Finite Group Databasebeta

← C2×#19148936 #26004280

Subgroups — C2×#19148936 #26004280

Order 11008.

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#19148936C2132yesmaximal, direct product factor
2C2×#14583650C214yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583614C211yesmaximal, characteristic, complemented
5C2×#14583610C211yesmaximal, characteristic, complemented
6C2×#14583587C212yesmaximal, complemented
7C2×#14583583C212yesmaximal, complemented
8C2×#14583554C212yesmaximal, complemented
9C2×#14583550C212yesmaximal, complemented
10C2×#14583530C212yesmaximal, complemented
11C2×#14583529C212yesmaximal, complemented
12C2×#14583522C212yesmaximal, complemented
13C2×#14583514C212yesmaximal, complemented
14C2×#14583472C214yesmaximal, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583436C211yesmaximal, characteristic, complemented
17C2×#14583431C211yesmaximal, characteristic, complemented
18C2×C43×#554C211yesmaximal, characteristic, complemented
19C22×#10621898C2214yes—
20C22×Q8×D43C2212yes—
21#14583650C22164yescomplemented
22Q8×Dic86C22116yescomplemented
23#14583614C22116yescomplemented
24#14583610C22116yescomplemented
25#14583587C22132yescomplemented
26#14583583C22132yescomplemented
27#14583554C22132yescomplemented
28#14583550C22132yescomplemented
29#14583530C22132yescomplemented
30#14583529C22132yescomplemented
31#14583522C22132yescomplemented
32#14583514C22132yescomplemented
33#14583472C22164yescomplemented
34C2×#13063325C2212yes—
35C2×#13063325C2211yescharacteristic
36C2×#13063324C2212yes—
37C2×#13063324C2212yes—
38C2×#13063324C2212yes—
39C2×#13063324C2214yes—
40C2×#13063324C2214yes—
41C2×#13063323C2212yes—
42C4⋊Q8×D43C22116yescomplemented
43#14583436C22116yescomplemented
44#14583431C22116yescomplemented
45C2×#13063320C2214yes—
46C2×#13063320C2212yes—
47C2×#13063318C2214yes—
48C2×#13063318C2212yes—
49C2×#13063316C2212yes—
50C2×#13063316C2214yes—
51C2×#13063316C2211yescharacteristic
52C2×#13063316C2211yescharacteristic
53C2×#13063315C2214yes—
54C2×#13063314C2211yescharacteristic
55C2×#13063312C2211yescharacteristic
56C2×#13063311C2214yes—
57C2×#13063311C2214yes—
58C2×#13063310C2214yes—
59C2×#13063310C2212yes—
60C2×#13063308C2214yes—
61C2×#13063307C2214yes—
62C2×#13063307C2214yes—
63C2×#13063307C2212yes—
64C2×#13063305C2211yescharacteristic
65C2×#13063305C2212yes—
66C2×#13063305C2214yes—
67C2×#13063304C2214yes—
68C2×#13063304C2214yes—
69C2×#13063303C2214yes—
70C2×#13063301C2211yescharacteristic
71C2×#13063301C2214yes—
72C2×#13063300C2211yescharacteristic
73C2×#13063299C2212yes—
74C2×#13063296C2211yescharacteristic
75C2×#13063296C2212yes—
76C2×Q8×Dic43C2212yes—
77C2×C4×Dic86C2212yes—
78C2×C4×Dic86C2211yescharacteristic
79C2×C4×D172C2212yes—
80C2×C4×D172C2211yescharacteristic
81C2×#13063287C2212yes—
82C2×C4×C22⋊D43C2212yes—
83C2×#13063284C2212yes—
