yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2312yes—
207C42×D83C23116yes—
208C42×D83C2318yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2312yes—
211C22×D4×C83C2311yescharacteristic
212C23×C4×C83C2312yes—
213C4⋊Q8×C83C2318yes—
214#126×C83C23132yes—
215#124×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C4×Q8×C83C2318yes—
218C4×Q8×C83C23116yes—
219C4×D4×C83C2318yes—
220#117×C83C23116yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2312yes—
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2314yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C22⋊C4×C83C2314yes—
228C2×C22⋊C4×C83C2312yes—
229C2×C22⋊C4×C83C2314yes—
230C2×C42×C83C2314yes—
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2312yes—
233C23×D83C2411yescharacteristic
234C2×Dic166—28no—
235C2×Dic166—24no—
236C2×Dic166—28no—
237C2×Dic166—216no—
238C2×Dic166—264no—
239C2×Dic166#4118yes—
240C2×Dic166C2418yes—
241C2×Dic166C24116yes—
242C2×Dic166C2418yes—
243C2×Dic166C2414yes—
244C2×Dic166C2414yes—
245Q8×D83—232no—
246C2×C22⋊D83—28no—
247C2×C22⋊D83C2418yes—
248C22×Dic83—216no—
249C22×Dic83C24116yes—
250C22×Dic83C2411yescharacteristic
251C22×Dic83C2411yescharacteristic
252C22×Dic83C2411yescharacteristic
253C22×Dic83C2412yes—
254C22×Dic83C2414yes—
255C22×Dic83C2412yes—
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C2×C4×D83—28no—
259C2×C4×D83—24no—
260C2×C4×D83—24no—
261C2×C4×D83—24no—
262C2×C4×D83—28no—
263C2×C4×D83C2414yes—
264C2×C4×D83C2418yes—
265C2×C4×D83C2414yes—
266C2×C4×D83C2418yes—
267C2×C4×D83C2414yes—
268C4⋊Dic83C2414yes—
269C4⋊Dic83C2418yes—
270C4⋊Dic83C2418yes—
271C4⋊Dic83C24116yes—
272C4⋊Dic83C2414yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C24116yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2418yes—
277Dic83⋊C4C24116yes—
278Dic83⋊C4C2418yes—
279Dic83⋊C4C24116yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C2418yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C24116yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289C22⋊Dic83C2418yes—
290C22⋊Dic83C2418yes—
291C22⋊Dic83C24116yes—
292C22⋊Dic83C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295C4×Dic83C2414yes—
296C4×Dic83C2418yes—
297C4×Dic83C24116yes—
298C4×Dic83C24116yes—
299C4×Dic83C2414yes—
300C4×Dic83C24116yes—
301C4×Dic83C2418yes—
302C4×Dic83C2418yes—
303C4×Dic83C2418yes—
304C4×Dic83C2414yes—
305C24×C83C2412yes—
306C2×Q8×C83—24no—
307C2×Q8×C83—28no—
308C2×Q8×C83C2418yes—
309C2×Q8×C83C2414yes—
310C2×D4×C83—24no—
311C2×D4×C83C2414yes—
312C22×C4×C83—28no—
313C22×C4×C83C2418yes—
314C22×C4×C83C2412yes—
315C22×C4×C83C2412yes—
316C22×C4×C83C2411yescharacteristic
317C22×C4×C83C2412yes—
318C22×C4×C83C2414yes—
319C22×C4×C83C2411yescharacteristic
320C22×C4×C83C2411yescharacteristic
321C4⋊C4×C83C24116yes—
322C4⋊C4×C83C2414yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2418yes—
325C4⋊C4×C83C2418yes—
