Finite Group Databasebeta

← C2×D11×#421 #15617363

Subgroups — C2×D11×#421 #15617363

Order 2816.

5198 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D11C211yesmaximal, characteristic
2C22×M16×D11C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4C2×#10622618C211yesmaximal, characteristic, complemented
5C2×#10622849C211yesmaximal, characteristic, complemented
6C2×#10622752C211yesmaximal, characteristic, complemented
7C2×#10622434C214yesmaximal, complemented
8D11×#421C2116yesmaximal, direct product factor
9C2×D11×#104C214yesmaximal, complemented
10C2×C11×#421C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12C2×#41×D11—21no—
13C2×#41×D11—21no—
14C2×#41×D11—24no—
15C2×#41×D11—21no—
16C2×#41×D11—21no—
17C2×#41×D11—24no—
18C2×#41×D11C412yescomplemented
19C2×#41×D11C412yescomplemented
20C2×#41×D11C418yescomplemented
21C2×#41×D11C2212yes—
22C2×#41×D11C2218yes—
23C2×#41×D11C2212yes—
24C22×#4343C411yescharacteristic, complemented
25C22×Q8×D11C411yescharacteristic, complemented
26C22×#4341—21no—
27C22×#4341C411yescharacteristic, complemented
28C22×D4×D11—21no—
29C22×D4×D11C411yescharacteristic, complemented
30C22×#4339—21no—
31C22×#4339C2211yescharacteristic
32C23×C4×D11—21no—
33C23×C4×D11C2211yescharacteristic
34C22×C11×M16C2211yescharacteristic, complemented
35C2×C11×#117C2211yescharacteristic, complemented
36C2×#66979C2211yescharacteristic, complemented
37C22×#4318C2211yescharacteristic, complemented
38C2×M16×D11—21no—
39C2×M16×D11—21no—
40C2×M16×D11—24no—
41C2×M16×D11C2212yescomplemented
42C2×M16×D11C2218yescomplemented
43C2×M16×D11C2212yescomplemented
44C22×#4313—21no—
45C22×C8×D11—21no—
46D11×#117—24no—
47D11×#117C2218yescomplemented
48C2×#66945—21no—
49C2×C4⋊C4×D11—21no—
50C2×C22⋊C4×D11—21no—
51C2×#66930—21no—
52C2×#66925C2212yescomplemented
53C2×C42×D11C2212yescomplemented
54C11×#421C2218yescomplemented
55C2×C11×#104C2214yescomplemented
56#10622849C2218yescomplemented
57C2×#66901C2214yescomplemented
58#10622752C2218yescomplemented
59C2×#66889C2214yescomplemented
60#10622618C2218yescomplemented
61C2×#66869C2214yescomplemented
62#10622434C22132yescomplemented
63D11×#104C22132yescomplemented
64C24×D11—21no—
65C24×D11D411yescharacteristic
66C2×C11×#41—21no—
67C2×C11×#41—22no—
68C2×C11×#41—21no—
69C2×C11×#41—22no—
70C2×C11×#41C2×C412yescomplemented
71C2×C11×#41C2×C414yescomplemented
72C2×C11×#41C2312yes—
73C2×C11×#41C2314yes—
74C22×Q8×C11C2×C411yescharacteristic, complemented
75C22×D4×C11—21no—
76C22×D4×C11C2×C411yescharacteristic, complemented
77C23×C4×C11—21no—
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C23×Dic11D411yescharacteristic
84#41×D11—28no—
85#41×D11—28no—
86#41×D11—28no—
87#41×D11—28no—
88#41×D11—28no—
89#41×D11—28no—
90#41×D11—24no—
91#41×D11—24no—
92#41×D11—28no—
93#41×D11—28no—
94#41×D11—28no—
95#41×D11—28no—
96#41×D11—24no—
97#41×D11—24no—
98#41×D11C2×C418yes—
99#41×D11C2×C418yescomplemented
100#41×D11C2×C4116yescomplemented
101#41×D11C2×C4116yescomplemented
102#41×D11C2318yes—
103#41×D11C2318yes—
104C2×#4343—21no—
105C2×#4343—21no—
106C2×#4343—24no—
107C2×#4343C2×C412yes—
108C2×#4343C2×C412yescomplemented
109C2×#4343C2×C418yescomplemented
110C2×Q8×D11—21no—
111C2×Q8×D11—21no—
112C2×Q8×D11—24no—
113C2×Q8×D11C2×C412yes—
114C2×Q8×D11C2×C412yescomplemented
115C2×Q8×D11C2×C418yescomplemented
116C2×#4341—22no—
117C2×#4341—22no—
118C2×#4341—28no—
119C2×#4341—22no—
120C2×#4341—28no—
