Finite Group Databasebeta

← C2×#13082354 #15662123

Subgroups — C2×#13082354 #15662123

Order 2816.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082354C2132yesmaximal, direct product factor
2C2×#10623265C212yesmaximal, complemented
3C2×#10623226C212yesmaximal, complemented
4C2×#10623226C212yesmaximal, complemented
5C2×#10623168C214yesmaximal, complemented
6C2×#10623257C212yesmaximal, complemented
7C2×#10623161C214yesmaximal, complemented
8C2×#10623264C212yesmaximal, complemented
9C2×#10623229C212yesmaximal, complemented
10C2×#10623056C211yesmaximal, characteristic, complemented
11C2×#10623256C212yesmaximal, complemented
12C2×#10623222C212yesmaximal, complemented
13C2×#10623055C211yesmaximal, characteristic, complemented
14C22×#66948C211yesmaximal, characteristic, complemented
15C2×#10623035C211yesmaximal, characteristic, complemented
16C2×#10623052C211yesmaximal, characteristic, complemented
17C2×D11×#117C211yesmaximal, characteristic, complemented
18C2×C11×#544C211yesmaximal, characteristic, complemented
19C22×#4343C2214yescomplemented
20C22×#4339C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2212yes—
23C23×C4×D11C2211yescharacteristic
24C11×#544C22116yescomplemented
25C2×C11×C4⋊Q8C2212yescomplemented
26C2×C11×C4⋊Q8C2212yescomplemented
27C2×C11×#125C2212yescomplemented
28C2×C11×#125C2212yescomplemented
29C2×C11×C22⋊Q8C2214yes—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C2×#67000C2214yescomplemented
34C2×#67000C2214yescomplemented
35C2×#66999C2214yescomplemented
36C2×C4×C22⋊D11C2214yes—
37C22×(C2×D11)⋊C4C2212yes—
38C2×#66979C2211yescharacteristic
39#10623265C22132yescomplemented
40#10623264C22132yescomplemented
41#10623257C22132yescomplemented
42#10623256C22132yescomplemented
43#10623229C22132yescomplemented
44#10623226C22132yescomplemented
45#10623226C22132yescomplemented
46#10623222C22132yescomplemented
47#10623168C22164yescomplemented
48#10623161C22164yescomplemented
49#10623056C22116yescomplemented
50#10623055C22116yescomplemented
51#10623052C22116yescomplemented
52D11×#117C22116yescomplemented
53C2×#66951C2214yescomplemented
54C2×#66951C2214yescomplemented
55C2×#66950C2211yescharacteristic, complemented
56C2×#66950C2211yescharacteristic, complemented
57C2×#66948C2212yes—
58C2×#66948C2212yes—
59C2×#66948C2212yes—
60C2×#66948C2212yes—
61C2×#66948C22116yescomplemented
62C2×#66948C2211yescharacteristic, complemented
63C2×#66948C2211yescharacteristic, complemented
64C2×#66948C2212yescomplemented
65C2×#66948C2214yescomplemented
66C2×#66948C2214yescomplemented
67C2×#66948C2212yescomplemented
68C2×#66948C2214yescomplemented
69C2×#66947C2214yescomplemented
70C2×#66947C2214yescomplemented
71C2×#66947C2214yescomplemented
72C2×#66947C2214yescomplemented
73#10623035C22116yescomplemented
74C2×#66946C2214yescomplemented
75C2×#66946C2214yescomplemented
76C2×#66946C2212yescomplemented
77C2×#66946C2212yescomplemented
78C2×#66946C2212yescomplemented
79C2×#66945C2214yescomplemented
80C2×#66945C2211yescharacteristic, complemented
81C2×#66945C2212yescomplemented
82C2×#66945C2211yescharacteristic, complemented
