Finite Group Databasebeta

← C2×#13082312 #15661822

Subgroups — C2×#13082312 #15661822

Order 2816.

7390 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082312C2132yesmaximal, direct product factor
2C2×#10623181C214yesmaximal, complemented
3C2×#10623044C214yesmaximal, complemented
4C2×#10623026C214yesmaximal, complemented
5C2×#10623189C214yesmaximal, complemented
6C2×#10623014C211yesmaximal, characteristic, complemented
7C2×#10623196C214yesmaximal, complemented
8C2×#10623335C211yesmaximal, characteristic
9C2×#10623180C214yesmaximal, complemented
10C22×#66982C211yesmaximal, characteristic, complemented
11C2×#10623329C211yesmaximal, characteristic, complemented
12C2×#10623017C211yesmaximal, characteristic, complemented
13C22×#66979C211yesmaximal, characteristic, complemented
14C22×C11×#123C211yesmaximal, characteristic, complemented
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C2×C11×#123C2214yes—
19C2×C11×#123C2212yescomplemented
20C2×C11×#123C2212yescomplemented
21C2×C11×#123C22116yescomplemented
22C22×C11×C4⋊C4C2212yescomplemented
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2212yescomplemented
25C2×#67006C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2212yescomplemented
30#10623335C22116yes—
31C2×#66992C2214yes—
32C2×#66990C2212yes—
33#10623329C22116yescomplemented
34C2×#66988C2212yes—
35C2×D4×Dic11C2214yes—
36C2×D4×Dic11C2214yescomplemented
37C2×#66982C2214yes—
38C2×#66982C2212yes—
39C2×#66982C2212yescomplemented
40C2×#66982C2212yescomplemented
41C2×#66982C22116yescomplemented
42C2×C4×C22⋊D11C2214yes—
43C22×(C2×D11)⋊C4C2212yescomplemented
44C2×#66979C2214yescomplemented
45C2×#66979C2212yescomplemented
46C2×#66979C2214yescomplemented
47C2×#66979C22116yescomplemented
48C22×C4⋊Dic11C2212yescomplemented
49C2×#66977C2214yescomplemented
50C22×Dic11⋊C4C2212yescomplemented
51C22×C4×Dic11C2212yescomplemented
52#10623196C22164yescomplemented
53#10623189C22164yescomplemented
54#10623181C22164yescomplemented
55#10623180C22164yescomplemented
56#10623044C22164yescomplemented
57C2×#66951C2214yescomplemented
58C2×#66951C2214yescomplemented
59C2×#66950C2214yescomplemented
60C2×#66945C2214yescomplemented
61C2×#66943C2214yescomplemented
62C2×#66942C2214yescomplemented
63C2×#66942C2214yescomplemented
64C2×#66940C2214yescomplemented
65#10623026C22164yescomplemented
66C2×#66939C2214yescomplemented
67C2×#66938C2214yescomplemented
68C2×#66936C2214yescomplemented
69#10623017C22116yescomplemented
70C2×(C22⋊D11)⋊C4C2214yescomplemented
71C2×(C22⋊D11)⋊C4C2214yescomplemented
72C2×C22⋊C4×D11C2212yescomplemented
73#10623014C22116yescomplemented
74C2×#66932C2214yescomplemented
75C2×#66932C2214yescomplemented
76C2×#66931C2214yescomplemented
77C2×#66931C2214yescomplemented
78C2×#66931C2214yescomplemented
79C2×#66930C2214yescomplemented
80C2×#66930C2212yescomplemented
81C25×C11C2311yescharacteristic
82C25×C11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C22×D4×C11—28no—
85C22×D4×C11C2312yes—
86C22×D4×C11C2312yes—
87C22×D4×C11C2318yes—
88C23×C4×C11—28no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2312yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2318yes—
95C23×C4×C11C2312yes—
96C22×C22⋊D11—28no—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2318yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2314yes—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C23×Dic11C2312yes—
