Finite Group Databasebeta

← C2×#24921848 #36312107

Subgroups — C2×#24921848 #36312107

Order 21248.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921848C2132yesmaximal, direct product factor
2C2×#19128447C214yesmaximal, complemented
3C2×#19128417C212yesmaximal, complemented
4C2×#19128416C211yesmaximal, characteristic, complemented
5C2×#19128411C211yesmaximal, characteristic, complemented
6C2×#19128401C212yesmaximal, complemented
7C2×#19128385C212yesmaximal, complemented
8C2×#19128362C212yesmaximal, complemented
9C2×#19128354C211yesmaximal, characteristic, complemented
10C2×#19128328C212yesmaximal, complemented
11C2×#19128321C214yesmaximal, complemented
12C2×#19128302C212yesmaximal, complemented
13C2×#19128281C212yesmaximal, complemented
14C2×#19128275C212yesmaximal, complemented
15C2×#19128256C211yesmaximal, characteristic, complemented
16C2×#19128248C211yesmaximal, characteristic, complemented
17C2×#19128238C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×#13050590C2212yes—
21#19128447C22164yescomplemented
22#19128417C22132yescomplemented
23#19128416C22116yescomplemented
24#19128411C22116yescomplemented
25#19128401C22132yescomplemented
26#19128385C22132yescomplemented
27#19128362C22132yescomplemented
28#19128354C22116yescomplemented
29#19128328C22132yescomplemented
30#19128321C22164yescomplemented
31#19128302C22132yescomplemented
32#19128281C22132yescomplemented
33#19128275C22132yescomplemented
34#19128256C22116yescomplemented
35#19128248C22116yescomplemented
36C2×#14581792C2211yescharacteristic
37C2×#14581791C2211yescharacteristic
38C2×#14581790C2214yes—
39C2×#14581788C2211yescharacteristic
40#19128238C22116yescomplemented
41C2×#14581787C2212yes—
42C2×#14581785C2214yes—
43C2×#14581784C2212yes—
44C2×#14581783C2212yes—
45C2×#14581783C2211yescharacteristic
46C2×#14581782C2214yes—
47C2×#14581781C2214yes—
48C2×#14581781C2211yescharacteristic
49C2×#14581781C2214yes—
50C2×#14581778C2212yes—
51C2×#14581778C2214yes—
52C2×#14581777C2214yes—
53C2×#14581777C2212yes—
54C2×#14581775C2214yes—
55C2×#14581775C2214yes—
56C2×#14581774C2214yes—
57C2×#14581772C2212yes—
58C2×#14581770C2214yes—
59C2×#14581770C2214yes—
60C2×#14581768C2214yes—
61C2×#14581768C2212yes—
62C2×#14581768C2212yes—
63C2×#14581768C2211yescharacteristic
64C2×#14581768C2212yes—
65C2×#14581767C2212yes—
66C2×#14581767C2211yescharacteristic
67C2×#14581767C2211yescharacteristic
68C2×#14581767C2214yes—
69C2×#14581766C2212yes—
70C2×#14581766C2214yes—
71C2×#14581765C2214yes—
72C2×#14581765C2214yes—
73C2×#14581765C2212yes—
74C2×#14581763C2211yescharacteristic
75C2×#14581763C2212yes—
76C2×Q8×Dic83C2212yes—