83C2×C4⋊C4×D11C2211yescharacteristic, complemented
84C2×C4⋊C4×D11C2212yescomplemented
85C2×C4⋊C4×D11C2211yescharacteristic, complemented
86C2×#66940C2212yescomplemented
87C2×#66939C2212yes—
88C2×#66935C2214yes—
89C2×#66935C2212yes—
90C2×C22⋊C4×D11C2214yes—
91C2×C22⋊C4×D11C2212yes—
92C2×#66930C2212yes—
93C2×#66928C2212yescomplemented
94C2×#66927C2212yescomplemented
95C2×C4×D44C2212yescomplemented
96C2×C4×D44C2212yescomplemented
97C2×C4×D44C2212yescomplemented
98C2×C4×D44C2212yescomplemented
99C2×#66925C2212yescomplemented
100C2×C42×D11C2212yescomplemented
101C24×D11C2311yescharacteristic
102C24×D11C2312yes—
103C22×Q8×C11C2314yes—
104C23×C4×C11C2312yes—
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11C2312yes—
107C23×Dic11C2311yescharacteristic
108C2×#4343—416no—
109C2×#4343C23132yescomplemented
110C2×#4339—28no—
111C2×#4339C2318yes—
112C22×D44—28no—
113C22×D44—48no—
114C22×D44C2312yes—
115C22×D44C2312yes—
116C22×D44C2311yescharacteristic
117C22×D44C2312yes—
118C22×D44C2314yes—
119C22×D44C2318yes—
120C22×D44C2312yes—
121C22×D44C2314yes—
122C22×D44C2314yes—
123C22×D44C2314yes—
124C22×D44C23116yes—
125C22×C4×D11—28no—
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2312yes—
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2312yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2318yes—
133C22×C4×D11C2312yes—
134C22×C4×D11C2314yes—
135C22×C4×D11C2314yes—
136C22×C4×D11C2314yes—
137C22×Dic22C2311yescharacteristic
138C11×C4⋊Q8C23116yescomplemented
139C11×C4⋊Q8C23116yescomplemented
140C11×#125C23116yescomplemented
141C11×#125C23116yescomplemented
142C11×C22⋊Q8C23132yes—
143C11×#117C2318yes—
144C11×#117C2318yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2314yes—
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2314yes—
153C2×C11×C4⋊C4C2314yes—
154C2×C11×C4⋊C4C2318yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C42×C11C2312yes—
158C2×C42×C11C2312yes—
159C2×C22⋊Dic11C2312yes—
160#67000C23132yescomplemented
161#67000C23132yescomplemented
162#66999C23132yescomplemented
163C4×C22⋊D11C23132yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2314yes—
176C2×(C2×D11)⋊C4C2314yes—
177C2×(C2×D11)⋊C4C23116yes—
178#66979C2318yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2312yes—
182C2×C4⋊Dic11C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2314yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2314yes—
190#66951C23132yescomplemented
191#66951C23132yescomplemented
192#66950C2318yescomplemented
193#66950C2318yescomplemented
194#66948C23116yes—
195#66948C23116yes—
196#66948C23116yes—
197#66948C23116yes—
198#66948C2318yescomplemented
199#66948C23132yescomplemented
200#66948C23116yescomplemented
201#66948C23132yescomplemented
202#66948C2318yescomplemented
203#66948C23116yescomplemented
204#66948C23132yescomplemented
205#66947C23132yescomplemented
206#66947C23132yescomplemented
207#66947C23132yescomplemented
208#66947C23132yescomplemented
209#66946C23116yescomplemented
210#66946C23116yescomplemented
211#66946C23132yescomplemented
212#66946C23116yescomplemented
