Finite Group Databasebeta

← C2×#13082388 #15662089

Subgroups — C2×#13082388 #15662089

Order 2816.

12982 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67037C212yesmaximal, complemented
2#13082388C2132yesmaximal, direct product factor
3C2×#10623084C211yesmaximal, characteristic, complemented
4C2×#10623249C211yesmaximal, characteristic, complemented
5C2×#10623130C212yesmaximal, complemented
6C2×D4×D44C211yesmaximal, characteristic, complemented
7C2×#10623140C212yesmaximal, complemented
8C2×D4×C22⋊D11C212yesmaximal, complemented
9C2×D4×C22⋊D11C212yesmaximal, complemented
10C2×#10623121C214yesmaximal, complemented
11C2×#10623138C212yesmaximal, complemented
12C2×#10623123C214yesmaximal, complemented
13C2×#10623079C211yesmaximal, characteristic, complemented
14C2×#10623127C212yesmaximal, complemented
15C22×#66993C212yesmaximal, complemented
16C2×D11×#127C211yesmaximal, characteristic, complemented
17C2×C4×#4341C211yesmaximal, characteristic, complemented
18C2×D42×C11C211yesmaximal, characteristic, complemented
19C23×D4×C11C2212yescomplemented
20C23×D4×C11C2212yescomplemented
21C23×C22⋊D11C2214yescomplemented
22C23×C22⋊D11C2214yescomplemented
23C23×C22⋊D11C2214yescomplemented
24C2×#67037—232no—
25C2×#67037C22132yescomplemented
26C22×#4341C2211yescharacteristic
27C22×#4341C2214yescomplemented
28C22×#4341C2212yescomplemented
29C22×D4×D11C2212yescomplemented
30C22×D4×D11C2214yescomplemented
31C22×D4×D11C2212yescomplemented
32C22×D4×D11C2212yescomplemented
33C22×D4×D11C2212yescomplemented
34C22×#4339C2212yescomplemented
35C22×#4339C2212yescomplemented
36C23×D44C2212yescomplemented
37D42×C11C22116yescomplemented
38C2×C11×#127C2211yescharacteristic, complemented
39C2×C11×#121C2212yescomplemented
40C2×C11×#121C2212yescomplemented
41C2×C11×#120C2214yescomplemented
42C2×C4×D4×C11C2211yescharacteristic, complemented
43C2×C4×D4×C11C2211yescharacteristic, complemented
44C2×#67006C2214yescomplemented
45C2×#66993C2212yescomplemented
46C2×#66993C2212yescomplemented
47C2×#66993C2212yescomplemented
48C2×#66993C2211yescharacteristic, complemented
49C2×#66993C2214yescomplemented
50C2×#66993C2214yescomplemented
51C2×#66993C2212yescomplemented
52C2×#66993C2212yescomplemented
53C2×#66993C22132yescomplemented
54C2×#66992C2214yescomplemented
55C2×#66992C2214yescomplemented
56C2×#66992C2214yescomplemented
57D4×C22⋊D11C22132yescomplemented
58D4×C22⋊D11C22132yescomplemented
59C2×#66991C2211yescharacteristic, complemented
60C2×#66991C2212yescomplemented
61C2×#66990C2214yescomplemented
62C2×#66990C2214yescomplemented
63C2×D4×Dic11C2212yescomplemented
64C2×D4×Dic11C2211yescharacteristic, complemented
65C2×#66983C2212yescomplemented
66C2×#66983C2212yescomplemented
67C2×C4×C22⋊D11C2212yescomplemented
68C2×C4×C22⋊D11C2212yescomplemented
69C22×C4×Dic11C2212yescomplemented
70#10623249C22116yescomplemented
71D11×#127C22116yescomplemented
72#10623140C22132yescomplemented
73#10623138C22132yescomplemented
74#10623130C22132yescomplemented
75#10623127C22132yescomplemented
76#10623123C22164yescomplemented
77#10623121C22164yescomplemented
78#10623084C22116yescomplemented
79D4×D44C22116yescomplemented
80#10623079C22116yescomplemented
81C4×#4341C22116yescomplemented
82C2×#66948C2211yescharacteristic, complemented
83C2×#66948C2212yescomplemented
84C2×#66946C2212yescomplemented
85C2×#66945C2211yescharacteristic, complemented
86C2×#66941C2211yescharacteristic, complemented
87C2×#66940C2211yescharacteristic, complemented
88C2×#66938C2214yescomplemented
89C2×#66938C2212yescomplemented
90C2×#66937C2212yescomplemented
91C2×#66937C2214yescomplemented
92C2×#66937C2214yescomplemented
93C2×#66935C2214yescomplemented
94C2×#66935C2214yescomplemented
95C2×(C22⋊D11)⋊C4C2214yescomplemented