77C2×#14581757C2212yes—
78C2×C4×D332C2211yescharacteristic
79C2×C4×D332C2211yescharacteristic
80C2×C4×D332C2212yes—
81C2×C4×D332C2212yes—
82C2×C4×C22⋊D83C2214yes—
83C2×C4×C22⋊D83C2212yes—
84C2×#14581751C2212yes—
85C2×#14581750C2214yes—
86C2×#14581750C2212yes—
87C2×#14581750C2212yes—
88C2×#14581749C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C4⋊C4×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92C23×Q8×C83C2212yes—
93D4×Q8×C83C22116yescomplemented
94C2×C4⋊Q8×C83C2212yes—
95C2×C4⋊Q8×C83C2211yescharacteristic
96C2×C22⋊Q8×C83C2214yes—
97C2×C22⋊Q8×C83C2212yes—
98C2×C4×Q8×C83C2211yescharacteristic
99C2×C4×D4×C83C2212yes—
100C2×C4×D4×C83C2211yescharacteristic
101C2×#13050591—48no—
102C2×#13050591C23116yes—
103C2×#13050590—48no—
104C2×#13050590C23116yes—
105C22×Dic166C2312yes—
106C22×Dic166C2312yes—
107C22×D332C2311yescharacteristic
108C22×D332C2311yescharacteristic
109C22×D332C2312yes—
110C22×D332C2314yes—
111C22×D332C2312yes—
112C22×C22⋊D83C2314yes—
113C22×C22⋊D83C2312yes—
114C22×C22⋊D83C2312yes—
115C22×C22⋊D83C2312yes—
116C22×C4×D83C2311yescharacteristic
117C22×C4×D83C2311yescharacteristic
118C22×C4×D83C2312yes—
119C22×C4×D83C2312yes—
120C22×C4×D83C2311yescharacteristic
121C22×C4×D83C2314yes—
122C22×C4×D83C2314yes—
123#14581792C2318yes—
124#14581791C2318yes—
125#14581790C23132yes—
126#14581788C2318yes—
127#14581787C23116yes—
128#14581785C23132yes—
129#14581784C23116yes—
130#14581783C23116yes—
131#14581783C2318yes—
132#14581782C23132yes—
133#14581781C23132yes—
134#14581781C2318yes—
135#14581781C23132yes—
136#14581778C23116yes—
137#14581778C23132yes—
138#14581777C23132yes—
139#14581777C23116yes—
140#14581775C23132yes—
141#14581775C23132yes—
142#14581774C23132yes—
143#14581772C23116yes—
144#14581770C23132yes—
145#14581770C23132yes—
146#14581768C23132yes—
147#14581768C23116yes—
148#14581768C23116yes—
149#14581768C2318yes—
150#14581768C23116yes—
151#14581767C23116yes—
152#14581767C2318yes—
153#14581767C23132yes—
154#14581767C2318yes—
155#14581766C23116yes—
156#14581766C23132yes—
157#14581765C23132yes—
158#14581765C23132yes—
159#14581765C23116yes—
160#14581763C2318yes—
161#14581763C23116yes—
162Q8×Dic83C23116yes—
163#14581757C23116yes—
164C4×D332C2318yes—
165C4×D332C2318yes—
166C4×D332C23116yes—
167C4×D332C23116yes—
168C4×C22⋊D83C23132yes—
169C4×C22⋊D83C23116yes—
170#14581751C23116yes—
171#14581750C23132yes—
172#14581750C23116yes—
173#14581750C23116yes—
174#14581749C23116yes—
175C2×C4⋊Dic83C2311yescharacteristic
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2312yes—
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2311yescharacteristic
