Finite Group Databasebeta

← C2×#24921893 #36312016

Subgroups — C2×#24921893 #36312016

Order 21248.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921893C2132yesmaximal, direct product factor
2C2×#19128453C214yesmaximal, complemented
3C2×#19128430C211yesmaximal, characteristic, complemented
4C2×#19128409C212yesmaximal, complemented
5C2×#19128395C212yesmaximal, complemented
6C2×Q8×D332C212yesmaximal, complemented
7C2×#19128366C211yesmaximal, characteristic, complemented
8C2×#19128359C212yesmaximal, complemented
9C2×#19128355C211yesmaximal, characteristic, complemented
10C2×#19128329C212yesmaximal, complemented
11C2×#19128324C212yesmaximal, complemented
12C2×#19128309C212yesmaximal, complemented
13C2×#19128292C214yesmaximal, complemented
14C2×#19128271C212yesmaximal, complemented
15C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
16C2×#19128238C211yesmaximal, characteristic, complemented
17C2×#19128233C211yesmaximal, characteristic, complemented
18C2×#556×C83C211yesmaximal, characteristic, complemented
19C22×#13050589C2212yes—
20C22×Q8×D83C2212yes—
21C22×Q8×D83C2212yes—
22#19128453C22164yescomplemented
23#19128430C22116yescomplemented
24#19128409C22132yescomplemented
25#19128395C22132yescomplemented
26Q8×D332C22132yescomplemented
27#19128366C22116yescomplemented
28#19128359C22132yescomplemented
29#19128355C22116yescomplemented
30#19128329C22132yescomplemented
31#19128324C22132yescomplemented
32#19128309C22132yescomplemented
33#19128292C22164yescomplemented
34#19128271C22132yescomplemented
35C2×#14581792C2214yes—
36C2×#14581792C2211yescharacteristic
37C2×#14581792C2212yes—
38C2×#14581791C2212yes—
39C2×#14581791C2212yes—
40C2×#14581791C2212yes—
41C2×#14581790C2212yes—
42C4⋊Q8×D83C22116yescomplemented
43#19128238C22116yescomplemented
44#19128233C22116yescomplemented
45C2×#14581787C2214yes—
46C2×#14581787C2212yes—
47C2×#14581786C2214yes—
48C2×#14581785C2212yes—
49C2×#14581784C2214yes—
50C2×#14581783C2211yescharacteristic
51C2×#14581783C2212yes—
52C2×#14581783C2211yescharacteristic
53C2×#14581783C2214yes—
54C2×#14581782C2214yes—
55C2×#14581781C2211yescharacteristic
56C2×#14581779C2211yescharacteristic
57C2×#14581778C2214yes—
58C2×#14581777C2212yes—
59C2×#14581776C2214yes—
60C2×#14581774C2214yes—
61C2×#14581774C2214yes—
62C2×#14581774C2212yes—
63C2×#14581772C2214yes—
64C2×#14581772C2212yes—
65C2×#14581772C2211yescharacteristic
66C2×#14581772C2214yes—
67C2×#14581770C2214yes—
68C2×#14581769C2214yes—
69C2×#14581769C2214yes—
70C2×#14581769C2214yes—
71C2×#14581768C2212yes—
72C2×#14581768C2211yescharacteristic
73C2×#14581767C2211yescharacteristic
74C2×#14581766C2212yes—
75C2×#14581765C2214yes—
76C2×#14581763C2211yescharacteristic
77C2×Q8×Dic83C2212yes—
78C2×C4×Dic166C2212yes—
79C2×C4×Dic166C2211yescharacteristic
80C2×C4×D332C2211yescharacteristic
81C2×C4×D332C2212yes—
82C2×C4×D332C2214yes—
83C2×#14581754C2212yes—
84C2×C4×C22⋊D83C2212yes—
85C2×(C22⋊D83)⋊C4C2214yes—
86C2×#14581751C2212yes—
87C2×#14581749C2212yes—