213#66946C23132yescomplemented
214#66945C2318yescomplemented
215#66945C23116yescomplemented
216#66945C23132yescomplemented
217#66945C2318yescomplemented
218C4⋊C4×D11C2318yescomplemented
219C4⋊C4×D11C23116yescomplemented
220C4⋊C4×D11C2318yescomplemented
221#66940C23116yescomplemented
222#66939C23116yes—
223#66935C23116yes—
224#66935C23132yes—
225C22⋊C4×D11C23116yes—
226C22⋊C4×D11C23132yes—
227#66930C23116yes—
228#66928C23116yescomplemented
229#66927C23116yescomplemented
230C4×D44C23116yescomplemented
231C4×D44C23116yescomplemented
232C4×D44C23116yescomplemented
233C4×D44C23116yescomplemented
234#66925C23116yescomplemented
235C42×D11C23116yescomplemented
236C2×#3494—111nomaximal, Sylow
237C24×C11C2411yescharacteristic
238C23×D11—24no—
239C23×D11—28no—
240C23×D11—24no—
241C23×D11—42no—
242C23×D11—44no—
243C23×D11—44no—
244C23×D11C2411yescharacteristic
245C23×D11C2414yes—
246C23×D11C2412yes—
247C23×D11C2414yes—
248C23×D11C2411yescharacteristic
249C23×D11C2418yes—
250C2×Q8×C11—48no—
251C2×Q8×C11C24116yes—
252C22×C4×C11—44no—
253C22×C4×C11#4118yescomplemented
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2414yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2418yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2414yes—
263C2×C22⋊D11—28no—
264C2×C22⋊D11C2418yes—
265C22×Dic11—24no—
266C22×Dic11C2414yes—
267C22×Dic11C2412yes—
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2411yescharacteristic
272#4343—464no—
273#4339—232no—
274C2×D44—216no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—28no—
278C2×D44—24no—
279C2×D44—232no—
280C2×D44—48no—
281C2×D44—44no—
282C2×D44—48no—
283C2×D44—48no—
284C2×D44—432no—
285C2×D44C2418yes—
286C2×D44C2418yes—
287C2×D44C2414yes—
288C2×D44C2418yes—
289C2×D44C24116yes—
290C2×D44C2418yes—
291C2×D44C24116yes—
292C2×D44C24116yes—
293C2×D44C24116yes—
294C2×C4×D11—28no—
295C2×C4×D11—24no—
296C2×C4×D11—24no—
297C2×C4×D11—24no—
298C2×C4×D11—24no—
299C2×C4×D11—28no—
300C2×C4×D11—232no—
301C2×C4×D11—48no—
302C2×C4×D11—44no—
303C2×C4×D11—48no—
304C2×C4×D11—48no—
305C2×C4×D11C2414yes—
306C2×C4×D11C2418yes—
307C2×C4×D11C2414yes—
308C2×C4×D11C2414yes—
309C2×C4×D11C2418yes—
310C2×C4×D11C2414yes—
311C2×C4×D11C2418yes—
312C2×C4×D11C24116yes—
313C2×C4×D11C24116yes—
314C2×C4×D11C24116yes—
315C2×Dic22—24no—
316C2×Dic22C2414yes—
317C11×C4⋊C4C2418yes—
318C11×C4⋊C4C2418yes—
319C11×C4⋊C4C2414yes—
320C11×C4⋊C4C2414yes—
321C11×C4⋊C4C24116yes—
322C11×C4⋊C4C2414yes—
323C11×C4⋊C4C2414yes—
324C11×C4⋊C4C24116yes—
325C11×C4⋊C4C24116yes—
326C11×C22⋊C4C2418yes—
327C11×C22⋊C4C2418yes—
328C42×C11C2418yes—
329C42×C11C2418yes—
330C22⋊Dic11C2418yes—
331(C2×D11)⋊C4C2418yes—
332(C2×D11)⋊C4C2418yes—
333(C2×D11)⋊C4C24116yes—
334(C2×D11)⋊C4C24116yes—
335(C2×D11)⋊C4C2418yes—
336(C2×D11)⋊C4C2418yes—
337(C2×D11)⋊C4C2418yes—
338(C2×D11)⋊C4C2418yes—
339(C2×D11)⋊C4C24116yes—
340(C2×D11)⋊C4C24116yes—
341(C2×D11)⋊C4C24116yes—
342(C2×D11)⋊C4C24116yes—
343(C2×D11)⋊C4C24116yes—
344C4⋊Dic11C2414yes—
345C4⋊Dic11C2414yes—
346C4⋊Dic11C2418yes—
347C4⋊Dic11C2418yes—
348Dic11⋊C4C2418yes—
349Dic11⋊C4C2418yes—
350Dic11⋊C4C24116yes—