121C2×#4341—22no—
122C2×#4341—24no—
123C2×#4341—21no—
124C2×#4341—21no—
125C2×#4341C2×C412yes—
126C2×#4341C2×C412yescomplemented
127C2×#4341C2×C418yescomplemented
128C2×D4×D11—22no—
129C2×D4×D11—22no—
130C2×D4×D11—28no—
131C2×D4×D11—22no—
132C2×D4×D11—28no—
133C2×D4×D11—22no—
134C2×D4×D11—24no—
135C2×D4×D11—21no—
136C2×D4×D11—21no—
137C2×D4×D11C2×C412yes—
138C2×D4×D11C2×C412yescomplemented
139C2×D4×D11C2×C418yescomplemented
140C2×#4339—21no—
141C2×#4339—22no—
142C2×#4339—21no—
143C2×#4339—22no—
144C2×#4339—22no—
145C2×#4339—22no—
146C2×#4339—28no—
147C2×#4339—22no—
148C2×#4339—22no—
149C2×#4339—28no—
150C2×#4339C2×C412yescomplemented
151C2×#4339C2×C414yescomplemented
152C2×#4339C2312yes—
153C2×#4339C2314yes—
154C22×D44—21no—
155C22×D44C2×C411yescharacteristic, complemented
156C22×C4×D11—21no—
157C22×C4×D11—21no—
158C22×C4×D11—21no—
159C22×C4×D11—22no—
160C22×C4×D11—28no—
161C22×C4×D11—22no—
162C22×C4×D11—22no—
163C22×C4×D11—22no—
164C22×C4×D11—28no—
165C22×C4×D11—22no—
166C22×C4×D11C2×C411yescharacteristic
167C22×C4×D11C2×C411yescharacteristic
168C22×C4×D11C2×C411yescharacteristic
169C22×C4×D11C2×C411yescharacteristic
170C22×C4×D11C2×C414yes—
171C22×C4×D11D411yescharacteristic
172C22×C4×D11D411yescharacteristic
173C22×C4×D11D414yes—
174C22×C4×D11D411yescharacteristic
175C22×C4×D11D411yescharacteristic
176C22×C4×D11D411yescharacteristic
177C22×C4×D11D411yescharacteristic
178C22×C4×D11D414yes—
179C22×C4×D11C2311yescharacteristic
180C22×C4×D11C2311yescharacteristic
181C22×C4×D11C2314yes—
182C22×Dic22—21no—
183C22×Dic22C2×C411yescharacteristic, complemented
184C2×C11×M16—21no—
185C2×C11×M16—22no—
186C2×C11×M16C2312yescomplemented
187C2×C11×M16C2314yescomplemented
188C22×C8×C11—21no—
189C11×#117—22no—
190C11×#117C2314yescomplemented
191C2×C11×C4⋊C4—21no—
192C2×C11×C22⋊C4—21no—
193C2×C42×C11C2312yescomplemented
194C2×C22⋊Dic11—21no—
195C2×(C2×D11)⋊C4—22no—
196#66979—22no—
197#66979C2314yescomplemented
198C2×C4⋊Dic11—21no—
199C2×Dic11⋊C4—22no—
200C2×C4×Dic11—22no—
201C2×C4×Dic11C2312yescomplemented
202C2×#4318—21no—
203C2×#4318—22no—
204C2×#4318C2312yescomplemented
205C2×#4318C2314yescomplemented
206C22×C11⋊C8—21no—
207M16×D11—28no—
208M16×D11—28no—
209M16×D11—24no—
210M16×D11—24no—
211M16×D11C2318yescomplemented
212M16×D11C2318yescomplemented
213C2×#4313—22no—
214C2×#4313—22no—
215C2×#4313—28no—
216C2×C8×D11—22no—
217C2×C8×D11—22no—
218C2×C8×D11—28no—
219#66945—28no—
220C4⋊C4×D11—28no—
221C22⋊C4×D11—28no—
222#66930—28no—
223#66925—24no—
224#66925C2318yescomplemented
225C42×D11—24no—
226C42×D11C2318yescomplemented
227C11×#104C23116yescomplemented
228#66901C23116yescomplemented
229#66889C23116yescomplemented
230#66869C23116yescomplemented
231C22×#421—111nomaximal, Sylow
232C24×C11—21no—
233C24×C11C2×D411yescharacteristic
234C23×D11—21no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—28no—
238C23×D11—44no—
239C23×D11—48no—
240C23×D11C22⋊C411yescharacteristic
241C23×D11C22⋊C411yescharacteristic
242C23×D11C22⋊C411yescharacteristic
243C23×D11C22⋊C414yes—
244C23×D11C22⋊C411yescharacteristic
245C23×D11C2×D411yescharacteristic
246C23×D11C2×D414yes—
247C23×D11C2×D411yescharacteristic
248C11×#41—24no—
249C11×#41—24no—
250C11×#41—24no—
251C11×#41—22no—
252C11×#41—24no—
253C11×#41—24no—
254C11×#41—22no—
255C11×#41C22×C414yes—
256C11×#41C22×C418yescomplemented
257C11×#41C2414yes—
258C2×Q8×C11—21no—
259C2×Q8×C11—22no—
260C2×Q8×C11C22×C412yes—