88C22×C4⋊Dic83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C4⋊C4×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#556×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#126×C83C2214yes—
95C2×#124×C83C2212yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2212yes—
98C2×C4×Q8×C83C2211yescharacteristic
99C2×C4×D4×C83C2211yescharacteristic
100C2×#117×C83C2212yes—
101C2×#13050589—48no—
102C2×#13050589C23116yes—
103C22×Dic166C2311yescharacteristic
104C22×Dic166C2312yes—
105C22×Dic166C2314yes—
106C22×Dic166C2314yes—
107C2×Q8×D83—48no—
108C2×Q8×D83—48no—
109C2×Q8×D83C23116yes—
110C2×Q8×D83C23116yes—
111C22×D332C2311yescharacteristic
112C22×D332C2312yes—
113C22×C22⋊D83C2312yes—
114C22×C22⋊D83C2314yes—
115C23×Dic83C2314yes—
116C22×C4×D83C2311yescharacteristic
117C22×C4×D83C2311yescharacteristic
118C22×C4×D83C2311yescharacteristic
119C22×C4×D83C2312yes—
120C22×C4×D83C2314yes—
121C22×C4×D83C2314yes—
122#14581792C23132yes—
123#14581792C2318yes—
124#14581792C23116yes—
125#14581791C23116yes—
126#14581791C23116yes—
127#14581791C23116yes—
128#14581790C23116yes—
129#14581787C23132yes—
130#14581787C23116yes—
131#14581786C23132yes—
132#14581785C23116yes—
133#14581784C23132yes—
134#14581783C2318yes—
135#14581783C23116yes—
136#14581783C23132yes—
137#14581783C2318yes—
138#14581782C23132yes—
139#14581781C2318yes—
140#14581779C2318yes—
141#14581778C23132yes—
142#14581777C23116yes—
143#14581776C23132yes—
144#14581774C23132yes—
145#14581774C23132yes—
146#14581774C23116yes—
147#14581772C23132yes—
148#14581772C23116yes—
149#14581772C2318yes—
150#14581772C23132yes—
151#14581770C23132yes—
152#14581769C23132yes—
153#14581769C23132yes—
154#14581769C23132yes—
155#14581768C23116yes—
156#14581768C2318yes—
157#14581767C2318yes—
158#14581766C23116yes—
159#14581765C23132yes—
160#14581763C2318yes—
161Q8×Dic83C23116yes—
162C4×Dic166C23116yes—
163C4×Dic166C2318yes—
164C4×D332C2318yes—
165C4×D332C23116yes—
166C4×D332C23132yes—
167#14581754C23116yes—
168C4×C22⋊D83C23116yes—
169(C22⋊D83)⋊C4C23132yes—
170#14581751C23116yes—
171#14581749C23116yes—
172C2×C4⋊Dic83C23116yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2312yes—
175C2×C4⋊Dic83C2311yescharacteristic
176C2×C4⋊Dic83C2314yes—
177C2×C4⋊Dic83C2312yes—
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2312yes—
180C2×C4⋊Dic83C2314yes—
181C2×C4⋊Dic83C2311yescharacteristic
182C2×C4⋊Dic83C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2314yes—
188C2×Dic83⋊C4C2312yes—
189C2×Dic83⋊C4C2314yes—
190C2×Dic83⋊C4C2312yes—
191C4⋊C4×D83C23116yes—
192C4⋊C4×D83C23116yes—
193C2×C22⋊Dic83C2312yes—
194C2×C22⋊Dic83C2312yes—
195C2×C22⋊Dic83C2312yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2312yes—
200C2×(C2×D83)⋊C4C2314yes—
201C2×(C2×D83)⋊C4C2314yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×(C2×D83)⋊C4C2312yes—
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2311yescharacteristic
206C2×C4×Dic83C2311yescharacteristic
207C2×C4×Dic83C2312yes—