96C2×(C22⋊D11)⋊C4C2212yescomplemented
97C2×#66930C2212yescomplemented
98C2×#66927C2211yescharacteristic, complemented
99C2×C4×D44C2211yescharacteristic, complemented
100C2×C42×D11C2211yescharacteristic, complemented
101C2×C4×Dic22C2211yescharacteristic, complemented
102C25×C11C2314yes—
103C24×D11C2314yes—
104C24×D11C2314yes—
105C22×D4×C11—216no—
106C22×D4×C11—48no—
107C22×D4×C11C2312yes—
108C22×D4×C11C2314yes—
109C22×D4×C11C2311yescharacteristic
110C22×D4×C11C2312yes—
111C22×D4×C11C2314yes—
112C22×D4×C11C2312yes—
113C22×D4×C11C2311yescharacteristic
114C22×D4×C11C23116yescomplemented
115C22×D4×C11C23116yescomplemented
116C23×C4×C11C2312yes—
117C23×C4×C11C2312yes—
118C22×C22⋊D11—232no—
119C22×C22⋊D11—232no—
120C22×C22⋊D11—416no—
121C22×C22⋊D11C2314yes—
122C22×C22⋊D11C2314yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2314yes—
126C22×C22⋊D11C2314yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2314yes—
129C22×C22⋊D11C2314yes—
130C22×C22⋊D11C2314yes—
131C22×C22⋊D11C2314yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C23132yescomplemented
134C22×C22⋊D11C23132yescomplemented
135C22×C22⋊D11C23132yescomplemented
136C23×Dic11C2312yes—
137C23×Dic11C2314yes—
138C23×Dic11C2312yes—
139#67037—2256no—
140C2×#4341—232no—
141C2×#4341—216no—
142C2×#4341D4116yescomplemented
143C2×#4341C2318yes—
144C2×#4341C23116yescomplemented
145C2×#4341C23132yescomplemented
146C2×D4×D11—216no—
147C2×D4×D11—232no—
148C2×D4×D11—216no—
149C2×D4×D11—48no—
150C2×D4×D11—48no—
151C2×D4×D11C23116yescomplemented
152C2×D4×D11C23116yescomplemented
153C2×D4×D11C23132yescomplemented
154C2×D4×D11C23116yescomplemented
155C2×D4×D11C23116yescomplemented
156C2×#4339—216no—
157C2×#4339—216no—
158C2×#4339C23116yescomplemented
159C2×#4339C23116yescomplemented
160C22×D44—48no—
161C22×D44C2311yescharacteristic
162C22×D44C2312yes—
163C22×D44C2312yes—
164C22×D44C2312yes—
165C22×D44C2312yes—
166C22×D44C2314yes—
167C22×D44C23116yescomplemented
168C22×C4×D11C2311yescharacteristic
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2312yes—
171C22×C4×D11C2314yes—
172C22×C4×D11C2311yescharacteristic
173C22×Dic22C2312yes—
174C22×Dic22C2311yescharacteristic
175C11×#127C2318yescomplemented
176C11×#121C23116yescomplemented
177C11×#121C23116yescomplemented
178C11×#120C23132yescomplemented
179C4×D4×C11C2318yescomplemented
180C4×D4×C11C2318yescomplemented
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2314yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C42×C11C2311yescharacteristic
187#67006C23132yescomplemented
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2314yes—
191#66993C23116yescomplemented
192#66993C23116yescomplemented
193#66993C23116yescomplemented
194#66993C23116yescomplemented
195#66993C23116yescomplemented
196#66993C2318yescomplemented
197#66993C23132yescomplemented
198#66993C23132yescomplemented
199#66992C23132yescomplemented
200#66992C23132yescomplemented
201#66992C23132yescomplemented
202#66991C23116yescomplemented
203#66991C2318yescomplemented
204#66990C23132yescomplemented
205#66990C23132yescomplemented
206D4×Dic11C23116yescomplemented
207D4×Dic11C2318yescomplemented
208#66983C23116yescomplemented
209#66983C23116yescomplemented
210C4×C22⋊D11C23116yescomplemented
211C4×C22⋊D11C23116yescomplemented
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2314yes—
215C2×(C2×D11)⋊C4C2314yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×C4⋊Dic11C2311yescharacteristic
218C2×C4⋊Dic11C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C23116yescomplemented
229#66948C2318yescomplemented
230#66948C23116yescomplemented
231#66946C23116yescomplemented
232#66945C2318yescomplemented
233#66941C2318yescomplemented
234#66940C2318yescomplemented
235#66938C23116yescomplemented