326C4⋊C4×C83C2414yes—
327C22⋊C4×C83C2418yes—
328C22⋊C4×C83C24116yes—
329C22⋊C4×C83C24116yes—
330C42×C83C24116yes—
331C42×C83C2418yes—
332C42×C83C2414yes—
333C23×C83—24no—
334C23×C83—24no—
335C23×C83—24no—
336C23×C83C2514yes—
337C23×C83C2511yescharacteristic
338C22×D83—22no—
339C22×D83—22no—
340C22×D832−1+414yes—
341C22×D83C2512yes—
342Q8×C83—28no—
343Q8×C83—216no—
344D4×C83—28no—
345C2×C4×C83—24no—
346C2×C4×C83—24no—
347C2×C4×C83—28no—
348C2×C4×C83—24no—
349C2×C4×C83—22no—
350C2×C4×C83—216no—
351C2×C4×C83C2×#4114yes—
352C2×C4×C832−1+414yes—
353C2×C4×C83C2514yes—
354C2×C4×C83C2514yes—
355C2×C4×C83C2512yes—
356C2×C4×C83C2518yes—
357C2×C4×C83C2514yes—
358C2×C4×C83C2512yes—
359C2×C4×C83C2512yes—
360C22⋊D83—216no—
361C2×Dic83—22no—
362C2×Dic83—28no—
363C2×Dic83—22no—
364C2×Dic83—24no—
365C2×Dic83—22no—
366C2×Dic83—24no—
367C2×Dic83—24no—
368C2×Dic83—232no—
369C2×Dic83C2×#4118yes—
370C2×Dic83C2512yes—
371C2×Dic83C2512yes—
372C2×Dic83C2514yes—
373C2×Dic83C2514yes—
374C2×Dic83C2518yes—
375C2×Dic83C2514yes—
376C2×Dic83C2512yes—
377C2×Dic83C2514yes—
378C4×D83—216no—
379C4×D83—28no—
380C4×D83—28no—
381C4×D83—28no—
382C4×D83—216no—
383Dic166—216no—
384Dic166—28no—
385Dic166—216no—
386Dic166—232no—
387Dic166C2×#41116yes—
388C22×C83—24no—
389C22×C83—24no—
390C22×C83—24no—
391C22×C83—48no—
392C22×C83C22×#4112yes—
393C22×C83C2×2−1+412yes—
394C22×C83C2×2−1+412yes—
395C22×C83C2611yescharacteristic
396C2×D83—22no—
397C2×D83—22no—
398C2×D83—28no—
399C2×D83C2×2−1+414yes—
400C4×C83—24no—
401C4×C83—24no—
402C4×C83—24no—
403C4×C83—22no—
404C4×C83—28no—
405C4×C83C22×#4114yes—
406C4×C83C2×2−1+414yes—
407Dic83—22no—
408Dic83—28no—
409Dic83—24no—
410Dic83—22no—
411Dic83—24no—
412Dic83—22no—
413Dic83—24no—
414Dic83C22×#4118yes—
415C2×#3523—831nomaximal, Sylow
416C2×C83—44no—
417C2×C83#352314yescomplemented
418C2×C83C23×#4111yescharacteristic
419C2×C83C22×2−1+411yescharacteristic
420C2×C83C22×2−1+411yescharacteristic
421D83—24no—
422#3523—8332no—
423C2×#557—831no—
424C2×#557—832no—
425C2×#557—831no—
426C2×#556—832no—
427C2×#556D8311yescharacteristic, complemented
428C2×#552—834no—
429C2×#552—832no—
430C2×D4×Q8—832no—
431C2×D4×Q8—831no—
432C2×#541—834no—
433C2×#541—832no—
434C2×#533—831no—
435C2×#533—832no—
436C2×#529—832no—
437C2×#529—831no—
438C2×#519—832no—
439C22×C4×Q8—831no—
440C83C2×#352311yescharacteristic, complemented, Sylow
441C23×Q8—831no—
442C23×Q8—832no—
443#557—8316no—
444#557—8332no—
445#557—8316no—
446#556—8332no—
447#556C2×D83116yescomplemented
448#552—8364no—
449#552—8332no—
450D4×Q8—8332no—
451D4×Q8—8316no—
452#541—8364no—
453#541—8332no—
454#533—8316no—
455#533—8332no—
456C2×C4⋊Q8—832no—
457C2×C4⋊Q8—832no—
458C2×C4⋊Q8—832no—
459C2×C4⋊Q8—834no—
460C2×C4⋊Q8—831no—
461C2×C4⋊Q8C2×D8311yescharacteristic
462#529—8332no—
463#529—8316no—
464C2×#126—834no—
465C2×#126—832no—
466C2×#126—834no—
467C2×#126—834no—
