Finite Group Databasebeta

← C2×#19148464 #26004950

Subgroups — C2×#19148464 #26004950

Order 11008.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C2132yesmaximal, direct product factor
2C2×#14583632C212yesmaximal, complemented
3C2×#14583631C212yesmaximal, complemented
4C2×#14583568C212yesmaximal, complemented
5C2×#14583567C212yesmaximal, complemented
6C2×#14583546C212yesmaximal, complemented
7C2×#14583544C212yesmaximal, complemented
8C2×#14583542C212yesmaximal, complemented
9C2×#14583537C212yesmaximal, complemented
10C2×#14583502C212yesmaximal, complemented
11C2×#14583500C212yesmaximal, complemented
12C2×#14583465C212yesmaximal, complemented
13C2×#14583454C211yesmaximal, characteristic, complemented
14C2×#14583450C211yesmaximal, characteristic, complemented
15C2×#14583449C211yesmaximal, characteristic, complemented
16C2×#14583447C211yesmaximal, characteristic, complemented
17C2×#127×D43C211yesmaximal, characteristic, complemented
18C2×#14583371C212yesmaximal, complemented
19C2×C4×#10621898C211yesmaximal, characteristic, complemented
20C2×C43×#532C211yesmaximal, characteristic, complemented
21C22×#10621902C2212yescomplemented
22C22×#10621898C2211yescharacteristic
23C22×#10621898C2212yescomplemented
24C22×#10621900C2212yescomplemented
25C22×D4×D43C2212yes—
26C22×D4×D43C2212yes—
27C22×D4×D43C2212yes—
28#14583632C22132yescomplemented
29#14583631C22132yescomplemented
30#14583568C22132yescomplemented
31#14583567C22132yescomplemented
32#14583546C22132yescomplemented
33#14583544C22132yescomplemented
34#14583542C22132yescomplemented
35#14583537C22132yescomplemented
36#14583502C22132yescomplemented
37#14583500C22132yescomplemented
38#14583465C22132yescomplemented
39#14583454C22116yescomplemented
40#14583450C22116yescomplemented
41#14583449C22116yescomplemented
42#14583447C22116yescomplemented
43C2×#13063325C2211yescharacteristic, complemented
44C2×#13063322C2211yescharacteristic
45C2×#13063321C2212yes—
46C2×#13063321C2212yes—
47C2×#13063321C2212yes—
48C2×#13063321C2214yescomplemented
49#127×D43C22116yescomplemented
50C2×#13063316C2212yescomplemented
51C2×#13063314C2212yescomplemented
52C2×#13063313C2212yescomplemented
53C2×#13063312C2212yescomplemented
54C2×#13063311C2214yescomplemented
55C2×#13063309C2214yescomplemented
56C2×#13063308C2214yescomplemented
57C2×#13063307C2214yescomplemented
58C2×#13063307C2214yescomplemented
59C2×#13063305C2212yes—
60C2×#13063301C2212yes—
61C2×#13063300C2212yescomplemented
62C2×#13063300C2212yescomplemented
63C2×#13063299C2212yescomplemented
64C2×#13063299C2214yescomplemented
65C2×#13063299C2212yescomplemented
66C2×#13063298C2214yescomplemented
67C2×#13063297C2214yescomplemented
68C2×#13063296C2212yescomplemented
69C2×#13063296C2214yescomplemented
70C2×#13063296C2212yescomplemented
71C2×#13063295C2214yes—
72C2×#13063293C2214yes—
73#14583371C22132yescomplemented
74C4×#10621898C22116yescomplemented
75C2×Q8×Dic43C2212yescomplemented
76C2×C4×Dic86C2211yescharacteristic, complemented
77C2×C4×Dic86C2211yescharacteristic, complemented
78C2×#13063290C2212yescomplemented
79C2×C4×D172C2211yescharacteristic
80C2×C4×D172C2211yescharacteristic
81C2×C4×D172C2212yescomplemented
82C2×C4×D172C2212yescomplemented
83C2×D4×Dic43C2212yescomplemented
84C2×D4×Dic43C2212yescomplemented
85C2×#13063287C2212yescomplemented
86C2×#13063287C2212yescomplemented
87C2×C4×C22⋊D43C2211yescharacteristic
88C2×C4×C22⋊D43C2211yescharacteristic
89C2×C4×C22⋊D43C2214yescomplemented
90C2×C4×C22⋊D43C2211yescharacteristic, complemented
91C2×C4×C22⋊D43C2211yescharacteristic, complemented
92C2×(C22⋊D43)⋊C4C2214yescomplemented