208C2×C4×Dic83C2314yes—
209C42×D83C2318yes—
210C22×Q8×C83C2311yescharacteristic
211C22×Q8×C83C2312yes—
212C22×D4×C83C2311yescharacteristic
213C23×C4×C83C2312yes—
214C4⋊Q8×C83C2318yes—
215#126×C83C23132yes—
216#124×C83C23116yes—
217C22⋊Q8×C83C23116yes—
218C4×Q8×C83C23116yes—
219C4×Q8×C83C2318yes—
220C4×D4×C83C2318yes—
221#117×C83C23116yes—
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2312yes—
224C2×C4⋊C4×C83C2311yescharacteristic
225C2×C4⋊C4×C83C2314yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2312yes—
228C2×C22⋊C4×C83C2314yes—
229C2×C22⋊C4×C83C2312yes—
230C2×C22⋊C4×C83C2314yes—
231C2×C42×C83C2314yes—
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235C23×D83C2411yescharacteristic
236#13050589—432no—
237C2×Dic166—24no—
238C2×Dic166—28no—
239C2×Dic166—48no—
240C2×Dic166—48no—
241C2×Dic166C2414yes—
242C2×Dic166C2418yes—
243C2×Dic166C24116yes—
244C2×Dic166C24116yes—
245Q8×D83—432no—
246Q8×D83—432no—
247C2×D332—28no—
248C2×D332—24no—
249C2×D332C2418yes—
250C2×D332C2414yes—
251C2×C22⋊D83—28no—
252C2×C22⋊D83—48no—
253C2×C22⋊D83C2418yes—
254C2×C22⋊D83C24116yes—
255C22×Dic83—48no—
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C22×Dic83C2414yes—
259C22×Dic83C2411yescharacteristic
260C22×Dic83C2411yescharacteristic
261C22×Dic83C2411yescharacteristic
262C22×Dic83C2412yes—
263C22×Dic83C24116yes—
264C2×C4×D83—24no—
265C2×C4×D83—24no—
266C2×C4×D83—28no—
267C2×C4×D83—24no—
268C2×C4×D83—48no—
269C2×C4×D83—48no—
270C2×C4×D83C2414yes—
271C2×C4×D83C2414yes—
272C2×C4×D83C2418yes—
273C2×C4×D83C2414yes—
274C2×C4×D83C24116yes—
275C2×C4×D83C24116yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C2414yes—
279C4⋊Dic83C2418yes—
280C4⋊Dic83C24116yes—
281C4⋊Dic83C24116yes—
282C4⋊Dic83C2418yes—
283C4⋊Dic83C24116yes—
284C4⋊Dic83C2418yes—
285C4⋊Dic83C2418yes—
286Dic83⋊C4C24116yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C24116yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C24116yes—
291Dic83⋊C4C24116yes—
292Dic83⋊C4C2418yes—
293Dic83⋊C4C2418yes—
294C22⋊Dic83C2418yes—
295C22⋊Dic83C2418yes—
296C22⋊Dic83C2418yes—
297(C2×D83)⋊C4C24116yes—
298(C2×D83)⋊C4C24116yes—
299(C2×D83)⋊C4C2418yes—
300(C2×D83)⋊C4C2418yes—
301(C2×D83)⋊C4C2418yes—
302(C2×D83)⋊C4C2418yes—
303(C2×D83)⋊C4C2418yes—
304(C2×D83)⋊C4C2418yes—
305C4×Dic83C24116yes—
306C4×Dic83C2414yes—
307C4×Dic83C2414yes—
308C4×Dic83C2418yes—
309C4×Dic83C2414yes—
310C24×C83C2412yes—
311C2×Q8×C83—28no—
312C2×Q8×C83—24no—
313C2×Q8×C83C2414yes—
314C2×Q8×C83C2418yes—
315C2×D4×C83—24no—
316C2×D4×C83C2414yes—
317C22×C4×C83—28no—
318C22×C4×C83C2418yes—
319C22×C4×C83C2414yes—
320C22×C4×C83C2411yescharacteristic
321C22×C4×C83C2412yes—
322C22×C4×C83C2412yes—
323C22×C4×C83C2412yes—
324C22×C4×C83C2411yescharacteristic
325C22×C4×C83C2411yescharacteristic
326C4⋊C4×C83C2414yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C2414yes—
329C4⋊C4×C83C24116yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C2418yes—
332C22⋊C4×C83C24116yes—
333C22⋊C4×C83C24116yes—