236#66938C23132yescomplemented
237#66937C23116yescomplemented
238#66937C23132yescomplemented
239#66937C23132yescomplemented
240#66935C23132yescomplemented
241#66935C23132yescomplemented
242(C22⋊D11)⋊C4C23116yescomplemented
243(C22⋊D11)⋊C4C23132yescomplemented
244#66930C23116yescomplemented
245#66927C2318yescomplemented
246C4×D44C2318yescomplemented
247C42×D11C2318yescomplemented
248C4×Dic22C2318yescomplemented
249C2×#3498—111nomaximal, Sylow
250C24×C11—216no—
251C24×C11—48no—
252C24×C11—48no—
253C24×C11C2414yes—
254C24×C11C2412yes—
255C24×C11C2412yes—
256C24×C11C24116yes—
257C23×D11—216no—
258C23×D11—216no—
259C23×D11—48no—
260C23×D11—48no—
261C23×D11—48no—
262C23×D11—48no—
263C23×D11C2412yes—
264C23×D11C2414yes—
265C23×D11C2411yescharacteristic
266C23×D11C24116yes—
267C23×D11C24116yes—
268C2×D4×C11—216no—
269C2×D4×C11—264no—
270C2×D4×C11—28no—
271C2×D4×C11—28no—
272C2×D4×C11—24no—
273C2×D4×C11—432no—
274C2×D4×C11—44no—
275C2×D4×C11—48no—
276C2×D4×C11C2×D418yescomplemented
277C2×D4×C11C2418yes—
278C2×D4×C11C24116yes—
279C2×D4×C11C2414yes—
280C2×D4×C11C2418yes—
281C2×D4×C11C24116yes—
282C2×D4×C11C2418yes—
283C2×D4×C11C2414yes—
284C22×C4×C11—28no—
285C22×C4×C11—28no—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2418yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2418yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—2128no—
294C2×C22⋊D11—28no—
295C2×C22⋊D11—216no—
296C2×C22⋊D11—216no—
297C2×C22⋊D11—216no—
298C2×C22⋊D11—2128no—
299C2×C22⋊D11—216no—
300C2×C22⋊D11—28no—
301C2×C22⋊D11—216no—
302C2×C22⋊D11—28no—
303C2×C22⋊D11—48no—
304C2×C22⋊D11—48no—
305C2×C22⋊D11—48no—
306C2×C22⋊D11—464no—
307C2×C22⋊D11C2×D4116yescomplemented
308C2×C22⋊D11C24116yes—
309C2×C22⋊D11C24116yes—
310C2×C22⋊D11C2418yes—
311C2×C22⋊D11C2418yes—
312C2×C22⋊D11C24116yes—
313C2×C22⋊D11C24116yes—
314C2×C22⋊D11C2418yes—
315C2×C22⋊D11C24116yes—
316C2×C22⋊D11C24116yes—
317C2×C22⋊D11C24116yes—
318C2×C22⋊D11C24116yes—
319C2×C22⋊D11C2418yes—
320C22×Dic11—216no—
321C22×Dic11—28no—
322C22×Dic11C2×D4116yescomplemented
323C22×Dic11C2418yes—
324C22×Dic11C24116yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2412yes—
327C22×Dic11C2412yes—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2412yes—
330C22×Dic11C2418yes—
331C22×Dic11C2411yescharacteristic
332#4341—2128no—
333#4341—264no—
334#4341C2×D4164yescomplemented
335D4×D11—2128no—
336D4×D11—264no—
337D4×D11—264no—
338D4×D11—432no—
339D4×D11—432no—
340#4339—264no—
341#4339—264no—
342C2×D44—28no—
343C2×D44—28no—
344C2×D44—24no—
345C2×D44—28no—
346C2×D44—48no—
347C2×D44—44no—
348C2×D44—432no—
349C2×D44C2414yes—
350C2×D44C2418yes—
351C2×D44C2418yes—
352C2×D44C2418yes—
353C2×D44C2418yes—
354C2×D44C24116yes—
355C2×C4×D11—216no—
356C2×C4×D11—24no—
357C2×C4×D11—28no—
358C2×C4×D11—24no—
359C2×C4×D11C2×D418yescomplemented
360C2×C4×D11C2414yes—
361C2×C4×D11C2414yes—
362C2×C4×D11C2418yes—
363C2×C4×D11C24116yes—
364C2×C4×D11C2414yes—
365C2×Dic22—28no—
366C2×Dic22C2×D418yescomplemented
367C2×Dic22C2418yes—
368C2×Dic22C2414yes—
369C11×C4⋊C4C2414yes—
370C11×C4⋊C4C2414yes—
371C11×C22⋊C4C2418yes—
372C11×C22⋊C4C24116yes—
373C11×C22⋊C4C2418yes—
374C42×C11C2414yes—
375C22⋊Dic11C2418yes—
376C22⋊Dic11C2418yes—
377C22⋊Dic11C24116yes—
378(C2×D11)⋊C4C2418yes—
379(C2×D11)⋊C4C2418yes—
380(C2×D11)⋊C4C24116yes—
381(C2×D11)⋊C4C24116yes—
382(C2×D11)⋊C4C2418yes—
383C4⋊Dic11C2414yes—
384C4⋊Dic11C2414yes—
385Dic11⋊C4C2418yes—
386Dic11⋊C4C2418yes—
387Dic11⋊C4C2418yes—
388C4×Dic11C2418yes—
389C4×Dic11C2414yes—
390C4×Dic11C2414yes—
391C4×Dic11C2414yes—
392C4×Dic11C2418yes—
393C4×Dic11C2418yes—
394C22×H(5,𝔽2)—112no—
395#3498—1132no—
396C2×#550—111no—
397C2×#550—112no—
398C2×#550—111no—
399C2×D42—112no—
400C2×D42—112no—
401C2×D42—112no—