93C2×#13063284C2211yescharacteristic, complemented
94C2×#13063283C2212yes—
95C2×#13063282C2211yescharacteristic
96C2×#13063282C2211yescharacteristic, complemented
97C22×(C2×D43)⋊C4C2214yes—
98C2×C22⋊C4×D43C2214yes—
99C2×C42×D43C2211yescharacteristic
100C2×C42×D43C2211yescharacteristic, complemented
101C22×#41×C43C2212yescomplemented
102C43×#532C22116yescomplemented
103C2×C4⋊Q8×C43C2211yescharacteristic, complemented
104C2×#127×C43C2211yescharacteristic
105C2×#124×C43C2212yescomplemented
106C2×#121×C43C2212yescomplemented
107C2×#121×C43C2212yescomplemented
108C2×C4×D4×C43C2212yescomplemented
109C2×C4×D4×C43C2212yescomplemented
110C22×C42×C43C2211yescharacteristic, complemented
111C24×D43C2314yes—
112C2×#10621902—48no—
113C2×#10621902C23116yescomplemented
114C2×#10621898—28no—
115C2×#10621898—48no—
116C2×#10621898C2318yes—
117C2×#10621898C23116yescomplemented
118C2×#10621900—48no—
119C2×#10621900C23116yescomplemented
120C22×Dic86C2312yes—
121C22×Dic86C2311yescharacteristic
122C22×D172C2312yes—
123C22×D172C2312yes—
124C22×D172C2311yescharacteristic
125C22×D172C2312yes—
126C22×D172C2314yes—
127C22×C22⋊D43C2314yes—
128C22×C22⋊D43C2311yescharacteristic
129C22×C22⋊D43C2311yescharacteristic
130C22×C22⋊D43C2314yes—
131C22×C22⋊D43C2314yes—
132C22×C22⋊D43C2314yes—
133C22×C22⋊D43C2314yes—
134C2×D4×D43—216no—
135C2×D4×D43—48no—
136C2×D4×D43—48no—
137C2×D4×D43C23116yes—
138C2×D4×D43C23116yes—
139C2×D4×D43C23116yes—
140C23×Dic43C2314yes—
141C22×C4×D43C2311yescharacteristic
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2314yes—
147C22×C4×D43C2314yes—
148C22×C4×D43C2311yescharacteristic
149#13063325C2318yescomplemented
150#13063322C2318yes—
151#13063321C23116yes—
152#13063321C23116yes—
153#13063321C23116yes—
154#13063321C23132yescomplemented
155#13063316C23116yescomplemented
156#13063314C23116yescomplemented
157#13063313C23116yescomplemented
158#13063312C23116yescomplemented
159#13063311C23132yescomplemented
160#13063309C23132yescomplemented
161#13063308C23132yescomplemented
162#13063307C23132yescomplemented
163#13063307C23132yescomplemented
164#13063305C23116yes—
165#13063301C23116yes—
166#13063300C23116yescomplemented
167#13063300C23116yescomplemented
168#13063299C23116yescomplemented
169#13063299C23132yescomplemented
170#13063299C23116yescomplemented
171#13063298C23132yescomplemented
172#13063297C23132yescomplemented
173#13063296C23116yescomplemented
174#13063296C23132yescomplemented
175#13063296C23116yescomplemented
176#13063295C23132yes—
177#13063293C23132yes—
178Q8×Dic43C23116yescomplemented
179C4×Dic86C2318yescomplemented
180C4×Dic86C2318yescomplemented
181#13063290C23116yescomplemented
182C4×D172C2318yes—
183C4×D172C2318yes—
184C4×D172C23116yescomplemented
185C4×D172C23116yescomplemented
186D4×Dic43C23116yescomplemented
187D4×Dic43C23116yescomplemented
188#13063287C23116yescomplemented
189#13063287C23116yescomplemented
190C4×C22⋊D43C2318yes—
191C4×C22⋊D43C2318yes—
192C4×C22⋊D43C2318yescomplemented
193C4×C22⋊D43C2318yescomplemented
194C4×C22⋊D43C23132yescomplemented
195(C22⋊D43)⋊C4C23132yescomplemented
196#13063284C2318yescomplemented
197#13063283C23116yes—
198#13063282C2318yes—
199#13063282C2318yescomplemented
200C2×C4⋊Dic43C2312yes—
201C2×C4⋊Dic43C2311yescharacteristic
202C2×C4⋊Dic43C2311yescharacteristic
203C2×C4⋊Dic43C2312yes—
204C2×C4⋊Dic43C2314yes—
205C2×Dic43⋊C4C2311yescharacteristic
206C2×Dic43⋊C4C2311yescharacteristic
207C2×Dic43⋊C4C2311yescharacteristic
208C2×Dic43⋊C4C2311yescharacteristic
209C2×Dic43⋊C4C2314yes—
210C2×C22⋊Dic43C2314yes—
211C2×C22⋊Dic43C2311yescharacteristic
212C2×C22⋊Dic43C2311yescharacteristic
213C2×C22⋊Dic43C2314yes—
