Finite Group Databasebeta

← C2×#13082838 #15660997

Subgroups — C2×#13082838 #15660997

Order 2816.

7962 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082838C2132yesmaximal, direct product factor
2C2×#10623152C214yesmaximal, complemented
3C2×#10623042C212yesmaximal, complemented
4C2×#10623129C212yesmaximal, complemented
5C2×#10623142C212yesmaximal, complemented
6C2×#10623337C214yesmaximal, complemented
7C2×#10623337C212yesmaximal, complemented
8C2×#10623014C212yesmaximal, complemented
9C2×#10623134C212yesmaximal, complemented
10C2×#10623133C212yesmaximal, complemented
11C2×#10623025C212yesmaximal, complemented
12C2×#10623139C212yesmaximal, complemented
13C2×#10623128C212yesmaximal, complemented
14C2×#10623322C211yesmaximal, characteristic, complemented
15C22×#66977C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2212yes—
19C24×C4×C11C2211yescharacteristic
20C22×#4341C2214yescomplemented
21C22×#4341C2212yescomplemented
22C22×#4339C2211yescharacteristic, complemented
23C23×Dic22C2211yescharacteristic, complemented
24C2×C11×#121C2212yes—
25C2×C11×#121C2212yes—
26C2×C11×#121C2212yes—
27C2×C11×#121C2212yes—
28C2×C11×#121C22116yescomplemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2212yes—
31C2×#67006C2212yes—
32C2×#67006C2214yes—
33C22×C22⋊Dic11C2214yes—
34C22×C22⋊Dic11C2212yes—
35#10623337C22164yescomplemented
36#10623337C22132yescomplemented
37C2×#66992C2214yescomplemented
38C2×#66992C2214yescomplemented
39C2×#66992C2214yescomplemented
40C2×#66991C2214yescomplemented
41C2×#66991C2212yescomplemented
42C2×#66989C2214yescomplemented
43C2×#66989C2212yescomplemented
44C2×#66988C2214yescomplemented
45C2×#66988C2214yescomplemented
46C2×#66988C2214yescomplemented
47C2×D4×Dic11C2214yescomplemented
48C2×D4×Dic11C2212yescomplemented
49#10623322C22116yescomplemented
50C2×#66983C2211yescharacteristic
51C2×#66983C2211yescharacteristic, complemented
52C2×#66982C2212yescomplemented
53C2×C4×C22⋊D11C2212yes—
54C2×C4×C22⋊D11C2214yes—
55C2×C4×C22⋊D11C2212yescomplemented
56C2×#66979C2211yescharacteristic, complemented
57C22×C4⋊Dic11C2211yescharacteristic, complemented
58C2×#66977C2211yescharacteristic
59C2×#66977C2214yes—
60C2×#66977C2212yes—
61C2×#66977C2212yes—
62C2×#66977C2211yescharacteristic, complemented
63C2×#66977C2212yescomplemented
64C2×#66977C2212yescomplemented
65C2×#66977C22116yescomplemented
66C22×Dic11⋊C4C2212yescomplemented
67#10623152C22164yescomplemented
68#10623142C22132yescomplemented
69#10623139C22132yescomplemented
70#10623134C22132yescomplemented
71#10623133C22132yescomplemented
72#10623129C22132yescomplemented
73#10623128C22132yescomplemented
74#10623042C22132yescomplemented
75C2×#66950C2212yescomplemented
76C2×#66949C2214yescomplemented
77C2×C4⋊C4×D11C2212yescomplemented
78C2×#66942C2214yescomplemented
79C2×#66941C2212yescomplemented
80C2×#66940C2212yescomplemented
81#10623025C22132yescomplemented
82C2×#66938C2214yescomplemented
83C2×#66937C2214yescomplemented
84C2×#66936C2214yescomplemented
85#10623014C22132yescomplemented
86C2×#66932C2214yescomplemented
87C2×#66931C2214yescomplemented
88C2×#66931C2214yescomplemented
89C2×#66931C2214yescomplemented
90C2×#66931C2214yescomplemented
91C25×C11C2311yescharacteristic
