Finite Group Databasebeta

← C2×#19148512 #26005098

Subgroups — C2×#19148512 #26005098

Order 11008.

7238 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148512C2132yesmaximal, direct product factor
2C2×#14583598C214yesmaximal, complemented
3C2×#14583597C212yesmaximal, complemented
4C2×#14583595C214yesmaximal, complemented
5C2×#14583593C212yesmaximal, complemented
6C2×#14583588C212yesmaximal, complemented
7C2×#14583584C212yesmaximal, complemented
8C2×#14583507C212yesmaximal, complemented
9C2×#14583500C212yesmaximal, complemented
10C2×#14583480C211yesmaximal, characteristic, complemented
11C2×#14583477C211yesmaximal, characteristic, complemented
12C2×#14583445C211yesmaximal, characteristic, complemented
13C2×#14583436C212yesmaximal, complemented
14C2×#14583431C212yesmaximal, complemented
15C22×#13063316C211yesmaximal, characteristic, complemented
16C2×#14583379C211yesmaximal, characteristic, complemented
17C2×#14583367C211yesmaximal, characteristic, complemented
18C2×C43×#520C211yesmaximal, characteristic, complemented
19C22×#10621898C2211yescharacteristic
20C22×#10621898C2211yescharacteristic
21#14583598C22164yescomplemented
22#14583597C22132yescomplemented
23#14583595C22164yescomplemented
24#14583593C22132yescomplemented
25#14583588C22132yescomplemented
26#14583584C22132yescomplemented
27#14583507C22132yescomplemented
28#14583500C22132yescomplemented
29#14583480C22116yescomplemented
30#14583477C22116yescomplemented
31#14583445C22116yescomplemented
32C2×#13063323C2211yescharacteristic
33C2×#13063321C2211yescharacteristic
34#14583436C22132yescomplemented
35#14583431C22132yescomplemented
36C2×#13063320C2214yes—
37C2×#13063320C2214yes—
38C2×#13063319C2214yes—
39C2×#13063318C2214yes—
40C2×#13063317C2214yes—
41C2×#13063316C2212yes—
42C2×#13063316C2212yes—
43C2×#13063316C2212yes—
44C2×#13063316C2212yes—
45C2×#13063316C22116yescomplemented
46C2×#13063315C2214yes—
47C2×#13063314C2211yescharacteristic
48C2×#13063312C2211yescharacteristic
49C2×#13063310C2214yes—
50C2×#13063308C2214yes—
51C2×#13063307C2214yes—
52C2×#13063307C2214yes—
53C2×#13063305C2212yes—
54C2×#13063305C2212yes—
55C2×#13063304C2212yes—
56C2×#13063301C2212yes—
57C2×#13063300C2212yes—
58C2×#13063300C2212yes—
59C2×#13063299C2212yes—
60C2×#13063299C2214yes—
61C2×#13063299C2214yes—
62C2×#13063298C2214yes—
63C2×#13063297C2212yes—
64C2×#13063297C2214yes—
65C2×#13063297C2212yes—
66C2×#13063296C2212yes—
67#14583379C22116yescomplemented
68#14583367C22116yescomplemented
69C2×C4×Dic86C2212yes—
70C2×#13063290C2211yescharacteristic
71C2×#13063290C2211yescharacteristic
72C2×C4×D172C2212yes—
73C2×C4×D172C2214yes—
74C2×#13063287C2211yescharacteristic
75C2×#13063287C2211yescharacteristic
76C2×C4×C22⋊D43C2212yes—
77C2×C4×C22⋊D43C2212yes—
78C2×C4×C22⋊D43C2214yes—
79C2×(C22⋊D43)⋊C4C2214yes—
80C2×(C22⋊D43)⋊C4C2212yes—
81C2×(C22⋊D43)⋊C4C2212yes—
82C2×#13063284C2214yes—
83C2×#13063283C2212yes—
84C2×#13063282C2214yes—
85C2×#13063282C2212yes—
86C22×C4⋊Dic43C2211yescharacteristic