468C2×#126C2×D8314yes—
469C2×#125—831no—
470C2×#125—834no—
471C2×#125—832no—
472C2×#125—834no—
473C2×#125—834no—
474C2×#125—834no—
475C2×#125—832no—
476C2×#125—832no—
477C2×#125—834no—
478C2×#124—831no—
479C2×#124C2×D8312yes—
480C2×#123—832no—
481C2×#123—834no—
482C2×C22⋊Q8—832no—
483C2×C22⋊Q8—832no—
484C2×C22⋊Q8—831no—
485C2×C22⋊Q8—834no—
486C2×C22⋊Q8—832no—
487C2×C22⋊Q8—834no—
488C2×C22⋊Q8—834no—
489C2×C22⋊Q8C2×D8312yes—
490C2×#121—831no—
491#519—8332no—
492C2×C4×Q8—831no—
493C2×C4×Q8—832no—
494C2×C4×Q8—832no—
495C2×C4×Q8—8316no—
496C2×C4×Q8—831no—
497C2×C4×Q8—832no—
498C2×C4×Q8—832no—
499C2×C4×Q8—832no—
500C2×C4×Q8—832no—
501C2×C4×Q8—831no—
502C2×C4×Q8—832no—
503C2×C4×Q8—834no—
504C2×C4×Q8—834no—
505C2×C4×Q8—831no—
506C2×C4×Q8—832no—
507C2×C4×Q8C2×D8311yescharacteristic
508C2×C4×Q8C2×D8312yes—
509C2×C4×D4—832no—
510C2×C4×D4—832no—
511C2×C4×D4—834no—
512C2×C4×D4C2×D8311yescharacteristic
513C2×#117—832no—
514C2×#117—832no—
515C2×#117—834no—
516C2×#117—834no—
517C2×#117—834no—
518C2×#117C2×D8312yes—
519C22×C4⋊C4—832no—
520C22×C4⋊C4—831no—
521C22×C42—832no—
522C22×C42—831no—
523C22×Q8—838no—
524C22×Q8—831no—
525C22×Q8—831no—
526C22×Q8—832no—
527C22×Q8—834no—
528C22×Q8—832no—
529C22×Q8—8316no—
530C22×Q8—16616no—
531C22×Q8—1668no—
532C22×Q8C22×D8312yes—
533C22×Q8C22×D8311yescharacteristic
534C22×D4—832no—
535C22×D4C22×D8311yescharacteristic
536C23×C4—834no—
537C23×C4—831no—
538C23×C4—832no—
539C23×C4—832no—
540C23×C4—831no—
541C23×C4—831no—
542C23×C4C22×D8312yes—
543C4⋊Q8—8316no—
544C4⋊Q8—8316no—
545C4⋊Q8—8316no—
546C4⋊Q8—8332no—
547C4⋊Q8—838no—
548C4⋊Q8C22×D8318yes—
549#126—8332no—
550#126—8316no—
551#126—8332no—
552#126—8332no—
553#126C22×D83132yes—
554#125—838no—
555#125—8332no—
556#125—8316no—
557#125—8332no—
558#125—8332no—
559#125—8332no—
560#125—8316no—
561#125—8316no—
562#125—8332no—
563#124—838no—
564#124C22×D83116yes—
565#123—8316no—
566#123—8332no—
567C22⋊Q8—8316no—
568C22⋊Q8—8316no—
569C22⋊Q8—8332no—
570C22⋊Q8—838no—
571C22⋊Q8—8316no—
572C22⋊Q8—8332no—
573C22⋊Q8—8332no—
574C22⋊Q8C22×D83116yes—
575#121—838no—
576C4×Q8—838no—
577C4×Q8—8316no—
578C4×Q8—8316no—
579C4×Q8—838no—
580C4×Q8—8316no—
581C4×Q8—8316no—
582C4×Q8—8316no—
583C4×Q8—8316no—
584C4×Q8—838no—
585C4×Q8—8316no—
586C4×Q8—8332no—
587C4×Q8—8332no—
588C4×Q8—838no—
589C4×Q8—8316no—
590C4×Q8C22×D8318yes—
591C4×Q8C22×D83116yes—
592C4×D4—8316no—
593C4×D4—8316no—
594C4×D4—8332no—
595C4×D4C22×D8318yes—
596#117—8316no—
597#117—8316no—
598#117—8332no—
599#117—8332no—
600#117—8332no—
601#117C22×D83116yes—
602C2×C4⋊C4—832no—
603C2×C4⋊C4—832no—
604C2×C4⋊C4—831no—
605C2×C4⋊C4—832no—
606C2×C4⋊C4—832no—
607C2×C4⋊C4—834no—
608C2×C4⋊C4—834no—
609C2×C4⋊C4—832no—
610C2×C4⋊C4—834no—
611C2×C4⋊C4—832no—
612C2×C4⋊C4—834no—
613C2×C4⋊C4—832no—
614C2×C4⋊C4—834no—
615C2×C4⋊C4—832no—
616C2×C4⋊C4—834no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—831no—