104C23×Dic11C2312yes—
105C23×Dic11C2312yes—
106C22×C4×D11C2314yes—
107C22×Dic22C2314yes—
108C11×#123C23132yes—
109C11×#123C23116yescomplemented
110C11×#123C23116yescomplemented
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C23116yescomplemented
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2318yes—
119C2×C11×C22⋊C4C23116yescomplemented
120#67006C23116yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2318yes—
127C2×C22⋊Dic11C2318yes—
128C2×C22⋊Dic11C2318yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C23116yescomplemented
133#66992C23132yes—
134#66990C23116yes—
135#66988C23116yes—
136D4×Dic11C23132yes—
137D4×Dic11C23132yescomplemented
138#66982C23132yes—
139#66982C23116yes—
140#66982C23116yescomplemented
141#66982C23116yescomplemented
142C4×C22⋊D11C23132yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C23116yescomplemented
148#66979C23132yescomplemented
149#66979C23116yescomplemented
150#66979C23132yescomplemented
151C2×C4⋊Dic11C2314yes—
152C2×C4⋊Dic11C2314yes—
153C2×C4⋊Dic11C2314yes—
154C2×C4⋊Dic11C2314yes—
155C2×C4⋊Dic11C23116yescomplemented
156#66977C23132yescomplemented
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×Dic11⋊C4C2314yes—
163C2×Dic11⋊C4C23116yescomplemented
164C2×C4×Dic11C2314yes—
165C2×C4×Dic11C2314yes—
166C2×C4×Dic11C2314yes—
167C2×C4×Dic11C2314yes—
168C2×C4×Dic11C23116yescomplemented
169#66951C23132yescomplemented
170#66951C23132yescomplemented
171#66950C23132yescomplemented
172#66945C23132yescomplemented
173#66943C23132yescomplemented
174#66942C23132yescomplemented
175#66942C23132yescomplemented
176#66940C23132yescomplemented
177#66939C23132yescomplemented
178#66938C23132yescomplemented
179#66936C23132yescomplemented
180(C22⋊D11)⋊C4C23132yescomplemented
181(C22⋊D11)⋊C4C23132yescomplemented
182C22⋊C4×D11C23116yescomplemented
183#66932C23132yescomplemented
184#66932C23132yescomplemented
185#66931C23132yescomplemented
186#66931C23132yescomplemented
187#66931C23132yescomplemented
188#66930C23116yescomplemented
189#66930C23132yescomplemented
190C2×#3491—111nomaximal, Sylow
191C24×C11—24no—
192C24×C11—44no—
193C24×C11—44no—
194C24×C11#4118yes—
195C24×C11C2412yes—
196C24×C11C2411yescharacteristic
197C24×C11C2411yescharacteristic
198C24×C11C2411yescharacteristic
199C24×C11C2414yes—
200C24×C11C2414yes—
201C23×D11—24no—
202C23×D11—44no—
203C23×D11C2412yes—
204C23×D11C2414yes—
205C2×D4×C11—28no—
206C2×D4×C11—28no—
207C2×D4×C11—232no—
208C2×D4×C11C2418yes—
209C2×D4×C11C2418yes—
210C22×C4×C11—28no—
211C22×C4×C11—28no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—232no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2414yes—
220C22×C4×C11C2414yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2418yes—
223C22×C4×C11C2414yes—
224C22×C4×C11C2418yes—
225C22×C4×C11C2414yes—
226C22×C4×C11C2418yes—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—232no—
230C2×C22⋊D11—48no—
231C2×C22⋊D11C2418yes—
232C2×C22⋊D11C2418yes—
233C2×C22⋊D11C24116yes—
234C22×Dic11—24no—
235C22×Dic11—44no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11—48no—
239C22×Dic11C2414yes—
240C22×Dic11C2414yes—
241C22×Dic11C2412yes—
242C22×Dic11C2414yes—
243C22×Dic11C2414yes—
244C22×Dic11C24116yes—
245C22×Dic11C2418yes—
246C22×Dic11C2418yes—