214C2×(C2×D43)⋊C4C2311yescharacteristic
215C2×(C2×D43)⋊C4C2314yes—
216C2×(C2×D43)⋊C4C2311yescharacteristic
217C2×(C2×D43)⋊C4C2314yes—
218C2×(C2×D43)⋊C4C2314yes—
219C2×(C2×D43)⋊C4C23132yes—
220C2×(C2×D43)⋊C4C2311yescharacteristic
221C2×(C2×D43)⋊C4C2311yescharacteristic
222C2×(C2×D43)⋊C4C2314yes—
223C2×(C2×D43)⋊C4C2314yes—
224C22⋊C4×D43C23132yes—
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C2×C4×Dic43C2311yescharacteristic
229C2×C4×Dic43C2311yescharacteristic
230C2×C4×Dic43C2311yescharacteristic
231C2×C4×Dic43C2314yes—
232C42×D43C2318yes—
233C42×D43C2318yescomplemented
234C2×#41×C43—48no—
235C2×#41×C43C23116yescomplemented
236C22×Q8×C43C2312yes—
237C22×D4×C43C2312yes—
238C22×D4×C43C2312yes—
239C22×D4×C43C2312yes—
240C22×D4×C43C2314yes—
241C23×C4×C43C2311yescharacteristic
242C23×C4×C43C2311yescharacteristic
243C23×C4×C43C2311yescharacteristic
244C23×C4×C43C2314yes—
245C4⋊Q8×C43C2318yescomplemented
246#127×C43C2318yes—
247#124×C43C23116yescomplemented
248#121×C43C23116yescomplemented
249#121×C43C23116yescomplemented
250C4×D4×C43C23116yescomplemented
251C4×D4×C43C23116yescomplemented
252C2×C4⋊C4×C43C2312yes—
253C2×C4⋊C4×C43C2312yes—
254C2×C22⋊C4×C43C2314yes—
255C2×C22⋊C4×C43C2314yes—
256C2×C42×C43C2311yescharacteristic
257C2×C42×C43C2311yescharacteristic
258C2×C42×C43C2311yescharacteristic
259C2×C42×C43C2311yescharacteristic
260C2×C42×C43C2318yescomplemented
261C24×C43C2414yes—
262C24×C43C2411yescharacteristic
263C23×D43—216no—
264C23×D43—48no—
265C23×D43—48no—
266C23×D43C2414yes—
267C23×D43C2411yescharacteristic
268C23×D43C2411yescharacteristic
269C23×D43C24116yes—
270#41×C43—432no—
271C2×Q8×C43—28no—
272C2×Q8×C43C2418yes—
273C2×D4×C43—28no—
274C2×D4×C43—28no—
275C2×D4×C43—28no—
276C2×D4×C43—48no—
277C2×D4×C43C2418yes—
278C2×D4×C43C2418yes—
279C2×D4×C43C2418yes—
280C2×D4×C43C24116yes—
281C22×C4×C43—24no—
282C22×C4×C43—24no—
283C22×C4×C43—24no—
284C22×C4×C43—48no—
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C22×C4×C43C2414yes—
289C22×C4×C43C2414yes—
290C22×C4×C43C2414yes—
291C22×C4×C43C2414yes—
292C22×C4×C43C24116yes—
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C2×C22⋊D43—216no—
297C2×C22⋊D43—24no—
298C2×C22⋊D43—24no—
299C2×C22⋊D43—48no—
300C2×C22⋊D43—48no—
301C2×C22⋊D43—48no—
302C2×C22⋊D43—48no—
303C2×C22⋊D43C24116yes—
304C2×C22⋊D43C2414yes—
305C2×C22⋊D43C2414yes—
306C2×C22⋊D43C24116yes—
307C2×C22⋊D43C24116yes—
308C2×C22⋊D43C24116yes—
309C2×C22⋊D43C24116yes—
310C22×Dic43—48no—
311C22×Dic43C2411yescharacteristic
312C22×Dic43C2411yescharacteristic
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316C22×Dic43C2414yes—
317C22×Dic43C24116yes—
318C22×Dic43C2411yescharacteristic
319#10621902—432no—
320#10621900—432no—
321D4×D43—264no—
322D4×D43—432no—
323D4×D43—432no—
324#10621898—232no—
325#10621898—432no—
326C2×D172—28no—
327C2×D172—28no—
328C2×D172—28no—
329C2×D172—24no—
330C2×D172—48no—
331C2×D172C2418yes—
332C2×D172C2418yes—
333C2×D172C2414yes—
334C2×D172C2418yes—
335C2×D172C24116yes—
336C2×C4×D43—24no—
337C2×C4×D43—24no—
338C2×C4×D43—24no—
339C2×C4×D43—24no—
340C2×C4×D43—24no—
341C2×C4×D43—48no—
342C2×C4×D43—48no—
343C2×C4×D43#4118yescomplemented
344C2×C4×D43C2414yes—
345C2×C4×D43C2414yes—
346C2×C4×D43C2414yes—
347C2×C4×D43C2414yes—
348C2×C4×D43C2414yes—
349C2×C4×D43C24116yes—
350C2×C4×D43C24116yes—
351C2×C4×D43C2414yes—
352C2×Dic86—28no—
353C2×Dic86—24no—
354C2×Dic86C2418yes—
355C2×Dic86C2414yes—
356C4⋊C4×C43C2418yes—
357C4⋊C4×C43C2418yes—
358C22⋊C4×C43C24116yes—
359C22⋊C4×C43C24116yes—
360C42×C43C2414yes—
361C42×C43C2414yes—
362C42×C43C2414yes—
363C42×C43C2414yes—
364C22⋊Dic43C24116yes—
365C22⋊Dic43C2414yes—