92C25×C11C2312yes—
93C22×D4×C11—44no—
94C22×D4×C11—48no—
95C22×D4×C11C2314yes—
96C22×D4×C11C2312yes—
97C22×D4×C11C2312yes—
98C22×D4×C11C2314yes—
99C22×D4×C11C2318yes—
100C22×D4×C11C23116yes—
101C23×C4×C11—44no—
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2312yes—
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2318yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2312yes—
115C23×Dic11C2312yes—
116C23×Dic11C2314yes—
117C23×Dic11C2314yes—
118C23×Dic11C2312yes—
119C2×#4341—48no—
120C2×#4341—416no—
121C2×#4341C23132yescomplemented
122C2×#4341C23116yescomplemented
123C2×#4339—44no—
124C2×#4339C2318yescomplemented
125C22×D44C2311yescharacteristic
126C22×C4×D11C2312yes—
127C22×C4×D11C2314yes—
128C22×Dic22—44no—
129C22×Dic22C2312yes—
130C22×Dic22C2311yescharacteristic
131C22×Dic22C2312yes—
132C22×Dic22C2314yes—
133C22×Dic22C2318yescomplemented
134C11×#121C23116yes—
135C11×#121C23116yes—
136C11×#121C23116yes—
137C11×#121C23116yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2318yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C23116yes—
144#67006C23132yes—
145#67006C23116yes—
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2314yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C23132yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2314yes—
154C2×C22⋊Dic11C23116yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157#66992C23132yescomplemented
158#66992C23132yescomplemented
159#66992C23132yescomplemented
160#66991C23116yescomplemented
161#66991C23132yescomplemented
162#66989C23116yescomplemented
163#66989C23132yescomplemented
164#66988C23132yescomplemented
165#66988C23132yescomplemented
166#66988C23132yescomplemented
167D4×Dic11C23132yescomplemented
168D4×Dic11C23116yescomplemented
169#66983C2318yes—
170#66983C2318yescomplemented
171#66982C23116yescomplemented
172C4×C22⋊D11C23132yes—
173C4×C22⋊D11C23116yes—
174C4×C22⋊D11C23116yescomplemented
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2314yes—
177C2×(C2×D11)⋊C4C2312yes—
178#66979C2318yescomplemented
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2314yes—
182C2×C4⋊Dic11C2311yescharacteristic
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2318yescomplemented
185#66977C2318yes—
186#66977C23116yes—
187#66977C23132yes—
188#66977C23116yes—
189#66977C23116yescomplemented
190#66977C23116yescomplemented
191#66977C2318yescomplemented
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×Dic11⋊C4C2314yes—
196C2×Dic11⋊C4C2314yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2314yes—
199C2×Dic11⋊C4C23116yescomplemented
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C2312yes—
202#66950C23116yescomplemented
203#66949C23132yescomplemented
204C4⋊C4×D11C23116yescomplemented
205#66942C23132yescomplemented
206#66941C23116yescomplemented
207#66940C23116yescomplemented
208#66938C23132yescomplemented
209#66937C23132yescomplemented
210#66936C23132yescomplemented
211#66932C23132yescomplemented
212#66931C23132yescomplemented
213#66931C23132yescomplemented
214#66931C23132yescomplemented
215#66931C23132yescomplemented
216C2×#3536—111nomaximal, Sylow
217C24×C11—24no—
218C24×C11—24no—
219C24×C11—28no—
220C24×C11—42no—
221C24×C11—44no—
