Finite Group Databasebeta

← C2×#19149068 #26004218

Subgroups — C2×#19149068 #26004218

Order 11008.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149068C2132yesmaximal, direct product factor
2C2×#14583646C214yesmaximal, complemented
3C2×#14583634C211yesmaximal, characteristic, complemented
4C2×#14583631C212yesmaximal, complemented
5C2×#14583628C211yesmaximal, characteristic, complemented
6C2×#14583605C212yesmaximal, complemented
7C2×#14583570C211yesmaximal, characteristic, complemented
8C2×D4×Dic86C211yesmaximal, characteristic, complemented
9C2×#14583558C212yesmaximal, complemented
10C2×#14583554C212yesmaximal, complemented
11C2×#14583522C212yesmaximal, complemented
12C2×#14583520C212yesmaximal, complemented
13C2×#14583502C212yesmaximal, complemented
14C2×#14583490C214yesmaximal, complemented
15C2×#14583475C212yesmaximal, complemented
16C2×#14583456C211yesmaximal, characteristic, complemented
17C2×#14583449C211yesmaximal, characteristic, complemented
18C2×C43×#529C211yesmaximal, characteristic, complemented
19C22×#10621898C2212yes—
20C22×#10621898C2212yes—
21C23×Dic86C2212yes—
22#14583646C22164yescomplemented
23#14583634C22116yescomplemented
24#14583631C22132yescomplemented
25#14583628C22116yescomplemented
26#14583605C22132yescomplemented
27#14583570C22116yescomplemented
28D4×Dic86C22116yescomplemented
29#14583558C22132yescomplemented
30#14583554C22132yescomplemented
31#14583522C22132yescomplemented
32#14583520C22132yescomplemented
33#14583502C22132yescomplemented
34#14583490C22164yescomplemented
35#14583475C22132yescomplemented
36#14583456C22116yescomplemented
37#14583449C22116yescomplemented
38C2×#13063325C2212yes—
39C2×#13063325C2211yescharacteristic
40C2×#13063325C2211yescharacteristic
41C2×#13063325C2211yescharacteristic
42C2×#13063324C2212yes—
43C2×#13063322C2211yescharacteristic
44C2×#13063321C2212yes—
45C2×#13063320C2214yes—
46C2×#13063317C2212yes—
47C2×#13063316C2212yes—
48C2×#13063316C2214yes—
49C2×#13063314C2212yes—
50C2×#13063313C2212yes—
51C2×#13063313C2212yes—
52C2×#13063311C2214yes—
53C2×#13063311C2214yes—
54C2×#13063310C2214yes—
55C2×#13063309C2214yes—
56C2×#13063309C2214yes—
57C2×#13063307C2214yes—
58C2×#13063307C2214yes—
59C2×#13063307C2214yes—
60C2×#13063305C2214yes—
61C2×#13063305C2214yes—
62C2×#13063304C2211yescharacteristic
63C2×#13063304C2212yes—
64C2×#13063304C2211yescharacteristic
65C2×#13063304C2212yes—
66C2×#13063303C2214yes—
67C2×#13063303C2214yes—
68C2×#13063302C2214yes—
69C2×#13063299C2212yes—
70C2×#13063299C2212yes—
71C2×#13063299C2212yes—
72C2×#13063298C2214yes—
73C2×#13063297C2214yes—
74C2×#13063296C2214yes—
75C2×Q8×Dic43C2212yes—
76C2×C4×Dic86C2212yes—
77C2×C4×Dic86C2211yescharacteristic
78C2×C4×Dic86C2211yescharacteristic
79C2×C4×Dic86C2212yes—
80C2×C4×D172C2212yes—
81C2×C4×D172C2212yes—
82C2×C4×D172C2212yes—
83C2×D4×Dic43C2212yes—
84C2×#13063287C2212yes—
85C2×#13063287C2212yes—