351C4×Dic11C2418yes—
352C4×Dic11C2418yes—
353C4×Dic11C2418yes—
354C4×Dic11C24116yes—
355#3494—1132no—
356C2×#555—112no—
357C2×#553—112no—
358C2×#553—112no—
359C2×#551—114no—
360C2×#547—112no—
361C2×#546—114no—
362C2×#544D1111yescharacteristic, complemented
363C2×#542—112no—
364C2×#540—112no—
365C2×#535—111no—
366C2×#532—112no—
367C2×#529—112no—
368C2×#525—111no—
369C22×#121—111no—
370C2×#520—111no—
371C2×#518—111no—
372C22×#117—111no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11C2×#4114yes—
376C23×C11C2512yes—
377C23×C11C2511yescharacteristic
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—28no—
381C22×D11—22no—
382C22×D11—24no—
383C22×D11—28no—
384C22×D11—24no—
385C22×D11—28no—
386C22×D11—22no—
387C22×D11—28no—
388C22×D11—24no—
389C22×D11—22no—
390C22×D11—216no—
391C22×D11—28no—
392C22×D11—44no—
393C22×D11—48no—
394C22×D11—48no—
395C22×D11—416no—
396C22×D11—816no—
397C22×D11H(5,𝔽2)14yes—
398C22×D11C2512yes—
399C22×D11C2518yes—
400C22×D11C2514yes—
401C22×D11C2512yes—
402Q8×C11—416no—
403C2×C4×C11—24no—
404C2×C4×C11—24no—
405C2×C4×C11—28no—
406C2×C4×C11—24no—
407C2×C4×C11—24no—
408C2×C4×C11—48no—
409C2×C4×C11C2×#4114yes—
410C2×C4×C11C2×#4114yes—
411C2×C4×C11C2×#41116yescomplemented
412C2×C4×C11C2514yes—
413C2×C4×C11C2514yes—
414C2×C4×C11C2518yes—
415C2×C4×C11C2514yes—
416C2×C4×C11C2514yes—
417C2×C4×C11C2512yes—
418C2×C4×C11C2512yes—
419C22⋊D11—216no—
420C2×Dic11—24no—
421C2×Dic11—28no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—24no—
425C2×Dic11—24no—
426C2×Dic11C2514yes—
427C2×Dic11C2512yes—
428C2×Dic11C2514yes—
429C2×Dic11C2514yes—
430C2×Dic11C2512yes—
431D44—232no—
432D44—216no—
433D44—216no—
434D44—216no—
435D44—28no—
436D44—416no—
437D44—48no—
438D44—416no—
439D44—416no—
440C4×D11—216no—
441C4×D11—28no—
442C4×D11—28no—
443C4×D11—28no—
444C4×D11—28no—
445C4×D11—216no—
446C4×D11—416no—
447C4×D11—48no—
448C4×D11—416no—
449C4×D11—416no—
450Dic22—28no—
451C22×#41—114no—
452C22×#41—111no—
453C23×D4—111no—
454C23×D4—112no—
455C24×C4—111no—
456#555—1132no—
457#553—1132no—
458#553—1132no—
459#551—1164no—
460#547—1132no—
461#546—1164no—
462#544C2×D11116yescomplemented
463#542—1132no—
464#540—1132no—
465#535—1116no—
466#532—1132no—
467C2×C4⋊Q8C2×D1112yescomplemented
468C2×C4⋊Q8C2×D1112yescomplemented
469C2×#127—112no—
470#529—1132no—
471C2×#126—114no—
472C2×#126—114no—
473C2×#125C2×D1112yescomplemented
474C2×#125C2×D1112yescomplemented
475C2×#124—114no—
476C2×#124—114no—
477C2×#124—112no—
478#525—1116no—
479C2×#123—114no—
480C2×#123—114no—
481C2×#123—114no—
482C2×#123—114no—
483C2×#123—112no—
484C2×C22⋊Q8—114no—
485C2×C22⋊Q8—111no—
486C2×C22⋊Q8—111no—
487C2×C22⋊Q8C2×D1114yes—
488C2×#121—112no—
489C2×#121—112no—
490C2×#121—112no—
491C2×#121—112no—
492C2×#121—1116no—
493C2×#121—111no—
494C2×#121—111no—
495C2×#121—114no—
496C2×#121—112no—
497C2×#121—112no—
498C2×#121—114no—
499C2×#121—114no—
500C2×#120—112no—
501C2×#120—114no—
502#520—1116no—
503#518—1116no—
504C2×C4×Q8—112no—
505C2×C4×D4—114no—
506C2×C4×D4—112no—
507C2×C4×D4—112no—
508C2×C4×D4—112no—
509C2×C4×D4—114no—
510C2×C4×D4—114no—