366C22⋊Dic43C2414yes—
367C22⋊Dic43C24116yes—
368(C2×D43)⋊C4C2414yes—
369(C2×D43)⋊C4C24116yes—
370(C2×D43)⋊C4C2414yes—
371(C2×D43)⋊C4C24116yes—
372(C2×D43)⋊C4C24116yes—
373(C2×D43)⋊C4C2414yes—
374(C2×D43)⋊C4C2414yes—
375(C2×D43)⋊C4C24116yes—
376(C2×D43)⋊C4C24116yes—
377C4⋊Dic43C2418yes—
378C4⋊Dic43C2414yes—
379C4⋊Dic43C2414yes—
380C4⋊Dic43C2418yes—
381C4⋊Dic43C24116yes—
382Dic43⋊C4C2414yes—
383Dic43⋊C4C2414yes—
384Dic43⋊C4C2414yes—
385Dic43⋊C4C2414yes—
386Dic43⋊C4C24116yes—
387C4×Dic43C2414yes—
388C4×Dic43C2414yes—
389C4×Dic43C2414yes—
390C4×Dic43C2414yes—
391C4×Dic43C2414yes—
392C4×Dic43C2414yes—
393C4×Dic43C24116yes—
394C23×C43—22no—
395C23×C43—28no—
396C23×C43—28no—
397C23×C43—22no—
398C23×C43—28no—
399C23×C43—22no—
400C23×C43C2518yes—
401C23×C43C2512yes—
402C23×C43C2511yescharacteristic
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—28no—
407C22×D43—22no—
408C22×D43—22no—
409C22×D43—28no—
410C22×D43—28no—
411C22×D43—232no—
412C22×D43—416no—
413C22×D43—416no—
414C22×D43—832no—
415C22×D43C2×#4114yes—
416C22×D43C2518yes—
417C22×D43C2512yes—
418C22×D43C2512yes—
419Q8×C43—216no—
420D4×C43—216no—
421D4×C43—216no—
422D4×C43—216no—
423D4×C43—416no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—28no—
427C2×C4×C43—22no—
428C2×C4×C43—28no—
429C2×C4×C43—28no—
430C2×C4×C43—28no—
431C2×C4×C43—416no—
432C2×C4×C43C2×#4114yes—
433C2×C4×C43H(5,𝔽2)14yes—
434C2×C4×C43H(5,𝔽2)14yes—
435C2×C4×C43C2518yes—
436C2×C4×C43C2512yes—
437C2×C4×C43C2512yes—
438C2×C4×C43C2512yes—
439C2×C4×C43C2512yes—
440C2×C4×C43C2512yes—
441C2×C4×C43C2512yes—
442C22⋊D43—28no—
443C22⋊D43—28no—
444C22⋊D43—232no—
445C22⋊D43—416no—
446C22⋊D43—416no—
447C22⋊D43—416no—
448C22⋊D43—416no—
449C2×Dic43—22no—
450C2×Dic43—28no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—416no—
456C2×Dic43C2×#4114yes—
457C2×Dic43C2512yes—
458C2×Dic43C2512yes—
459C2×Dic43C2512yes—
460C2×Dic43C2512yes—
461C2×Dic43C2512yes—
462C2×Dic43C2518yes—
463C2×Dic43C2512yes—
464D172—28no—
465D172—216no—
466D172—216no—
467D172—216no—
468D172—416no—
469C4×D43—28no—
470C4×D43—28no—
471C4×D43—28no—
472C4×D43—28no—
473C4×D43—28no—
474C4×D43—416no—
475C4×D43—416no—
476C4×D43C2×#41116yescomplemented
477Dic86—216no—
478Dic86—28no—
479C2×#3508—431nomaximal, Sylow
480C22×C43—28no—
481C22×C43—22no—
482C22×C43—28no—
483C22×C43—28no—
484C22×C43—22no—
485C22×C43—22no—
486C22×C43—416no—
487C22×C43—44no—
488C22×C43C22×#4112yes—
489C22×C43C2×H(5,𝔽2)12yes—
490C22×C43C2×H(5,𝔽2)12yes—
491C22×C43C2611yescharacteristic
492C2×D43—22no—
493C2×D43—22no—
494C2×D43—28no—
495C2×D43—28no—
496C2×D43—22no—
497C2×D43—28no—
498C2×D43—28no—
499C2×D43—22no—
500C2×D43—22no—
501C2×D43—44no—
502C2×D43—416no—
503C2×D43—832no—
504C2×D43C22×#4114yes—
505C4×C43—22no—
506C4×C43—22no—
507C4×C43—28no—
508C4×C43—22no—
509C4×C43C22×#4114yes—
510C4×C43C2×H(5,𝔽2)14yes—
511C4×C43C2×H(5,𝔽2)14yes—
512Dic43—22no—
513Dic43—28no—
514Dic43—22no—
515Dic43—22no—
516Dic43—22no—
517Dic43—22no—
518Dic43C22×#4114yes—
519#3508—4332no—
520C2×#559—432no—
521C2×#559—432no—
522C2×#550—432no—
523C2×#550—432no—
524C2×#546—432no—
525C2×#546—432no—
526C2×#546—432no—
527C2×#546—432no—
528C2×#540—432no—
529C2×#540—432no—
530C2×#535—432no—
531C2×#533—431no—
532C2×#532—431no—
533C2×#532—431no—
534C2×#532—431no—
535C2×#532D4311yescharacteristic, complemented
536C22×#127—431no—
537C2×#518—432no—
538C2×C4×#41—431no—
539C2×C43—48no—
540C2×C43—42no—
541C2×C43#350814yescomplemented
542C2×C43C23×#4111yescharacteristic
543C2×C43C22×H(5,𝔽2)11yescharacteristic
544C2×C43C22×H(5,𝔽2)11yescharacteristic
545D43—24no—
546D43—42no—
547D43—48no—
548C22×#41—432no—
549C22×#41—432no—