402C2×D42—114no—
403C2×D42—111no—
404C2×D42D1111yescharacteristic, complemented
405C2×#535—112no—
406C2×#535—114no—
407C2×#532—112no—
408C2×#532—111no—
409C22×#127—112no—
410C22×#127—111no—
411C2×C4×#41—111no—
412C23×C11—24no—
413C23×C11—24no—
414C23×C11—28no—
415C23×C11—24no—
416C23×C11—24no—
417C23×C11—28no—
418C23×C11—28no—
419C23×C11—24no—
420C23×C11—232no—
421C23×C11—416no—
422C23×C11—416no—
423C23×C11—832no—
424C23×C11C22×D418yes—
425C23×C11C2518yes—
426C23×C11C2514yes—
427C23×C11C2514yes—
428C23×C11C2511yescharacteristic
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—28no—
432C22×D11—24no—
433C22×D11—24no—
434C22×D11—28no—
435C22×D11—28no—
436C22×D11—24no—
437C22×D11—232no—
438C22×D11—232no—
439C22×D11—416no—
440C22×D11—416no—
441C22×D11—416no—
442C22×D11—416no—
443C22×D11—832no—
444C22×D11—832no—
445C22×D11C22×D414yes—
446C22×D11C2514yes—
447C22×D11C2518yes—
448C22×D11C2512yes—
449D4×C11—232no—
450D4×C11—216no—
451D4×C11—216no—
452D4×C11—28no—
453D4×C11—48no—
454D4×C11—416no—
455D4×C11C22×D4116yescomplemented
456C2×C4×C11—24no—
457C2×C4×C11—22no—
458C2×C4×C11—24no—
459C2×C4×C11—216no—
460C2×C4×C11—216no—
461C2×C4×C11C22×D414yes—
462C2×C4×C11H(5,𝔽2)14yescomplemented
463C2×C4×C11C2514yes—
464C2×C4×C11C2512yes—
465C2×C4×C11C2514yes—
466C2×C4×C11C2512yes—
467C2×C4×C11C2512yes—
468C22⋊D11—232no—
469C22⋊D11—216no—
470C22⋊D11—216no—
471C22⋊D11—232no—
472C22⋊D11—232no—
473C22⋊D11—232no—
474C22⋊D11—232no—
475C22⋊D11—216no—
476C22⋊D11—416no—
477C22⋊D11—416no—
478C22⋊D11—416no—
479C22⋊D11C22×D4132yescomplemented
480C2×Dic11—24no—
481C2×Dic11—22no—
482C2×Dic11—24no—
483C2×Dic11—232no—
484C2×Dic11—216no—
485C2×Dic11C22×D414yes—
486C2×Dic11C22×D418yes—
487C2×Dic11C22×D4132yescomplemented
488C2×Dic11H(5,𝔽2)14yescomplemented
489C2×Dic11C2512yes—
490C2×Dic11C2514yes—
491C2×Dic11C2514yes—
492C2×Dic11C2512yes—
493C2×Dic11C2514yes—
494C2×Dic11C2512yes—
495D44—216no—
496D44—216no—
497D44—28no—
498D44—216no—
499D44—416no—
500D44—48no—
501C4×D11—216no—
502C4×D11—28no—
503C4×D11—232no—
504C4×D11—28no—
505C4×D11C22×D4116yescomplemented
506Dic22—216no—
507Dic22C22×D4116yescomplemented
508C2×H(5,𝔽2)—1132no—
509C2×H(5,𝔽2)—2232no—
510C22×#41—111no—
511C22×#41—114no—
512C22×#41—112no—
513C22×#41—112no—
514C22×#41—112no—
515C23×D4—114no—
516C23×D4—114no—
517C23×D4—114no—
518C23×D4—112no—
519C23×D4—114no—
520C23×D4—112no—
521C23×D4—112no—
522C23×D4—112no—
523C23×D4—112no—
524C23×D4C2×D1112yescomplemented
525C23×D4C2×D1112yescomplemented
526#550—1116no—
527#550—1132no—
528#550—1116no—
529D42—1132no—
530D42—1132no—
531D42—1132no—
532D42—1164no—
533D42—1116no—
534D42C2×D11116yescomplemented
535#535—1132no—
536#535—1164no—
537#532—1132no—
538#532—1116no—
539C2×C4⋊Q8—111no—
540C2×#127—112no—
541C2×#127—111no—
542C2×#127—114no—
543C2×#127—112no—
544C2×#127—114no—
545C2×#127—112no—
546C2×#127—112no—
547C2×#127—112no—
548C2×#127—1132no—
549C2×#127—1116no—
550C2×#127—111no—
551C2×#127C2×D1111yescharacteristic, complemented
552C2×#124—114no—
553C2×#124—112no—
554C2×#121—111no—
555C2×#121—112no—
556C2×#121—114no—
557C2×#121—114no—
558C2×#121—114no—
559C2×#121—112no—
560C2×#121—112no—
561C2×#121—111no—
562C2×#121—112no—
563C2×#121—112no—
564C2×#121—114no—
565C2×#121—114no—
566C2×#121C2×D1112yescomplemented
567C2×#121C2×D1112yescomplemented
568C2×#120—114no—
569C2×#120—114no—
570C2×#120—114no—
571C2×#120—114no—
572C2×#120—114no—
573C2×#120C2×D1114yescomplemented
574C4×#41—1116no—
575C2×C4×Q8—111no—
576C2×C4×Q8—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—112no—
583C2×C4×D4—114no—
584C2×C4×D4—111no—
585C2×C4×D4C2×D1111yescharacteristic, complemented
586C2×C4×D4C2×D1111yescharacteristic, complemented
587C2×#117—111no—
588C2×#117—112no—
589C22×C42—112no—