180C2×C4⋊Dic83C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2314yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C23116yes—
190C2×C22⋊Dic83C2314yes—
191C2×C22⋊Dic83C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2314yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2312yes—
200C2×(C2×D83)⋊C4C2314yes—
201C2×(C2×D83)⋊C4C2312yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×C4×Dic83C2311yescharacteristic
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2311yescharacteristic
206C2×C4×Dic83C2314yes—
207C2×C4×Dic83C2314yes—
208C42×D83C2318yes—
209C22×Q8×C83—48no—
210C22×Q8×C83C2311yescharacteristic
211C22×Q8×C83C2312yes—
212C22×Q8×C83C23116yes—
213C22×Q8×C83C2314yes—
214C22×D4×C83C2311yescharacteristic
215C23×C4×C83C2312yes—
216C23×C4×C83C2314yes—
217C4⋊Q8×C83C23116yes—
218C4⋊Q8×C83C2318yes—
219C22⋊Q8×C83C23132yes—
220C22⋊Q8×C83C23116yes—
221C4×Q8×C83C2318yes—
222C4×D4×C83C23116yes—
223C4×D4×C83C2318yes—
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2311yescharacteristic
226C2×C4⋊C4×C83C2311yescharacteristic
227C2×C4⋊C4×C83C2312yes—
228C2×C4⋊C4×C83C2314yes—
229C2×C4⋊C4×C83C2312yes—
230C2×C22⋊C4×C83C2314yes—
231C2×C22⋊C4×C83C2312yes—
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2312yes—
234C23×D83C2411yescharacteristic
235C23×D83C2412yes—
236C23×D83C2412yes—
237#13050591—432no—
238#13050590—432no—
239C2×Dic166—44no—
240C2×Dic166—44no—
241C2×Dic166C2418yes—
242C2×Dic166C2418yes—
243C2×D332—24no—
244C2×D332—24no—
245C2×D332—44no—
246C2×D332—44no—
247C2×D332—48no—
248C2×D332C2414yes—
249C2×D332C2414yes—
250C2×D332C2418yes—
251C2×D332C24116yes—
252C2×D332C2418yes—
253C2×C22⋊D83—44no—
254C2×C22⋊D83—48no—
255C2×C22⋊D83—44no—
256C2×C22⋊D83—44no—
257C2×C22⋊D83C2418yes—
258C2×C22⋊D83C24116yes—
259C2×C22⋊D83C2418yes—
260C2×C22⋊D83C2418yes—
261C22×Dic83C2412yes—
262C22×Dic83C2411yescharacteristic
263C22×Dic83C2411yescharacteristic
264C22×Dic83C2414yes—
265C22×Dic83C2411yescharacteristic
266C22×Dic83C2412yes—
267C2×C4×D83—24no—
268C2×C4×D83—28no—
269C2×C4×D83—24no—
270C2×C4×D83—28no—
271C2×C4×D83—42no—
272C2×C4×D83—48no—
273C2×C4×D83—48no—
274C2×C4×D83C2414yes—
275C2×C4×D83C2418yes—
276C2×C4×D83C2414yes—
277C2×C4×D83C2418yes—
278C2×C4×D83C2414yes—
279C2×C4×D83C24116yes—
280C2×C4×D83C24116yes—
281C4⋊Dic83C2418yes—
282C4⋊Dic83C2414yes—
283C4⋊Dic83C2418yes—
284C4⋊Dic83C24116yes—
285C4⋊Dic83C2414yes—
286C4⋊Dic83C2418yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C24116yes—
289Dic83⋊C4C24116yes—
290Dic83⋊C4C24116yes—
291Dic83⋊C4C2418yes—
292Dic83⋊C4C24116yes—
293Dic83⋊C4C2418yes—
294C22⋊Dic83C24116yes—