550C22×#41—431no—
551C22×#41—432no—
552C22×#41C2×D4312yescomplemented
553C23×D4—432no—
554C23×D4—432no—
555C23×D4—432no—
556#559—4332no—
557#559—4332no—
558#550—4332no—
559#550—4332no—
560#546—4332no—
561#546—4332no—
562#546—4332no—
563#546—4332no—
564#540—4332no—
565#540—4332no—
566#535—4332no—
567#533—4316no—
568#532—4316no—
569#532—4316no—
570#532—4316no—
571#532C2×D43116yescomplemented
572C2×C4⋊Q8—431no—
573C2×C4⋊Q8C2×D4311yescharacteristic, complemented
574C2×#127—432no—
575C2×#127—432no—
576C2×#127—432no—
577C2×#127—434no—
578C2×#127—4316no—
579C2×#127—431no—
580C2×#127C2×D4311yescharacteristic
581C2×#125—432no—
582C2×#124—432no—
583C2×#124—432no—
584C2×#124—434no—
585C2×#124—432no—
586C2×#124C2×D4312yescomplemented
587C2×#123—434no—
588C2×#123—434no—
589C2×#123—434no—
590C2×#123—434no—
591C2×C22⋊Q8—432no—
592C2×C22⋊Q8—432no—
593C2×#121—432no—
594C2×#121—432no—
595C2×#121—434no—
596C2×#121—434no—
597C2×#121—432no—
598C2×#121—432no—
599C2×#121—434no—
600C2×#121—432no—
601C2×#121—432no—
602C2×#121—434no—
603C2×#121C2×D4312yescomplemented
604C2×#121C2×D4312yescomplemented
605C2×#120—434no—
606C2×#120—434no—
607#518—4332no—
608C4×#41—4316no—
609C2×C4×Q8—432no—
610C2×C4×Q8—432no—
611C2×C4×Q8—431no—
612C2×C4×Q8—431no—
613C2×C4×D4—432no—
614C2×C4×D4—432no—
615C2×C4×D4—431no—
616C2×C4×D4—431no—
617C2×C4×D4—431no—
618C2×C4×D4—431no—
619C2×C4×D4—434no—
620C2×C4×D4—432no—
621C2×C4×D4—432no—
622C2×C4×D4—434no—
623C2×C4×D4—431no—
624C2×C4×D4—431no—
625C2×C4×D4—432no—
626C2×C4×D4—432no—
627C2×C4×D4C2×D4312yescomplemented
628C2×C4×D4C2×D4312yescomplemented
629C2×#117—431no—
630C2×#117—432no—
631C2×#117—431no—
632C2×#117—431no—
633C22×C22⋊C4—434no—
634C22×C22⋊C4—434no—
635C22×C42—431no—
636C22×C42—431no—
637C22×C42C2×D4311yescharacteristic, complemented
638C43C2×#350811yescharacteristic, complemented, Sylow
639C25—434no—
640C2×#41—48no—
641C2×#41—4316no—
642C2×#41—4316no—
643C2×#41—438no—
644C2×#41—4316no—
645C2×#41—868no—
646C2×#41—1728no—
647C2×#41—1728no—
648C2×#41—1728no—
649C2×#41C22×D43116yescomplemented
650C22×Q8—431no—
651C22×Q8—432no—
652C22×Q8C22×D4312yes—
653C22×D4—431no—
654C22×D4—434no—
655C22×D4—431no—
656C22×D4—434no—
657C22×D4—434no—
658C22×D4—434no—
659C22×D4—434no—
660C22×D4—4316no—
661C22×D4—4316no—
662C22×D4—4316no—
663C22×D4—431no—
664C22×D4—432no—
665C22×D4—432no—
666C22×D4—432no—
667C22×D4—434no—
668C22×D4—8616no—
669C22×D4—1728no—
670C22×D4—1728no—
671C22×D4C22×D4312yes—
672C22×D4C22×D4312yes—
673C22×D4C22×D4312yes—
674C22×D4C22×D4314yes—
675C23×C4—431no—
676C23×C4—434no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—431no—
680C23×C4—431no—
681C23×C4—431no—
682C23×C4—434no—
683C23×C4—434no—
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687C23×C4C22×D4314yes—
688C4⋊Q8—438no—
689C4⋊Q8C22×D4318yescomplemented
690#127—4316no—
691#127—4316no—
692#127—4316no—
693#127—4332no—
694#127—438no—
695#127C22×D4318yes—
696#125—4316no—
697#124—4316no—
698#124—4316no—
699#124—4332no—
700#124—4316no—
701#124C22×D43116yescomplemented
702#123—4332no—
703#123—4332no—
704#123—4332no—
705#123—4332no—
706C22⋊Q8—4316no—
707C22⋊Q8—4316no—
708#121—4316no—
709#121—4316no—
710#121—4332no—
711#121—4332no—
712#121—4316no—
713#121—4316no—
714#121—4332no—
715#121—4316no—
716#121—4316no—
717#121—4332no—
718#121C22×D43116yescomplemented
719#121C22×D43116yescomplemented
720#120—4332no—
721#120—4332no—
722C4×Q8—4316no—
723C4×Q8—4316no—
724C4×Q8—438no—
725C4×Q8—438no—
726C4×D4—4316no—
727C4×D4—4316no—
728C4×D4—438no—
729C4×D4—438no—
730C4×D4—438no—
731C4×D4—438no—
732C4×D4—4332no—
733C4×D4—4316no—
734C4×D4—4316no—
735C4×D4—4332no—
736C4×D4—438no—