86C2×(C22⋊D43)⋊C4C2214yes—
87C2×#13063284C2212yes—
88C2×C4⋊C4×D43C2214yes—
89C43×#529C22116yescomplemented
90C2×#126×C43C2212yes—
91C2×#125×C43C2211yescharacteristic
92C2×#124×C43C2211yescharacteristic
93C2×#123×C43C2212yes—
94C2×C22⋊Q8×C43C2211yescharacteristic
95C2×#121×C43C2211yescharacteristic
96C2×C4×Q8×C43C2211yescharacteristic
97C2×C4×D4×C43C2212yes—
98C2×C4×D4×C43C2211yescharacteristic
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C2×#10621898—48no—
102C2×#10621898—48no—
103C2×#10621898C23116yes—
104C2×#10621898C23116yes—
105C22×Dic86—48no—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C2312yes—
108C22×Dic86C2311yescharacteristic
109C22×Dic86C23116yes—
110C22×Dic86C2312yes—
111C22×Dic86C2314yes—
112C22×D172C2312yes—
113C22×D172C2312yes—
114C22×D172C2312yes—
115C22×C22⋊D43C2314yes—
116C22×C22⋊D43C2314yes—
117C22×C22⋊D43C2314yes—
118C23×Dic43C2314yes—
119C22×C4×D43C2314yes—
120C22×C4×D43C2314yes—
121C22×C4×D43C2314yes—
122#13063325C23116yes—
123#13063325C2318yes—
124#13063325C2318yes—
125#13063325C2318yes—
126#13063324C23116yes—
127#13063322C2318yes—
128#13063321C23116yes—
129#13063320C23132yes—
130#13063317C23116yes—
131#13063316C23116yes—
132#13063316C23132yes—
133#13063314C23116yes—
134#13063313C23116yes—
135#13063313C23116yes—
136#13063311C23132yes—
137#13063311C23132yes—
138#13063310C23132yes—
139#13063309C23132yes—
140#13063309C23132yes—
141#13063307C23132yes—
142#13063307C23132yes—
143#13063307C23132yes—
144#13063305C23132yes—
145#13063305C23132yes—
146#13063304C2318yes—
147#13063304C23116yes—
148#13063304C2318yes—
149#13063304C23116yes—
150#13063303C23132yes—
151#13063303C23132yes—
152#13063302C23132yes—
153#13063299C23116yes—
154#13063299C23116yes—
155#13063299C23116yes—
156#13063298C23132yes—
157#13063297C23132yes—
158#13063296C23132yes—
159Q8×Dic43C23116yes—
160C4×Dic86C23116yes—
161C4×Dic86C2318yes—
162C4×Dic86C2318yes—
163C4×Dic86C23116yes—
164C4×D172C23116yes—
165C4×D172C23116yes—
166C4×D172C23116yes—
167D4×Dic43C23116yes—
168#13063287C23116yes—
169#13063287C23116yes—
170(C22⋊D43)⋊C4C23132yes—
171#13063284C23116yes—
172C2×C4⋊Dic43C2314yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2314yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C4⋊C4×D43C23132yes—
188C2×C22⋊Dic43C2312yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2314yes—
191C2×(C2×D43)⋊C4C2314yes—
192C2×(C2×D43)⋊C4C2314yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2314yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2314yes—
200C22×Q8×C43C2311yescharacteristic
201C22×D4×C43C2311yescharacteristic
202C22×D4×C43C2312yes—
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C23×C4×C43C2312yes—
206C23×C4×C43C2311yescharacteristic
207#126×C43C23116yes—
208#125×C43C2318yes—
209#124×C43C2318yes—
210#123×C43C23116yes—
211C22⋊Q8×C43C2318yes—
212#121×C43C2318yes—
213C4×Q8×C43C2318yes—
214C4×D4×C43C23116yes—
215C4×D4×C43C2318yes—