87C22×C4⋊Dic43C2212yes—
88C22×Dic43⋊C4C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C22×C4×Dic43C2211yescharacteristic
91C2×C42×D43C2212yes—
92C22×#41×C43C2211yescharacteristic
93C43×#520C22116yescomplemented
94C2×C4×Q8×C43C2212yes—
95C2×C4×D4×C43C2214yes—
96C2×C4×D4×C43C2212yes—
97C2×#117×C43C2211yescharacteristic
98C2×#117×C43C2212yes—
99C22×C4⋊C4×C43C2212yes—
100C22×C4⋊C4×C43C2211yescharacteristic
101C2×#10621898—28no—
102C2×#10621898—28no—
103C2×#10621898C2318yes—
104C2×#10621898C2318yes—
105C22×Dic86C2311yescharacteristic
106C22×Dic86C2311yescharacteristic
107C22×D172C2311yescharacteristic
108C22×D172C2311yescharacteristic
109C22×D172C2314yes—
110C22×C22⋊D43C2312yes—
111C22×C22⋊D43C2312yes—
112C22×C22⋊D43C2314yes—
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2312yes—
115C23×Dic43C2311yescharacteristic
116C23×Dic43C2311yescharacteristic
117C23×Dic43C2312yes—
118C22×C4×D43C2312yes—
119C22×C4×D43C2312yes—
120C22×C4×D43C2312yes—
121C22×C4×D43C2312yes—
122C22×C4×D43C2314yes—
123#13063323C2318yes—
124#13063321C2318yes—
125#13063320C23132yes—
126#13063320C23132yes—
127#13063319C23132yes—
128#13063318C23132yes—
129#13063317C23132yes—
130#13063316C23116yes—
131#13063316C23116yes—
132#13063316C23116yes—
133#13063316C23116yes—
134#13063315C23132yes—
135#13063314C2318yes—
136#13063312C2318yes—
137#13063310C23132yes—
138#13063308C23132yes—
139#13063307C23132yes—
140#13063307C23132yes—
141#13063305C23116yes—
142#13063305C23116yes—
143#13063304C23116yes—
144#13063301C23116yes—
145#13063300C23116yes—
146#13063300C23116yes—
147#13063299C23116yes—
148#13063299C23132yes—
149#13063299C23132yes—
150#13063298C23132yes—
151#13063297C23116yes—
152#13063297C23132yes—
153#13063297C23116yes—
154#13063296C23116yes—
155C4×Dic86C23116yes—
156#13063290C2318yes—
157#13063290C2318yes—
158C4×D172C23132yes—
159C4×D172C23116yes—
160#13063287C2318yes—
161#13063287C2318yes—
162C4×C22⋊D43C23116yes—
163C4×C22⋊D43C23116yes—
164C4×C22⋊D43C23132yes—
165(C22⋊D43)⋊C4C23116yes—
166(C22⋊D43)⋊C4C23132yes—
167(C22⋊D43)⋊C4C23116yes—
168#13063284C23132yes—
169#13063283C23116yes—
170#13063282C23132yes—
171#13063282C23116yes—
172C2×C4⋊Dic43C23116yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2314yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2318yes—
177C2×C4⋊Dic43C2314yes—
178C2×C4⋊Dic43C2314yes—
179C2×Dic43⋊C4C23116yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C4⋊C4×D43C23116yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2314yes—
191C2×C22⋊Dic43C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2314yes—
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2312yes—
202C2×C4×Dic43C2312yes—
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2318yes—
207C2×C4×Dic43C2314yes—
208C42×D43C23116yes—
209C2×#41×C43—28no—
210C2×#41×C43C2318yes—
211C22×Q8×C43C2311yescharacteristic
212C22×D4×C43C2311yescharacteristic
213C22×D4×C43C2312yes—
214C23×C4×C43C2312yes—
215C23×C4×C43C2312yes—
216C23×C4×C43C2314yes—
217C23×C4×C43C2311yescharacteristic