511C2×C4×D4—112no—
512C2×C4×D4—112no—
513C2×C4×D4—112no—
514C2×C4×D4—112no—
515C2×#117—111no—
516C2×#117—1116no—
517C2×#117—111no—
518C2×#117—111no—
519C2×#117—112no—
520C2×#117—114no—
521C2×#117—112no—
522C2×#117—112no—
523C2×#117C2×D1111yescharacteristic
524C2×#117C2×D1111yescharacteristic
525C22×C4⋊C4—111no—
526C22×C4⋊C4—111no—
527C22×C4⋊C4—112no—
528C22×C4⋊C4C2×D1111yescharacteristic
529C22×C22⋊C4—112no—
530C22×C22⋊C4—112no—
531C22×C22⋊C4—114no—
532C22×C42—112no—
533C22×C11—22no—
534C22×C11—22no—
535C22×C11—28no—
536C22×C11C22×#4114yes—
537C22×C11C22×#4112yes—
538C22×C11C2×H(5,𝔽2)12yes—
539C22×C11#58512yes—
540C22×C11C2611yescharacteristic
541C2×D11—22no—
542C2×D11—22no—
543C2×D11—28no—
544C2×D11—22no—
545C2×D11—28no—
546C2×D11—24no—
547C2×D11—22no—
548C2×D11—28no—
549C2×D11—24no—
550C2×D11—28no—
551C2×D11—22no—
552C2×D11—24no—
553C2×D11—416no—
554C2×D11—48no—
555C2×D11—44no—
556C2×D11—416no—
557C2×D11—816no—
558C2×D11C2×H(5,𝔽2)14yes—
559C4×C11—28no—
560C4×C11—24no—
561C4×C11—24no—
562C4×C11—24no—
563C4×C11—24no—
564C4×C11C22×#4114yes—
565C4×C11C22×#4114yes—
566Dic11—24no—
567Dic11—22no—
568Dic11—22no—
569Dic11—24no—
570Dic11—24no—
571C25—111no—
572C25—112no—
573C2×#41—1132no—
574C2×#41—118no—
575C2×#41—228no—
576C2×#41—4416no—
577C22×Q8—111no—
578C22×Q8C22×D1114yes—
579C22×D4—112no—
580C22×D4—112no—
581C22×D4—112no—
582C22×D4—111no—
583C22×D4—112no—
584C22×D4—114no—
585C22×D4—118no—
586C22×D4—112no—
587C22×D4—114no—
588C22×D4—114no—
589C22×D4—114no—
590C22×D4—1116no—
591C22×D4—228no—
592C22×D4—448no—
593C23×C4—111no—
594C23×C4—112no—
595C23×C4—111no—
596C23×C4—112no—
597C23×C4—111no—
598C23×C4—111no—
599C23×C4—118no—
600C23×C4—111no—
601C23×C4—112no—
602C23×C4—114no—
603C23×C4—114no—
604C23×C4—114no—
605C23×C4—228no—
606C23×C4C22×D1112yes—
607C23×C4C22×D1111yescharacteristic
608C4⋊Q8C22×D11116yescomplemented
609C4⋊Q8C22×D11116yescomplemented
610#127—1116no—
611#126—1132no—
612#126—1132no—
613#125C22×D11116yescomplemented
614#125C22×D11116yescomplemented
615#124—1132no—
616#124—1132no—
617#124—1116no—
618#123—1132no—
619#123—1132no—
620#123—1132no—
621#123—1132no—
622#123—1116no—
623C22⋊Q8—1132no—
624C22⋊Q8—118no—
625C22⋊Q8—118no—
626C22⋊Q8C22×D11132yes—
627#121—1116no—
628#121—1116no—
629#121—1116no—
630#121—1116no—
631#121—118no—
632#121—118no—
633#121—1132no—
634#121—1116no—
635#121—1116no—
636#121—1132no—
637#121—1132no—
638#120—1116no—
639#120—1132no—
640C4×Q8—1116no—
641C4×D4—1132no—
642C4×D4—1116no—
643C4×D4—1116no—
644C4×D4—1116no—
645C4×D4—1132no—
646C4×D4—1132no—
647C4×D4—1116no—
648C4×D4—1116no—
649C4×D4—1116no—
650C4×D4—1116no—
651#117—118no—
652#117—118no—
653#117—118no—
654#117—1116no—
655#117—1132no—
656#117—1116no—
657#117—1116no—
658#117C22×D1118yes—
659#117C22×D1118yes—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4—114no—
665C2×C4⋊C4—112no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—118no—
668C2×C4⋊C4—118no—
669C2×C4⋊C4—1116no—
670C2×C4⋊C4C22×D1112yes—
671C2×C4⋊C4C22×D1111yescharacteristic
672C2×C4⋊C4C22×D1111yescharacteristic
673C2×C4⋊C4C22×D1112yes—
674C2×C4⋊C4C22×D1118yes—