84C2×#13063284C2212yes—
85C2×#13063283C2214yes—
86C2×#13063283C2212yes—
87C2×#13063282C2212yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#554C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#125×C43C2212yes—
95C2×C22⋊Q8×C43C2212yes—
96C2×C22⋊Q8×C43C2214yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×D4×C43C2212yes—
99C2×C4×D4×C43C2211yescharacteristic
100C22×C4⋊C4×C43C2212yes—
101C2×#10621898—416no—
102C2×#10621898C23132yes—
103C22×Dic86C2311yescharacteristic
104C22×Dic86C2314yes—
105C22×Dic86C2314yes—
106C22×Dic86C2312yes—
107C2×Q8×D43—48no—
108C2×Q8×D43C23116yes—
109C22×D172C2311yescharacteristic
110C22×D172C2312yes—
111C22×C22⋊D43C2312yes—
112C22×C22⋊D43C2314yes—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2311yescharacteristic
116C22×C4×D43C2314yes—
117C22×C4×D43C2312yes—
118C22×C4×D43C2314yes—
119#13063325C23116yes—
120#13063325C2318yes—
121#13063324C23132yes—
122#13063324C23116yes—
123#13063324C23116yes—
124#13063324C23116yes—
125#13063324C23132yes—
126#13063323C23116yes—
127#13063320C23132yes—
128#13063320C23116yes—
129#13063318C23132yes—
130#13063318C23116yes—
131#13063316C23116yes—
132#13063316C23132yes—
133#13063316C2318yes—
134#13063316C2318yes—
135#13063315C23132yes—
136#13063314C2318yes—
137#13063312C2318yes—
138#13063311C23132yes—
139#13063311C23132yes—
140#13063310C23132yes—
141#13063310C23116yes—
142#13063308C23132yes—
143#13063307C23132yes—
144#13063307C23132yes—
145#13063307C23116yes—
146#13063305C2318yes—
147#13063305C23116yes—
148#13063305C23132yes—
149#13063304C23132yes—
150#13063304C23132yes—
151#13063303C23132yes—
152#13063301C2318yes—
153#13063301C23132yes—
154#13063300C2318yes—
155#13063299C23116yes—
156#13063296C2318yes—
157#13063296C23116yes—
158Q8×Dic43C23116yes—
159C4×Dic86C23116yes—
160C4×Dic86C2318yes—
161C4×D172C23116yes—
162C4×D172C2318yes—
163#13063287C23116yes—
164C4×C22⋊D43C23116yes—
165#13063284C23116yes—
166#13063284C23116yes—
167#13063283C23132yes—
168#13063283C23116yes—
169#13063282C23116yes—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2314yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2314yes—
187C4⋊C4×D43C23116yes—
188C4⋊C4×D43C23116yes—
189C4⋊C4×D43C23116yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2314yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2314yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2314yes—
207C2×C4×Dic43C2312yes—
208C42×D43C2318yes—
209C22×Q8×C43C2311yescharacteristic
210C22×Q8×C43C2312yes—
211C22×D4×C43C2311yescharacteristic
212C23×C4×C43C2312yes—
213C23×C4×C43C2314yes—
214C4⋊Q8×C43C2318yes—
215#125×C43C23116yes—
216C22⋊Q8×C43C23116yes—
217C22⋊Q8×C43C23132yes—
218C4×Q8×C43C2318yes—
219C4×D4×C43C23116yes—
220C4×D4×C43C2318yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2314yes—
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C23116yes—