619C2×C4⋊C4—834no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—832no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—8316no—
624C2×C4⋊C4—838no—
625C2×C4⋊C4C22×D8311yescharacteristic
626C2×C4⋊C4C22×D8312yes—
627C2×C4⋊C4C22×D8312yes—
628C2×C4⋊C4C22×D8312yes—
629C2×C4⋊C4C22×D8311yescharacteristic
630C2×C4⋊C4C22×D8314yes—
631C2×C22⋊C4—832no—
632C2×C22⋊C4—832no—
633C2×C22⋊C4—834no—
634C2×C22⋊C4—832no—
635C2×C22⋊C4—832no—
636C2×C22⋊C4—834no—
637C2×C22⋊C4C22×D8314yes—
638C2×C22⋊C4C22×D8314yes—
639C2×C22⋊C4C22×D8312yes—
640C2×C42—832no—
641C2×C42—831no—
642C2×C42—834no—
643C2×C42—834no—
644C2×C42—834no—
645C2×C42—832no—
646C2×C42—832no—
647C2×C42—831no—
648C2×C42—832no—
649C2×C42—831no—
650C2×C42—8316no—
651C2×C42—838no—
652C2×C42C22×D8314yes—
653C2×C42C22×D8311yescharacteristic
654C2×C42C22×D8312yes—
655C24—831no—
656C24C23×D8312yes—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—838no—
660C2×Q8—834no—
661C2×Q8—834no—
662C2×Q8—838no—
663C2×Q8—8316no—
664C2×Q8—838no—
665C2×Q8—16616no—
666C2×Q8—1668no—
667C2×Q8—16664no—
668C2×Q8—16632no—
669C2×Q8—1668no—
670C2×Q8—1664no—
671C2×Q8C23×D8318yes—
672C2×Q8C23×D8314yes—
673C2×D4—24no—
674C2×D4—838no—
675C2×D4—1668no—
676C2×D4C23×D8314yes—
677C22×C4—28no—
678C22×C4—832no—
679C22×C4—8316no—
680C22×C4—831no—
681C22×C4—831no—
682C22×C4—832no—
683C22×C4—832no—
684C22×C4—832no—
685C22×C4—834no—
686C22×C4—831no—
687C22×C4—834no—
688C22×C4—834no—
689C22×C4—838no—
690C22×C4—838no—
691C22×C4—834no—
692C22×C4—1668no—
693C22×C4—1668no—
694C22×C4—1664no—
695C22×C4—16616no—
696C22×C4—1664no—
697C22×C4—1664no—
698C22×C4C23×D8318yes—
699C22×C4C23×D8312yes—
700C22×C4C23×D8314yes—
701C22×C4C23×D8311yescharacteristic
702C22×C4C23×D8312yes—
703C22×C4C23×D8312yes—
704C22×C4C23×D8311yescharacteristic
705C22×C4C23×D8311yescharacteristic
706C4⋊C4—838no—
707C4⋊C4—838no—
708C4⋊C4—834no—
709C4⋊C4—838no—
710C4⋊C4—838no—
711C4⋊C4—8316no—
712C4⋊C4—8316no—
713C4⋊C4—838no—
714C4⋊C4—8316no—
715C4⋊C4—838no—
716C4⋊C4—8316no—
717C4⋊C4—838no—
718C4⋊C4—8316no—
719C4⋊C4—838no—
720C4⋊C4—8316no—
721C4⋊C4—838no—
722C4⋊C4—834no—
723C4⋊C4—8316no—
724C4⋊C4—8316no—
725C4⋊C4—838no—
726C4⋊C4—8316no—
727C4⋊C4C23×D8314yes—
728C4⋊C4C23×D8318yes—
729C4⋊C4C23×D8318yes—
730C4⋊C4C23×D8318yes—
731C4⋊C4C23×D8314yes—
732C4⋊C4C23×D83116yes—
733C22⋊C4—838no—
734C22⋊C4—838no—
735C22⋊C4—8316no—
736C22⋊C4—838no—
737C22⋊C4—838no—
738C22⋊C4—8316no—
739C22⋊C4C23×D83116yes—
740C22⋊C4C23×D83116yes—
741C22⋊C4C23×D8318yes—
742C42—838no—
743C42—834no—
744C42—838no—
745C42—834no—
746C42—838no—
747C42—834no—
748C42—8316no—
749C42—8316no—
750C42—8316no—
751C42—838no—
752C42C23×D8314yes—
753C42C23×D8318yes—
754C42C23×D83116yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—834no—
759C23—832no—
760C23—1662no—
761C23—1662no—
762C23C24×D8314yes—
763C23C24×D8311yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—8316no—