675C2×C4⋊C4C22×D1114yes—
676C2×C4⋊C4C22×D1111yescharacteristic
677C2×C4⋊C4C22×D1111yescharacteristic
678C2×C4⋊C4C22×D1114yes—
679C2×C4⋊C4C22×D1114yes—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
685C2×C22⋊C4—114no—
686C2×C22⋊C4—114no—
687C2×C22⋊C4—1116no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—1116no—
696C2×C22⋊C4—1132no—
697C2×C22⋊C4C22×D1112yes—
698C2×C22⋊C4C22×D1112yes—
699C2×C42—112no—
700C2×C42—112no—
701C2×C42—114no—
702C2×C42—112no—
703C2×C42—1116no—
704C2×C42C22×D1112yes—
705C2×C42C22×D1112yes—
706C2×C11—24no—
707C2×C11#349414yescomplemented
708C2×C11C23×#4111yescharacteristic
709C2×C11C22×H(5,𝔽2)11yescharacteristic
710C2×C11C2×#58511yescharacteristic
711D11—24no—
712D11—44no—
713D11—42no—
714D11—48no—
715C24—111no—
716C24—111no—
717C24—114no—
718C24—112no—
719C24—114no—
720C24—118no—
721C24—224no—
722C24—224no—
723C24—228no—
724C24—442no—
725C24—444no—
726C24—444no—
727C24C23×D1111yescharacteristic
728#41—2232no—
729#41—4464no—
730C2×Q8—48no—
731C2×Q8—114no—
732C2×Q8—224no—
733C2×Q8C23×D11116yes—
734C2×D4—118no—
735C2×D4—118no—
736C2×D4—118no—
737C2×D4—114no—
738C2×D4—118no—
739C2×D4—1116no—
740C2×D4—118no—
741C2×D4—1116no—
742C2×D4—1116no—
743C2×D4—1116no—
744C2×D4—2216no—
745C2×D4—228no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—224no—
750C2×D4—2232no—
751C2×D4—448no—
752C2×D4—448no—
753C2×D4—444no—
754C2×D4—448no—
755C2×D4—4432no—
756C22×C4—44no—
757C22×C4—114no—
758C22×C4—111no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—111no—
763C22×C4—114no—
764C22×C4—118no—
765C22×C4—114no—
766C22×C4—118no—
767C22×C4—114no—
768C22×C4—114no—
769C22×C4—118no—
770C22×C4—1116no—
771C22×C4—1116no—
772C22×C4—1116no—
773C22×C4—228no—
774C22×C4—224no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—224no—
778C22×C4—224no—
779C22×C4—228no—
780C22×C4—2232no—
781C22×C4—448no—
782C22×C4—448no—
783C22×C4—448no—
784C22×C4—444no—
785C22×C4#434318yescomplemented
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C22×C4C23×D1114yes—
789C22×C4C23×D1112yes—
790C22×C4C23×D1112yes—
791C22×C4C23×D1118yes—
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C22×C4C23×D1114yes—
795C4⋊C4—114no—
796C4⋊C4—114no—
797C4⋊C4—118no—
798C4⋊C4—118no—
799C4⋊C4—1116no—
800C4⋊C4—118no—
801C4⋊C4—118no—
802C4⋊C4C23×D1118yes—
803C4⋊C4C23×D1114yes—
804C4⋊C4C23×D1114yes—
805C4⋊C4C23×D1118yes—
806C4⋊C4C23×D11116yes—
807C4⋊C4C23×D1114yes—
808C4⋊C4C23×D1114yes—
809C4⋊C4C23×D11116yes—
810C4⋊C4C23×D11116yes—
811C22⋊C4—118no—
812C22⋊C4—118no—
813C22⋊C4—118no—
814C22⋊C4—1116no—
815C22⋊C4—1116no—
816C22⋊C4—1116no—
817C22⋊C4—1116no—
818C22⋊C4—1116no—
819C22⋊C4—1116no—
820C22⋊C4—118no—
821C22⋊C4—118no—
822C22⋊C4—1116no—
823C22⋊C4—118no—
824C22⋊C4—118no—
825C22⋊C4C23×D1118yes—
826C22⋊C4C23×D1118yes—
827C42—118no—
828C42—118no—
829C42—118no—
830C42—1116no—
831C42C23×D1118yes—
832C42C23×D1118yes—
833C11C2×#349411yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—114no—
837C23—112no—
838C23—112no—
839C23—118no—
840C23—114no—
841C23—228no—
842C23—222no—
843C23—222no—
844C23—228no—
845C23—222no—
846C23—224no—