295C22⋊Dic83C2418yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C24116yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C2418yes—
300(C2×D83)⋊C4C24116yes—
301(C2×D83)⋊C4C24116yes—
302(C2×D83)⋊C4C24116yes—
303(C2×D83)⋊C4C2418yes—
304(C2×D83)⋊C4C2418yes—
305(C2×D83)⋊C4C2418yes—
306(C2×D83)⋊C4C2418yes—
307C4×Dic83C2414yes—
308C4×Dic83C24116yes—
309C4×Dic83C2414yes—
310C4×Dic83C24116yes—
311C4×Dic83C2414yes—
312C24×C83C2412yes—
313C2×Q8×C83—28no—
314C2×Q8×C83—24no—
315C2×Q8×C83—48no—
316C2×Q8×C83—432no—
317C2×Q8×C83C2414yes—
318C2×Q8×C83C2418yes—
319C2×Q8×C83C24116yes—
320C2×D4×C83—24no—
321C2×D4×C83C2414yes—
322C22×C4×C83—28no—
323C22×C4×C83—48no—
324C22×C4×C83C2418yes—
325C22×C4×C83C2412yes—
326C22×C4×C83C2414yes—
327C22×C4×C83C2411yescharacteristic
328C22×C4×C83C2412yes—
329C22×C4×C83C2412yes—
330C22×C4×C83C24116yes—
331C22×C4×C83C2411yescharacteristic
332C22×C4×C83C2411yescharacteristic
333C4⋊C4×C83C24116yes—
334C4⋊C4×C83C2418yes—
335C4⋊C4×C83C2414yes—
336C4⋊C4×C83C2414yes—
337C4⋊C4×C83C2418yes—
338C4⋊C4×C83C2418yes—
339C22⋊C4×C83C24116yes—
340C22⋊C4×C83C2418yes—
341C42×C83C2418yes—
342C42×C83C2414yes—
343C23×C83—24no—
344C23×C83—24no—
345C23×C83—24no—
346C23×C83C2514yes—
347C23×C83C2511yescharacteristic
348C22×D83—22no—
349C22×D83—24no—
350C22×D83—24no—
351C22×D83—22no—
352C22×D83—24no—
353C22×D83—24no—
354C22×D83—24no—
355C22×D83—22no—
356C22×D83—24no—
357C22×D83C2514yes—
358C22×D83C2512yes—
359C22×D83C2514yes—
360Q8×C83—28no—
361Q8×C83—216no—
362Q8×C83—416no—
363D4×C83—28no—
364C2×C4×C83—24no—
365C2×C4×C83—24no—
366C2×C4×C83—28no—
367C2×C4×C83—24no—
368C2×C4×C83—22no—
369C2×C4×C83—216no—
370C2×C4×C83—416no—
371C2×C4×C83H(5,𝔽2)14yes—
372C2×C4×C832−1+414yes—
373C2×C4×C83C2512yes—
374C2×C4×C83C2514yes—
375C2×C4×C83C2514yes—
376C2×C4×C83C2514yes—
377C2×C4×C83C2518yes—
378C2×C4×C83C2512yes—
379C2×C4×C83C2512yes—
380C22⋊D83—416no—
381C22⋊D83—48no—
382C22⋊D83—48no—
383C22⋊D83—48no—
384C2×Dic83—24no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—24no—
388C2×Dic83—22no—
389C2×Dic83—28no—
390C2×Dic83C2512yes—
391C2×Dic83C2514yes—
392C2×Dic83C2518yes—
393C2×Dic83C2512yes—
394C2×Dic83C2512yes—
395C2×Dic83C2514yes—
396D332—28no—
397D332—28no—
398D332—48no—
399D332—48no—
400D332—416no—
401C4×D83—28no—
402C4×D83—216no—
403C4×D83—28no—
404C4×D83—216no—
405C4×D83—416no—
406C4×D83—44no—
407C4×D83—416no—
408Dic166—48no—
409Dic166—48no—
410C22×C83—24no—
411C22×C83—24no—
412C22×C83—24no—
413C22×C83—48no—
414C22×C83C2×H(5,𝔽2)12yes—
415C22×C83C2×2−1+412yes—
416C22×C83#58512yes—
417C22×C83C2611yescharacteristic
418C2×D83—24no—
419C2×D83—22no—
420C2×D83—24no—
421C2×D83—22no—
422C2×D83—24no—
423C2×D83—24no—
424C2×D83—24no—