218C4×Q8×C43C23116yes—
219C4×D4×C43C23132yes—
220C4×D4×C43C23116yes—
221#117×C43C23116yes—
222#117×C43C2318yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2312yes—
225C2×C4⋊C4×C43C2312yes—
226C2×C4⋊C4×C43C2314yes—
227C2×C4⋊C4×C43C23116yes—
228C2×C4⋊C4×C43C2318yes—
229C2×C4⋊C4×C43C2311yescharacteristic
230C2×C22⋊C4×C43C2312yes—
231C2×C22⋊C4×C43C2314yes—
232C2×C42×C43C2312yes—
233C2×C42×C43C2314yes—
234C24×C43C2412yes—
235C24×C43C2411yescharacteristic
236C23×D43C2412yes—
237C23×D43C2412yes—
238#41×C43—232no—
239C2×Q8×C43—24no—
240C2×Q8×C43C2414yes—
241C2×D4×C43—24no—
242C2×D4×C43—28no—
243C2×D4×C43C2414yes—
244C2×D4×C43C2418yes—
245C22×C4×C43—28no—
246C22×C4×C43—44no—
247C22×C4×C43—48no—
248C22×C4×C43#4118yes—
249C22×C4×C43C2412yes—
250C22×C4×C43C2412yes—
251C22×C4×C43C2412yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2418yes—
254C22×C4×C43C2418yes—
255C22×C4×C43C24116yes—
256C22×C4×C43C2411yescharacteristic
257C22×C4×C43C2411yescharacteristic
258C22×C4×C43C2414yes—
259C2×C22⋊D43—28no—
260C2×C22⋊D43—28no—
261C2×C22⋊D43—44no—
262C2×C22⋊D43—48no—
263C2×C22⋊D43—44no—
264C2×C22⋊D43C2418yes—
265C2×C22⋊D43C2418yes—
266C2×C22⋊D43C24116yes—
267C2×C22⋊D43C2418yes—
268C2×C22⋊D43C2418yes—
269C22×Dic43—42no—
270C22×Dic43—44no—
271C22×Dic43—42no—
272C22×Dic43C2411yescharacteristic
273C22×Dic43C2411yescharacteristic
274C22×Dic43C2412yes—
275C22×Dic43C2412yes—
276C22×Dic43C2411yescharacteristic
277C22×Dic43C2411yescharacteristic
278C22×Dic43C2414yes—
279C22×Dic43C2414yes—
280C22×Dic43C2414yes—
281C22×Dic43C2418yes—
282#10621898—232no—
283#10621898—232no—
284C2×D172—24no—
285C2×D172—24no—
286C2×D172—48no—
287C2×D172C2414yes—
288C2×D172C2414yes—
289C2×D172C24116yes—
290C2×C4×D43—28no—
291C2×C4×D43—28no—
292C2×C4×D43—48no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43C2418yes—
296C2×C4×D43C2418yes—
297C2×C4×D43C2418yes—
298C2×C4×D43C2418yes—
299C2×C4×D43C24116yes—
300C2×Dic86—24no—
301C2×Dic86—24no—
302C2×Dic86C2414yes—
303C2×Dic86C2414yes—
304C4⋊C4×C43C2414yes—
305C4⋊C4×C43C2418yes—
306C4⋊C4×C43C2418yes—
307C4⋊C4×C43C24116yes—
308C4⋊C4×C43C2414yes—
309C22⋊C4×C43C2418yes—
310C22⋊C4×C43C24116yes—
311C42×C43C2418yes—
312C42×C43C24116yes—
313C22⋊Dic43C2418yes—
314C22⋊Dic43C24116yes—
315C22⋊Dic43C2418yes—
316(C2×D43)⋊C4C2418yes—
317(C2×D43)⋊C4C2418yes—
318(C2×D43)⋊C4C2418yes—
319(C2×D43)⋊C4C24116yes—
320(C2×D43)⋊C4C24116yes—
321(C2×D43)⋊C4C2418yes—
322(C2×D43)⋊C4C24116yes—
323(C2×D43)⋊C4C24116yes—
324C4⋊Dic43C2418yes—
325C4⋊Dic43C24116yes—
326C4⋊Dic43C2418yes—
327C4⋊Dic43C24116yes—
328C4⋊Dic43C24116yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C24116yes—
331Dic43⋊C4C24116yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C2418yes—
334Dic43⋊C4C24116yes—
335Dic43⋊C4C2418yes—
336Dic43⋊C4C2418yes—
337C4×Dic43C2414yes—
338C4×Dic43C2418yes—
339C4×Dic43C2418yes—
340C4×Dic43C2414yes—
341C4×Dic43C2414yes—
342C4×Dic43C2414yes—
343C4×Dic43C24116yes—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—24no—
347C23×C43—24no—
348C23×C43—24no—