225C2×C4⋊C4×C43C2311yescharacteristic
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C4⋊C4×C43C2314yes—
229C2×C22⋊C4×C43C2314yes—
230C2×C22⋊C4×C43C2312yes—
231C2×C42×C43C2312yes—
232C2×C42×C43C2311yescharacteristic
233C24×C43C2412yes—
234C23×D43C2412yes—
235C23×D43C2411yescharacteristic
236C2×Q8×C43—24no—
237C2×Q8×C43—44no—
238C2×Q8×C43C2414yes—
239C2×Q8×C43C2418yes—
240C2×D4×C43—24no—
241C2×D4×C43C2414yes—
242C22×C4×C43—28no—
243C22×C4×C43—48no—
244C22×C4×C43C2412yes—
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2414yes—
249C22×C4×C43C2418yes—
250C22×C4×C43C24116yes—
251C22×C4×C43C2411yescharacteristic
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—28no—
254C2×C22⋊D43—48no—
255C2×C22⋊D43C2418yes—
256C2×C22⋊D43C24116yes—
257C22×Dic43C2412yes—
258C22×Dic43C2411yescharacteristic
259C22×Dic43C2411yescharacteristic
260C22×Dic43C2412yes—
261C22×Dic43C2411yescharacteristic
262C22×Dic43C2414yes—
263C22×Dic43C2412yes—
264Q8×D43—432no—
265#10621898—464no—
266C2×D172—24no—
267C2×D172—28no—
268C2×D172C2414yes—
269C2×D172C2418yes—
270C2×C4×D43—24no—
271C2×C4×D43—24no—
272C2×C4×D43—28no—
273C2×C4×D43—24no—
274C2×C4×D43—216no—
275C2×C4×D43—48no—
276C2×C4×D43C2414yes—
277C2×C4×D43C2414yes—
278C2×C4×D43C2414yes—
279C2×C4×D43C24116yes—
280C2×C4×D43C2418yes—
281C2×C4×D43C24116yes—
282C2×Dic86—24no—
283C2×Dic86—48no—
284C2×Dic86—44no—
285C2×Dic86—48no—
286C2×Dic86C2414yes—
287C2×Dic86C24116yes—
288C2×Dic86C24116yes—
289C2×Dic86C2418yes—
290C4⋊C4×C43C2414yes—
291C4⋊C4×C43C24116yes—
292C4⋊C4×C43C2418yes—
293C4⋊C4×C43C2414yes—
294C4⋊C4×C43C2418yes—
295C4⋊C4×C43C2418yes—
296C4⋊C4×C43C24116yes—
297C22⋊C4×C43C24116yes—
298C22⋊C4×C43C2418yes—
299C42×C43C2418yes—
300C42×C43C2414yes—
301C22⋊Dic43C2418yes—
302C22⋊Dic43C24116yes—
303C22⋊Dic43C2418yes—
304C22⋊Dic43C2418yes—
305(C2×D43)⋊C4C2418yes—
306(C2×D43)⋊C4C2418yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C2418yes—
309(C2×D43)⋊C4C24116yes—
310(C2×D43)⋊C4C24116yes—
311(C2×D43)⋊C4C2418yes—
312(C2×D43)⋊C4C2418yes—
313C4⋊Dic43C2414yes—
314C4⋊Dic43C2418yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C24116yes—
317C4⋊Dic43C2414yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C2418yes—
321C4⋊Dic43C24116yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C24116yes—
324Dic43⋊C4C24116yes—
325Dic43⋊C4C2418yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C24116yes—
330C4×Dic43C2414yes—
331C4×Dic43C2414yes—
332C4×Dic43C2414yes—
333C4×Dic43C24116yes—
334C4×Dic43C24116yes—
335C4×Dic43C2418yes—
336C23×C43—24no—
337C23×C43—24no—
338C23×C43—24no—
339C23×C43C2514yes—
340C23×C43C2511yescharacteristic
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—24no—
344C22×D43—24no—
345C22×D43—24no—
346C22×D43H(5,𝔽2)14yes—
347C22×D43C2514yes—
348C22×D43C2512yes—
349Q8×C43—28no—