425C2×D83—22no—
426C2×D83—24no—
427C2×D83—44no—
428C2×D83—48no—
429C2×D83—48no—
430C4×C83—24no—
431C4×C83—28no—
432C4×C83—24no—
433C4×C83—22no—
434C4×C83—24no—
435C4×C83C2×H(5,𝔽2)14yes—
436C4×C83C2×2−1+414yes—
437Dic83—22no—
438Dic83—24no—
439Dic83—22no—
440Dic83—24no—
441Dic83—28no—
442Dic83—22no—
443C2×#3547—831nomaximal, Sylow
444C2×C83—44no—
445C2×C83#354714yescomplemented
446C2×C83C22×H(5,𝔽2)11yescharacteristic
447C2×C83C22×2−1+411yescharacteristic
448C2×C83C2×#58511yescharacteristic
449D83—44no—
450D83—42no—
451D83—44no—
452#3547—8332no—
453C2×#562—834no—
454C2×#555—832no—
455C2×#555—831no—
456C2×#554—831no—
457C2×#553—832no—
458C2×#552—832no—
459C2×D4×Q8D8311yescharacteristic, complemented
460C2×#548—832no—
461C2×#547—831no—
462C2×#544—832no—
463C2×#542—834no—
464C2×#540—832no—
465C2×#537—832no—
466C2×#536—832no—
467C2×#533—831no—
468C2×#532—831no—
469C2×#529—831no—
470C83C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—832no—
472C22×#41—832no—
473C23×Q8C2×D8312yes—
474#562—8364no—
475#555—8332no—
476#555—8316no—
477#554—8316no—
478#553—8332no—
479#552—8332no—
480D4×Q8C2×D83116yescomplemented
481#548—8332no—
482#547—8316no—
483#544—8332no—
484#542—8364no—
485#540—8332no—
486#537—8332no—
487#536—8332no—
488#533—8316no—
489#532—8316no—
490C2×C4⋊Q8—834no—
491C2×C4⋊Q8—831no—
492C2×C4⋊Q8—831no—
493C2×C4⋊Q8C2×D8311yescharacteristic
494C2×C4⋊Q8C2×D8312yes—
495C2×#127—831no—
496#529—8316no—
497C2×#126—832no—
498C2×#126—834no—
499C2×#125—831no—
500C2×#125—832no—
501C2×#125—834no—
502C2×#125—832no—
503C2×#124—831no—
504C2×#124—834no—
505C2×#124—834no—
506C2×#124—832no—
507C2×#124—834no—
508C2×#123—834no—
509C2×#123—834no—
510C2×#123—832no—
511C2×#123—834no—
512C2×#123—834no—
513C2×C22⋊Q8—831no—
514C2×C22⋊Q8—832no—
515C2×C22⋊Q8—832no—
516C2×C22⋊Q8—832no—
517C2×C22⋊Q8—834no—
518C2×C22⋊Q8—832no—
519C2×C22⋊Q8—834no—
520C2×C22⋊Q8—834no—
521C2×C22⋊Q8C2×D8312yes—
522C2×C22⋊Q8C2×D8314yes—
523C2×#121—831no—
524C2×#121—832no—
525C2×#121—832no—
526C2×#121—834no—
527C2×#121—831no—
528C2×#121—831no—
529C2×#121—834no—
530C2×#121—832no—
531C2×#121—832no—
532C2×#121—834no—
533C2×#121—834no—
534C2×C4×Q8—832no—
535C2×C4×Q8—832no—
536C2×C4×Q8C2×D8311yescharacteristic
537C2×C4×D4—832no—
538C2×C4×D4—834no—
539C2×C4×D4—831no—
540C2×C4×D4—832no—
541C2×C4×D4—831no—
542C2×C4×D4—832no—
543C2×C4×D4C2×D8311yescharacteristic
544C2×C4×D4C2×D8312yes—
545C2×#117—832no—
546C2×#117—832no—
547C2×#117—834no—
548C2×#117—832no—
549C2×#117—832no—
550C22×C4⋊C4—832no—
551C22×C4⋊C4—832no—
552C22×C42—831no—
553C2×#41—3328no—
554C2×#41—3328no—
555C2×#41—8316no—
556C2×#41—8316no—
557C22×Q8—48no—