349C23×C43C2×#4114yes—
350C23×C43C2514yes—
351C23×C43C2512yes—
352C23×C43C2511yescharacteristic
353C22×D43—24no—
354C22×D43—24no—
355C22×D43—24no—
356C22×D43—24no—
357C22×D43—24no—
358C22×D43—24no—
359C22×D43C2514yes—
360C22×D43C2514yes—
361Q8×C43—28no—
362D4×C43—216no—
363D4×C43—28no—
364C2×C4×C43—24no—
365C2×C4×C43—24no—
366C2×C4×C43—24no—
367C2×C4×C43—28no—
368C2×C4×C43—216no—
369C2×C4×C43—416no—
370C2×C4×C43—48no—
371C2×C4×C43C2×#4114yes—
372C2×C4×C43C2×#4114yes—
373C2×C4×C43C2×#41116yes—
374C2×C4×C43C2514yes—
375C2×C4×C43C2514yes—
376C2×C4×C43C2514yes—
377C2×C4×C43C2518yes—
378C2×C4×C43C2512yes—
379C2×C4×C43C2512yes—
380C22⋊D43—216no—
381C22⋊D43—216no—
382C22⋊D43—416no—
383C22⋊D43—48no—
384C22⋊D43—48no—
385C2×Dic43—24no—
386C2×Dic43—24no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—28no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—44no—
393C2×Dic43—44no—
394C2×Dic43—48no—
395C2×Dic43C2512yes—
396C2×Dic43C2512yes—
397C2×Dic43C2512yes—
398C2×Dic43C2512yes—
399C2×Dic43C2514yes—
400C2×Dic43C2514yes—
401C2×Dic43C2518yes—
402D172—28no—
403D172—28no—
404D172—416no—
405C4×D43—216no—
406C4×D43—216no—
407C4×D43—48no—
408C4×D43—48no—
409C4×D43—416no—
410Dic86—28no—
411Dic86—28no—
412C2×#3512—431nomaximal, Sylow
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—28no—
416C22×C43—24no—
417C22×C43—24no—
418C22×C43—24no—
419C22×C43—48no—
420C22×C43C22×#4114yes—
421C22×C43C22×#4112yes—
422C22×C43#58512yes—
423C22×C43#58512yes—
424C22×C43C2611yescharacteristic
425C2×D43—24no—
426C2×D43—24no—
427C2×D43—24no—
428C2×D43—24no—
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—48no—
432C2×D43—48no—
433C4×C43—24no—
434C4×C43—24no—
435C4×C43—24no—
436C4×C43—28no—
437C4×C43C22×#4114yes—
438C4×C43C22×#4114yes—
439Dic43—24no—
440Dic43—24no—
441Dic43—22no—
442Dic43—22no—
443Dic43—28no—
444Dic43—22no—
445Dic43—22no—
446#3512—4332no—
447C2×#553—434no—
448C2×#553—434no—
449C2×#553—432no—
450C2×#553—432no—
451C2×#552—432no—
452C2×#552—432no—
453C2×#541—432no—
454C2×#540—432no—
455C2×#537—431no—
456C2×#537—431no—
457C2×#532—431no—
458C2×#529—432no—
459C2×#529—432no—
460C22×#125—431no—
461C2×#520—431no—
462C2×#520D4311yescharacteristic, complemented
463C2×C4×#41—431no—
464C2×C43—24no—
465C2×C43—44no—
466C2×C43#351214yescomplemented
467C2×C43C23×#4111yescharacteristic
468C2×C43C2×#58511yescharacteristic
469C2×C43C2×#58511yescharacteristic
470D43—44no—
471D43—44no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41C2×D4311yescharacteristic
475#553—4364no—
476#553—4364no—
477#553—4332no—
478#553—4332no—
479#552—4332no—
480#552—4332no—
481#541—4332no—
482#540—4332no—
483#537—4316no—
484#537—4316no—
485#532—4316no—
486C2×C4⋊Q8—431no—
487C2×#127—431no—
488#529—4332no—
489#529—4332no—
490C2×#126—434no—
491C2×#126—434no—
492C2×#126—434no—
493C2×#126—434no—
494C2×#125—432no—
495C2×#125—432no—
496C2×#125—432no—
497C2×#125—432no—
498C2×#125—4316no—
499C2×#125—434no—
500C2×#125—434no—
501C2×#124—431no—
502C2×#124—431no—
503C2×#123—434no—