334C22⋊C4×C83C2418yes—
335C42×C83C24116yes—
336C42×C83C2414yes—
337C42×C83C2418yes—
338C23×C83—24no—
339C23×C83—24no—
340C23×C83—24no—
341C23×C83C2514yes—
342C23×C83C2511yescharacteristic
343C22×D83—22no—
344C22×D83—22no—
345C22×D83—24no—
346C22×D83—24no—
347C22×D83—24no—
348C22×D832−1+414yes—
349C22×D83C2514yes—
350C22×D83C2512yes—
351Q8×C83—216no—
352Q8×C83—28no—
353D4×C83—28no—
354C2×C4×C83—28no—
355C2×C4×C83—24no—
356C2×C4×C83—24no—
357C2×C4×C83—22no—
358C2×C4×C83—24no—
359C2×C4×C83—216no—
360C2×C4×C83H(5,𝔽2)14yes—
361C2×C4×C832−1+414yes—
362C2×C4×C83C2514yes—
363C2×C4×C83C2514yes—
364C2×C4×C83C2512yes—
365C2×C4×C83C2514yes—
366C2×C4×C83C2518yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2512yes—
369C22⋊D83—216no—
370C22⋊D83—416no—
371C2×Dic83—24no—
372C2×Dic83—22no—
373C2×Dic83—24no—
374C2×Dic83—28no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—24no—
378C2×Dic83—416no—
379C2×Dic83C2514yes—
380C2×Dic83C2512yes—
381C2×Dic83C2512yes—
382C2×Dic83C2512yes—
383C2×Dic83C2514yes—
384C2×Dic83C2518yes—
385C2×Dic83C2514yes—
386D332—216no—
387D332—28no—
388C4×D83—28no—
389C4×D83—28no—
390C4×D83—216no—
391C4×D83—28no—
392C4×D83—416no—
393C4×D83—416no—
394Dic166—28no—
395Dic166—216no—
396Dic166—416no—
397Dic166—416no—
398C22×C83—24no—
399C22×C83—24no—
400C22×C83—24no—
401C22×C83—48no—
402C22×C83C2×H(5,𝔽2)12yes—
403C22×C83C2×2−1+412yes—
404C22×C83C2×2−1+412yes—
405C22×C83C2611yescharacteristic
406C2×D83—22no—
407C2×D83—22no—
408C2×D83—28no—
409C2×D83—24no—
410C2×D83—24no—
411C2×D83—24no—
412C2×D83—48no—
413C2×D83C2×2−1+414yes—
414C4×C83—28no—
415C4×C83—22no—
416C4×C83—24no—
417C4×C83—24no—
418C4×C83—24no—
419C4×C83C2×H(5,𝔽2)14yes—
420C4×C83C2×2−1+414yes—
421Dic83—24no—
422Dic83—28no—
423Dic83—22no—
424Dic83—24no—
425Dic83—22no—
426Dic83—22no—
427Dic83—24no—
428C2×#3552—831nomaximal, Sylow
429C2×C83—44no—
430C2×C83#355214yescomplemented
431C2×C83C22×H(5,𝔽2)11yescharacteristic
432C2×C83C22×2−1+411yescharacteristic
433C2×C83C22×2−1+411yescharacteristic
434D83—24no—
435D83—44no—
436#3552—8332no—
437C2×#563—834no—
438C2×#557—831no—
439C2×#556D8311yescharacteristic, complemented
440C2×#554—832no—
441C2×#553—832no—
442C2×D4×Q8—831no—
443C2×D4×Q8—832no—
444C2×#548—832no—
445C2×#547—831no—
446C2×#544—832no—
447C2×#542—832no—
448C2×#541—832no—
449C2×#539—834no—
450C2×#536—832no—
451C22×C4⋊Q8—831no—
452C2×#529—831no—
453C2×#529—831no—
454C83C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—832no—
456C23×Q8—832no—
457C23×Q8—832no—
458#563—8364no—
459#557—8316no—
460#556C2×D83116yescomplemented
461#554—8332no—
462#553—8332no—
463D4×Q8—8316no—
464D4×Q8—8332no—
465#548—8332no—
466#547—8316no—
467#544—8332no—
468#542—8332no—
469#541—8332no—
470#539—8364no—
471#536—8332no—
472C2×C4⋊Q8—832no—
473C2×C4⋊Q8—8316no—
474C2×C4⋊Q8—832no—
475C2×C4⋊Q8—832no—
476C2×C4⋊Q8—832no—
477C2×C4⋊Q8—831no—
478C2×C4⋊Q8—832no—
479C2×C4⋊Q8—834no—
480C2×C4⋊Q8C2×D8311yescharacteristic
481#529—8316no—
482#529—8316no—
483C2×#126—832no—