558C22×Q8—832no—
559C22×Q8—832no—
560C22×Q8C22×D8312yes—
561C22×Q8C22×D8311yescharacteristic
562C22×Q8C22×D8314yes—
563C22×Q8C22×D83116yes—
564C22×D4—834no—
565C22×D4—832no—
566C22×D4—832no—
567C22×D4—832no—
568C22×D4—832no—
569C22×D4—834no—
570C22×D4—832no—
571C22×D4—831no—
572C22×D4—831no—
573C22×D4C22×D8311yescharacteristic
574C23×C4—834no—
575C23×C4—834no—
576C23×C4—831no—
577C23×C4—832no—
578C23×C4—832no—
579C23×C4—831no—
580C23×C4—831no—
581C23×C4C22×D8312yes—
582C23×C4C22×D8314yes—
583C4⋊Q8—8332no—
584C4⋊Q8—838no—
585C4⋊Q8—838no—
586C4⋊Q8C22×D8318yes—
587C4⋊Q8C22×D83116yes—
588#127—838no—
589#126—8316no—
590#126—8332no—
591#125—838no—
592#125—8316no—
593#125—8332no—
594#125—8316no—
595#124—838no—
596#124—8332no—
597#124—8332no—
598#124—8316no—
599#124—8332no—
600#123—8332no—
601#123—8332no—
602#123—8316no—
603#123—8332no—
604#123—8332no—
605C22⋊Q8—838no—
606C22⋊Q8—8316no—
607C22⋊Q8—8316no—
608C22⋊Q8—8316no—
609C22⋊Q8—8332no—
610C22⋊Q8—8332no—
611C22⋊Q8—8332no—
612C22⋊Q8—8316no—
613C22⋊Q8C22×D83116yes—
614C22⋊Q8C22×D83132yes—
615#121—838no—
616#121—8316no—
617#121—8316no—
618#121—8332no—
619#121—838no—
620#121—838no—
621#121—8332no—
622#121—8316no—
623#121—8316no—
624#121—8332no—
625#121—8332no—
626C4×Q8—8316no—
627C4×Q8—8316no—
628C4×Q8C22×D8318yes—
629C4×D4—8316no—
630C4×D4—8332no—
631C4×D4—838no—
632C4×D4—8316no—
633C4×D4—838no—
634C4×D4—8316no—
635C4×D4C22×D8318yes—
636C4×D4C22×D83116yes—
637#117—8316no—
638#117—8316no—
639#117—8332no—
640#117—8316no—
641#117—8316no—
642C2×C4⋊C4—831no—
643C2×C4⋊C4—832no—
644C2×C4⋊C4—834no—
645C2×C4⋊C4—834no—
646C2×C4⋊C4—832no—
647C2×C4⋊C4—831no—
648C2×C4⋊C4—832no—
649C2×C4⋊C4—832no—
650C2×C4⋊C4—832no—
651C2×C4⋊C4—832no—
652C2×C4⋊C4—834no—
653C2×C4⋊C4—834no—
654C2×C4⋊C4—834no—
655C2×C4⋊C4—8316no—
656C2×C4⋊C4—8316no—
657C2×C4⋊C4C22×D8311yescharacteristic
658C2×C4⋊C4C22×D8312yes—
659C2×C4⋊C4C22×D8311yescharacteristic
660C2×C4⋊C4C22×D8314yes—
661C2×C4⋊C4C22×D8312yes—
662C2×C4⋊C4C22×D8312yes—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—832no—
665C2×C22⋊C4—832no—
666C2×C22⋊C4—832no—
667C2×C22⋊C4—834no—
668C2×C22⋊C4—832no—
669C2×C22⋊C4—834no—
670C2×C22⋊C4—834no—
671C2×C22⋊C4—832no—
672C2×C22⋊C4—832no—
673C2×C22⋊C4—834no—
674C2×C22⋊C4—832no—
675C2×C22⋊C4—832no—
676C2×C22⋊C4C22×D8314yes—
677C2×C22⋊C4C22×D8312yes—
678C2×C42—834no—
679C2×C42—834no—
680C2×C42—831no—
681C2×C42—831no—
682C2×C42—831no—
683C2×C42—838no—
684C2×C42C22×D8312yes—
685C2×C42C22×D8311yescharacteristic
686C24—832no—
687C24—831no—
688C24—832no—
689C24C23×D8312yes—
690#41—33232no—
691#41—33232no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—48no—
695C2×Q8—432no—