261C2×Q8×C11C22×C414yescomplemented
262C2×D4×C11—22no—
263C2×D4×C11—24no—
264C2×D4×C11—22no—
265C2×D4×C11—24no—
266C2×D4×C11—22no—
267C2×D4×C11—21no—
268C2×D4×C11C22×C412yes—
269C2×D4×C11C22×C414yescomplemented
270C22×C4×C11—21no—
271C22×C4×C11—22no—
272C22×C4×C11—24no—
273C22×C4×C11—22no—
274C22×C4×C11—24no—
275C22×C4×C11—22no—
276C22×C4×C11C22×C411yescharacteristic
277C22×C4×C11C22×C411yescharacteristic
278C22×C4×C11C22×C412yes—
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D412yes—
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C2×C22⋊D11—22no—
287C2×C22⋊D11—22no—
288C2×C22⋊D11—28no—
289C2×C22⋊D11—22no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—24no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—28no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—28no—
299C22×Dic11—21no—
300C22×Dic11—22no—
301C22×Dic11C22⋊C411yescharacteristic
302C22×Dic11C22⋊C411yescharacteristic
303C22×Dic11C22⋊C411yescharacteristic
304C22×Dic11C22⋊C411yescharacteristic
305C22×Dic11C22⋊C414yes—
306C22×Dic11C2×D414yes—
307C22×Dic11C2×D411yescharacteristic
308C22×Dic11C2×D411yescharacteristic
309#4343—24no—
310#4343—24no—
311#4343—28no—
312#4343—28no—
313#4343C22×C418yes—
314#4343C22×C418yescomplemented
315Q8×D11—24no—
316Q8×D11—24no—
317Q8×D11—28no—
318Q8×D11—28no—
319Q8×D11C22×C418yes—
320Q8×D11C22×C418yescomplemented
321#4341—28no—
322#4341—28no—
323#4341—216no—
324#4341—216no—
325#4341—28no—
326#4341—28no—
327#4341—24no—
328#4341—24no—
329#4341—28no—
330#4341—28no—
331#4341C22×C418yes—
332#4341C22×C418yescomplemented
333D4×D11—24no—
334D4×D11—24no—
335D4×D11—28no—
336D4×D11—28no—
337D4×D11—28no—
338D4×D11—28no—
339D4×D11—216no—
340D4×D11—216no—
341D4×D11—28no—
342D4×D11—28no—
343D4×D11C22×C418yes—
344D4×D11C22×C418yescomplemented
345#4339—28no—
346#4339—28no—
347#4339—216no—
348#4339—216no—
349#4339—28no—
350#4339—28no—
351#4339—24no—
352#4339—24no—
353#4339—24no—
354#4339—22no—
355#4339—24no—
356#4339—24no—
357#4339—22no—
358#4339C22×C414yes—
359#4339C22×C418yescomplemented
360#4339C2414yes—
361C2×D44—22no—
362C2×D44—22no—
363C2×D44—28no—
364C2×D44—21no—
365C2×D44—22no—
366C2×D44C22×C412yes—
367C2×D44C22×C414yescomplemented
368C2×C4×D11—22no—
369C2×C4×D11—22no—
370C2×C4×D11—28no—
371C2×C4×D11—28no—
372C2×C4×D11—28no—
373C2×C4×D11—216no—
374C2×C4×D11—216no—
375C2×C4×D11—28no—
376C2×C4×D11—28no—
377C2×C4×D11—22no—
378C2×C4×D11—22no—
379C2×C4×D11—28no—
380C2×C4×D11—28no—
381C2×C4×D11—22no—
382C2×C4×D11—24no—
383C2×C4×D11—24no—
384C2×C4×D11—22no—
385C2×C4×D11—48no—
386C2×C4×D11C22⋊C411yescharacteristic
387C2×C4×D11C22⋊C414yes—
388C2×C4×D11C22⋊C411yescharacteristic
389C2×C4×D11C22⋊C411yescharacteristic
390C2×C4×D11C22⋊C411yescharacteristic
391C2×C4×D11C22⋊C414yes—
392C2×C4×D11C22⋊C411yescharacteristic
393C2×C4×D11C22⋊C414yes—
394C2×C4×D11C22⋊C411yescharacteristic
395C2×C4×D11C22⋊C411yescharacteristic
396C2×C4×D11C22⋊C411yescharacteristic
397C2×C4×D11C22⋊C414yes—
398C2×C4×D11C22⋊C414yes—
399C2×C4×D11C22⋊C414yes—
400C2×C4×D11C22⋊C414yes—
401C2×C4×D11C22⋊C414yes—
402C2×C4×D11C22⋊C414yes—
403C2×C4×D11C22⋊C414yes—
404C2×C4×D11C22×C411yescharacteristic
405C2×C4×D11C22×C411yescharacteristic
406C2×C4×D11C22×C414yes—
407C2×C4×D11C22×C411yescharacteristic
408C2×C4×D11C22×C411yescharacteristic
409C2×C4×D11C22×C414yes—
410C2×C4×D11C22×C412yes—
411C2×C4×D11C22×C412yes—
412C2×C4×D11C22×C414yes—
413C2×C4×D11C22×C414yes—