504C2×#123—434no—
505C2×#123—434no—
506C2×#123—434no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—432no—
509C2×C22⋊Q8—432no—
510C2×C22⋊Q8—432no—
511C2×#121—432no—
512C2×#121—432no—
513C2×#121—432no—
514C2×#121—434no—
515C2×#121—434no—
516C2×#121—432no—
517C2×#121—434no—
518C2×#121—432no—
519C2×#121—432no—
520C2×#121—434no—
521#520—4316no—
522#520C2×D43116yescomplemented
523C4×#41—4316no—
524C2×C4×Q8—431no—
525C2×C4×Q8—431no—
526C2×C4×Q8—432no—
527C2×C4×Q8C2×D4312yes—
528C2×C4×D4—434no—
529C2×C4×D4—432no—
530C2×C4×D4—432no—
531C2×C4×D4—431no—
532C2×C4×D4—431no—
533C2×C4×D4—432no—
534C2×C4×D4—432no—
535C2×C4×D4—434no—
536C2×C4×D4—432no—
537C2×C4×D4—434no—
538C2×C4×D4C2×D4312yes—
539C2×C4×D4C2×D4314yes—
540C2×#117—434no—
541C2×#117—432no—
542C2×#117—432no—
543C2×#117—434no—
544C2×#117C2×D4311yescharacteristic
545C2×#117C2×D4312yes—
546C22×C4⋊C4—432no—
547C22×C4⋊C4—431no—
548C22×C4⋊C4—432no—
549C22×C4⋊C4—432no—
550C22×C4⋊C4C2×D4311yescharacteristic
551C22×C4⋊C4C2×D4312yes—
552C22×C42—431no—
553C22×C42—432no—
554C43C2×#351211yescharacteristic, complemented, Sylow
555C2×#41—28no—
556C2×#41—438no—
557C2×#41—438no—
558C2×#41—868no—
559C2×#41—868no—
560C2×#41C22×D4318yes—
561C22×Q8—431no—
562C22×Q8—431no—
563C22×Q8C22×D4311yescharacteristic
564C22×D4—432no—
565C22×D4—432no—
566C22×D4—434no—
567C22×D4—432no—
568C22×D4—432no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—434no—
572C22×D4C22×D4312yes—
573C22×D4C22×D4311yescharacteristic
574C23×C4—432no—
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—432no—
578C23×C4—432no—
579C23×C4—434no—
580C23×C4—432no—
581C23×C4—432no—
582C23×C4C22×D4312yes—
583C23×C4C22×D4312yes—
584C23×C4C22×D4314yes—
585C23×C4C22×D4311yescharacteristic
586C4⋊Q8—438no—
587#127—438no—
588#126—4332no—
589#126—4332no—
590#126—4332no—
591#126—4332no—
592#125—4316no—
593#125—4316no—
594#125—4316no—
595#125—4316no—
596#125—4332no—
597#125—4332no—
598#124—438no—
599#124—438no—
600#123—4332no—
601#123—4332no—
602#123—4332no—
603#123—4332no—
604C22⋊Q8—4316no—
605C22⋊Q8—4316no—
606C22⋊Q8—4316no—
607C22⋊Q8—4316no—
608#121—4316no—
609#121—4316no—
610#121—4316no—
611#121—4332no—
612#121—4332no—
613#121—4316no—
614#121—4332no—
615#121—4316no—
616#121—4316no—
617#121—4332no—
618C4×Q8—438no—
619C4×Q8—438no—
620C4×Q8—4316no—
621C4×Q8C22×D43116yes—
622C4×D4—4332no—
623C4×D4—4316no—
624C4×D4—4316no—
625C4×D4—438no—
626C4×D4—438no—
627C4×D4—4316no—
628C4×D4—4316no—
629C4×D4—4332no—
630C4×D4—4316no—
631C4×D4—4332no—
632C4×D4C22×D43116yes—
633C4×D4C22×D43132yes—
634#117—4332no—
635#117—4316no—
636#117—4316no—
637#117—4332no—
638#117C22×D4318yes—
639#117C22×D43116yes—
640C2×C4⋊C4—432no—
641C2×C4⋊C4—434no—
642C2×C4⋊C4—434no—
643C2×C4⋊C4—432no—
644C2×C4⋊C4—434no—
645C2×C4⋊C4—438no—
646C2×C4⋊C4—434no—
647C2×C4⋊C4—434no—
648C2×C4⋊C4—4316no—
649C2×C4⋊C4—4316no—
650C2×C4⋊C4—432no—
651C2×C4⋊C4—432no—
652C2×C4⋊C4—434no—
653C2×C4⋊C4—434no—
654C2×C4⋊C4—432no—
655C2×C4⋊C4—432no—
656C2×C4⋊C4—4316no—
657C2×C4⋊C4C22×D4311yescharacteristic