216#117×C43C23116yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2311yescharacteristic
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C22⋊C4×C43C2312yes—
225C2×C22⋊C4×C43C2312yes—
226C2×C22⋊C4×C43C2312yes—
227C2×C22⋊C4×C43C2312yes—
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2318yes—
233C2×C42×C43C2312yes—
234C24×C43C2412yes—
235C24×C43C2411yescharacteristic
236C23×D43C2414yes—
237C2×Q8×C43—24no—
238C2×Q8×C43C2414yes—
239C2×D4×C43—24no—
240C2×D4×C43—44no—
241C2×D4×C43C2414yes—
242C2×D4×C43C2418yes—
243C22×C4×C43—28no—
244C22×C4×C43—24no—
245C22×C4×C43—24no—
246C22×C4×C43—42no—
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2414yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2418yes—
257C22×C4×C43C2414yes—
258C22×C4×C43C2411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C2×C22⋊D43—48no—
261C2×C22⋊D43—48no—
262C2×C22⋊D43—48no—
263C2×C22⋊D43C24116yes—
264C2×C22⋊D43C24116yes—
265C2×C22⋊D43C24116yes—
266C22×Dic43—48no—
267C22×Dic43C2412yes—
268C22×Dic43C2412yes—
269C22×Dic43C2412yes—
270C22×Dic43C2414yes—
271C22×Dic43C2412yes—
272C22×Dic43C24116yes—
273#10621898—432no—
274#10621898—432no—
275C2×D172—28no—
276C2×D172—28no—
277C2×D172—44no—
278C2×D172C2418yes—
279C2×D172C2418yes—
280C2×D172C2418yes—
281C2×C4×D43—48no—
282C2×C4×D43—48no—
283C2×C4×D43—48no—
284C2×C4×D43C24116yes—
285C2×C4×D43C24116yes—
286C2×C4×D43C24116yes—
287C2×Dic86—24no—
288C2×Dic86—28no—
289C2×Dic86—24no—
290C2×Dic86—432no—
291C2×Dic86—48no—
292C2×Dic86—44no—
293C2×Dic86C2414yes—
294C2×Dic86C2418yes—
295C2×Dic86C2414yes—
296C2×Dic86C2418yes—
297C2×Dic86C24116yes—
298C4⋊C4×C43C2418yes—
299C4⋊C4×C43C2418yes—
300C4⋊C4×C43C2414yes—
301C4⋊C4×C43C2418yes—
302C4⋊C4×C43C2414yes—
303C4⋊C4×C43C2418yes—
304C22⋊C4×C43C2418yes—
305C22⋊C4×C43C2418yes—
306C22⋊C4×C43C2418yes—
307C22⋊C4×C43C2418yes—
308C22⋊C4×C43C2418yes—
309C42×C43C2414yes—
310C42×C43C2414yes—
311C42×C43C2414yes—
312C42×C43C2414yes—
313C42×C43C2418yes—
314C22⋊Dic43C2418yes—
315C22⋊Dic43C2418yes—
316C22⋊Dic43C24116yes—
317(C2×D43)⋊C4C24116yes—
318(C2×D43)⋊C4C24116yes—
319(C2×D43)⋊C4C24116yes—
320(C2×D43)⋊C4C24116yes—
321(C2×D43)⋊C4C24116yes—
322(C2×D43)⋊C4C24116yes—
323C4⋊Dic43C24116yes—
324C4⋊Dic43C2418yes—
325C4⋊Dic43C2418yes—
326C4⋊Dic43C2418yes—
327C4⋊Dic43C2414yes—
328C4⋊Dic43C2418yes—
329C4⋊Dic43C2414yes—
330C4⋊Dic43C2418yes—
331C4⋊Dic43C24116yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C24116yes—
334Dic43⋊C4C2418yes—
335Dic43⋊C4C24116yes—
336Dic43⋊C4C2418yes—
337Dic43⋊C4C2418yes—
338C4×Dic43C2418yes—
339C4×Dic43C2418yes—
340C4×Dic43C24116yes—
341C23×C43—24no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—24no—
345C23×C43—24no—
346C23×C43—22no—
347C23×C43C2512yes—
348C23×C43C2514yes—
349C23×C43C2511yescharacteristic
350C22×D43—28no—
351C22×D43—28no—
352C22×D43—28no—
353C22×D43C2518yes—
354Q8×C43—28no—
355D4×C43—28no—
356D4×C43—48no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—24no—