414C2×C4×D11C2×D411yescharacteristic
415C2×C4×D11C2×D411yescharacteristic
416C2×C4×D11C2×D414yes—
417C2×C4×D11C2×D411yescharacteristic
418C2×C4×D11C2×D411yescharacteristic
419C2×C4×D11C2×D414yes—
420C2×C4×D11C2×D414yes—
421C2×C4×D11C2×D414yes—
422C2×C4×D11C2×D412yes—
423C2×C4×D11C2×D412yes—
424C2×C4×D11C2×D412yes—
425C2×C4×D11C2×D412yes—
426C2×C4×D11C2×D414yes—
427C2×C4×D11C2×D414yes—
428C2×C4×D11C2412yes—
429C2×C4×D11C2412yes—
430C2×Dic22—22no—
431C2×Dic22—22no—
432C2×Dic22—28no—
433C2×Dic22—22no—
434C2×Dic22—21no—
435C2×Dic22C22×C412yes—
436C2×Dic22C22×C414yescomplemented
437C11×M16—24no—
438C11×M16—22no—
439C11×M16C2414yescomplemented
440C2×C8×C11—24no—
441C2×C8×C11—22no—
442C11×C4⋊C4—24no—
443C11×C22⋊C4—24no—
444C42×C11—22no—
445C42×C11C2414yescomplemented
446C22⋊Dic11—24no—
447(C2×D11)⋊C4—28no—
448C4⋊Dic11—24no—
449Dic11⋊C4—28no—
450C4×Dic11—28no—
451C4×Dic11—22no—
452C4×Dic11C2414yescomplemented
453#4318—24no—
454#4318—22no—
455#4318C2414yescomplemented
456C2×C11⋊C8—24no—
457C2×C11⋊C8—22no—
458#4313—28no—
459#4313—28no—
460C8×D11—28no—
461C8×D11—28no—
462C23×#41—111no—
463C23×M16—111no—
464C22×#117—111no—
465C2×#421—1116no—
466C2×#421—114no—
467C2×#421—111no—
468C2×#421—111no—
469C2×#421—111no—
470C2×#421D1111yescharacteristic, direct product factor
471C22×#104—114no—
472C23×C11—22no—
473C23×C11—24no—
474C23×C11—42no—
475C23×C11—44no—
476C23×C11C2×C22⋊C411yescharacteristic
477C23×C11C2×C22⋊C411yescharacteristic
478C23×C11C2×C22⋊C412yes—
479C23×C11C22×D411yescharacteristic
480C23×C11C22×D412yes—
481C22×D11—24no—
482C22×D11—24no—
483C22×D11—24no—
484C22×D11—22no—
485C22×D11—24no—
486C22×D11—28no—
487C22×D11—28no—
488C22×D11—48no—
489C22×D11—48no—
490C22×D11—42no—
491C22×D11—42no—
492C22×D11—42no—
493C22×D11—48no—
494C22×D11—432no—
495C22×D11—44no—
496C22×D11—48no—
497C22×D11C2×C22⋊C411yescharacteristic
498C22×D11C2×C22⋊C414yes—
499C22×D11C2×C22⋊C411yescharacteristic
500C22×D11C2×C22⋊C411yescharacteristic
501C22×D11C2×C22⋊C412yes—
502C22×D11C2×C22⋊C414yes—
503C22×D11C2×C22⋊C414yes—
504C22×D11C2×C22⋊C414yes—
505C22×D11C2×C22⋊C412yes—
506C22×D11C2×C22⋊C411yescharacteristic
507C22×D11C22×D412yes—
508C22×D11C22×D412yes—
509Q8×C11—22no—
510Q8×C11—24no—
511Q8×C11C23×C414yes—
512D4×C11—24no—
513D4×C11—28no—
514D4×C11—24no—
515D4×C11—22no—
516D4×C11—24no—
517D4×C11C23×C414yes—
518C2×C4×C11—22no—
519C2×C4×C11—24no—
520C2×C4×C11—24no—
521C2×C4×C11—28no—
522C2×C4×C11—24no—
523C2×C4×C11—24no—
524C2×C4×C11—44no—
525C2×C4×C11C2×C22⋊C412yes—
526C2×C4×C11C2×C22⋊C411yescharacteristic
527C2×C4×C11C2×C22⋊C412yes—
528C2×C4×C11C2×C22⋊C411yescharacteristic
529C2×C4×C11C2×C22⋊C412yes—
530C2×C4×C11C2×C22⋊C412yes—
531C2×C4×C11C2×C22⋊C412yes—
532C2×C4×C11C23×C411yescharacteristic
533C2×C4×C11C23×C412yes—
534C2×C4×C11C23×C411yescharacteristic
535C2×C4×C11C23×C412yes—
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D412yes—
538C2×C4×C11C22×D412yes—
539C2×C4×C11C22×D412yes—
540C2×C4×C11C22×D411yescharacteristic
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C2511yescharacteristic
543C22⋊D11—24no—
544C22⋊D11—28no—
545C22⋊D11—24no—
546C22⋊D11—28no—
547C22⋊D11—28no—
548C22⋊D11—28no—
549C22⋊D11—28no—
550C2×Dic11—22no—
551C2×Dic11—24no—
552C2×Dic11—28no—
553C2×Dic11—28no—
554C2×Dic11—24no—
555C2×Dic11—44no—
556C2×Dic11C2×C22⋊C414yes—
557C2×Dic11C2×C22⋊C411yescharacteristic
558C2×Dic11C2×C22⋊C411yescharacteristic
559C2×Dic11C2×C22⋊C414yes—