767Q8—16632no—
768Q8—16616no—
769Q8—16616no—
770Q8—1668no—
771D4—28no—
772D4—16616no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—216no—
779C2×C4—838no—
780C2×C4—834no—
781C2×C4—832no—
782C2×C4—832no—
783C2×C4—834no—
784C2×C4—834no—
785C2×C4—834no—
786C2×C4—832no—
787C2×C4—838no—
788C2×C4—16616no—
789C2×C4—16616no—
790C2×C4—1668no—
791C2×C4—16632no—
792C2×C4—1668no—
793C2×C4—1662no—
794C2×C4—1662no—
795C2×C4—1664no—
796C2×C4—1664no—
797C2×C4—1662no—
798C2×C4—1664no—
799C2×C4—1668no—
800C2×C4—1668no—
801C2×C4#41×D8314yes—
802C2×C4#1458183914yes—
803C2×C4C24×D8314yes—
804C2×C4C24×D8318yes—
805C2×C4C24×D8312yes—
806C2×C4C24×D8314yes—
807C2×C4C24×D8314yes—
808C2×C4C24×D8312yes—
809C2×C4C24×D8312yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—834no—
815C22—1662no—
816C22—1662no—
817C22—1668no—
818C22C2×#41×D8312yes—
819C222−1+4×D8312yes—
820C22C2×#1458183912yes—
821C22C25×D8311yescharacteristic
822C4—24no—
823C4—24no—
824C4—24no—
825C4—22no—
826C4—28no—
827C4—838no—
828C4—1668no—
829C4—1662no—
830C4—1662no—
831C4—1664no—
832C4—1664no—
833C4—1662no—
834C4—1664no—
835C4C2×#41×D8314yes—
836C4C2×#1458183914yes—
837C2—44no—
838C2—1664no—
839C2#2492155814yesdirect product factor
840C2C22×#41×D8311yescharacteristic
841C2C2×2−1+4×D8311yescharacteristic
842C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#556×C83C2
socleC23×C83C25
prime radicalC2×#14581763C22
hypercenterC2×#556D83
hypocenterC83C2×#3523
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #24921558C2direct (N × H)
2. C2×#19128429C2semidirect
3. C2×#19128427C2semidirect
4. C2×#19128426C2semidirect
5. C2×#19128420C2semidirect
6. C2×#19128390C2semidirect
7. C2×#19128387C2semidirect
8. C2×D4×Dic166C2semidirect
9. C2×#19128364C2semidirect
10. C2×#19128311C2semidirect
11. C2×#19128308C2semidirect
12. C2×#19128256C2semidirect
13. C2×#19128255C2semidirect
16. C2×#19128178C2semidirect
17. C2×C4×Q8×D83C2semidirect
18. C2×#556×C83C2semidirect
21. #19128429C22semidirect
22. #19128427C22semidirect
23. #19128426C22semidirect
24. #19128420C22semidirect
25. #19128390C22semidirect
26. #19128387C22semidirect
27. D4×Dic166C22semidirect
28. #19128364C22semidirect
29. #19128311C22semidirect
30. #19128308C22semidirect
31. #19128256C22semidirect
32. #19128255C22semidirect
64. #19128178C22semidirect
79. C4×Q8×D83C22semidirect
92. #556×C83C22semidirect
417. C2×C83#3523semidirect
427. C2×#556D83semidirect
440. C83C2×#3523semidirect
447. #556C2×D83semidirect
839. C2#24921558direct (N × H)

Maximal subgroups

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

subgroupindex
#249215582
C2×#191284292
C2×#191284272
C2×#191284262
C2×#191284202
C2×#191283902
C2×#191283872
C2×D4×Dic1662
C2×#191283642
C2×#191283112
C2×#191283082
C2×#191282562
C2×#191282552
C2×#191282332
C2×#191282302
C2×#191281782
C2×C4×Q8×D832
C2×#556×C832
C2×#352383