361C2×C4×C43—22no—
362C2×C4×C43—24no—
363C2×C4×C43—22no—
364C2×C4×C43—216no—
365C2×C4×C43—28no—
366C2×C4×C43—28no—
367C2×C4×C43—44no—
368C2×C4×C43H(5,𝔽2)14yes—
369C2×C4×C432−1+414yes—
370C2×C4×C43C2514yes—
371C2×C4×C43C2512yes—
372C2×C4×C43C2512yes—
373C2×C4×C43C2514yes—
374C2×C4×C43C2514yes—
375C2×C4×C43C2512yes—
376C2×C4×C43C2512yes—
377C2×C4×C43C2512yes—
378C2×C4×C43C2512yes—
379C22⋊D43—416no—
380C22⋊D43—416no—
381C22⋊D43—416no—
382C2×Dic43—24no—
383C2×Dic43—28no—
384C2×Dic43—24no—
385C2×Dic43—24no—
386C2×Dic43—24no—
387C2×Dic43—416no—
388C2×Dic43C2514yes—
389C2×Dic43C2514yes—
390C2×Dic43C2514yes—
391C2×Dic43C2518yes—
392C2×Dic43C2514yes—
393D172—216no—
394D172—216no—
395D172—48no—
396C4×D43—416no—
397C4×D43—416no—
398C4×D43—416no—
399Dic86—28no—
400Dic86—216no—
401Dic86—28no—
402Dic86—416no—
403Dic86—48no—
404C2×#3554—431nomaximal, Sylow
405C22×C43—24no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—24no—
409C22×C43—24no—
410C22×C43—22no—
411C22×C43—48no—
412C22×C43—44no—
413C22×C43C2×H(5,𝔽2)12yes—
414C22×C43C2×2−1+412yes—
415C22×C43#58512yes—
416C22×C43C2611yescharacteristic
417C2×D43—28no—
418C2×D43—28no—
419C2×D43—28no—
420C2×D43—416no—
421C4×C43—24no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—24no—
425C4×C43—22no—
426C4×C43—24no—
427C4×C43—22no—
428C4×C43C2×H(5,𝔽2)14yes—
429C4×C43C2×2−1+414yes—
430Dic43—24no—
431Dic43—28no—
432Dic43—24no—
433Dic43—24no—
434Dic43—24no—
435#3554—4332no—
436C2×#562—434no—
437C2×#559—432no—
438C2×#559—431no—
439C2×#557—431no—
440C2×#554—432no—
441C2×#550—431no—
442C2×D4×Q8—431no—
443C2×#548—432no—
444C2×#547—432no—
445C2×#542—432no—
446C2×#542—432no—
447C2×#540—432no—
448C2×#539—434no—
449C2×#536—432no—
450C2×#533—431no—
451C2×#532—431no—
452C2×#529D4311yescharacteristic, complemented
453C2×C43—44no—
454C2×C43—42no—
455C2×C43#355414yescomplemented
456C2×C43C22×H(5,𝔽2)11yescharacteristic
457C2×C43C22×2−1+411yescharacteristic
458C2×C43C2×#58511yescharacteristic
459D43—48no—
460C22×#41—432no—
461C22×#41—432no—
462C23×Q8—432no—
463#562—4364no—
464#559—4332no—
465#559—4316no—
466#557—4316no—
467#554—4332no—
468#550—4316no—
469D4×Q8—4316no—
470#548—4332no—
471#547—4332no—
472#542—4332no—
473#542—4332no—
474#540—4332no—
475#539—4364no—
476#536—4332no—
477#533—4316no—
478#532—4316no—
479C2×C4⋊Q8—432no—
480C2×C4⋊Q8—431no—
481C2×C4⋊Q8—431no—
482C2×C4⋊Q8—431no—
483C2×C4⋊Q8—432no—
484C2×#127—432no—
485C2×#127—431no—
486#529C2×D43116yescomplemented
487C2×#126—434no—
488C2×#126C2×D4312yes—
489C2×#125—434no—
490C2×#125—432no—
491C2×#125—432no—
492C2×#125C2×D4311yescharacteristic
493C2×#124—432no—
494C2×#124—434no—
495C2×#124—434no—
496C2×#124—432no—
497C2×#124—432no—
498C2×#124C2×D4311yescharacteristic
499C2×#123—434no—
500C2×#123—434no—
501C2×#123—434no—
502C2×#123—434no—
503C2×#123—434no—
504C2×#123—434no—
505C2×#123C2×D4312yes—
506C2×C22⋊Q8—431no—