560C2×Dic11C2×C22⋊C411yescharacteristic
561C2×Dic11C2×C22⋊C411yescharacteristic
562C2×Dic11C2×C22⋊C412yes—
563C2×Dic11C2×C22⋊C414yes—
564C2×Dic11C2×C22⋊C414yes—
565C2×Dic11C2×C22⋊C412yes—
566C2×Dic11C22×D412yes—
567C2×Dic11C22×D412yes—
568D44—28no—
569D44—28no—
570D44—22no—
571D44—24no—
572D44C23×C414yes—
573C4×D11—28no—
574C4×D11—28no—
575C4×D11—24no—
576C4×D11—28no—
577C4×D11—24no—
578C4×D11—28no—
579C4×D11—28no—
580C4×D11—416no—
581C4×D11C2×C22⋊C412yes—
582C4×D11C2×C22⋊C414yes—
583C4×D11C2×C22⋊C412yes—
584C4×D11C2×C22⋊C414yes—
585C4×D11C2×C22⋊C412yes—
586C4×D11C2×C22⋊C412yes—
587C4×D11C2×C22⋊C414yes—
588C4×D11C2×C22⋊C414yes—
589C4×D11C2×C22⋊C414yes—
590C4×D11C2×C22⋊C412yes—
591C4×D11C2×C22⋊C412yes—
592C4×D11C2×C22⋊C414yes—
593C4×D11C2×C22⋊C412yes—
594C4×D11C2×C22⋊C414yes—
595C4×D11C2×C22⋊C414yes—
596C4×D11C2×C22⋊C412yes—
597C4×D11C23×C412yes—
598C4×D11C23×C412yes—
599C4×D11C23×C412yes—
600C4×D11C23×C412yes—
601C4×D11C22×D412yes—
602C4×D11C22×D412yes—
603C4×D11C22×D412yes—
604C4×D11C22×D412yes—
605Dic22—22no—
606Dic22—24no—
607Dic22—28no—
608Dic22—28no—
609Dic22C23×C414yes—
610C8×C11—24no—
611C11⋊C8—24no—
612C22×#41—112no—
613C22×#41—112no—
614C22×#41—118no—
615C22×#41—112no—
616C22×#41—112no—
617C22×#41—118no—
618C22×#41—111no—
619C22×#41—111no—
620C22×#41—111no—
621C22×#41—221no—
622C22×#41—221no—
623C22×#41—221no—
624C22×#41—221no—
625C22×#41—224no—
626C22×#41—221no—
627C22×#41—224no—
628C22×#41—221no—
629C22×#41C2×D1111yescharacteristic
630C23×Q8—111no—
631C23×D4—111no—
632C23×D4—221no—
633C24×C4—111no—
634C24×C4—221no—
635C22×M16—111no—
636C22×M16—112no—
637C22×M16—112no—
638C22×M16—118no—
639C22×M16—221no—
640C22×M16—221no—
641C22×M16—224no—
642C22×M16—221no—
643C22×M16C2×D1111yescharacteristic, complemented
644C23×C8—221no—
645C2×#117—111no—
646C2×#117—118no—
647C2×#117—112no—
648C2×#117—221no—
649C2×#117—221no—
650C2×#117—224no—
651C2×#117C2×D1111yescharacteristic, complemented
652C22×C4⋊C4—221no—
653C22×C22⋊C4—221no—
654C22×C42—112no—
655#421—118no—
656#421—118no—
657#421—118no—
658#421—1132no—
659#421C2×D1118yesdirect product factor
660C2×#104—114no—
661C2×#104—114no—
662C2×#104—114no—
663C2×#104—1132no—
664C2×#104C2×D1114yescomplemented
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—24no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—48no—
672C22×C11—44no—
673C22×C11C22×C22⋊C412yes—
674C22×C11C22×C22⋊C411yescharacteristic
675C22×C11C22×C22⋊C412yes—
676C22×C11C22×C22⋊C411yescharacteristic
677C22×C11C23×D411yescharacteristic
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—28no—
682C2×D11—24no—
683C2×D11—28no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—42no—
687C2×D11—44no—
688C2×D11—44no—
689C2×D11—42no—
690C2×D11—416no—
691C2×D11—48no—
692C2×D11—44no—
693C2×D11—416no—
694C2×D11#42114yesdirect product factor
695C2×D11C22×C22⋊C412yes—
696C2×D11C22×C22⋊C412yes—
697C2×D11C22×C22⋊C412yes—
698C2×D11C22×C22⋊C412yes—
699C4×C11—24no—
700C4×C11—44no—
701C4×C11C22×C22⋊C412yes—
702C4×C11C22×C22⋊C411yescharacteristic
703C4×C11C22×C22⋊C411yescharacteristic
704C4×C11C22×C22⋊C412yes—
705C4×C11C24×C411yescharacteristic
706C4×C11C23×D411yescharacteristic
707Dic11—24no—
708Dic11—44no—
709Dic11C22×C22⋊C412yes—
710Dic11C22×C22⋊C412yes—
711Dic11C22×C22⋊C412yes—
712Dic11C22×C22⋊C412yes—
713C25—111no—
714C25—221no—
715C2×#41—21no—
716C2×#41—22no—
717C2×#41—22no—
718C2×#41—21no—
719C2×#41—118no—
720C2×#41—118no—
721C2×#41—1116no—