484C2×#126—834no—
485C2×#126—832no—
486C2×#126—834no—
487C2×#126C2×D8314yes—
488C2×#125—831no—
489C2×#125—831no—
490C2×#125—834no—
491C2×#125—834no—
492C2×#125—832no—
493C2×#125—834no—
494C2×#124—831no—
495C2×#124—831no—
496C2×#124—834no—
497C2×#124C2×D8312yes—
498C2×#123—832no—
499C2×#123—832no—
500C2×#123—834no—
501C2×#123—834no—
502C2×#123—834no—
503C2×C22⋊Q8—831no—
504C2×C22⋊Q8—832no—
505C2×C22⋊Q8—831no—
506C2×C22⋊Q8—834no—
507C2×C22⋊Q8—834no—
508C2×C22⋊Q8—832no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—834no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8—834no—
513C2×C22⋊Q8C2×D8312yes—
514C2×#121—831no—
515C2×#121—832no—
516C2×#121—831no—
517C2×#121—834no—
518C2×C4×Q8—832no—
519C2×C4×Q8—831no—
520C2×C4×Q8—832no—
521C2×C4×Q8C2×D8311yescharacteristic
522C2×C4×Q8C2×D8312yes—
523C2×C4×D4—832no—
524C2×C4×D4—832no—
525C2×C4×D4—834no—
526C2×C4×D4—831no—
527C2×C4×D4—832no—
528C2×C4×D4—834no—
529C2×C4×D4C2×D8311yescharacteristic
530C2×#117—832no—
531C2×#117—832no—
532C2×#117C2×D8312yes—
533C22×C4⋊C4—832no—
534C22×C4⋊C4—832no—
535C22×C4⋊C4—832no—
536C22×C42—831no—
537C2×#41—3328no—
538C2×#41—8316no—
539C22×Q8—3328no—
540C22×Q8—3328no—
541C22×Q8—8316no—
542C22×Q8—8316no—
543C22×Q8—834no—
544C22×Q8—834no—
545C22×Q8—831no—
546C22×Q8—832no—
547C22×Q8C22×D8311yescharacteristic
548C22×Q8C22×D8312yes—
549C22×D4—834no—
550C22×D4—832no—
551C22×D4—832no—
552C22×D4—831no—
553C22×D4C22×D8311yescharacteristic
554C23×C4—834no—
555C23×C4—834no—
556C23×C4—834no—
557C23×C4—831no—
558C23×C4—831no—
559C23×C4—832no—
560C23×C4—831no—
561C23×C4C22×D8312yes—
562C4⋊Q8—8316no—
563C4⋊Q8—8316no—
564C4⋊Q8—8316no—
565C4⋊Q8—8316no—
566C4⋊Q8—838no—
567C4⋊Q8—8316no—
568C4⋊Q8—8332no—
569C4⋊Q8C22×D8318yes—
570#126—8316no—
571#126—8332no—
572#126—8316no—
573#126—8332no—
574#126C22×D83132yes—
575#125—838no—
576#125—838no—
577#125—8332no—
578#125—8332no—
579#125—8316no—
580#125—8332no—
581#124—838no—
582#124—838no—
583#124—8332no—
584#124C22×D83116yes—
585#123—8316no—
586#123—8316no—
587#123—8332no—
588#123—8332no—
589#123—8332no—
590C22⋊Q8—838no—
591C22⋊Q8—8316no—
592C22⋊Q8—8332no—
593C22⋊Q8—838no—
594C22⋊Q8—8332no—
595C22⋊Q8—8316no—
596C22⋊Q8—8332no—
597C22⋊Q8—8332no—
598C22⋊Q8—8332no—
599C22⋊Q8—8332no—
600C22⋊Q8C22×D83116yes—
601#121—838no—
602#121—8316no—
603#121—838no—
604#121—8332no—
605C4×Q8—8316no—
606C4×Q8—838no—
607C4×Q8—8316no—
608C4×Q8C22×D8318yes—
609C4×Q8C22×D83116yes—
610C4×D4—8316no—
611C4×D4—8316no—
612C4×D4—8332no—
613C4×D4—838no—
614C4×D4—8316no—
615C4×D4—8332no—
616C4×D4C22×D8318yes—
617#117—8316no—
618#117—8316no—
619#117C22×D83116yes—
620C2×C4⋊C4—831no—
621C2×C4⋊C4—832no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—832no—
626C2×C4⋊C4—8316no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—832no—
629C2×C4⋊C4—832no—
630C2×C4⋊C4—832no—
631C2×C4⋊C4—834no—
632C2×C4⋊C4—832no—
633C2×C4⋊C4—834no—
634C2×C4⋊C4—832no—
635C2×C4⋊C4—831no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—834no—