658C2×C4⋊C4C22×D4311yescharacteristic
659C2×C4⋊C4C22×D4312yes—
660C2×C4⋊C4C22×D4312yes—
661C2×C4⋊C4C22×D4314yes—
662C2×C4⋊C4C22×D4318yes—
663C2×C4⋊C4C22×D43116yes—
664C2×C22⋊C4—432no—
665C2×C22⋊C4—434no—
666C2×C22⋊C4—432no—
667C2×C22⋊C4—432no—
668C2×C22⋊C4—432no—
669C2×C22⋊C4—432no—
670C2×C22⋊C4—434no—
671C2×C22⋊C4—434no—
672C2×C22⋊C4—432no—
673C2×C22⋊C4—434no—
674C2×C22⋊C4—434no—
675C2×C22⋊C4C22×D4312yes—
676C2×C22⋊C4C22×D4314yes—
677C2×C42—434no—
678C2×C42—432no—
679C2×C42—432no—
680C2×C42—431no—
681C2×C42—431no—
682C2×C42—431no—
683C2×C42—438no—
684C2×C42—431no—
685C2×C42—4316no—
686C2×C42C22×D4312yes—
687C2×C42C22×D4314yes—
688C24—432no—
689C24—432no—
690C24C23×D4312yes—
691C24C23×D4311yescharacteristic
692#41—232no—
693#41—8632no—
694#41—8632no—
695C2×Q8—24no—
696C2×Q8—434no—
697C2×Q8—434no—
698C2×Q8—864no—
699C2×Q8—864no—
700C2×Q8C23×D4314yes—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—438no—
704C2×D4—438no—
705C2×D4—4316no—
706C2×D4—438no—
707C2×D4—438no—
708C2×D4—434no—
709C2×D4—434no—
710C2×D4—4316no—
711C2×D4—868no—
712C2×D4—868no—
713C2×D4—864no—
714C2×D4—864no—
715C2×D4—1728no—
716C2×D4—1724no—
717C2×D4—1728no—
718C2×D4—1724no—
719C2×D4C23×D4318yes—
720C2×D4C23×D4314yes—
721C22×C4—28no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—432no—
727C22×C4—432no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—434no—
731C22×C4—434no—
732C22×C4—434no—
733C22×C4—438no—
734C22×C4—438no—
735C22×C4—438no—
736C22×C4—438no—
737C22×C4—438no—
738C22×C4—4316no—
739C22×C4—868no—
740C22×C4—868no—
741C22×C4—1724no—
742C22×C4—1724no—
743C22×C4—1728no—
744C22×C4—1722no—
745C22×C4—1722no—
746C22×C4—1724no—
747C22×C4#1062189818yes—
748C22×C4C23×D4318yes—
749C22×C4C23×D4312yes—
750C22×C4C23×D4312yes—
751C22×C4C23×D4312yes—
752C22×C4C23×D4314yes—
753C22×C4C23×D4318yes—
754C22×C4C23×D43116yes—
755C22×C4C23×D4314yes—
756C22×C4C23×D4311yescharacteristic
757C22×C4C23×D4311yescharacteristic
758C4⋊C4—438no—
759C4⋊C4—4316no—
760C4⋊C4—4316no—
761C4⋊C4—438no—
762C4⋊C4—4316no—
763C4⋊C4—4316no—
764C4⋊C4—4316no—
765C4⋊C4—438no—
766C4⋊C4—438no—
767C4⋊C4—4316no—
768C4⋊C4—4316no—
769C4⋊C4—438no—
770C4⋊C4—438no—
771C4⋊C4C23×D4314yes—
772C4⋊C4C23×D4314yes—
773C4⋊C4C23×D4318yes—
774C4⋊C4C23×D4318yes—
775C4⋊C4C23×D43116yes—
776C22⋊C4—438no—
777C22⋊C4—4316no—
778C22⋊C4—438no—
779C22⋊C4—438no—
780C22⋊C4—438no—
781C22⋊C4—438no—
782C22⋊C4—4316no—
783C22⋊C4—4316no—
784C22⋊C4—438no—
785C22⋊C4—4316no—
786C22⋊C4—4316no—
787C22⋊C4C23×D4318yes—
788C22⋊C4C23×D43116yes—
789C42—434no—
790C42—438no—
791C42—438no—
792C42—434no—
793C42—434no—
794C42—434no—
795C42—4316no—
796C42C23×D4318yes—
797C42C23×D43116yes—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—434no—
804C23—434no—
805C23—864no—
806C23—864no—
807C23—864no—
808C23—864no—
809C23—864no—
810C23—864no—
811C23C2×#1062189814yes—
812C23C24×D4314yes—
813C23C24×D4312yes—
814C23C24×D4311yescharacteristic
815Q8—28no—
816Q8—868no—
817Q8—868no—
818D4—216no—
819D4—28no—
820D4—8616no—
821D4—8616no—