247C22×Dic11C2418yes—
248C2×C4×D11—48no—
249C2×C4×D11C24116yes—
250C2×Dic22—48no—
251C2×Dic22C24116yes—
252C11×C4⋊C4C24116yes—
253C11×C4⋊C4C24116yes—
254C11×C22⋊C4C2418yes—
255C11×C22⋊C4C24116yes—
256C11×C22⋊C4C2418yes—
257C11×C22⋊C4C24116yes—
258C22⋊Dic11C24116yes—
259C22⋊Dic11C2418yes—
260C22⋊Dic11C2418yes—
261C22⋊Dic11C2418yes—
262C22⋊Dic11C24116yes—
263C22⋊Dic11C2418yes—
264C22⋊Dic11C2418yes—
265C22⋊Dic11C2418yes—
266(C2×D11)⋊C4C24116yes—
267(C2×D11)⋊C4C24116yes—
268(C2×D11)⋊C4C24116yes—
269(C2×D11)⋊C4C24116yes—
270C4⋊Dic11C24116yes—
271C4⋊Dic11C24116yes—
272C4⋊Dic11C24116yes—
273C4⋊Dic11C24116yes—
274Dic11⋊C4C24116yes—
275Dic11⋊C4C24116yes—
276Dic11⋊C4C24116yes—
277Dic11⋊C4C24116yes—
278Dic11⋊C4C24116yes—
279Dic11⋊C4C24116yes—
280C4×Dic11C24116yes—
281C4×Dic11C24116yes—
282C4×Dic11C24116yes—
283C4×Dic11C24116yes—
284#3491—1132no—
285C2×#552—114no—
286C2×#552—114no—
287C2×#551—114no—
288C2×#551—114no—
289C2×#543—111no—
290C2×#539—114no—
291C2×#534—111no—
292C2×#529—114no—
293C22×#123—111no—
294C22×#123D1111yescharacteristic, complemented
295C2×#518—111no—
296C2×#518—111no—
297C22×#117—111no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—24no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—416no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—88no—
308C23×C11C2×#4114yes—
309C23×C11C2×#4114yes—
310C23×C11C2×#4114yes—
311C23×C11C2×#41116yes—
312C23×C11C2514yes—
313C23×C11C2512yes—
314C23×C11C2512yes—
315C23×C11C2512yes—
316C23×C11C2511yescharacteristic
317C22×D11—24no—
318C22×D11—28no—
319C22×D11—28no—
320C22×D11—48no—
321C22×D11—88no—
322C22×D11C2514yes—
323D4×C11—216no—
324D4×C11—216no—
325C2×C4×C11—216no—
326C2×C4×C11—216no—
327C2×C4×C11—28no—
328C2×C4×C11—28no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—28no—
332C2×C4×C11—24no—
333C2×C4×C11—28no—
334C2×C4×C11—48no—
335C2×C4×C11C2514yes—
336C2×C4×C11C2514yes—
337C2×C4×C11C2518yes—
338C2×C4×C11C2514yes—
339C22⋊D11—216no—
340C22⋊D11—216no—
341C22⋊D11—416no—
342C2×Dic11—28no—
343C2×Dic11—24no—
344C2×Dic11—28no—
345C2×Dic11—28no—
346C2×Dic11—28no—
347C2×Dic11—48no—
348C2×Dic11—416no—
349C2×Dic11—48no—
350C2×Dic11—48no—
351C2×Dic11C2518yes—
352C2×Dic11C2514yes—
353C2×Dic11C2518yes—
354C2×Dic11C2518yes—
355C4×D11—416no—
356Dic22—416no—
357C23×D4—111no—
358C23×D4C2×D1111yescharacteristic
359C24×C4C2×D1111yescharacteristic
360#552—1164no—
361#552—1164no—
362#551—1164no—
363#551—1164no—
364#543—1116no—
365#539—1164no—
366#534—1116no—
367#529—1164no—
368C2×#126—114no—
369C2×#126—114no—
370C2×#126—114no—
371C2×#126—114no—
372C2×#125—114no—
373C2×#125—114no—
374C2×#125—114no—
375C2×#124—114no—
376C2×#123—112no—
377C2×#123—114no—
378C2×#123—112no—
379C2×#123—112no—
380C2×#123—112no—
381C2×#123—1116no—
382C2×#123—114no—
383C2×#123—114no—
384C2×#123C2×D1114yes—
385C2×#123C2×D1112yescomplemented
386C2×#123C2×D1112yescomplemented
387C2×#123C2×D11116yescomplemented
388C2×C22⋊Q8—114no—
389C2×C22⋊Q8—114no—
390C2×C22⋊Q8—114no—
391C2×C22⋊Q8—114no—
392C2×C22⋊Q8—114no—
393C2×#121—114no—
394C2×#120—112no—
395C2×#120—112no—
396#518—1116no—
397#518—1116no—
398C2×C4×Q8—114no—
399C2×C4×D4—114no—
400C2×C4×D4—114no—
401C2×C4×D4—114no—
402C2×C4×D4—114no—
403C2×C4×D4—114no—
404C2×#117—114no—
405C2×#117—114no—
406C2×#117—1116no—
407C2×#117—112no—
408C2×#117—114no—
409C2×#117—112no—