507C2×C22⋊Q8—431no—
508C2×C22⋊Q8—432no—
509C2×C22⋊Q8—432no—
510C2×C22⋊Q8—434no—
511C2×C22⋊Q8—434no—
512C2×C22⋊Q8—434no—
513C2×C22⋊Q8—434no—
514C2×C22⋊Q8—434no—
515C2×C22⋊Q8C2×D4311yescharacteristic
516C2×#121—434no—
517C2×#121—434no—
518C2×#121—432no—
519C2×#121—432no—
520C2×#121—432no—
521C2×#121—434no—
522C2×#121C2×D4311yescharacteristic
523C2×C4×Q8—432no—
524C2×C4×Q8—431no—
525C2×C4×Q8—431no—
526C2×C4×Q8—432no—
527C2×C4×Q8—432no—
528C2×C4×Q8C2×D4311yescharacteristic
529C2×C4×D4—432no—
530C2×C4×D4—432no—
531C2×C4×D4—432no—
532C2×C4×D4—434no—
533C2×C4×D4—432no—
534C2×C4×D4—432no—
535C2×C4×D4—432no—
536C2×C4×D4C2×D4312yes—
537C2×C4×D4C2×D4311yescharacteristic
538C2×#117—432no—
539C2×#117C2×D4312yes—
540C22×C4⋊C4—434no—
541C22×C42C2×D4311yescharacteristic
542C43C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—4316no—
544C2×#41—4316no—
545C2×#41—1728no—
546C2×#41—1728no—
547C22×Q8—431no—
548C22×Q8—432no—
549C22×Q8—431no—
550C22×Q8—432no—
551C22×Q8—434no—
552C22×Q8—4316no—
553C22×Q8—1728no—
554C22×Q8C22×D4311yescharacteristic
555C22×D4—434no—
556C22×D4—434no—
557C22×D4—434no—
558C22×D4—432no—
559C22×D4—432no—
560C22×D4—432no—
561C22×D4C22×D4311yescharacteristic
562C22×D4C22×D4312yes—
563C23×C4—434no—
564C23×C4—434no—
565C23×C4—434no—
566C23×C4—434no—
567C23×C4C22×D4311yescharacteristic
568C23×C4C22×D4312yes—
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571C4⋊Q8—4316no—
572C4⋊Q8—438no—
573C4⋊Q8—438no—
574C4⋊Q8—438no—
575C4⋊Q8—4316no—
576#127—4316no—
577#127—438no—
578#126—4332no—
579#126C22×D43116yes—
580#125—4332no—
581#125—4316no—
582#125—4316no—
583#125C22×D4318yes—
584#124—4316no—
585#124—4332no—
586#124—4332no—
587#124—4316no—
588#124—4316no—
589#124C22×D4318yes—
590#123—4332no—
591#123—4332no—
592#123—4332no—
593#123—4332no—
594#123—4332no—
595#123—4332no—
596#123C22×D43116yes—
597C22⋊Q8—438no—
598C22⋊Q8—438no—
599C22⋊Q8—4316no—
600C22⋊Q8—4316no—
601C22⋊Q8—4332no—
602C22⋊Q8—4332no—
603C22⋊Q8—4332no—
604C22⋊Q8—4332no—
605C22⋊Q8—4332no—
606C22⋊Q8C22×D4318yes—
607#121—4332no—
608#121—4332no—
609#121—4316no—
610#121—4316no—
611#121—4316no—
612#121—4332no—
613#121C22×D4318yes—
614C4×Q8—4316no—
615C4×Q8—438no—
616C4×Q8—438no—
617C4×Q8—4316no—
618C4×Q8—4316no—
619C4×Q8C22×D4318yes—
620C4×D4—4316no—
621C4×D4—4316no—
622C4×D4—4316no—
623C4×D4—4332no—
624C4×D4—4316no—
625C4×D4—4316no—
626C4×D4—4316no—
627C4×D4C22×D43116yes—
628C4×D4C22×D4318yes—
629#117—4316no—
630#117C22×D43116yes—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—434no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—432no—
636C2×C4⋊C4—432no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—431no—
639C2×C4⋊C4—432no—
640C2×C4⋊C4—431no—
641C2×C4⋊C4—432no—
642C2×C4⋊C4—434no—
643C2×C4⋊C4—432no—
644C2×C4⋊C4—432no—
645C2×C4⋊C4—434no—
646C2×C4⋊C4—4332no—
647C2×C4⋊C4C22×D4312yes—
648C2×C4⋊C4C22×D4312yes—
649C2×C4⋊C4C22×D4312yes—
650C2×C4⋊C4C22×D4311yescharacteristic