222C24×C11—44no—
223C24×C11C2411yescharacteristic
224C24×C11C2414yes—
225C24×C11C2414yes—
226C24×C11C2411yescharacteristic
227C24×C11C2411yescharacteristic
228C24×C11C2418yes—
229C23×D11C2412yes—
230C2×D4×C11—216no—
231C2×D4×C11—28no—
232C2×D4×C11—416no—
233C2×D4×C11—48no—
234C2×D4×C11—44no—
235C2×D4×C11—432no—
236C2×D4×C11C24116yes—
237C2×D4×C11C2418yes—
238C2×D4×C11C2418yes—
239C2×D4×C11C24116yes—
240C22×C4×C11—24no—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—416no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11—44no—
248C22×C4×C11C2414yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2414yes—
253C22×C4×C11C2414yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2414yes—
256C22×C4×C11C2414yes—
257C22×C4×C11C2418yes—
258C22×C4×C11C2414yes—
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—48no—
264C2×C22⋊D11—48no—
265C2×C22⋊D11C2418yes—
266C2×C22⋊D11C2418yes—
267C2×C22⋊D11C24116yes—
268C2×C22⋊D11C24116yes—
269C2×C22⋊D11C2418yes—
270C22×Dic11—28no—
271C22×Dic11—44no—
272C22×Dic11—48no—
273C22×Dic11—48no—
274C22×Dic11C2412yes—
275C22×Dic11C2414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2414yes—
279C22×Dic11C2418yes—
280C22×Dic11C24116yes—
281C22×Dic11C24116yes—
282C22×Dic11C2418yes—
283#4341—432no—
284#4341—464no—
285#4339—416no—
286C2×D44—42no—
287C2×D44C2414yes—
288C2×C4×D11—28no—
289C2×C4×D11—48no—
290C2×C4×D11C2418yes—
291C2×C4×D11C24116yes—
292C2×Dic22—28no—
293C2×Dic22—416no—
294C2×Dic22—44no—
295C2×Dic22—42no—
296C2×Dic22—48no—
297C2×Dic22C2418yes—
298C2×Dic22C2414yes—
299C2×Dic22C2418yes—
300C2×Dic22C24116yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2418yes—
303C11×C22⋊C4C24116yes—
304C11×C22⋊C4C24116yes—
305C22⋊Dic11C24116yes—
306C22⋊Dic11C24116yes—
307C22⋊Dic11C24116yes—
308C22⋊Dic11C24116yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C24116yes—
311C22⋊Dic11C24116yes—
312C22⋊Dic11C2418yes—
313C22⋊Dic11C2418yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C24116yes—
316(C2×D11)⋊C4C2418yes—
317C4⋊Dic11C2414yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C24116yes—
320C4⋊Dic11C2414yes—
321C4⋊Dic11C2418yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C24116yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C24116yes—
329C4×Dic11C24116yes—
330C4×Dic11C2418yes—
331#3536—1132no—
332C2×#562—114no—
333C2×#554—112no—
334C2×#548—112no—
335C2×#547—112no—
336C2×#546—114no—
337C2×#546—112no—
338C2×#543—112no—
339C2×#542—112no—
340C2×#539—112no—
341C2×#538—112no—
342C2×#537—112no—
343C2×#537—112no—
344C2×#525—111no—
345C22×C22⋊Q8—111no—
346C22×#121D1111yescharacteristic, complemented
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—28no—
352C23×C11—28no—
353C23×C11—22no—
354C23×C11—28no—
355C23×C11—22no—
356C23×C11—28no—
357C23×C11—22no—
358C23×C11—28no—
359C23×C11—216no—
360C23×C11—44no—
361C23×C11—48no—
362C23×C11—48no—
363C23×C11—416no—
364C23×C11—816no—
365C23×C11H(5,𝔽2)14yes—
366C23×C112−1+414yes—
367C23×C11C2512yes—
368C23×C11C2518yes—
369C23×C11C2512yes—
370C23×C11C2512yes—
371C23×C11C2511yescharacteristic
372C22×D11—24no—
373C22×D11—24no—
374C22×D11—24no—
375C22×D11C2514yes—
376D4×C11—232no—
377D4×C11—216no—
378D4×C11—48no—
379D4×C11—416no—