410C2×#117—114no—
411C22×C4⋊C4—112no—
412C22×C4⋊C4—112no—
413C22×C4⋊C4C2×D1112yescomplemented
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—112no—
418C22×C22⋊C4—112no—
419C22×C22⋊C4—112no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1112yescomplemented
422C22×C42—112no—
423C22×C11—24no—
424C22×C11—24no—
425C22×C11—24no—
426C22×C11—28no—
427C22×C11—28no—
428C22×C11—28no—
429C22×C11—24no—
430C22×C11—28no—
431C22×C11—416no—
432C22×C11—48no—
433C22×C11—88no—
434C22×C11C22×#4114yes—
435C22×C11C22×#4114yes—
436C22×C11C22×#4114yes—
437C22×C11C22×#4112yes—
438C22×C11#58514yes—
439C22×C11C2611yescharacteristic
440C2×D11—24no—
441C2×D11—28no—
442C2×D11—48no—
443C2×D11—88no—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—24no—
447C4×C11—28no—
448Dic11—24no—
449Dic11—28no—
450Dic11—28no—
451Dic11—28no—
452C25—111no—
453C25C22×D1111yescharacteristic
454C25C22×D1111yescharacteristic
455C22×Q8—114no—
456C22×D4—28no—
457C22×D4—112no—
458C22×D4—112no—
459C22×D4—118no—
460C22×D4—114no—
461C22×D4—228no—
462C22×D4C22×D1112yes—
463C22×D4C22×D1112yes—
464C22×D4C22×D1118yes—
465C23×C4—28no—
466C23×C4—111no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4—112no—
470C23×C4—114no—
471C23×C4—114no—
472C23×C4C22×D1112yes—
473C23×C4C22×D1112yes—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1118yes—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1112yes—
479#126—1132no—
480#126—1132no—
481#126—1132no—
482#126—1132no—
483#125—1132no—
484#125—1132no—
485#125—1132no—
486#124—1132no—
487#123—1116no—
488#123—1116no—
489#123—1116no—
490#123—1132no—
491#123—1116no—
492#123—1132no—
493#123—1132no—
494#123C22×D11132yes—
495#123C22×D11116yescomplemented
496#123C22×D11116yescomplemented
497C22⋊Q8—1132no—
498C22⋊Q8—1132no—
499C22⋊Q8—1132no—
500C22⋊Q8—1132no—
501C22⋊Q8—1132no—
502#121—1132no—
503#120—1116no—
504#120—1116no—
505C4×Q8—1132no—
506C4×D4—1132no—
507C4×D4—1132no—
508C4×D4—1132no—
509C4×D4—1132no—
510C4×D4—1132no—
511#117—1132no—
512#117—1132no—
513#117—1116no—
514#117—1132no—
515#117—1116no—
516#117—1132no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—1116no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—1116no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4C22×D1114yes—
530C2×C4⋊C4C22×D1114yes—
531C2×C4⋊C4C22×D11116yescomplemented
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—118no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—118no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—118no—
542C2×C22⋊C4—1116no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—1116no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—1116no—
550C2×C22⋊C4C22×D1112yes—
551C2×C22⋊C4C22×D1112yes—
552C2×C22⋊C4C22×D1118yes—
553C2×C22⋊C4C22×D1114yes—
554C2×C22⋊C4C22×D1114yes—
555C2×C22⋊C4C22×D11116yescomplemented
556C2×C42—114no—
557C2×C42—114no—
558C2×C42—114no—
559C2×C42—114no—
560C2×C42—1116no—
561C2×C11—24no—
562C2×C11—24no—
563C2×C11—24no—
564C2×C11—44no—
565C2×C11#349114yescomplemented
566C2×C11C23×#4111yescharacteristic
567C2×C11C2×#58512yes—
568D11—44no—
569C24—24no—
570C24—44no—
571C24—44no—
572C24—112no—
573C24—114no—
574C24—224no—
575C24—444no—
576C24#434118yes—
577C24C23×D1112yes—
578C24C23×D1111yescharacteristic
579C24C23×D1111yescharacteristic
580C24C23×D1111yescharacteristic
581C24C23×D1114yes—