737C4×D4—438no—
738C4×D4—4316no—
739C4×D4—4316no—
740C4×D4C22×D43116yescomplemented
741C4×D4C22×D43116yescomplemented
742#117—438no—
743#117—4316no—
744#117—438no—
745#117—438no—
746C2×C4⋊C4—431no—
747C2×C4⋊C4—431no—
748C2×C4⋊C4—432no—
749C2×C4⋊C4—431no—
750C2×C4⋊C4—431no—
751C2×C4⋊C4—431no—
752C2×C4⋊C4—431no—
753C2×C4⋊C4—432no—
754C2×C4⋊C4—434no—
755C2×C4⋊C4—434no—
756C2×C4⋊C4C22×D4312yes—
757C2×C4⋊C4C22×D4312yes—
758C2×C22⋊C4—434no—
759C2×C22⋊C4—431no—
760C2×C22⋊C4—431no—
761C2×C22⋊C4—434no—
762C2×C22⋊C4—431no—
763C2×C22⋊C4—431no—
764C2×C22⋊C4—434no—
765C2×C22⋊C4—434no—
766C2×C22⋊C4—434no—
767C2×C22⋊C4—4332no—
768C2×C22⋊C4—431no—
769C2×C22⋊C4—431no—
770C2×C22⋊C4—434no—
771C2×C22⋊C4—434no—
772C2×C22⋊C4—4332no—
773C2×C22⋊C4C22×D4314yes—
774C2×C22⋊C4C22×D4314yes—
775C2×C42—431no—
776C2×C42—431no—
777C2×C42—434no—
778C2×C42—431no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42—431no—
782C2×C42—438no—
783C2×C42—438no—
784C2×C42C22×D4311yescharacteristic
785C2×C42C22×D4311yescharacteristic
786C2×C42C22×D4311yescharacteristic
787C2×C42C22×D4311yescharacteristic
788C2×C42C22×D4318yescomplemented
789C24—431no—
790C24—434no—
791C24—431no—
792C24—4316no—
793C24—8616no—
794C24—1728no—
795C24—1728no—
796C24C23×D4314yes—
797C24C23×D4311yescharacteristic
798#41—432no—
799#41—8632no—
800#41—17232no—
801#41—17232no—
802#41—17232no—
803C2×Q8—28no—
804C2×Q8—434no—
805C2×Q8—438no—
806C2×Q8—864no—
807C2×Q8—868no—
808C2×Q8C23×D4318yes—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—48no—
813C2×D4—434no—
814C2×D4—4316no—
815C2×D4—434no—
816C2×D4—4316no—
817C2×D4—4316no—
818C2×D4—4316no—
819C2×D4—4316no—
820C2×D4—434no—
821C2×D4—438no—
822C2×D4—438no—
823C2×D4—438no—
824C2×D4—4316no—
825C2×D4—864no—
826C2×D4—8664no—
827C2×D4—8616no—
828C2×D4—864no—
829C2×D4—864no—
830C2×D4—868no—
831C2×D4—868no—
832C2×D4—868no—
833C2×D4—1728no—
834C2×D4—17232no—
835C2×D4—17232no—
836C2×D4—1728no—
837C2×D4—1728no—
838C2×D4—1728no—
839C2×D4—1728no—
840C2×D4C23×D4318yes—
841C2×D4C23×D4318yes—
842C2×D4C23×D4318yes—
843C2×D4C23×D43116yes—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—48no—
848C22×C4—431no—
849C22×C4—438no—
850C22×C4—434no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—434no—
857C22×C4—4316no—
858C22×C4—434no—
859C22×C4—434no—
860C22×C4—434no—
861C22×C4—434no—
862C22×C4—434no—
863C22×C4—4316no—
864C22×C4—4316no—
865C22×C4—864no—
866C22×C4—864no—
867C22×C4—864no—
868C22×C4—864no—
869C22×C4—864no—
870C22×C4—1728no—
871C22×C4—1728no—
872C22×C4—1728no—
873C22×C4C23×D4314yes—
874C22×C4C23×D4314yes—
875C22×C4C23×D4314yes—
876C22×C4C23×D4314yes—
877C22×C4C23×D4311yescharacteristic
878C22×C4C23×D4311yescharacteristic
879C22×C4C23×D4311yescharacteristic
880C22×C4C23×D43116yes—
881C22×C4C23×D4311yescharacteristic
882C22×C4C23×D4311yescharacteristic
883C22×C4C23×D4311yescharacteristic
884C4⋊C4—434no—
885C4⋊C4—434no—
886C4⋊C4—438no—
887C4⋊C4—434no—
888C4⋊C4—434no—
889C4⋊C4—434no—
890C4⋊C4—434no—
891C4⋊C4—438no—
892C4⋊C4—4316no—
893C4⋊C4—4316no—
894C4⋊C4C23×D4318yes—
895C4⋊C4C23×D4318yes—
896C22⋊C4—4316no—
897C22⋊C4—434no—
898C22⋊C4—434no—
899C22⋊C4—4316no—
900C22⋊C4—434no—
901C22⋊C4—434no—
902C22⋊C4—4316no—
903C22⋊C4—4316no—
904C22⋊C4—4316no—
905C22⋊C4—434no—
906C22⋊C4—434no—
907C22⋊C4—4316no—
908C22⋊C4—4316no—
909C22⋊C4C23×D43116yes—
910C22⋊C4C23×D43116yes—
911C42—434no—
912C42—434no—
913C42—434no—
914C42—434no—
915C42—434no—
916C42—434no—
917C42—4316no—
918C42C23×D4314yes—
919C42C23×D4314yes—
920C42C23×D4314yes—
921C42C23×D4314yes—
922C23—22no—
923C23—28no—
924C23—22no—
925C23—28no—
926C23—22no—
927C23—28no—
928C23—434no—
929C23—432no—