590C22×C42—111no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—216no—
594C22×C11—24no—
595C22×C11—28no—
596C22×C11—24no—
597C22×C11—28no—
598C22×C11—28no—
599C22×C11—24no—
600C22×C11—416no—
601C22×C11—48no—
602C22×C11—832no—
603C22×C11C23×D418yes—
604C22×C11C23×D412yes—
605C22×C11C2×H(5,𝔽2)12yes—
606C22×C11C2×H(5,𝔽2)12yes—
607C22×C11C2611yescharacteristic
608C2×D11—22no—
609C2×D11—22no—
610C2×D11—28no—
611C2×D11—24no—
612C2×D11—28no—
613C2×D11—24no—
614C2×D11—28no—
615C2×D11—28no—
616C2×D11—24no—
617C2×D11—48no—
618C2×D11—416no—
619C2×D11—832no—
620C2×D11—832no—
621C2×D11C23×D414yes—
622C4×C11—24no—
623C4×C11—24no—
624C4×C11—22no—
625C4×C11C23×D414yes—
626C4×C11C2×H(5,𝔽2)14yescomplemented
627Dic11—24no—
628Dic11—22no—
629Dic11—24no—
630Dic11C23×D414yes—
631Dic11C23×D418yes—
632Dic11C2×H(5,𝔽2)14yescomplemented
633C25—114no—
634C25—114no—
635C25C22×D1114yes—
636H(5,𝔽2)—22256no—
637C2×#41—1116no—
638C2×#41—118no—
639C2×#41—1132no—
640C2×#41—1116no—
641C2×#41—1116no—
642C2×#41—1116no—
643C2×#41—2216no—
644C2×#41—2216no—
645C2×#41—2232no—
646C2×#41—2216no—
647C22×Q8—111no—
648C22×Q8—112no—
649C22×D4—216no—
650C22×D4—48no—
651C22×D4—112no—
652C22×D4—114no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—114no—
656C22×D4—114no—
657C22×D4—114no—
658C22×D4—114no—
659C22×D4—112no—
660C22×D4—1132no—
661C22×D4—1132no—
662C22×D4—114no—
663C22×D4—114no—
664C22×D4—114no—
665C22×D4—1132no—
666C22×D4—1116no—
667C22×D4—1132no—
668C22×D4—1116no—
669C22×D4—1116no—
670C22×D4—1116no—
671C22×D4—112no—
672C22×D4—111no—
673C22×D4—112no—
674C22×D4—112no—
675C22×D4—114no—
676C22×D4—112no—
677C22×D4—1116no—
678C22×D4—2216no—
679C22×D4—2232no—
680C22×D4—2232no—
681C22×D4—2232no—
682C22×D4—2216no—
683C22×D4—448no—
684C22×D4—448no—
685C22×D4—448no—
686C22×D4—4416no—
687C22×D4C22×D1112yes—
688C22×D4C22×D1111yescharacteristic
689C22×D4C22×D1114yes—
690C22×D4C22×D1112yes—
691C22×D4C22×D1114yes—
692C22×D4C22×D1112yes—
693C22×D4C22×D1111yescharacteristic
694C22×D4C22×D11116yescomplemented
695C22×D4C22×D11116yescomplemented
696C23×C4—112no—
697C23×C4—111no—
698C23×C4—112no—
699C23×C4—114no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—114no—
703C23×C4—112no—
704C23×C4C22×D1112yes—
705C23×C4C22×D1112yes—
706C4⋊Q8—118no—
707#127—1116no—
708#127—118no—
709#127—1132no—
710#127—1116no—
711#127—1132no—
712#127—1116no—
713#127—1116no—
714#127—1116no—
715#127—118no—
716#127C22×D1118yescomplemented
717#124—1132no—
718#124—1116no—
719#121—118no—
720#121—1132no—
721#121—1116no—
722#121—1132no—
723#121—1132no—
724#121—1116no—
725#121—1116no—
726#121—118no—
727#121—1116no—
728#121—1116no—
729#121—1132no—
730#121—1132no—
731#121C22×D11116yescomplemented
732#121C22×D11116yescomplemented
733#120—1132no—
734#120—1132no—
735#120—1132no—
736#120—1132no—
737#120—1132no—
738#120C22×D11132yescomplemented
739C4×Q8—118no—
740C4×Q8—118no—
741C4×D4—118no—
742C4×D4—1116no—
743C4×D4—1116no—
744C4×D4—1116no—
745C4×D4—1116no—
746C4×D4—1116no—
747C4×D4—1132no—
748C4×D4—118no—
749C4×D4C22×D1118yescomplemented
750C4×D4C22×D1118yescomplemented
751#117—118no—
752#117—1116no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4C22×D1111yescharacteristic
759C2×C4⋊C4C22×D1111yescharacteristic
760C2×C22⋊C4—112no—
761C2×C22⋊C4—114no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—114no—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4C22×D1112yes—
769C2×C22⋊C4C22×D1114yes—
770C2×C22⋊C4C22×D1112yes—
771C2×C42—112no—
772C2×C42—111no—
773C2×C42—112no—
774C2×C42—111no—
775C2×C42—112no—
776C2×C42—1116no—
777C2×C42—111no—
778C2×C42—118no—
779C2×C42C22×D1111yescharacteristic
780C2×C11—28no—
781C2×C11—48no—
782C2×C11—44no—
783C2×C11#349814yescomplemented
784C2×C11C24×D411yescharacteristic