380C2×C4×C11—22no—
381C2×C4×C11—28no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—28no—
385C2×C4×C11—28no—
386C2×C4×C11—28no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—48no—
391C2×C4×C11H(5,𝔽2)14yes—
392C2×C4×C11C2518yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2512yes—
395C2×C4×C11C2512yes—
396C2×C4×C11C2512yes—
397C22⋊D11—216no—
398C22⋊D11—216no—
399C22⋊D11—48no—
400C22⋊D11—416no—
401C22⋊D11—416no—
402C2×Dic11—28no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—28no—
406C2×Dic11—216no—
407C2×Dic11—24no—
408C2×Dic11—48no—
409C2×Dic11—416no—
410C2×Dic11—416no—
411C2×Dic11C2514yes—
412C2×Dic11C2518yes—
413C2×Dic11C2514yes—
414C2×Dic11C2514yes—
415C2×Dic11C2518yes—
416D44—44no—
417C4×D11—216no—
418C4×D11—416no—
419Dic22—216no—
420Dic22—48no—
421Dic22—44no—
422Dic22—416no—
423C22×#41—114no—
424C22×#41—112no—
425C22×#41—111no—
426C23×Q8—111no—
427C23×D4C2×D1111yescharacteristic
428C23×D4C2×D1112yes—
429C24×C4C2×D1111yescharacteristic
430#562—1164no—
431#554—1132no—
432#548—1132no—
433#547—1132no—
434#546—1164no—
435#546—1132no—
436#543—1132no—
437#542—1132no—
438#539—1132no—
439#538—1132no—
440#537—1132no—
441#537—1132no—
442C2×C4⋊Q8—112no—
443C2×#126—114no—
444C2×#125—114no—
445C2×#124—112no—
446C2×#124—114no—
447C2×#124—114no—
448#525—1116no—
449C2×#123—114no—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—112no—
453C2×#123—114no—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8—112no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—114no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—1116no—
461C2×C22⋊Q8—111no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—114no—
466C2×C22⋊Q8—114no—
467C2×C22⋊Q8—114no—
468C2×#121—112no—
469C2×#121—114no—
470C2×#121—114no—
471C2×#121—114no—
472C2×#121—114no—
473C2×#121—111no—
474C2×#121—111no—
475C2×#121—114no—
476C2×#121C2×D1112yes—
477C2×#121C2×D1112yes—
478C2×#121C2×D1112yes—
479C2×#121C2×D1112yes—
480C2×#121C2×D11116yescomplemented
481C2×#120—112no—
482C2×#120—114no—
483C2×C4×Q8—112no—
484C2×C4×D4—114no—
485C2×C4×D4—112no—
486C2×C4×D4—112no—
487C2×C4×D4—114no—
488C2×C4×D4—112no—
489C2×#117—111no—
490C22×C4⋊C4—112no—
491C22×C4⋊C4—111no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4—112no—
495C22×C22⋊C4—114no—
496C22×C22⋊C4C2×D1112yes—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—28no—
502C22×C11—28no—
503C22×C11—22no—
504C22×C11—28no—
505C22×C11—28no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—28no—
509C22×C11—416no—
510C22×C11—44no—
511C22×C11—416no—
512C22×C11—816no—
513C22×C11C2×H(5,𝔽2)14yes—
514C22×C11C2×H(5,𝔽2)12yes—
515C22×C11C2×H(5,𝔽2)12yes—
516C22×C11C2×2−1+414yes—
517C22×C11C2×2−1+412yes—
518C22×C11C2611yescharacteristic
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—24no—
522C2×D11—48no—
523C4×C11—22no—
524C4×C11—22no—
525C4×C11—22no—
526C4×C11—28no—
527C4×C11C2×H(5,𝔽2)14yes—
528Dic11—28no—
529Dic11—24no—
530Dic11—24no—
531Dic11—28no—
532Dic11—24no—
533C25C22×D1111yescharacteristic
534C25C22×D1112yes—
535C2×#41—1132no—
536C2×#41—1116no—
537C2×#41—118no—
538C2×#41—444no—
539C2×#41—4416no—
540C2×#41—448no—
541C22×Q8—112no—
542C22×Q8—111no—
543C22×Q8—112no—
544C22×Q8—114no—
545C22×Q8—118no—
546C22×Q8—444no—