638C2×C4⋊C4—832no—
639C2×C4⋊C4—8316no—
640C2×C4⋊C4—8316no—
641C2×C4⋊C4C22×D8312yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C4⋊C4C22×D8311yescharacteristic
644C2×C4⋊C4C22×D8311yescharacteristic
645C2×C4⋊C4C22×D8314yes—
646C2×C4⋊C4C22×D8312yes—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—832no—
649C2×C22⋊C4—832no—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—832no—
652C2×C22⋊C4—832no—
653C2×C22⋊C4—832no—
654C2×C22⋊C4—834no—
655C2×C22⋊C4—834no—
656C2×C22⋊C4—832no—
657C2×C22⋊C4—832no—
658C2×C22⋊C4C22×D8314yes—
659C2×C22⋊C4C22×D8314yes—
660C2×C22⋊C4C22×D8312yes—
661C2×C42—831no—
662C2×C42—831no—
663C2×C42—832no—
664C2×C42—834no—
665C2×C42—831no—
666C2×C42—838no—
667C2×C42C22×D8312yes—
668C2×C42C22×D8314yes—
669C2×C42C22×D8311yescharacteristic
670C24—831no—
671C24—832no—
672C24C23×D8312yes—
673#41—33232no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—3328no—
677C2×Q8—3328no—
678C2×Q8—33232no—
679C2×Q8—33232no—
680C2×Q8—8316no—
681C2×Q8—8316no—
682C2×Q8—834no—
683C2×Q8—838no—
684C2×Q8—1664no—
685C2×Q8—1668no—
686C2×Q8C23×D8314yes—
687C2×Q8C23×D8318yes—
688C2×D4—24no—
689C2×D4—3328no—
690C2×D4—8316no—
691C2×D4—838no—
692C2×D4—838no—
693C2×D4—834no—
694C2×D4—1668no—
695C2×D4—1668no—
696C2×D4—1664no—
697C2×D4C23×D8314yes—
698C22×C4—28no—
699C22×C4—3328no—
700C22×C4—3328no—
701C22×C4—3328no—
702C22×C4—8316no—
703C22×C4—8316no—
704C22×C4—8316no—
705C22×C4—832no—
706C22×C4—831no—
707C22×C4—831no—
708C22×C4—831no—
709C22×C4—832no—
710C22×C4—834no—
711C22×C4—832no—
712C22×C4—834no—
713C22×C4—834no—
714C22×C4—834no—
715C22×C4—838no—
716C22×C4—1664no—
717C22×C4—1664no—
718C22×C4—1668no—
719C22×C4—1664no—
720C22×C4C23×D8318yes—
721C22×C4C23×D8312yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8312yes—
724C22×C4C23×D8312yes—
725C22×C4C23×D8314yes—
726C22×C4C23×D8311yescharacteristic
727C22×C4C23×D8311yescharacteristic
728C4⋊C4—834no—
729C4⋊C4—838no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—8316no—
733C4⋊C4—838no—
734C4⋊C4—838no—
735C4⋊C4—838no—
736C4⋊C4—838no—
737C4⋊C4—838no—
738C4⋊C4—8316no—
739C4⋊C4—838no—
740C4⋊C4—8316no—
741C4⋊C4—838no—
742C4⋊C4—834no—
743C4⋊C4—8316no—
744C4⋊C4—8316no—
745C4⋊C4—838no—
746C4⋊C4C23×D8318yes—
747C4⋊C4C23×D8318yes—
748C4⋊C4C23×D8314yes—
749C4⋊C4C23×D8314yes—
750C4⋊C4C23×D83116yes—
751C4⋊C4C23×D8318yes—
752C22⋊C4—838no—
753C22⋊C4—838no—
754C22⋊C4—838no—
755C22⋊C4—838no—
756C22⋊C4—838no—
757C22⋊C4—838no—
758C22⋊C4—838no—
759C22⋊C4—8316no—
760C22⋊C4—8316no—
761C22⋊C4—838no—
762C22⋊C4—838no—
763C22⋊C4C23×D83116yes—
764C22⋊C4C23×D83116yes—
765C22⋊C4C23×D8318yes—
766C42—834no—
767C42—834no—
768C42—834no—
769C42—838no—
770C42—8316no—
771C42C23×D8314yes—
772C42C23×D8318yes—
773C42C23×D83116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—834no—
778C23—832no—
779C23—834no—
780C23—1664no—
781C23—1664no—
782C23—1664no—
783C23—1662no—
784C23—1662no—
785C23C24×D8314yes—
786C23C24×D8311yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—33216no—