722C2×#41—1116no—
723C2×#41—118no—
724C2×#41—118no—
725C2×#41—112no—
726C2×#41—112no—
727C2×#41—118no—
728C2×#41—112no—
729C2×#41—112no—
730C2×#41—118no—
731C2×#41—112no—
732C2×#41—114no—
733C2×#41—112no—
734C2×#41—114no—
735C2×#41—222no—
736C2×#41—222no—
737C2×#41—228no—
738C2×#41—228no—
739C2×#41—222no—
740C2×#41—222no—
741C2×#41—222no—
742C2×#41—222no—
743C2×#41—228no—
744C2×#41—222no—
745C2×#41—222no—
746C2×#41—228no—
747C2×#41—221no—
748C2×#41—221no—
749C2×#41—224no—
750C2×#41—221no—
751C2×#41—221no—
752C2×#41—224no—
753C2×#41—228no—
754C2×#41—228no—
755C2×#41—228no—
756C2×#41—228no—
757C2×#41—228no—
758C2×#41—228no—
759C2×#41—224no—
760C2×#41—228no—
761C2×#41—228no—
762C2×#41—224no—
763C2×#41—228no—
764C2×#41—224no—
765C2×#41—224no—
766C2×#41—228no—
767C2×#41—221no—
768C2×#41—222no—
769C2×#41—222no—
770C2×#41—221no—
771C2×#41C4×D1112yescomplemented
772C2×#41C4×D1114yescomplemented
773C2×#41C22×D1112yes—
774C2×#41C22×D1114yes—
775C22×Q8—112no—
776C22×Q8—112no—
777C22×Q8—118no—
778C22×Q8—111no—
779C22×Q8—221no—
780C22×Q8—221no—
781C22×Q8—221no—
782C22×Q8—224no—
783C22×Q8C4×D1111yescharacteristic, complemented
784C22×D4—21no—
785C22×D4—112no—
786C22×D4—112no—
787C22×D4—118no—
788C22×D4—111no—
789C22×D4—221no—
790C22×D4—221no—
791C22×D4—224no—
792C22×D4—221no—
793C22×D4—221no—
794C22×D4—222no—
795C22×D4—222no—
796C22×D4—228no—
797C22×D4—222no—
798C22×D4—222no—
799C22×D4—228no—
800C22×D4—221no—
801C22×D4—221no—
802C22×D4C4×D1111yescharacteristic, complemented
803C23×C4—21no—
804C23×C4—111no—
805C23×C4—111no—
806C23×C4—111no—
807C23×C4—111no—
808C23×C4—111no—
809C23×C4—114no—
810C23×C4—111no—
811C23×C4—111no—
812C23×C4—114no—
813C23×C4—111no—
814C23×C4—111no—
815C23×C4—111no—
816C23×C4—114no—
817C23×C4—111no—
818C23×C4—111no—
819C23×C4—114no—
820C23×C4—111no—
821C23×C4—221no—
822C23×C4—222no—
823C23×C4—222no—
824C23×C4—228no—
825C23×C4—228no—
826C23×C4—222no—
827C23×C4—222no—
828C23×C4—221no—
829C23×C4—222no—
830C23×C4—221no—
831C23×C4—221no—
832C23×C4C22×D1111yescharacteristic
833C2×M16—22no—
834C2×M16—21no—
835C2×M16—112no—
836C2×M16—114no—
837C2×M16—118no—
838C2×M16—118no—
839C2×M16—228no—
840C2×M16—222no—
841C2×M16—222no—
842C2×M16—228no—
843C2×M16—224no—
844C2×M16—228no—
845C2×M16—224no—
846C2×M16—222no—
847C2×M16—221no—
848C2×M16C22×D1112yescomplemented
849C2×M16C22×D1114yescomplemented
850C22×C8—21no—
851C22×C8—228no—
852C22×C8—222no—
853C22×C8—222no—
854C22×C8—221no—
855#117—22no—
856#117—114no—
857#117—118no—
858#117—224no—
859#117—228no—
860#117—228no—
861#117—222no—
862#117C22×D1114yescomplemented
863C2×C4⋊C4—21no—
864C2×C4⋊C4—228no—
865C2×C4⋊C4—222no—
866C2×C4⋊C4—221no—
867C2×C22⋊C4—21no—
868C2×C22⋊C4—228no—
869C2×C22⋊C4—222no—
870C2×C22⋊C4—221no—
871C2×C42—112no—
872C2×C42—118no—
873C2×C42—224no—
874C2×C42—222no—
875C2×C42C22×D1112yescomplemented
876#104—1116no—
877#104—1116no—
878#104—1116no—
879#104C22×D11116yescomplemented
880C2×C11—21no—
881C2×C11—22no—
882C2×C11—21no—
883C2×C11—22no—
884C2×C11—44no—
885C2×C11C2×#42112yescomplemented
886C2×C11C23×C22⋊C411yescharacteristic
887D11—22no—
888D11—22no—
889D11—22no—
890D11—44no—
891D11C2×#42114yesdirect product factor
892C24—21no—
893C24—111no—
894C24—111no—
895C24—111no—
896C24—114no—
897C24—111no—
898C24—111no—
899C24—114no—
900C24—111no—
901C24—222no—
902C24—222no—
903C24—228no—
904C24—221no—
905C24—444no—
906C24—448no—
907C24D4×D1111yescharacteristic