582C24C23×D1114yes—
583C2×Q8—1116no—
584C2×Q8—448no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—232no—
588C2×D4—118no—
589C2×D4—118no—
590C2×D4—1116no—
591C2×D4—228no—
592C2×D4—228no—
593C2×D4—2232no—
594C2×D4—448no—
595C2×D4C23×D1118yes—
596C2×D4C23×D1118yes—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—232no—
602C22×C4—24no—
603C22×C4—44no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—114no—
607C22×C4—112no—
608C22×C4—114no—
609C22×C4—118no—
610C22×C4—118no—
611C22×C4—118no—
612C22×C4—1116no—
613C22×C4—1116no—
614C22×C4—224no—
615C22×C4—448no—
616C22×C4—444no—
617C22×C4—448no—
618C22×C4—444no—
619C22×C4—444no—
620C22×C4C23×D1114yes—
621C22×C4C23×D1118yes—
622C22×C4C23×D1118yes—
623C22×C4C23×D1114yes—
624C22×C4C23×D1114yes—
625C22×C4C23×D1112yes—
626C22×C4C23×D1112yes—
627C22×C4C23×D1114yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1118yes—
630C4⋊C4—1116no—
631C4⋊C4—1116no—
632C4⋊C4—1116no—
633C4⋊C4—1116no—
634C4⋊C4—1116no—
635C4⋊C4—1116no—
636C4⋊C4—1116no—
637C4⋊C4—1116no—
638C4⋊C4—1116no—
639C4⋊C4—1116no—
640C4⋊C4C23×D11116yes—
641C4⋊C4C23×D11116yes—
642C22⋊C4—118no—
643C22⋊C4—118no—
644C22⋊C4—118no—
645C22⋊C4—118no—
646C22⋊C4—118no—
647C22⋊C4—118no—
648C22⋊C4—1116no—
649C22⋊C4—1116no—
650C22⋊C4—1116no—
651C22⋊C4—1116no—
652C22⋊C4—1116no—
653C22⋊C4—1116no—
654C22⋊C4C23×D1118yes—
655C22⋊C4C23×D1118yes—
656C22⋊C4C23×D11116yes—
657C22⋊C4C23×D11116yes—
658C42—1116no—
659C42—1116no—
660C42—1116no—
661C42—1116no—
662C11C2×#349111yescharacteristic, complemented, Sylow
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—416no—
670C23—48no—
671C23—48no—
672C23—88no—
673C23—114no—
674C23—224no—
675C23—228no—
676C23—228no—
677C23—448no—
678C23—888no—
679C23C2×#434114yes—
680C23C2×#434114yes—
681C23C2×#434114yes—
682C23C2×#4341116yes—
683C23C24×D1114yes—
684C23C24×D1112yes—
685C23C24×D1112yes—
686C23C24×D1112yes—
687C23C24×D1111yescharacteristic
688Q8—4416no—
689D4—216no—
690D4—216no—
691D4—2216no—
692D4—2216no—
693D4—4416no—
694C2×C4—216no—
695C2×C4—216no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—48no—
704C2×C4—118no—
705C2×C4—118no—
706C2×C4—114no—
707C2×C4—118no—
708C2×C4—228no—
709C2×C4—224no—
710C2×C4—228no—
711C2×C4—228no—
712C2×C4—228no—
713C2×C4—4416no—
714C2×C4—448no—
715C2×C4—4416no—
716C2×C4—448no—
717C2×C4—448no—
718C2×C4C24×D1114yes—
719C2×C4C24×D1114yes—
720C2×C4C24×D1118yes—
721C2×C4C24×D1114yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—24no—
729C22—28no—
730C22—416no—
731C22—48no—
732C22—88no—
733C22—224no—
734C22—228no—
735C22—448no—
736C22—888no—
737C22C22×#434114yes—
738C22C22×#434114yes—
739C22C22×#434114yes—
740C22C22×#434112yes—
741C22#1062345314yes—
742C22C25×D1111yescharacteristic
743C4—24no—
744C4—24no—
745C4—24no—
746C4—28no—
747C4—224no—
748C4—228no—
749C4—228no—
750C4—228no—
751C2—24no—
752C2—24no—
753C2—24no—
754C2—44no—
755C2—444no—
756C2#1308231214yesdirect product factor
757C2C23×#434111yescharacteristic
758C2C2×#1062345312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#123C2
socleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC22×#123D11
hypocenterC11C2×#3491
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #13082312C2direct (N × H)
2. C2×#10623181C2semidirect
3. C2×#10623044C2semidirect
4. C2×#10623026C2semidirect
5. C2×#10623189C2semidirect