547C22×D4—44no—
548C22×D4—48no—
549C22×D4—112no—
550C22×D4—112no—
551C22×D4—112no—
552C22×D4—114no—
553C22×D4—114no—
554C22×D4—111no—
555C22×D4C22×D1114yes—
556C22×D4C22×D1112yes—
557C22×D4C22×D1112yes—
558C22×D4C22×D1114yes—
559C22×D4C22×D1118yes—
560C22×D4C22×D11116yes—
561C23×C4—44no—
562C23×C4—112no—
563C23×C4—112no—
564C23×C4—114no—
565C23×C4—114no—
566C23×C4—112no—
567C23×C4—114no—
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1112yes—
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1118yes—
576C4⋊Q8—1116no—
577#126—1132no—
578#125—1132no—
579#124—1116no—
580#124—1132no—
581#124—1132no—
582#123—1132no—
583#123—1132no—
584#123—1132no—
585#123—1116no—
586#123—1132no—
587C22⋊Q8—1116no—
588C22⋊Q8—1116no—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—118no—
592C22⋊Q8—118no—
593C22⋊Q8—1132no—
594C22⋊Q8—1116no—
595C22⋊Q8—1132no—
596C22⋊Q8—1132no—
597C22⋊Q8—1132no—
598C22⋊Q8—1132no—
599C22⋊Q8—1132no—
600#121—1116no—
601#121—1132no—
602#121—1132no—
603#121—1132no—
604#121—1132no—
605#121—118no—
606#121—118no—
607#121—1132no—
608#121C22×D11116yes—
609#121C22×D11116yes—
610#121C22×D11116yes—
611#121C22×D11116yes—
612#120—1116no—
613#120—1132no—
614C4×Q8—1116no—
615C4×D4—1132no—
616C4×D4—1116no—
617C4×D4—1116no—
618C4×D4—1116no—
619C4×D4—1132no—
620#117—118no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—114no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—1116no—
627C2×C4⋊C4—118no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—1116no—
636C2×C4⋊C4C22×D1112yes—
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1118yes—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—1116no—
645C2×C22⋊C4—1132no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4C22×D1114yes—
654C2×C22⋊C4C22×D1114yes—
655C2×C22⋊C4C22×D11116yes—
656C2×C42—112no—
657C2×C42—114no—
658C2×C11—24no—
659C2×C11—24no—
660C2×C11—42no—
661C2×C11—48no—
662C2×C11#353614yescomplemented
663C2×C11C22×H(5,𝔽2)11yescharacteristic
664C2×C11C22×H(5,𝔽2)11yescharacteristic
665C2×C11C22×2−1+411yescharacteristic
666D11—44no—
667C24—24no—
668C24—24no—
669C24—28no—
670C24—42no—
671C24—44no—
672C24—44no—
673C24—112no—
674C24C23×D1111yescharacteristic
675C24C23×D1114yes—
676C24C23×D1114yes—
677C24C23×D1111yescharacteristic
678C24C23×D1111yescharacteristic
679C24C23×D1118yes—
680#41—4416no—
681#41—4464no—
682#41—4432no—
683C2×Q8—118no—
684C2×Q8—114no—
685C2×Q8—118no—
686C2×Q8—1116no—
687C2×Q8—228no—
688C2×Q8—444no—
689C2×Q8—442no—
690C2×Q8—448no—
691C2×Q8—4416no—
692C2×D4—216no—
693C2×D4—28no—
694C2×D4—416no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—432no—
698C2×D4—118no—
699C2×D4—118no—
700C2×D4—118no—
701C2×D4—1116no—
702C2×D4—1116no—
703C2×D4—114no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—442no—
707C2×D4—444no—
708C2×D4—448no—
709C2×D4—448no—
710C2×D4C23×D11116yes—
711C2×D4C23×D1118yes—
712C2×D4C23×D1118yes—
713C2×D4C23×D11116yes—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—416no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—44no—
722C22×C4—118no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—114no—
726C22×C4—112no—
727C22×C4—114no—
728C22×C4—118no—
729C22×C4—1116no—
730C22×C4—1116no—
731C22×C4—118no—