908#41—24no—
909#41—24no—
910#41—24no—
911#41—22no—
912#41—24no—
913#41—24no—
914#41—22no—
915#41—118no—
916#41—118no—
917#41—118no—
918#41—118no—
919#41—114no—
920#41—118no—
921#41—114no—
922#41—228no—
923#41—228no—
924#41—2216no—
925#41—2216no—
926#41—228no—
927#41—228no—
928#41—228no—
929#41—228no—
930#41—2216no—
931#41—2216no—
932#41—228no—
933#41—228no—
934#41—224no—
935#41—224no—
936#41—228no—
937#41—228no—
938#41—224no—
939#41—224no—
940#41—228no—
941#41—228no—
942#41—224no—
943#41—224no—
944#41—224no—
945#41—222no—
946#41—224no—
947#41—224no—
948#41—222no—
949#41C2×C4×D1114yes—
950#41C2×C4×D1118yescomplemented
951#41C23×D1114yes—
952C2×Q8—21no—
953C2×Q8—22no—
954C2×Q8—118no—
955C2×Q8—118no—
956C2×Q8—112no—
957C2×Q8—114no—
958C2×Q8—222no—
959C2×Q8—222no—
960C2×Q8—228no—
961C2×Q8—224no—
962C2×Q8—224no—
963C2×Q8—228no—
964C2×Q8—228no—
965C2×Q8—222no—
966C2×Q8—221no—
967C2×Q8C2×C4×D1112yes—
968C2×Q8C2×C4×D1114yescomplemented
969C2×D4—22no—
970C2×D4—24no—
971C2×D4—22no—
972C2×D4—24no—
973C2×D4—22no—
974C2×D4—21no—
975C2×D4—118no—
976C2×D4—118no—
977C2×D4—112no—
978C2×D4—114no—
979C2×D4—222no—
980C2×D4—222no—
981C2×D4—228no—
982C2×D4—224no—
983C2×D4—224no—
984C2×D4—228no—
985C2×D4—228no—
986C2×D4—222no—
987C2×D4—222no—
988C2×D4—228no—
989C2×D4—228no—
990C2×D4—228no—
991C2×D4—2216no—
992C2×D4—2216no—
993C2×D4—228no—
994C2×D4—228no—
995C2×D4—222no—
996C2×D4—222no—
997C2×D4—228no—
998C2×D4—222no—
999C2×D4—224no—
1000C2×D4—222no—
1001C2×D4—224no—
1002C2×D4—222no—
1003C2×D4—221no—
1004C2×D4C2×C4×D1112yes—
1005C2×D4C2×C4×D1114yescomplemented
1006C22×C4—21no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—111no—
1015C22×C4—111no—
1016C22×C4—114no—
1017C22×C4—111no—
1018C22×C4—111no—
1019C22×C4—114no—
1020C22×C4—111no—
1021C22×C4—114no—
1022C22×C4—111no—
1023C22×C4—111no—
1024C22×C4—114no—
1025C22×C4—111no—
1026C22×C4—111no—
1027C22×C4—111no—
1028C22×C4—114no—
1029C22×C4—111no—
1030C22×C4—111no—
1031C22×C4—114no—
1032C22×C4—114no—
1033C22×C4—114no—
1034C22×C4—114no—
1035C22×C4—114no—
1036C22×C4—114no—
1037C22×C4—114no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—114no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—114no—
1044C22×C4—112no—
1045C22×C4—112no—
1046C22×C4—114no—
1047C22×C4—114no—
1048C22×C4—112no—
1049C22×C4—114no—
1050C22×C4—114no—
1051C22×C4—112no—
1052C22×C4—114no—
1053C22×C4—114no—
1054C22×C4—114no—
1055C22×C4—112no—
1056C22×C4—112no—
1057C22×C4—114no—
1058C22×C4—111no—
1059C22×C4—111no—
1060C22×C4—111no—
1061C22×C4—111no—
1062C22×C4—112no—
1063C22×C4—112no—
1064C22×C4—222no—
1065C22×C4—222no—
1066C22×C4—228no—
1067C22×C4—228no—
1068C22×C4—228no—
1069C22×C4—2216no—
1070C22×C4—2216no—
1071C22×C4—228no—
1072C22×C4—228no—
1073C22×C4—222no—
1074C22×C4—222no—
1075C22×C4—228no—
1076C22×C4—228no—
1077C22×C4—222no—
1078C22×C4—222no—
1079C22×C4—228no—
1080C22×C4—221no—
1081C22×C4—224no—
1082C22×C4—222no—
1083C22×C4—224no—
1084C22×C4—222no—
1085C22×C4—222no—
1086C22×C4—448no—
1087C22×C4C2×C4×D1111yescharacteristic
1088C22×C4C2×C4×D1111yescharacteristic
1089C22×C4C2×C4×D1112yes—
1090C22×C4D4×D1111yescharacteristic
1091C22×C4D4×D1112yes—
1092C22×C4D4×D1112yes—
1093C22×C4D4×D1111yescharacteristic
1094C22×C4D4×D1111yescharacteristic
1095C22×C4C23×D1112yes—
1096C22×C4C23×D1111yescharacteristic
1097M16—24no—
1098M16—22no—
1099M16—114no—
1100M16—228no—
1101M16—228no—
1102M16—224no—
1103M16—222no—