696C2×Q8—3324no—
697C2×Q8—3324no—
698C2×Q8—838no—
699C2×Q8—838no—
700C2×Q8C23×D8318yes—
701C2×Q8C23×D8314yes—
702C2×Q8C23×D83116yes—
703C2×D4—24no—
704C2×D4—3324no—
705C2×D4—3328no—
706C2×D4—3324no—
707C2×D4—3324no—
708C2×D4—3324no—
709C2×D4—3324no—
710C2×D4—3328no—
711C2×D4—8316no—
712C2×D4—838no—
713C2×D4—838no—
714C2×D4—838no—
715C2×D4—838no—
716C2×D4—8316no—
717C2×D4—838no—
718C2×D4—834no—
719C2×D4—834no—
720C2×D4—1664no—
721C2×D4—1664no—
722C2×D4C23×D8314yes—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—3328no—
726C22×C4—3328no—
727C22×C4—3322no—
728C22×C4—834no—
729C22×C4—8316no—
730C22×C4—8316no—
731C22×C4—831no—
732C22×C4—832no—
733C22×C4—834no—
734C22×C4—831no—
735C22×C4—831no—
736C22×C4—832no—
737C22×C4—834no—
738C22×C4—834no—
739C22×C4—838no—
740C22×C4—838no—
741C22×C4—1668no—
742C22×C4—1664no—
743C22×C4—1668no—
744C22×C4—1664no—
745C22×C4C23×D8318yes—
746C22×C4C23×D8312yes—
747C22×C4C23×D8311yescharacteristic
748C22×C4C23×D8314yes—
749C22×C4C23×D8312yes—
750C22×C4C23×D8312yes—
751C22×C4C23×D83116yes—
752C22×C4C23×D8311yescharacteristic
753C22×C4C23×D8311yescharacteristic
754C4⋊C4—834no—
755C4⋊C4—838no—
756C4⋊C4—8316no—
757C4⋊C4—8316no—
758C4⋊C4—838no—
759C4⋊C4—834no—
760C4⋊C4—838no—
761C4⋊C4—838no—
762C4⋊C4—838no—
763C4⋊C4—838no—
764C4⋊C4—8316no—
765C4⋊C4—8316no—
766C4⋊C4—8316no—
767C4⋊C4C23×D8314yes—
768C4⋊C4C23×D8318yes—
769C4⋊C4C23×D8314yes—
770C4⋊C4C23×D83116yes—
771C4⋊C4C23×D8318yes—
772C4⋊C4C23×D8318yes—
773C22⋊C4—8316no—
774C22⋊C4—838no—
775C22⋊C4—838no—
776C22⋊C4—838no—
777C22⋊C4—8316no—
778C22⋊C4—838no—
779C22⋊C4—8316no—
780C22⋊C4—8316no—
781C22⋊C4—838no—
782C22⋊C4—838no—
783C22⋊C4—8316no—
784C22⋊C4—838no—
785C22⋊C4—838no—
786C22⋊C4C23×D83116yes—
787C22⋊C4C23×D8318yes—
788C42—834no—
789C42—834no—
790C42—834no—
791C42—8316no—
792C42—8316no—
793C42C23×D8314yes—
794C42C23×D8318yes—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—834no—
799C23—832no—
800C23—834no—
801C23—1664no—
802C23—1664no—
803C23—1662no—
804C23—1664no—
805C23—1662no—
806C23—1664no—
807C23—1664no—
808C23—1662no—
809C23—1664no—
810C23C24×D8314yes—
811C23C24×D8311yescharacteristic
812Q8—28no—
813Q8—216no—
814Q8—416no—
815Q8—3328no—
816Q8—3328no—
817D4—28no—
818D4—3328no—
819D4—33216no—
820D4—3328no—
821D4—3328no—
822D4—3328no—
823D4—3328no—
824D4—33216no—
825D4—1668no—
826D4—1668no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—33216no—
835C2×C4—33216no—
836C2×C4—3324no—
837C2×C4—832no—
838C2×C4—834no—
839C2×C4—838no—
840C2×C4—832no—
841C2×C4—832no—
842C2×C4—834no—
843C2×C4—1664no—
844C2×C4—1662no—
845C2×C4—1662no—
846C2×C4—1664no—
847C2×C4—1662no—