785C2×C11C22×H(5,𝔽2)11yescharacteristic
786C2×C11C22×H(5,𝔽2)11yescharacteristic
787D11—24no—
788D11—44no—
789D11—48no—
790C24—216no—
791C24—48no—
792C24—48no—
793C24—111no—
794C24—114no—
795C24—112no—
796C24—1116no—
797C24—1116no—
798C24—2216no—
799C24—2216no—
800C24—448no—
801C24—448no—
802C24—448no—
803C24—448no—
804C24C23×D1114yes—
805C24C23×D1112yes—
806C24C23×D1112yes—
807C24C23×D11116yes—
808#41—1164no—
809#41—2264no—
810#41—2264no—
811#41—22128no—
812#41—2264no—
813C2×Q8—118no—
814C2×Q8—114no—
815C2×Q8—118no—
816C2×Q8—228no—
817C2×D4—216no—
818C2×D4—264no—
819C2×D4—28no—
820C2×D4—24no—
821C2×D4—28no—
822C2×D4—432no—
823C2×D4—48no—
824C2×D4—44no—
825C2×D4—1116no—
826C2×D4—118no—
827C2×D4—1116no—
828C2×D4—118no—
829C2×D4—118no—
830C2×D4—1116no—
831C2×D4—1116no—
832C2×D4—1116no—
833C2×D4—1116no—
834C2×D4—118no—
835C2×D4—1116no—
836C2×D4—1116no—
837C2×D4—1116no—
838C2×D4—118no—
839C2×D4—114no—
840C2×D4—118no—
841C2×D4—118no—
842C2×D4—1116no—
843C2×D4—118no—
844C2×D4—228no—
845C2×D4—2264no—
846C2×D4—228no—
847C2×D4—2216no—
848C2×D4—2216no—
849C2×D4—2216no—
850C2×D4—22128no—
851C2×D4—2216no—
852C2×D4—228no—
853C2×D4—22128no—
854C2×D4—22128no—
855C2×D4—228no—
856C2×D4—2216no—
857C2×D4—2264no—
858C2×D4—228no—
859C2×D4—224no—
860C2×D4—228no—
861C2×D4—4432no—
862C2×D4—448no—
863C2×D4—444no—
864C2×D4—4432no—
865C2×D4—4432no—
866C2×D4—4464no—
867C2×D4—448no—
868C2×D4—448no—
869C2×D4—448no—
870C2×D4D4×D1118yescomplemented
871C2×D4C23×D1118yes—
872C2×D4C23×D1114yes—
873C2×D4C23×D11116yes—
874C2×D4C23×D1118yes—
875C2×D4C23×D11116yes—
876C2×D4C23×D1118yes—
877C2×D4C23×D1114yes—
878C22×C4—28no—
879C22×C4—28no—
880C22×C4—1116no—
881C22×C4—118no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—112no—
885C22×C4—118no—
886C22×C4—114no—
887C22×C4—118no—
888C22×C4—1116no—
889C22×C4—111no—
890C22×C4—112no—
891C22×C4—112no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—1116no—
895C22×C4—118no—
896C22×C4—2216no—
897C22×C4—224no—
898C22×C4—2216no—
899C22×C4—228no—
900C22×C4—228no—
901C22×C4—224no—
902C22×C4C23×D1118yes—
903C22×C4C23×D1118yes—
904C22×C4C23×D1112yes—
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C4⋊C4—118no—
910C4⋊C4—118no—
911C4⋊C4—114no—
912C4⋊C4—118no—
913C4⋊C4—114no—
914C4⋊C4C23×D1114yes—
915C4⋊C4C23×D1114yes—
916C22⋊C4—118no—
917C22⋊C4—1116no—
918C22⋊C4—118no—
919C22⋊C4—118no—
920C22⋊C4—118no—
921C22⋊C4—1116no—
922C22⋊C4—1116no—
923C22⋊C4—118no—
924C22⋊C4C23×D1118yes—
925C22⋊C4C23×D11116yes—
926C22⋊C4C23×D1118yes—
927C42—114no—
928C42—118no—
929C42—114no—
930C42—118no—
931C42—114no—
932C42—118no—
933C42C23×D1114yes—
934C11C2×#349811yescharacteristic, complemented, Sylow
935C23—24no—
936C23—24no—
937C23—24no—
938C23—28no—
939C23—24no—
940C23—28no—
941C23—28no—
942C23—24no—
943C23—232no—
944C23—416no—
945C23—416no—
946C23—832no—
947C23—114no—
948C23—112no—
949C23—118no—
950C23—114no—
951C23—2232no—
952C23—222no—
953C23—222no—
954C23—228no—
955C23—224no—
956C23—224no—
957C23—228no—
958C23—228no—
959C23—224no—
960C23—2232no—
961C23—4416no—
962C23—4416no—
963C23—4416no—
964C23—4416no—
965C23—8832no—
966C23—8832no—
967C23C2×D4×D1118yes—
968C23C24×D1118yes—
969C23C24×D1114yes—
970C23C24×D1114yes—
971C23C24×D1111yescharacteristic
972Q8—1116no—
973Q8—2216no—
974D4—232no—
975D4—216no—
976D4—28no—
977D4—216no—
978D4—416no—
979D4—48no—
980D4—1132no—
981D4—2216no—
982D4—2216no—
983D4—2232no—
984D4—2232no—
985D4—2232no—
986D4—2232no—
987D4—2216no—
988D4—2216no—
989D4—2232no—
990D4—2216no—
991D4—228no—
992D4—2216no—
993D4—448no—
994D4—4416no—
995D4—4416no—
996D4—4416no—
997D4—4416no—
998D4C2×D4×D11116yescomplemented
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—216no—
1003C2×C4—216no—
1004C2×C4—114no—
1005C2×C4—118no—
1006C2×C4—1132no—