847C23—228no—
848C23—224no—
849C23—228no—
850C23—222no—
851C23—228no—
852C23—224no—
853C23—222no—
854C23—2216no—
855C23—444no—
856C23—448no—
857C23—448no—
858C23—4416no—
859C23—8816no—
860C23C2×#434314yes—
861C23C24×D1112yes—
862C23C24×D1111yescharacteristic
863Q8—416no—
864Q8—228no—
865D4—2232no—
866D4—2216no—
867D4—2216no—
868D4—2216no—
869D4—2216no—
870D4—228no—
871D4—4416no—
872D4—4416no—
873D4—448no—
874D4—4416no—
875C2×C4—28no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—48no—
881C2×C4—112no—
882C2×C4—114no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—112no—
886C2×C4—2216no—
887C2×C4—228no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—224no—
891C2×C4—224no—
892C2×C4—224no—
893C2×C4—228no—
894C2×C4—228no—
895C2×C4—228no—
896C2×C4—228no—
897C2×C4—2216no—
898C2×C4—4416no—
899C2×C4—4416no—
900C2×C4—4416no—
901C2×C4—448no—
902C2×C4C2×#434314yes—
903C2×C4C2×#434314yes—
904C2×C4C2×#4343116yescomplemented
905C2×C4C24×D1114yes—
906C2×C4C24×D1114yes—
907C2×C4C24×D1118yes—
908C2×C4C24×D1114yes—
909C2×C4C24×D1114yes—
910C2×C4C24×D1112yes—
911C2×C4C24×D1112yes—
912C22—22no—
913C22—22no—
914C22—28no—
915C22—114no—
916C22—222no—
917C22—222no—
918C22—228no—
919C22—222no—
920C22—224no—
921C22—228no—
922C22—224no—
923C22—228no—
924C22—222no—
925C22—228no—
926C22—224no—
927C22—222no—
928C22—4416no—
929C22—444no—
930C22—4416no—
931C22—448no—
932C22—8816no—
933C22C22×#434314yes—
934C22C22×#434312yes—
935C22D11×H(5,𝔽2)12yes—
936C22#1062345712yes—
937C22C25×D1111yescharacteristic
938C4—28no—
939C4—24no—
940C4—24no—
941C4—24no—
942C4—24no—
943C4—222no—
944C4—222no—
945C4—224no—
946C4—224no—
947C4—224no—
948C4C22×#434314yes—
949C4C22×#434314yes—
950C2—24no—
951C2—224no—
952C2—442no—
953C2—448no—
954C2—444no—
955C2#1308235414yesdirect product factor
956C2C23×#434311yescharacteristic
957C2C2×D11×H(5,𝔽2)11yescharacteristic
958C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
hypercenterC2×#544D11
hypocenterC11C2×#3494
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082354C2direct (N × H)
2. C2×#10623265C2semidirect
3. C2×#10623226C2semidirect
4. C2×#10623226C2semidirect
5. C2×#10623168C2semidirect
6. C2×#10623257C2semidirect
7. C2×#10623161C2semidirect
8. C2×#10623264C2semidirect
9. C2×#10623229C2semidirect
10. C2×#10623056C2semidirect
11. C2×#10623256C2semidirect
12. C2×#10623222C2semidirect
13. C2×#10623055C2semidirect
14. C22×#66948C2semidirect
15. C2×#10623035C2semidirect
16. C2×#10623052C2semidirect
17. C2×D11×#117C2semidirect
18. C2×C11×#544C2semidirect
19. C22×#4343C22semidirect
24. C11×#544C22semidirect
25. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×C4⋊Q8C22semidirect
27. C2×C11×#125C22semidirect
28. C2×C11×#125C22semidirect
33. C2×#67000C22semidirect
34. C2×#67000C22semidirect
35. C2×#66999C22semidirect
39. #10623265C22semidirect
40. #10623264C22semidirect
41. #10623257C22semidirect
42. #10623256C22semidirect
43. #10623229C22semidirect
44. #10623226C22semidirect
45. #10623226C22semidirect
46. #10623222C22semidirect
47. #10623168C22semidirect
48. #10623161C22semidirect
49. #10623056C22semidirect