732C22×C4—1116no—
733C22×C4—228no—
734C22×C4—228no—
735C22×C4—448no—
736C22×C4—444no—
737C22×C4—448no—
738C22×C4—448no—
739C22×C4C23×D1114yes—
740C22×C4C23×D1114yes—
741C22×C4C23×D1114yes—
742C22×C4C23×D1114yes—
743C22×C4C23×D1111yescharacteristic
744C22×C4C23×D1111yescharacteristic
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1114yes—
747C22×C4C23×D1118yes—
748C22×C4C23×D1114yes—
749C22×C4C23×D1114yes—
750C22×C4C23×D1111yescharacteristic
751C4⋊C4—118no—
752C4⋊C4—1116no—
753C4⋊C4—1116no—
754C4⋊C4—1116no—
755C4⋊C4—118no—
756C4⋊C4—114no—
757C4⋊C4—114no—
758C4⋊C4—1116no—
759C4⋊C4—118no—
760C4⋊C4—118no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4C23×D1118yes—
764C4⋊C4C23×D1118yes—
765C22⋊C4—1116no—
766C22⋊C4—118no—
767C22⋊C4—1116no—
768C22⋊C4—1116no—
769C22⋊C4—1116no—
770C22⋊C4—118no—
771C22⋊C4—118no—
772C22⋊C4—1116no—
773C22⋊C4—1116no—
774C22⋊C4—118no—
775C22⋊C4—1116no—
776C22⋊C4—118no—
777C22⋊C4C23×D11116yes—
778C22⋊C4C23×D11116yes—
779C42—118no—
780C42—1116no—
781C11C2×#353611yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—28no—
788C23—28no—
789C23—28no—
790C23—22no—
791C23—28no—
792C23—22no—
793C23—28no—
794C23—216no—
795C23—44no—
796C23—48no—
797C23—48no—
798C23—416no—
799C23—816no—
800C23—114no—
801C23—224no—
802C23—224no—
803C23—224no—
804C23#6703714yes—
805C23#6704314yes—
806C23C24×D1112yes—
807C23C24×D1118yes—
808C23C24×D1112yes—
809C23C24×D1112yes—
810C23C24×D1111yescharacteristic
811Q8—2216no—
812Q8—448no—
813Q8—444no—
814Q8—4416no—
815D4—232no—
816D4—216no—
817D4—48no—
818D4—416no—
819D4—2216no—
820D4—2216no—
821D4—444no—
822D4—448no—
823D4—4416no—
824D4—4416no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—48no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—118no—
839C2×C4—114no—
840C2×C4—118no—
841C2×C4—228no—
842C2×C4—224no—
843C2×C4—2216no—
844C2×C4—224no—
845C2×C4—228no—
846C2×C4—224no—
847C2×C4—2216no—
848C2×C4—4416no—
849C2×C4—448no—
850C2×C4—4416no—
851C2×C4—4416no—
852C2×C4#6703714yes—
853C2×C4C24×D1118yes—
854C2×C4C24×D1112yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C2×C4C24×D1112yes—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—28no—
863C22—28no—
864C22—22no—
865C22—28no—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—28no—
870C22—416no—
871C22—44no—
872C22—416no—
873C22—816no—
874C22—224no—
875C22—224no—
876C22—224no—
877C22—448no—
878C22C2×#6703714yes—
879C22C2×#6703712yes—
880C22C2×#6703712yes—
881C22C2×#6704314yes—
882C22C2×#6704312yes—
883C22C25×D1111yescharacteristic
884C4—22no—
885C4—22no—
886C4—22no—
887C4—28no—
888C4—228no—
889C4—224no—
890C4—224no—
891C4—228no—
892C4—224no—
893C4C2×#6703714yes—
894C2—24no—
895C2—24no—
896C2—42no—
897C2—48no—
898C2—444no—
899C2#1308283814yesdirect product factor
900C2C22×#6703711yescharacteristic
901C2C22×#6703711yescharacteristic
902C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#121C2
socleC23×C11C25
hypercenterC22×#121D11
hypocenterC11C2×#3536
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. #13082838C2direct (N × H)
2. C2×#10623152C2semidirect
3. C2×#10623042C2semidirect
4. C2×#10623129C2semidirect
5. C2×#10623142C2semidirect
6. C2×#10623337C2semidirect
7. C2×#10623337C2semidirect