350Q8×C43—48no—
351D4×C43—28no—
352C2×C4×C43—22no—
353C2×C4×C43—24no—
354C2×C4×C43—28no—
355C2×C4×C43—24no—
356C2×C4×C43—24no—
357C2×C4×C43—216no—
358C2×C4×C43—416no—
359C2×C4×C432−1+414yes—
360C2×C4×C432−1+414yes—
361C2×C4×C43C2514yes—
362C2×C4×C43C2514yes—
363C2×C4×C43C2512yes—
364C2×C4×C43C2514yes—
365C2×C4×C43C2518yes—
366C2×C4×C43C2512yes—
367C2×C4×C43C2512yes—
368C22⋊D43—216no—
369C22⋊D43—416no—
370C2×Dic43—22no—
371C2×Dic43—28no—
372C2×Dic43—24no—
373C2×Dic43—24no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—24no—
377C2×Dic43C2514yes—
378C2×Dic43C2512yes—
379C2×Dic43C2512yes—
380C2×Dic43C2514yes—
381C2×Dic43C2518yes—
382C2×Dic43C2512yes—
383C2×Dic43C2514yes—
384D172—216no—
385D172—28no—
386C4×D43—232no—
387C4×D43—28no—
388C4×D43—28no—
389C4×D43—28no—
390C4×D43—216no—
391C4×D43—416no—
392Dic86—28no—
393Dic86—416no—
394Dic86—416no—
395Dic86—48no—
396C2×#3544—431nomaximal, Sylow
397C22×C43—24no—
398C22×C43—24no—
399C22×C43—24no—
400C22×C43—48no—
401C22×C43C2×H(5,𝔽2)12yes—
402C22×C43C2×2−1+412yes—
403C22×C43C2×2−1+412yes—
404C22×C43C2611yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—28no—
408C2×D43—24no—
409C2×D43—24no—
410C2×D43—24no—
411C2×D43—48no—
412C2×D43C2×H(5,𝔽2)14yes—
413C4×C43—22no—
414C4×C43—24no—
415C4×C43—28no—
416C4×C43—24no—
417C4×C43—24no—
418C4×C43C2×2−1+414yes—
419C4×C43C2×2−1+414yes—
420Dic43—22no—
421Dic43—28no—
422Dic43—24no—
423Dic43—24no—
424Dic43—22no—
425Dic43—22no—
426Dic43—24no—
427#3544—4332no—
428C2×#563—434no—
429C2×Q82—431no—
430C2×#555—431no—
431C2×#554—431no—
432C2×#554D4311yescharacteristic, complemented
433C2×#552—432no—
434C2×#552—432no—
435C2×#547—432no—
436C2×#547—432no—
437C2×#544—432no—
438C2×#544—432no—
439C2×#542—432no—
440C2×#542—432no—
441C2×#536—434no—
442C22×C4⋊Q8—431no—
443C2×#529—431no—
444C2×#529—431no—
445C2×C43—44no—
446C2×C43#354414yescomplemented
447C2×C43C22×H(5,𝔽2)11yescharacteristic
448C2×C43C22×2−1+411yescharacteristic
449C2×C43C22×2−1+411yescharacteristic
450D43—24no—
451D43—44no—
452C22×#41—434no—
453C23×Q8—432no—
454#563—4364no—
455Q82—4316no—
456#555—4316no—
457#554—4316no—
458#554C2×D43116yescomplemented
459#552—4332no—
460#552—4332no—
461#547—4332no—
462#547—4332no—
463#544—4332no—
464#544—4332no—
465#542—4332no—
466#542—4332no—
467#536—4364no—
468C2×C4⋊Q8—432no—
469C2×C4⋊Q8—4316no—
470C2×C4⋊Q8—432no—
471C2×C4⋊Q8—432no—
472C2×C4⋊Q8—434no—
473C2×C4⋊Q8—434no—
474C2×C4⋊Q8—432no—
475C2×C4⋊Q8—431no—
476C2×C4⋊Q8—432no—
477C2×C4⋊Q8C2×D4311yescharacteristic
478#529—4316no—
479#529—4316no—
480C2×#126—432no—
481C2×#126—434no—
482C2×#126—432no—
483C2×#126—434no—
484C2×#125—431no—
485C2×#125—431no—
486C2×#125—434no—
487C2×#125—432no—
488C2×#125—434no—
489C2×#125C2×D4312yes—
490C2×#124—431no—
491C2×#124—431no—
492C2×#124—434no—
493C2×#124—434no—
494C2×#123—434no—
495C2×#123—432no—
496C2×#123—434no—