50. #10623055C22semidirect
51. #10623052C22semidirect
52. D11×#117C22semidirect
53. C2×#66951C22semidirect
54. C2×#66951C22semidirect
55. C2×#66950C22semidirect
56. C2×#66950C22semidirect
61. C2×#66948C22semidirect
62. C2×#66948C22semidirect
63. C2×#66948C22semidirect
64. C2×#66948C22semidirect
65. C2×#66948C22semidirect
66. C2×#66948C22semidirect
67. C2×#66948C22semidirect
68. C2×#66948C22semidirect
69. C2×#66947C22semidirect
70. C2×#66947C22semidirect
71. C2×#66947C22semidirect
72. C2×#66947C22semidirect
73. #10623035C22semidirect
74. C2×#66946C22semidirect
75. C2×#66946C22semidirect
76. C2×#66946C22semidirect
77. C2×#66946C22semidirect
78. C2×#66946C22semidirect
79. C2×#66945C22semidirect
80. C2×#66945C22semidirect
81. C2×#66945C22semidirect
82. C2×#66945C22semidirect
83. C2×C4⋊C4×D11C22semidirect
84. C2×C4⋊C4×D11C22semidirect
85. C2×C4⋊C4×D11C22semidirect
86. C2×#66940C22semidirect
93. C2×#66928C22semidirect
94. C2×#66927C22semidirect
95. C2×C4×D44C22semidirect
96. C2×C4×D44C22semidirect
97. C2×C4×D44C22semidirect
98. C2×C4×D44C22semidirect
99. C2×#66925C22semidirect
100. C2×C42×D11C22semidirect
109. C2×#4343C23semidirect
138. C11×C4⋊Q8C23semidirect
139. C11×C4⋊Q8C23semidirect
140. C11×#125C23semidirect
141. C11×#125C23semidirect
160. #67000C23semidirect
161. #67000C23semidirect
162. #66999C23semidirect
190. #66951C23semidirect
191. #66951C23semidirect
192. #66950C23semidirect
193. #66950C23semidirect
198. #66948C23semidirect
199. #66948C23semidirect
200. #66948C23semidirect
201. #66948C23semidirect
202. #66948C23semidirect
203. #66948C23semidirect
204. #66948C23semidirect
205. #66947C23semidirect
206. #66947C23semidirect
207. #66947C23semidirect
208. #66947C23semidirect
209. #66946C23semidirect
210. #66946C23semidirect
211. #66946C23semidirect
212. #66946C23semidirect
213. #66946C23semidirect
214. #66945C23semidirect
215. #66945C23semidirect
216. #66945C23semidirect
217. #66945C23semidirect
218. C4⋊C4×D11C23semidirect
219. C4⋊C4×D11C23semidirect
220. C4⋊C4×D11C23semidirect
221. #66940C23semidirect
228. #66928C23semidirect
229. #66927C23semidirect
230. C4×D44C23semidirect
231. C4×D44C23semidirect
232. C4×D44C23semidirect
233. C4×D44C23semidirect
234. #66925C23semidirect
235. C42×D11C23semidirect
253. C22×C4×C11#41semidirect
362. C2×#544D11semidirect
411. C2×C4×C11C2×#41semidirect
462. #544C2×D11semidirect
467. C2×C4⋊Q8C2×D11semidirect
468. C2×C4⋊Q8C2×D11semidirect
473. C2×#125C2×D11semidirect
474. C2×#125C2×D11semidirect
608. C4⋊Q8C22×D11semidirect
609. C4⋊Q8C22×D11semidirect
613. #125C22×D11semidirect
614. #125C22×D11semidirect
707. C2×C11#3494semidirect
785. C22×C4#4343semidirect
833. C11C2×#3494semidirect
904. C2×C4C2×#4343semidirect
955. C2#13082354direct (N × H)

Maximal subgroups

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

subgroupindex
#130823542
C2×#106232652
C2×#106232262
C2×#106231682
C2×#106232572
C2×#106231612
C2×#106232642
C2×#106232292
C2×#106230562
C2×#106232562
C2×#106232222
C2×#106230552
C22×#669482
C2×#106230352
C2×#106230522
C2×D11×#1172
C2×C11×#5442
C2×#349411