651C2×C4⋊C4C22×D4311yescharacteristic
652C2×C4⋊C4C22×D4312yes—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4—434no—
658C2×C22⋊C4—434no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4C22×D4312yes—
663C2×C22⋊C4C22×D4312yes—
664C2×C22⋊C4C22×D4312yes—
665C2×C22⋊C4C22×D4312yes—
666C2×C22⋊C4C22×D4312yes—
667C2×C42—432no—
668C2×C42—432no—
669C2×C42—434no—
670C2×C42C22×D4311yescharacteristic
671C2×C42C22×D4312yes—
672C2×C42C22×D4311yescharacteristic
673C2×C42C22×D4311yescharacteristic
674C2×C42C22×D4311yescharacteristic
675C2×C42C22×D4318yes—
676C24—434no—
677C24C23×D4311yescharacteristic
678C24C23×D4312yes—
679#41—17232no—
680#41—17232no—
681C2×Q8—24no—
682C2×Q8—434no—
683C2×Q8—438no—
684C2×Q8—434no—
685C2×Q8—438no—
686C2×Q8—4316no—
687C2×Q8—864no—
688C2×Q8—868no—
689C2×Q8—864no—
690C2×Q8—1728no—
691C2×Q8—1724no—
692C2×Q8—17232no—
693C2×Q8C23×D4314yes—
694C2×D4—24no—
695C2×D4—44no—
696C2×D4—4316no—
697C2×D4—4316no—
698C2×D4—4316no—
699C2×D4—438no—
700C2×D4—438no—
701C2×D4—438no—
702C2×D4—868no—
703C2×D4—868no—
704C2×D4—1724no—
705C2×D4—1728no—
706C2×D4—1728no—
707C2×D4—1728no—
708C2×D4C23×D4314yes—
709C2×D4C23×D4318yes—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—42no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—432no—
717C22×C4—434no—
718C22×C4—432no—
719C22×C4—4316no—
720C22×C4—4316no—
721C22×C4—4316no—
722C22×C4—4316no—
723C22×C4—1728no—
724C22×C4—1728no—
725C22×C4—1728no—
726C22×C4—1728no—
727C22×C4C23×D4314yes—
728C22×C4C23×D4314yes—
729C22×C4C23×D4318yes—
730C22×C4C23×D4312yes—
731C22×C4C23×D4311yescharacteristic
732C22×C4C23×D4311yescharacteristic
733C22×C4C23×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735C22×C4C23×D4312yes—
736C22×C4C23×D4312yes—
737C22×C4C23×D4314yes—
738C22×C4C23×D4311yescharacteristic
739C22×C4C23×D4311yescharacteristic
740C4⋊C4—438no—
741C4⋊C4—4316no—
742C4⋊C4—4316no—
743C4⋊C4—438no—
744C4⋊C4—438no—
745C4⋊C4—438no—
746C4⋊C4—438no—
747C4⋊C4—434no—
748C4⋊C4—438no—
749C4⋊C4—434no—
750C4⋊C4—438no—
751C4⋊C4—4316no—
752C4⋊C4—438no—
753C4⋊C4—438no—
754C4⋊C4—4316no—
755C4⋊C4C23×D4318yes—
756C4⋊C4C23×D4318yes—
757C4⋊C4C23×D4318yes—
758C4⋊C4C23×D4314yes—
759C4⋊C4C23×D4314yes—
760C4⋊C4C23×D4318yes—
761C22⋊C4—438no—
762C22⋊C4—438no—
763C22⋊C4—4316no—
764C22⋊C4—4316no—
765C22⋊C4—4316no—
766C22⋊C4—4316no—
767C22⋊C4—4316no—
768C22⋊C4—4316no—
769C22⋊C4—4316no—
770C22⋊C4C23×D4318yes—
771C22⋊C4C23×D4318yes—
772C22⋊C4C23×D4318yes—
773C22⋊C4C23×D4318yes—
774C22⋊C4C23×D4318yes—
775C42—438no—
776C42—438no—
777C42—4316no—
778C42C23×D4314yes—
779C42C23×D4314yes—
780C42C23×D4314yes—
781C42C23×D4314yes—
782C42C23×D4318yes—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—24no—
789C23—438no—
790C23—868no—
791C23—868no—
792C23—868no—
793C23C24×D4312yes—
794C23C24×D4314yes—
795C23C24×D4311yescharacteristic
796Q8—28no—
797Q8—868no—
798Q8—8616no—
799Q8—868no—
800Q8—17216no—
801Q8—1728no—