497C2×#123—432no—
498C2×#123—434no—
499C2×#123—434no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8—434no—
502C2×C22⋊Q8—434no—
503C2×C22⋊Q8—434no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—431no—
506C2×C22⋊Q8—434no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8C2×D4314yes—
509C2×C22⋊Q8C2×D4312yes—
510C2×#121—431no—
511C2×#121—432no—
512C2×#121—432no—
513C2×#121—431no—
514C2×C4×Q8—432no—
515C2×C4×Q8—431no—
516C2×C4×Q8—432no—
517C2×C4×Q8C2×D4311yescharacteristic
518C2×C4×D4—432no—
519C2×C4×D4—432no—
520C2×C4×D4—432no—
521C2×C4×D4—431no—
522C2×C4×D4C2×D4311yescharacteristic
523C2×C4×D4C2×D4312yes—
524C2×#117—432no—
525C2×#117—432no—
526C2×#117—434no—
527C2×#117—432no—
528C2×#117—432no—
529C22×C4⋊C4—432no—
530C22×C4⋊C4—432no—
531C22×C4⋊C4—432no—
532C22×C4⋊C4C2×D4312yes—
533C22×C42—431no—
534C43C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—4332no—
536C2×#41—17216no—
537C22×Q8—4316no—
538C22×Q8—431no—
539C22×Q8—434no—
540C22×Q8—434no—
541C22×Q8—432no—
542C22×Q8—1728no—
543C22×Q8C22×D4311yescharacteristic
544C22×Q8C22×D4312yes—
545C22×D4—432no—
546C22×D4—434no—
547C22×D4—431no—
548C22×D4—432no—
549C22×D4C22×D4311yescharacteristic
550C23×C4—434no—
551C23×C4—431no—
552C23×C4—431no—
553C23×C4—432no—
554C23×C4—431no—
555C23×C4—434no—
556C23×C4C22×D4312yes—
557C23×C4C22×D4314yes—
558C4⋊Q8—4316no—
559C4⋊Q8—4316no—
560C4⋊Q8—4316no—
561C4⋊Q8—4332no—
562C4⋊Q8—4332no—
563C4⋊Q8—4316no—
564C4⋊Q8—438no—
565C4⋊Q8—4316no—
566C4⋊Q8C22×D4318yes—
567#126—4316no—
568#126—4332no—
569#126—4316no—
570#126—4332no—
571#125—438no—
572#125—438no—
573#125—4316no—
574#125—4332no—
575#125—4332no—
576#125C22×D43116yes—
577#124—438no—
578#124—438no—
579#124—4332no—
580#124—4332no—
581#123—4332no—
582#123—4316no—
583#123—4332no—
584#123—4316no—
585#123—4332no—
586#123—4332no—
587C22⋊Q8—438no—
588C22⋊Q8—4332no—
589C22⋊Q8—4332no—
590C22⋊Q8—4332no—
591C22⋊Q8—438no—
592C22⋊Q8—4332no—
593C22⋊Q8—4316no—
594C22⋊Q8—4332no—
595C22⋊Q8C22×D43132yes—
596C22⋊Q8C22×D43116yes—
597#121—438no—
598#121—4316no—
599#121—4316no—
600#121—438no—
601C4×Q8—4316no—
602C4×Q8—438no—
603C4×Q8—4316no—
604C4×Q8C22×D4318yes—
605C4×D4—4316no—
606C4×D4—4316no—
607C4×D4—4316no—
608C4×D4—438no—
609C4×D4C22×D4318yes—
610C4×D4C22×D43116yes—
611#117—4316no—
612#117—4316no—
613#117—4332no—
614#117—4316no—
615#117—4316no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—432no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—434no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—431no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—432no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—432no—
631C2×C4⋊C4—434no—
632C2×C4⋊C4—434no—
633C2×C4⋊C4—4316no—
634C2×C4⋊C4—4316no—
635C2×C4⋊C4—4316no—
636C2×C4⋊C4C22×D4312yes—
637C2×C4⋊C4C22×D4312yes—
638C2×C4⋊C4C22×D4311yescharacteristic