8. C2×#10623014C2semidirect
9. C2×#10623134C2semidirect
10. C2×#10623133C2semidirect
11. C2×#10623025C2semidirect
12. C2×#10623139C2semidirect
13. C2×#10623128C2semidirect
14. C2×#10623322C2semidirect
15. C22×#66977C2semidirect
16. C22×C11×#121C2semidirect
20. C22×#4341C22semidirect
21. C22×#4341C22semidirect
22. C22×#4339C22semidirect
23. C23×Dic22C22semidirect
28. C2×C11×#121C22semidirect
35. #10623337C22semidirect
36. #10623337C22semidirect
37. C2×#66992C22semidirect
38. C2×#66992C22semidirect
39. C2×#66992C22semidirect
40. C2×#66991C22semidirect
41. C2×#66991C22semidirect
42. C2×#66989C22semidirect
43. C2×#66989C22semidirect
44. C2×#66988C22semidirect
45. C2×#66988C22semidirect
46. C2×#66988C22semidirect
47. C2×D4×Dic11C22semidirect
48. C2×D4×Dic11C22semidirect
49. #10623322C22semidirect
51. C2×#66983C22semidirect
52. C2×#66982C22semidirect
55. C2×C4×C22⋊D11C22semidirect
56. C2×#66979C22semidirect
57. C22×C4⋊Dic11C22semidirect
62. C2×#66977C22semidirect
63. C2×#66977C22semidirect
64. C2×#66977C22semidirect
65. C2×#66977C22semidirect
66. C22×Dic11⋊C4C22semidirect
67. #10623152C22semidirect
68. #10623142C22semidirect
69. #10623139C22semidirect
70. #10623134C22semidirect
71. #10623133C22semidirect
72. #10623129C22semidirect
73. #10623128C22semidirect
74. #10623042C22semidirect
75. C2×#66950C22semidirect
76. C2×#66949C22semidirect
77. C2×C4⋊C4×D11C22semidirect
78. C2×#66942C22semidirect
79. C2×#66941C22semidirect
80. C2×#66940C22semidirect
81. #10623025C22semidirect
82. C2×#66938C22semidirect
83. C2×#66937C22semidirect
84. C2×#66936C22semidirect
85. #10623014C22semidirect
86. C2×#66932C22semidirect
87. C2×#66931C22semidirect
88. C2×#66931C22semidirect
89. C2×#66931C22semidirect
90. C2×#66931C22semidirect
121. C2×#4341C23semidirect
122. C2×#4341C23semidirect
124. C2×#4339C23semidirect
133. C22×Dic22C23semidirect
157. #66992C23semidirect
158. #66992C23semidirect
159. #66992C23semidirect
160. #66991C23semidirect
161. #66991C23semidirect
162. #66989C23semidirect
163. #66989C23semidirect
164. #66988C23semidirect
165. #66988C23semidirect
166. #66988C23semidirect
167. D4×Dic11C23semidirect
168. D4×Dic11C23semidirect
170. #66983C23semidirect
171. #66982C23semidirect
174. C4×C22⋊D11C23semidirect
178. #66979C23semidirect
184. C2×C4⋊Dic11C23semidirect
189. #66977C23semidirect
190. #66977C23semidirect
191. #66977C23semidirect
199. C2×Dic11⋊C4C23semidirect
202. #66950C23semidirect
203. #66949C23semidirect
204. C4⋊C4×D11C23semidirect
205. #66942C23semidirect
206. #66941C23semidirect
207. #66940C23semidirect
208. #66938C23semidirect
209. #66937C23semidirect
210. #66936C23semidirect
211. #66932C23semidirect
212. #66931C23semidirect
213. #66931C23semidirect
214. #66931C23semidirect
215. #66931C23semidirect
346. C22×#121D11semidirect
480. C2×#121C2×D11semidirect
662. C2×C11#3536semidirect
781. C11C2×#3536semidirect
899. C2#13082838direct (N × H)

Maximal subgroups

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

subgroupindex
#130828382
C2×#106231522
C2×#106230422
C2×#106231292
C2×#106231422
C2×#106233372
C2×#106230142
C2×#106231342
C2×#106231332
C2×#106230252
C2×#106231392
C2×#106231282
C2×#106233222
C22×#669772
C22×C11×#1212
C2×#353611