822D4—868no—
823D4—868no—
824D4—17216no—
825D4—1728no—
826D4—17216no—
827D4—1728no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—48no—
835C2×C4—432no—
836C2×C4—432no—
837C2×C4—434no—
838C2×C4—434no—
839C2×C4—432no—
840C2×C4—432no—
841C2×C4—438no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—868no—
848C2×C4—862no—
849C2×C4—8616no—
850C2×C4—8616no—
851C2×C4—1728no—
852C2×C4—1728no—
853C2×C4—17216no—
854C2×C4—1724no—
855C2×C4—1724no—
856C2×C4—1728no—
857C2×C4C2×#1062189814yes—
858C2×C4C2×#1062189814yes—
859C2×C4C2×#10621898116yes—
860C2×C4C24×D4314yes—
861C2×C4C24×D4314yes—
862C2×C4C24×D4314yes—
863C2×C4C24×D4318yes—
864C2×C4C24×D4312yes—
865C2×C4C24×D4312yes—
866C22—22no—
867C22—22no—
868C22—28no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—48no—
873C22—864no—
874C22—864no—
875C22—864no—
876C22—864no—
877C22—864no—
878C22—864no—
879C22—1728no—
880C22—1728no—
881C22C22×#1062189814yes—
882C22C22×#1062189812yes—
883C22#1458373412yes—
884C22#1458373612yes—
885C22C25×D4311yescharacteristic
886C4—24no—
887C4—24no—
888C4—28no—
889C4—24no—
890C4—864no—
891C4—864no—
892C4—862no—
893C4—862no—
894C4—862no—
895C4—868no—
896C4—862no—
897C4C22×#1062189814yes—
898C4C22×#1062189814yes—
899C2—24no—
900C2—44no—
901C2—1724no—
902C2—1724no—
903C2#1914851214yesdirect product factor
904C2C23×#1062189811yescharacteristic
905C2C2×#1458373411yescharacteristic
906C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
hypercenterC2×#520D43
hypocenterC43C2×#3512
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19148512C2direct (N × H)
2. C2×#14583598C2semidirect
3. C2×#14583597C2semidirect
4. C2×#14583595C2semidirect
5. C2×#14583593C2semidirect
6. C2×#14583588C2semidirect
7. C2×#14583584C2semidirect
8. C2×#14583507C2semidirect
9. C2×#14583500C2semidirect
10. C2×#14583480C2semidirect
11. C2×#14583477C2semidirect
12. C2×#14583445C2semidirect
13. C2×#14583436C2semidirect
14. C2×#14583431C2semidirect
15. C22×#13063316C2semidirect
16. C2×#14583379C2semidirect
17. C2×#14583367C2semidirect
18. C2×C43×#520C2semidirect
21. #14583598C22semidirect
22. #14583597C22semidirect
23. #14583595C22semidirect
24. #14583593C22semidirect
25. #14583588C22semidirect
26. #14583584C22semidirect
27. #14583507C22semidirect
28. #14583500C22semidirect
29. #14583480C22semidirect
30. #14583477C22semidirect
31. #14583445C22semidirect
34. #14583436C22semidirect
35. #14583431C22semidirect
45. C2×#13063316C22semidirect
67. #14583379C22semidirect
68. #14583367C22semidirect
93. C43×#520C22semidirect
462. C2×#520D43semidirect
466. C2×C43#3512semidirect
522. #520C2×D43semidirect
554. C43C2×#3512semidirect
903. C2#19148512direct (N × H)

Maximal subgroups

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

subgroupindex
#191485122
C2×#145835982
C2×#145835972
C2×#145835952
C2×#145835932
C2×#145835882
C2×#145835842
C2×#145835072
C2×#145835002
C2×#145834802
C2×#145834772
C2×#145834452
C2×#145834362
C2×#145834312
C22×#130633162
C2×#145833792
C2×#145833672
C2×C43×#5202
C2×#351243