639C2×C4⋊C4C22×D4314yes—
640C2×C4⋊C4C22×D43116yes—
641C2×C4⋊C4C22×D4311yescharacteristic
642C2×C4⋊C4C22×D4314yes—
643C2×C4⋊C4C22×D4312yes—
644C2×C22⋊C4—432no—
645C2×C22⋊C4—434no—
646C2×C22⋊C4—432no—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—434no—
652C2×C22⋊C4—432no—
653C2×C22⋊C4—434no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4C22×D4314yes—
657C2×C22⋊C4C22×D4312yes—
658C2×C42—434no—
659C2×C42—431no—
660C2×C42—431no—
661C2×C42—432no—
662C2×C42—434no—
663C2×C42—431no—
664C2×C42—438no—
665C2×C42C22×D4312yes—
666C2×C42C22×D4311yescharacteristic
667C24—431no—
668C24—432no—
669C24C23×D4312yes—
670#41—17264no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—434no—
674C2×Q8—4316no—
675C2×Q8—4316no—
676C2×Q8—438no—
677C2×Q8—864no—
678C2×Q8—1728no—
679C2×Q8—1724no—
680C2×Q8—1728no—
681C2×Q8—17232no—
682C2×Q8C23×D4314yes—
683C2×Q8C23×D4318yes—
684C2×D4—24no—
685C2×D4—438no—
686C2×D4—4316no—
687C2×D4—434no—
688C2×D4—438no—
689C2×D4—868no—
690C2×D4—868no—
691C2×D4—864no—
692C2×D4—1728no—
693C2×D4C23×D4314yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—432no—
697C22×C4—431no—
698C22×C4—432no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—434no—
702C22×C4—432no—
703C22×C4—434no—
704C22×C4—434no—
705C22×C4—434no—
706C22×C4—4316no—
707C22×C4—438no—
708C22×C4—4316no—
709C22×C4—864no—
710C22×C4—8616no—
711C22×C4—864no—
712C22×C4—864no—
713C22×C4—868no—
714C22×C4—1728no—
715C22×C4C23×D4318yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4312yes—
718C22×C4C23×D4311yescharacteristic
719C22×C4C23×D4312yes—
720C22×C4C23×D4314yes—
721C22×C4C23×D43116yes—
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C4⋊C4—434no—
725C4⋊C4—438no—
726C4⋊C4—438no—
727C4⋊C4—4316no—
728C4⋊C4—4316no—
729C4⋊C4—4316no—
730C4⋊C4—434no—
731C4⋊C4—4316no—
732C4⋊C4—438no—
733C4⋊C4—438no—
734C4⋊C4—438no—
735C4⋊C4—438no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—438no—
739C4⋊C4—4316no—
740C4⋊C4—4316no—
741C4⋊C4C23×D4318yes—
742C4⋊C4C23×D4318yes—
743C4⋊C4C23×D4314yes—
744C4⋊C4C23×D43116yes—
745C4⋊C4C23×D4314yes—
746C4⋊C4C23×D43116yes—
747C4⋊C4C23×D4318yes—
748C22⋊C4—438no—
749C22⋊C4—4316no—
750C22⋊C4—438no—
751C22⋊C4—438no—
752C22⋊C4—438no—
753C22⋊C4—438no—
754C22⋊C4—438no—
755C22⋊C4—4316no—
756C22⋊C4—438no—
757C22⋊C4—4316no—
758C22⋊C4—438no—
759C22⋊C4—438no—
760C22⋊C4C23×D43116yes—
761C22⋊C4C23×D4318yes—
762C42—434no—
763C42—434no—
764C42—434no—
765C42—4316no—
766C42—438no—
767C42—4316no—
768C42C23×D4314yes—
769C42C23×D4318yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—434no—
774C23—432no—
775C23—434no—
776C23—862no—
777C23—862no—
778C23—864no—
779C23—864no—
780C23—864no—
781C23C24×D4314yes—
782C23C24×D4311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—868no—
786Q8—17216no—
787Q8—1728no—
788Q8—17216no—
789D4—28no—
790D4—8616no—