1007C2×C4—114no—
1008C2×C4—112no—
1009C2×C4—112no—
1010C2×C4—114no—
1011C2×C4—1116no—
1012C2×C4—114no—
1013C2×C4—112no—
1014C2×C4—114no—
1015C2×C4—2232no—
1016C2×C4—228no—
1017C2×C4—2232no—
1018C2×C4—2216no—
1019C2×C4—224no—
1020C2×C4—222no—
1021C2×C4—224no—
1022C2×C4—2216no—
1023C2×C4—228no—
1024C2×C4C2×D4×D1114yes—
1025C2×C4#6703714yescomplemented
1026C2×C4C24×D1114yes—
1027C2×C4C24×D1112yes—
1028C2×C4C24×D1114yes—
1029C2×C4C24×D1112yes—
1030C2×C4C24×D1112yes—
1031C22—216no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—28no—
1036C22—28no—
1037C22—24no—
1038C22—24no—
1039C22—28no—
1040C22—48no—
1041C22—416no—
1042C22—832no—
1043C22—114no—
1044C22—228no—
1045C22—222no—
1046C22—222no—
1047C22—228no—
1048C22—224no—
1049C22—228no—
1050C22—224no—
1051C22—224no—
1052C22—228no—
1053C22—448no—
1054C22—4416no—
1055C22—8832no—
1056C22—8832no—
1057C22C22×D4×D1118yes—
1058C22C22×D4×D1112yes—
1059C22C2×#6703712yes—
1060C22D11×H(5,𝔽2)12yes—
1061C22C25×D1111yescharacteristic
1062C4—24no—
1063C4—22no—
1064C4—24no—
1065C4—114no—
1066C4—118no—
1067C4—114no—
1068C4—224no—
1069C4—224no—
1070C4—222no—
1071C4C22×D4×D1114yes—
1072C4C2×#6703714yescomplemented
1073C2—28no—
1074C2—44no—
1075C2—48no—
1076C2—224no—
1077C2—444no—
1078C2—448no—
1079C2#1308238814yesdirect product factor
1080C2C23×D4×D1111yescharacteristic
1081C2C2×D11×H(5,𝔽2)11yescharacteristic
1082C2C22×#6703711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×D42×C11C2
socleC23×C11C25
hypercenterC2×D42D11
hypocenterC11C2×#3498
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. #13082388C2direct (N × H)
3. C2×#10623084C2semidirect
4. C2×#10623249C2semidirect
5. C2×#10623130C2semidirect
6. C2×D4×D44C2semidirect
7. C2×#10623140C2semidirect
8. C2×D4×C22⋊D11C2semidirect
9. C2×D4×C22⋊D11C2semidirect
10. C2×#10623121C2semidirect
11. C2×#10623138C2semidirect
12. C2×#10623123C2semidirect
13. C2×#10623079C2semidirect
14. C2×#10623127C2semidirect
15. C22×#66993C2semidirect
16. C2×D11×#127C2semidirect
17. C2×C4×#4341C2semidirect
18. C2×D42×C11C2semidirect
19. C23×D4×C11C22semidirect
20. C23×D4×C11C22semidirect
21. C23×C22⋊D11C22semidirect
22. C23×C22⋊D11C22semidirect
23. C23×C22⋊D11C22semidirect
25. C2×#67037C22semidirect
27. C22×#4341C22semidirect
28. C22×#4341C22semidirect
29. C22×D4×D11C22semidirect
30. C22×D4×D11C22semidirect
31. C22×D4×D11C22semidirect
32. C22×D4×D11C22semidirect
33. C22×D4×D11C22semidirect
34. C22×#4339C22semidirect
35. C22×#4339C22semidirect
36. C23×D44C22semidirect
37. D42×C11C22semidirect
38. C2×C11×#127C22semidirect
39. C2×C11×#121C22semidirect
40. C2×C11×#121C22semidirect
41. C2×C11×#120C22semidirect
42. C2×C4×D4×C11C22semidirect
43. C2×C4×D4×C11C22semidirect
44. C2×#67006C22semidirect
45. C2×#66993C22semidirect
46. C2×#66993C22semidirect
47. C2×#66993C22semidirect
48. C2×#66993C22semidirect
49. C2×#66993C22semidirect
50. C2×#66993C22semidirect
51. C2×#66993C22semidirect
52. C2×#66993C22semidirect
53. C2×#66993C22semidirect
54. C2×#66992C22semidirect
55. C2×#66992C22semidirect
56. C2×#66992C22semidirect
57. D4×C22⋊D11C22semidirect
58. D4×C22⋊D11C22semidirect
59. C2×#66991C22semidirect
60. C2×#66991C22semidirect
61. C2×#66990C22semidirect
62. C2×#66990C22semidirect
63. C2×D4×Dic11C22semidirect
64. C2×D4×Dic11C22semidirect
65. C2×#66983C22semidirect
66. C2×#66983C22semidirect
67. C2×C4×C22⋊D11C22semidirect
68. C2×C4×C22⋊D11C22semidirect
69. C22×C4×Dic11C22semidirect
70. #10623249C22semidirect
71. D11×#127C22semidirect
72. #10623140C22semidirect
73. #10623138C22semidirect
74. #10623130C22semidirect
75. #10623127C22semidirect
76. #10623123C22semidirect
77. #10623121C22semidirect
78. #10623084C22semidirect
79. D4×D44C22semidirect
80. #10623079C22semidirect
81. C4×#4341C22semidirect