6. C2×#10623014C2semidirect
7. C2×#10623196C2semidirect
9. C2×#10623180C2semidirect
10. C22×#66982C2semidirect
11. C2×#10623329C2semidirect
12. C2×#10623017C2semidirect
13. C22×#66979C2semidirect
14. C22×C11×#123C2semidirect
19. C2×C11×#123C22semidirect
20. C2×C11×#123C22semidirect
21. C2×C11×#123C22semidirect
22. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C22⋊C4C22semidirect
29. C22×C22⋊Dic11C22semidirect
33. #10623329C22semidirect
36. C2×D4×Dic11C22semidirect
39. C2×#66982C22semidirect
40. C2×#66982C22semidirect
41. C2×#66982C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C2×#66979C22semidirect
45. C2×#66979C22semidirect
46. C2×#66979C22semidirect
47. C2×#66979C22semidirect
48. C22×C4⋊Dic11C22semidirect
49. C2×#66977C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×C4×Dic11C22semidirect
52. #10623196C22semidirect
53. #10623189C22semidirect
54. #10623181C22semidirect
55. #10623180C22semidirect
56. #10623044C22semidirect
57. C2×#66951C22semidirect
58. C2×#66951C22semidirect
59. C2×#66950C22semidirect
60. C2×#66945C22semidirect
61. C2×#66943C22semidirect
62. C2×#66942C22semidirect
63. C2×#66942C22semidirect
64. C2×#66940C22semidirect
65. #10623026C22semidirect
66. C2×#66939C22semidirect
67. C2×#66938C22semidirect
68. C2×#66936C22semidirect
69. #10623017C22semidirect
70. C2×(C22⋊D11)⋊C4C22semidirect
71. C2×(C22⋊D11)⋊C4C22semidirect
72. C2×C22⋊C4×D11C22semidirect
73. #10623014C22semidirect
74. C2×#66932C22semidirect
75. C2×#66932C22semidirect
76. C2×#66931C22semidirect
77. C2×#66931C22semidirect
78. C2×#66931C22semidirect
79. C2×#66930C22semidirect
80. C2×#66930C22semidirect
109. C11×#123C23semidirect
110. C11×#123C23semidirect
113. C2×C11×C4⋊C4C23semidirect
119. C2×C11×C22⋊C4C23semidirect
132. C2×C22⋊Dic11C23semidirect
137. D4×Dic11C23semidirect
140. #66982C23semidirect
141. #66982C23semidirect
147. C2×(C2×D11)⋊C4C23semidirect
148. #66979C23semidirect
149. #66979C23semidirect
150. #66979C23semidirect
155. C2×C4⋊Dic11C23semidirect
156. #66977C23semidirect
163. C2×Dic11⋊C4C23semidirect
168. C2×C4×Dic11C23semidirect
169. #66951C23semidirect
170. #66951C23semidirect
171. #66950C23semidirect
172. #66945C23semidirect
173. #66943C23semidirect
174. #66942C23semidirect
175. #66942C23semidirect
176. #66940C23semidirect
177. #66939C23semidirect
178. #66938C23semidirect
179. #66936C23semidirect
180. (C22⋊D11)⋊C4C23semidirect
181. (C22⋊D11)⋊C4C23semidirect
182. C22⋊C4×D11C23semidirect
183. #66932C23semidirect
184. #66932C23semidirect
185. #66931C23semidirect
186. #66931C23semidirect
187. #66931C23semidirect
188. #66930C23semidirect
189. #66930C23semidirect
294. C22×#123D11semidirect
385. C2×#123C2×D11semidirect
386. C2×#123C2×D11semidirect
387. C2×#123C2×D11semidirect
413. C22×C4⋊C4C2×D11semidirect
421. C22×C22⋊C4C2×D11semidirect
495. #123C22×D11semidirect
496. #123C22×D11semidirect
531. C2×C4⋊C4C22×D11semidirect
555. C2×C22⋊C4C22×D11semidirect
565. C2×C11#3491semidirect
662. C11C2×#3491semidirect
756. C2#13082312direct (N × H)

Maximal subgroups

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

subgroupindex
#130823122
C2×#106231812
C2×#106230442
C2×#106230262
C2×#106231892
C2×#106230142
C2×#106231962
C2×#106233352
C2×#106231802
C22×#669822
C2×#106233292
C2×#106230172
C22×#669792
C22×C11×#1232
C2×#349111