930C23—438no—
931C23—432no—
932C23—8632no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—868no—
937C23—862no—
938C23—868no—
939C23—862no—
940C23—868no—
941C23—34432no—
942C23—17216no—
943C23—17216no—
944C23C24×D4318yes—
945C23C24×D4312yes—
946C23C24×D4311yescharacteristic
947Q8—216no—
948Q8—868no—
949Q8—8616no—
950D4—216no—
951D4—216no—
952D4—216no—
953D4—416no—
954D4—868no—
955D4—8632no—
956D4—868no—
957D4—868no—
958D4—8616no—
959D4—8616no—
960D4—8616no—
961D4—17216no—
962D4—17216no—
963D4—17216no—
964D4—17216no—
965D4—17216no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—416no—
974C2×C4—434no—
975C2×C4—432no—
976C2×C4—4316no—
977C2×C4—432no—
978C2×C4—432no—
979C2×C4—432no—
980C2×C4—432no—
981C2×C4—432no—
982C2×C4—438no—
983C2×C4—862no—
984C2×C4—862no—
985C2×C4—862no—
986C2×C4—862no—
987C2×C4—862no—
988C2×C4—868no—
989C2×C4—868no—
990C2×C4—868no—
991C2×C4—868no—
992C2×C4—868no—
993C2×C4—868no—
994C2×C4—17216no—
995C2×C4—17216no—
996C2×C4—17216no—
997C2×C4#41×D4314yes—
998C2×C4#1306337014yes—
999C2×C4#1306337114yes—
1000C2×C4C24×D4318yes—
1001C2×C4C24×D4312yes—
1002C2×C4C24×D4312yes—
1003C2×C4C24×D4312yes—
1004C2×C4C24×D4312yes—
1005C2×C4C24×D4312yes—
1006C2×C4C24×D4312yes—
1007C22—22no—
1008C22—28no—
1009C22—22no—
1010C22—28no—
1011C22—22no—
1012C22—28no—
1013C22—416no—
1014C22—44no—
1015C22—434no—
1016C22—862no—
1017C22—862no—
1018C22—868no—
1019C22—862no—
1020C22—868no—
1021C22—862no—
1022C22—868no—
1023C22—862no—
1024C22—868no—
1025C22—34432no—
1026C22—17216no—
1027C22—1724no—
1028C22C2×#41×D4312yes—
1029C22C2×#1306337012yes—
1030C22C2×#1306337112yes—
1031C22C25×D4311yescharacteristic
1032C4—22no—
1033C4—22no—
1034C4—28no—
1035C4—22no—
1036C4—434no—
1037C4—862no—
1038C4—862no—
1039C4—862no—
1040C4—862no—
1041C4—862no—
1042C4—868no—
1043C4C2×#41×D4314yes—
1044C4C2×#1306337014yes—
1045C4C2×#1306337114yes—
1046C2—48no—
1047C2—42no—
1048C2—864no—
1049C2—1728no—
1050C2—1722no—
1051C2#1914846414yesdirect product factor
1052C2C22×#41×D4311yescharacteristic
1053C2C22×#1306337011yescharacteristic
1054C2C22×#1306337111yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#532C2
socleC23×C43C25
hypercenterC2×#532D43
hypocenterC43C2×#3508
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #19148464C2direct (N × H)
2. C2×#14583632C2semidirect
3. C2×#14583631C2semidirect
4. C2×#14583568C2semidirect
5. C2×#14583567C2semidirect
6. C2×#14583546C2semidirect
7. C2×#14583544C2semidirect
8. C2×#14583542C2semidirect
9. C2×#14583537C2semidirect
10. C2×#14583502C2semidirect
11. C2×#14583500C2semidirect
12. C2×#14583465C2semidirect
13. C2×#14583454C2semidirect
14. C2×#14583450C2semidirect
15. C2×#14583449C2semidirect
16. C2×#14583447C2semidirect
17. C2×#127×D43C2semidirect
18. C2×#14583371C2semidirect
19. C2×C4×#10621898C2semidirect
20. C2×C43×#532C2semidirect
21. C22×#10621902C22semidirect
23. C22×#10621898C22semidirect
24. C22×#10621900C22semidirect
28. #14583632C22semidirect
29. #14583631C22semidirect
30. #14583568C22semidirect
31. #14583567C22semidirect
32. #14583546C22semidirect
33. #14583544C22semidirect
34. #14583542C22semidirect
35. #14583537C22semidirect
36. #14583502C22semidirect
37. #14583500C22semidirect
38. #14583465C22semidirect
39. #14583454C22semidirect
40. #14583450C22semidirect
41. #14583449C22semidirect
42. #14583447C22semidirect
43. C2×#13063325C22semidirect
48. C2×#13063321C22semidirect
49. #127×D43C22semidirect
50. C2×#13063316C22semidirect
51. C2×#13063314C22semidirect
52. C2×#13063313C22semidirect
53. C2×#13063312C22semidirect
54. C2×#13063311C22semidirect
55. C2×#13063309C22semidirect
56. C2×#13063308C22semidirect