790Q8—33216no—
791Q8—1668no—
792Q8—16616no—
793D4—28no—
794D4—33216no—
795D4—16616no—
796D4—16616no—
797D4—1668no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—33216no—
805C2×C4—33216no—
806C2×C4—33216no—
807C2×C4—834no—
808C2×C4—832no—
809C2×C4—832no—
810C2×C4—832no—
811C2×C4—834no—
812C2×C4—838no—
813C2×C4—834no—
814C2×C4—1668no—
815C2×C4—1664no—
816C2×C4—1668no—
817C2×C4—1664no—
818C2×C4—1662no—
819C2×C4—1662no—
820C2×C4—1664no—
821C2×C4—1662no—
822C2×C4—1668no—
823C2×C4—16616no—
824C2×C4—1668no—
825C2×C4#1458183814yes—
826C2×C4#1458183914yes—
827C2×C4C24×D8314yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8314yes—
830C2×C4C24×D8314yes—
831C2×C4C24×D8318yes—
832C2×C4C24×D8312yes—
833C2×C4C24×D8312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—3328no—
839C22—834no—
840C22—1664no—
841C22—1664no—
842C22—1664no—
843C22—1668no—
844C22—1662no—
845C22—1662no—
846C22C2×#1458183812yes—
847C222−1+4×D8312yes—
848C22C2×#1458183912yes—
849C22C25×D8311yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1664no—
856C4—1668no—
857C4—1664no—
858C4—1662no—
859C4—1662no—
860C4—1664no—
861C4—1662no—
862C4C2×#1458183814yes—
863C4C2×#1458183914yes—
864C2—44no—
865C2—3324no—
866C2—1664no—
867C2#2492189314yesdirect product factor
868C2C22×#1458183811yescharacteristic
869C2C2×2−1+4×D8311yescharacteristic
870C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#556×C83C2
socleC23×C83C25
hypercenterC2×#556D83
hypocenterC83C2×#3552
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #24921893C2direct (N × H)
2. C2×#19128453C2semidirect
3. C2×#19128430C2semidirect
4. C2×#19128409C2semidirect
5. C2×#19128395C2semidirect
6. C2×Q8×D332C2semidirect
7. C2×#19128366C2semidirect
8. C2×#19128359C2semidirect
9. C2×#19128355C2semidirect
10. C2×#19128329C2semidirect
11. C2×#19128324C2semidirect
12. C2×#19128309C2semidirect
13. C2×#19128292C2semidirect
14. C2×#19128271C2semidirect
15. C2×C4⋊Q8×D83C2semidirect
16. C2×#19128238C2semidirect
17. C2×#19128233C2semidirect
18. C2×#556×C83C2semidirect
22. #19128453C22semidirect
23. #19128430C22semidirect
24. #19128409C22semidirect
25. #19128395C22semidirect
26. Q8×D332C22semidirect
27. #19128366C22semidirect
28. #19128359C22semidirect
29. #19128355C22semidirect
30. #19128329C22semidirect
31. #19128324C22semidirect
32. #19128309C22semidirect
33. #19128292C22semidirect
34. #19128271C22semidirect
42. C4⋊Q8×D83C22semidirect
43. #19128238C22semidirect
44. #19128233C22semidirect
92. #556×C83C22semidirect
430. C2×C83#3552semidirect
439. C2×#556D83semidirect
454. C83C2×#3552semidirect
460. #556C2×D83semidirect
867. C2#24921893direct (N × H)

Maximal subgroups

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

subgroupindex
#249218932
C2×#191284532
C2×#191284302
C2×#191284092
C2×#191283952
C2×Q8×D3322
C2×#191283662
C2×#191283592
C2×#191283552
C2×#191283292
C2×#191283242
C2×#191283092
C2×#191282922
C2×#191282712
C2×C4⋊Q8×D832
C2×#191282382
C2×#191282332
C2×#556×C832
C2×#355283