82. C2×#66948C22semidirect
83. C2×#66948C22semidirect
84. C2×#66946C22semidirect
85. C2×#66945C22semidirect
86. C2×#66941C22semidirect
87. C2×#66940C22semidirect
88. C2×#66938C22semidirect
89. C2×#66938C22semidirect
90. C2×#66937C22semidirect
91. C2×#66937C22semidirect
92. C2×#66937C22semidirect
93. C2×#66935C22semidirect
94. C2×#66935C22semidirect
95. C2×(C22⋊D11)⋊C4C22semidirect
96. C2×(C22⋊D11)⋊C4C22semidirect
97. C2×#66930C22semidirect
98. C2×#66927C22semidirect
99. C2×C4×D44C22semidirect
100. C2×C42×D11C22semidirect
101. C2×C4×Dic22C22semidirect
114. C22×D4×C11C23semidirect
115. C22×D4×C11C23semidirect
133. C22×C22⋊D11C23semidirect
134. C22×C22⋊D11C23semidirect
135. C22×C22⋊D11C23semidirect
142. C2×#4341D4semidirect
144. C2×#4341C23semidirect
145. C2×#4341C23semidirect
151. C2×D4×D11C23semidirect
152. C2×D4×D11C23semidirect
153. C2×D4×D11C23semidirect
154. C2×D4×D11C23semidirect
155. C2×D4×D11C23semidirect
158. C2×#4339C23semidirect
159. C2×#4339C23semidirect
167. C22×D44C23semidirect
175. C11×#127C23semidirect
176. C11×#121C23semidirect
177. C11×#121C23semidirect
178. C11×#120C23semidirect
179. C4×D4×C11C23semidirect
180. C4×D4×C11C23semidirect
187. #67006C23semidirect
191. #66993C23semidirect
192. #66993C23semidirect
193. #66993C23semidirect
194. #66993C23semidirect
195. #66993C23semidirect
196. #66993C23semidirect
197. #66993C23semidirect
198. #66993C23semidirect
199. #66992C23semidirect
200. #66992C23semidirect
201. #66992C23semidirect
202. #66991C23semidirect
203. #66991C23semidirect
204. #66990C23semidirect
205. #66990C23semidirect
206. D4×Dic11C23semidirect
207. D4×Dic11C23semidirect
208. #66983C23semidirect
209. #66983C23semidirect
210. C4×C22⋊D11C23semidirect
211. C4×C22⋊D11C23semidirect
228. C2×C4×Dic11C23semidirect
229. #66948C23semidirect
230. #66948C23semidirect
231. #66946C23semidirect
232. #66945C23semidirect
233. #66941C23semidirect
234. #66940C23semidirect
235. #66938C23semidirect
236. #66938C23semidirect
237. #66937C23semidirect
238. #66937C23semidirect
239. #66937C23semidirect
240. #66935C23semidirect
241. #66935C23semidirect
242. (C22⋊D11)⋊C4C23semidirect
243. (C22⋊D11)⋊C4C23semidirect
244. #66930C23semidirect
245. #66927C23semidirect
246. C4×D44C23semidirect
247. C42×D11C23semidirect
248. C4×Dic22C23semidirect
276. C2×D4×C11C2×D4semidirect
307. C2×C22⋊D11C2×D4semidirect
322. C22×Dic11C2×D4semidirect
334. #4341C2×D4semidirect
359. C2×C4×D11C2×D4semidirect
366. C2×Dic22C2×D4semidirect
404. C2×D42D11semidirect
455. D4×C11C22×D4semidirect
462. C2×C4×C11H(5,𝔽2)semidirect
479. C22⋊D11C22×D4semidirect
487. C2×Dic11C22×D4semidirect
488. C2×Dic11H(5,𝔽2)semidirect
505. C4×D11C22×D4semidirect
507. Dic22C22×D4semidirect
524. C23×D4C2×D11semidirect
525. C23×D4C2×D11semidirect
534. D42C2×D11semidirect
551. C2×#127C2×D11semidirect
566. C2×#121C2×D11semidirect
567. C2×#121C2×D11semidirect
573. C2×#120C2×D11semidirect
585. C2×C4×D4C2×D11semidirect
586. C2×C4×D4C2×D11semidirect
626. C4×C11C2×H(5,𝔽2)semidirect
632. Dic11C2×H(5,𝔽2)semidirect
694. C22×D4C22×D11semidirect
695. C22×D4C22×D11semidirect
716. #127C22×D11semidirect
731. #121C22×D11semidirect
732. #121C22×D11semidirect
738. #120C22×D11semidirect
749. C4×D4C22×D11semidirect
750. C4×D4C22×D11semidirect
783. C2×C11#3498semidirect
870. C2×D4D4×D11semidirect
934. C11C2×#3498semidirect
998. D4C2×D4×D11semidirect
1025. C2×C4#67037semidirect
1072. C4C2×#67037semidirect
1079. C2#13082388direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670372
#130823882
C2×#106230842
C2×#106232492
C2×#106231302
C2×D4×D442
C2×#106231402
C2×D4×C22⋊D112
C2×#106231212
C2×#106231382
C2×#106231232
C2×#106230792
C2×#106231272
C22×#669932
C2×D11×#1272
C2×C4×#43412
C2×D42×C112
C2×#349811