57. C2×#13063307C22semidirect
58. C2×#13063307C22semidirect
61. C2×#13063300C22semidirect
62. C2×#13063300C22semidirect
63. C2×#13063299C22semidirect
64. C2×#13063299C22semidirect
65. C2×#13063299C22semidirect
66. C2×#13063298C22semidirect
67. C2×#13063297C22semidirect
68. C2×#13063296C22semidirect
69. C2×#13063296C22semidirect
70. C2×#13063296C22semidirect
73. #14583371C22semidirect
74. C4×#10621898C22semidirect
75. C2×Q8×Dic43C22semidirect
76. C2×C4×Dic86C22semidirect
77. C2×C4×Dic86C22semidirect
78. C2×#13063290C22semidirect
81. C2×C4×D172C22semidirect
82. C2×C4×D172C22semidirect
83. C2×D4×Dic43C22semidirect
84. C2×D4×Dic43C22semidirect
85. C2×#13063287C22semidirect
86. C2×#13063287C22semidirect
89. C2×C4×C22⋊D43C22semidirect
90. C2×C4×C22⋊D43C22semidirect
91. C2×C4×C22⋊D43C22semidirect
92. C2×(C22⋊D43)⋊C4C22semidirect
93. C2×#13063284C22semidirect
96. C2×#13063282C22semidirect
100. C2×C42×D43C22semidirect
101. C22×#41×C43C22semidirect
102. C43×#532C22semidirect
103. C2×C4⋊Q8×C43C22semidirect
105. C2×#124×C43C22semidirect
106. C2×#121×C43C22semidirect
107. C2×#121×C43C22semidirect
108. C2×C4×D4×C43C22semidirect
109. C2×C4×D4×C43C22semidirect
110. C22×C42×C43C22semidirect
113. C2×#10621902C23semidirect
117. C2×#10621898C23semidirect
119. C2×#10621900C23semidirect
149. #13063325C23semidirect
154. #13063321C23semidirect
155. #13063316C23semidirect
156. #13063314C23semidirect
157. #13063313C23semidirect
158. #13063312C23semidirect
159. #13063311C23semidirect
160. #13063309C23semidirect
161. #13063308C23semidirect
162. #13063307C23semidirect
163. #13063307C23semidirect
166. #13063300C23semidirect
167. #13063300C23semidirect
168. #13063299C23semidirect
169. #13063299C23semidirect
170. #13063299C23semidirect
171. #13063298C23semidirect
172. #13063297C23semidirect
173. #13063296C23semidirect
174. #13063296C23semidirect
175. #13063296C23semidirect
178. Q8×Dic43C23semidirect
179. C4×Dic86C23semidirect
180. C4×Dic86C23semidirect
181. #13063290C23semidirect
184. C4×D172C23semidirect
185. C4×D172C23semidirect
186. D4×Dic43C23semidirect
187. D4×Dic43C23semidirect
188. #13063287C23semidirect
189. #13063287C23semidirect
192. C4×C22⋊D43C23semidirect
193. C4×C22⋊D43C23semidirect
194. C4×C22⋊D43C23semidirect
195. (C22⋊D43)⋊C4C23semidirect
196. #13063284C23semidirect
199. #13063282C23semidirect
233. C42×D43C23semidirect
235. C2×#41×C43C23semidirect
245. C4⋊Q8×C43C23semidirect
247. #124×C43C23semidirect
248. #121×C43C23semidirect
249. #121×C43C23semidirect
250. C4×D4×C43C23semidirect
251. C4×D4×C43C23semidirect
260. C2×C42×C43C23semidirect
343. C2×C4×D43#41semidirect
476. C4×D43C2×#41semidirect
535. C2×#532D43semidirect
541. C2×C43#3508semidirect
552. C22×#41C2×D43semidirect
571. #532C2×D43semidirect
573. C2×C4⋊Q8C2×D43semidirect
586. C2×#124C2×D43semidirect
603. C2×#121C2×D43semidirect
604. C2×#121C2×D43semidirect
627. C2×C4×D4C2×D43semidirect
628. C2×C4×D4C2×D43semidirect
637. C22×C42C2×D43semidirect
638. C43C2×#3508semidirect
649. C2×#41C22×D43semidirect
689. C4⋊Q8C22×D43semidirect
701. #124C22×D43semidirect
718. #121C22×D43semidirect
719. #121C22×D43semidirect
740. C4×D4C22×D43semidirect
741. C4×D4C22×D43semidirect
788. C2×C42C22×D43semidirect
1051. C2#19148464direct (N × H)

Maximal subgroups

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

subgroupindex
#191484642
C2×#145836322
C2×#145836312
C2×#145835682
C2×#145835672
C2×#145835462
C2×#145835442
C2×#145835422
C2×#145835372
C2×#145835022
C2×#145835002
C2×#145834652
C2×#145834542
C2×#145834502
C2×#145834492
C2×#145834472
C2×#127×D432
C2×#145833712
C2×C4×#106218982
C2×C43×#5322
C2×#350843