802D4—28no—
803D4—48no—
804D4—8616no—
805D4—8616no—
806D4—1728no—
807D4—17216no—
808D4—17216no—
809D4—17216no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—216no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—434no—
822C2×C4—434no—
823C2×C4—434no—
824C2×C4—438no—
825C2×C4—434no—
826C2×C4—864no—
827C2×C4—868no—
828C2×C4—864no—
829C2×C4—864no—
830C2×C4—864no—
831C2×C4—17216no—
832C2×C4—17216no—
833C2×C4—17216no—
834C2×C4—17216no—
835C2×C4#1306337114yes—
836C2×C4#1306337214yes—
837C2×C4C24×D4314yes—
838C2×C4C24×D4312yes—
839C2×C4C24×D4312yes—
840C2×C4C24×D4312yes—
841C2×C4C24×D4312yes—
842C2×C4C24×D4314yes—
843C2×C4C24×D4314yes—
844C2×C4C24×D4312yes—
845C2×C4C24×D4312yes—
846C22—24no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—24no—
852C22—48no—
853C22—44no—
854C22—868no—
855C22—868no—
856C22—868no—
857C22—17216no—
858C22C2×#1306337112yes—
859C22C2×#1306337212yes—
860C22#1458373512yes—
861C22C25×D4311yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—864no—
870C4—868no—
871C4—864no—
872C4—864no—
873C4—864no—
874C4C2×#1306337114yes—
875C4C2×#1306337214yes—
876C2—44no—
877C2—42no—
878C2—1728no—
879C2#1914906814yesdirect product factor
880C2C22×#1306337111yescharacteristic
881C2C22×#1306337211yescharacteristic
882C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#529C2
socleC23×C43C25
hypercenterC2×#529D43
hypocenterC43C2×#3554
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #19149068C2direct (N × H)
2. C2×#14583646C2semidirect
3. C2×#14583634C2semidirect
4. C2×#14583631C2semidirect
5. C2×#14583628C2semidirect
6. C2×#14583605C2semidirect
7. C2×#14583570C2semidirect
8. C2×D4×Dic86C2semidirect
9. C2×#14583558C2semidirect
10. C2×#14583554C2semidirect
11. C2×#14583522C2semidirect
12. C2×#14583520C2semidirect
13. C2×#14583502C2semidirect
14. C2×#14583490C2semidirect
15. C2×#14583475C2semidirect
16. C2×#14583456C2semidirect
17. C2×#14583449C2semidirect
18. C2×C43×#529C2semidirect
22. #14583646C22semidirect
23. #14583634C22semidirect
24. #14583631C22semidirect
25. #14583628C22semidirect
26. #14583605C22semidirect
27. #14583570C22semidirect
28. D4×Dic86C22semidirect
29. #14583558C22semidirect
30. #14583554C22semidirect
31. #14583522C22semidirect
32. #14583520C22semidirect
33. #14583502C22semidirect
34. #14583490C22semidirect
35. #14583475C22semidirect
36. #14583456C22semidirect
37. #14583449C22semidirect
89. C43×#529C22semidirect
452. C2×#529D43semidirect
455. C2×C43#3554semidirect
486. #529C2×D43semidirect
542. C43C2×#3554semidirect
879. C2#19149068direct (N × H)

Maximal subgroups

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

subgroupindex
#191490682
C2×#145836462
C2×#145836342
C2×#145836312
C2×#145836282
C2×#145836052
C2×#145835702
C2×D4×Dic862
C2×#145835582
C2×#145835542
C2×#145835222
C2×#145835202
C2×#145835022
C2×#145834902
C2×#145834752
C2×#145834562
C2×#145834492
C2×C43×#5292
C2×#355443