791D4—8616no—
792D4—868no—
793D4—17216no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—434no—
802C2×C4—432no—
803C2×C4—432no—
804C2×C4—434no—
805C2×C4—432no—
806C2×C4—438no—
807C2×C4—434no—
808C2×C4—868no—
809C2×C4—8632no—
810C2×C4—868no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—864no—
815C2×C4—862no—
816C2×C4—864no—
817C2×C4—868no—
818C2×C4—868no—
819C2×C4—8616no—
820C2×C4—17216no—
821C2×C4#1306337214yes—
822C2×C4#1306337314yes—
823C2×C4C24×D4314yes—
824C2×C4C24×D4314yes—
825C2×C4C24×D4312yes—
826C2×C4C24×D4314yes—
827C2×C4C24×D4318yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—434no—
835C22—862no—
836C22—862no—
837C22—868no—
838C22—864no—
839C22—864no—
840C22—864no—
841C22—1728no—
842C22H(5,𝔽2)×D4312yes—
843C22C2×#1306337212yes—
844C22C2×#1306337312yes—
845C22C25×D4311yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—868no—
852C4—862no—
853C4—864no—
854C4—862no—
855C4—862no—
856C4—864no—
857C4—864no—
858C4C2×#1306337214yes—
859C4C2×#1306337314yes—
860C2—44no—
861C2—864no—
862C2—1724no—
863C2#1914893614yesdirect product factor
864C2C2×H(5,𝔽2)×D4311yescharacteristic
865C2C22×#1306337211yescharacteristic
866C2C22×#1306337311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#554C2
socleC23×C43C25
hypercenterC2×#554D43
hypocenterC43C2×#3544
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19148936C2direct (N × H)
2. C2×#14583650C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583614C2semidirect
5. C2×#14583610C2semidirect
6. C2×#14583587C2semidirect
7. C2×#14583583C2semidirect
8. C2×#14583554C2semidirect
9. C2×#14583550C2semidirect
10. C2×#14583530C2semidirect
11. C2×#14583529C2semidirect
12. C2×#14583522C2semidirect
13. C2×#14583514C2semidirect
14. C2×#14583472C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
16. C2×#14583436C2semidirect
17. C2×#14583431C2semidirect
18. C2×C43×#554C2semidirect
21. #14583650C22semidirect
22. Q8×Dic86C22semidirect
23. #14583614C22semidirect
24. #14583610C22semidirect
25. #14583587C22semidirect
26. #14583583C22semidirect
27. #14583554C22semidirect
28. #14583550C22semidirect
29. #14583530C22semidirect
30. #14583529C22semidirect
31. #14583522C22semidirect
32. #14583514C22semidirect
33. #14583472C22semidirect
42. C4⋊Q8×D43C22semidirect
43. #14583436C22semidirect
44. #14583431C22semidirect
92. C43×#554C22semidirect
432. C2×#554D43semidirect
446. C2×C43#3544semidirect
458. #554C2×D43semidirect
534. C43C2×#3544semidirect
863. C2#19148936direct (N × H)

Maximal subgroups

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

subgroupindex
#191489362
C2×#145836502
C2×Q8×Dic862
C2×#145836142
C2×#145836102
C2×#145835872
C2×#145835832
C2×#145835542
C2×#145835502
C2×#145835302
C2×#145835292
C2×#145835222
C2×#145835142
C2×#145834722
C2×C4⋊Q8×D432
C2×#145834362
C2×#145834312
C2×C43×#5542
C2×#354443