848C2×C4—1668no—
849C2×C4—16616no—
850C2×C4—1668no—
851C2×C4—1668no—
852C2×C4—16616no—
853C2×C4#1458183714yes—
854C2×C4#1458184014yes—
855C2×C4C24×D8314yes—
856C2×C4C24×D8312yes—
857C2×C4C24×D8318yes—
858C2×C4C24×D8314yes—
859C2×C4C24×D8314yes—
860C2×C4C24×D8312yes—
861C2×C4C24×D8312yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—48no—
866C22—3328no—
867C22—3324no—
868C22—3328no—
869C22—1664no—
870C22—1664no—
871C22—1662no—
872C22—1664no—
873C22—1662no—
874C22—1664no—
875C22—1664no—
876C22—1662no—
877C22—1664no—
878C22C2×#1458183712yes—
879C22C2×#1458184012yes—
880C22#1912853812yes—
881C22C25×D8311yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—22no—
887C4—1664no—
888C4—1662no—
889C4—1662no—
890C4—1664no—
891C4—1662no—
892C4—1668no—
893C4C2×#1458183714yes—
894C4C2×#1458184014yes—
895C2—44no—
896C2—3324no—
897C2—3322no—
898C2—3324no—
899C2#2492184814yesdirect product factor
900C2C22×#1458183711yescharacteristic
901C2C22×#1458184011yescharacteristic
902C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×D4×Q8×C83C2
socleC23×C83C25
hypercenterC2×D4×Q8D83
hypocenterC83C2×#3547
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #24921848C2direct (N × H)
2. C2×#19128447C2semidirect
3. C2×#19128417C2semidirect
4. C2×#19128416C2semidirect
5. C2×#19128411C2semidirect
6. C2×#19128401C2semidirect
7. C2×#19128385C2semidirect
8. C2×#19128362C2semidirect
9. C2×#19128354C2semidirect
10. C2×#19128328C2semidirect
11. C2×#19128321C2semidirect
12. C2×#19128302C2semidirect
13. C2×#19128281C2semidirect
14. C2×#19128275C2semidirect
15. C2×#19128256C2semidirect
16. C2×#19128248C2semidirect
17. C2×#19128238C2semidirect
18. C2×D4×Q8×C83C2semidirect
21. #19128447C22semidirect
22. #19128417C22semidirect
23. #19128416C22semidirect
24. #19128411C22semidirect
25. #19128401C22semidirect
26. #19128385C22semidirect
27. #19128362C22semidirect
28. #19128354C22semidirect
29. #19128328C22semidirect
30. #19128321C22semidirect
31. #19128302C22semidirect
32. #19128281C22semidirect
33. #19128275C22semidirect
34. #19128256C22semidirect
35. #19128248C22semidirect
40. #19128238C22semidirect
93. D4×Q8×C83C22semidirect
445. C2×C83#3547semidirect
459. C2×D4×Q8D83semidirect
470. C83C2×#3547semidirect
480. D4×Q8C2×D83semidirect
899. C2#24921848direct (N × H)

Maximal subgroups

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

subgroupindex
#249218482
C2×#191284472
C2×#191284172
C2×#191284162
C2×#191284112
C2×#191284012
C2×#191283852
C2×#191283622
C2×#191283542
C2×#191283282
C2×#191283212
C2×#191283022
C2×#191282812
C2×#191282752
C2×#191282562
C2×#191282482
C2×#191282382
C2×D4×Q8×C832
C2×#354783