1104M16C23×D1114yescomplemented
1105C2×C8—24no—
1106C2×C8—22no—
1107C2×C8—228no—
1108C2×C8—228no—
1109C2×C8—224no—
1110C2×C8—222no—
1111C4⋊C4—24no—
1112C4⋊C4—228no—
1113C4⋊C4—224no—
1114C22⋊C4—24no—
1115C22⋊C4—228no—
1116C22⋊C4—224no—
1117C42—22no—
1118C42—114no—
1119C42—228no—
1120C42—222no—
1121C42C23×D1114yescomplemented
1122C11C22×#42111yescharacteristic, complemented, Sylow
1123C23—22no—
1124C23—24no—
1125C23—42no—
1126C23—44no—
1127C23—111no—
1128C23—114no—
1129C23—111no—
1130C23—114no—
1131C23—112no—
1132C23—111no—
1133C23—111no—
1134C23—112no—
1135C23—112no—
1136C23—114no—
1137C23—114no—
1138C23—112no—
1139C23—224no—
1140C23—224no—
1141C23—224no—
1142C23—228no—
1143C23—228no—
1144C23—224no—
1145C23—222no—
1146C23—442no—
1147C23—442no—
1148C23—442no—
1149C23—444no—
1150C23—448no—
1151C23—448no—
1152C23—448no—
1153C23—4432no—
1154C23—448no—
1155C23C22⋊C4×D1111yescharacteristic
1156C23C22⋊C4×D1111yescharacteristic
1157C23C22⋊C4×D1112yes—
1158C23C2×D4×D1111yescharacteristic
1159C23C2×D4×D1112yes—
1160Q8—22no—
1161Q8—24no—
1162Q8—114no—
1163Q8—228no—
1164Q8—228no—
1165Q8—222no—
1166Q8—224no—
1167Q8C22×C4×D1114yes—
1168D4—24no—
1169D4—28no—
1170D4—24no—
1171D4—22no—
1172D4—24no—
1173D4—114no—
1174D4—228no—
1175D4—228no—
1176D4—228no—
1177D4—228no—
1178D4—228no—
1179D4—228no—
1180D4—224no—
1181D4—228no—
1182D4—224no—
1183D4—222no—
1184D4—224no—
1185D4C22×C4×D1114yes—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—28no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—44no—
1193C2×C4—114no—
1194C2×C4—111no—
1195C2×C4—111no—
1196C2×C4—114no—
1197C2×C4—111no—
1198C2×C4—111no—
1199C2×C4—112no—
1200C2×C4—112no—
1201C2×C4—114no—
1202C2×C4—114no—
1203C2×C4—112no—
1204C2×C4—112no—
1205C2×C4—114no—
1206C2×C4—114no—
1207C2×C4—112no—
1208C2×C4—112no—
1209C2×C4—112no—
1210C2×C4—114no—
1211C2×C4—114no—
1212C2×C4—112no—
1213C2×C4—112no—
1214C2×C4—114no—
1215C2×C4—114no—
1216C2×C4—112no—
1217C2×C4—114no—
1218C2×C4—114no—
1219C2×C4—112no—
1220C2×C4—112no—
1221C2×C4—112no—
1222C2×C4—112no—
1223C2×C4—112no—
1224C2×C4—112no—
1225C2×C4—112no—
1226C2×C4—112no—
1227C2×C4—112no—
1228C2×C4—112no—
1229C2×C4—228no—
1230C2×C4—228no—
1231C2×C4—228no—
1232C2×C4—228no—
1233C2×C4—228no—
1234C2×C4—228no—
1235C2×C4—224no—
1236C2×C4—222no—
1237C2×C4—228no—
1238C2×C4—224no—
1239C2×C4—224no—
1240C2×C4—224no—
1241C2×C4—4416no—
1242C2×C4—444no—
1243C2×C4C22⋊C4×D1111yescharacteristic
1244C2×C4C22⋊C4×D1112yes—
1245C2×C4C22⋊C4×D1112yes—
1246C2×C4C22⋊C4×D1111yescharacteristic
1247C2×C4C22⋊C4×D1112yes—
1248C2×C4C22⋊C4×D1112yes—
1249C2×C4C22⋊C4×D1112yes—
1250C2×C4C22×C4×D1111yescharacteristic
1251C2×C4C22×C4×D1112yes—
1252C2×C4C22×C4×D1111yescharacteristic
1253C2×C4C22×C4×D1112yes—
1254C2×C4C2×D4×D1111yescharacteristic
1255C2×C4C2×D4×D1112yes—
1256C2×C4C2×D4×D1112yes—
1257C2×C4C2×D4×D1112yes—
1258C2×C4C2×D4×D1111yescharacteristic
1259C2×C4C2×D4×D1111yescharacteristic
1260C2×C4C24×D1111yescharacteristic
1261C8—24no—
1262C8—224no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—24no—
1267C22—42no—
1268C22—42no—
1269C22—48no—
1270C22—44no—
1271C22—114no—
1272C22—112no—
1273C22—112no—
1274C22—112no—
1275C22—112no—
1276C22—224no—
1277C22—228no—
1278C22—224no—
1279C22—228no—
1280C22—222no—
1281C22—222no—
1282C22—222no—
1283C22—224no—
1284C22—442no—
1285C22—444no—
1286C22—442no—
1287C22—444no—
1288C22—448no—
1289C22—4416no—
1290C22—4416no—
1291C22—444no—
1292C22C2×C22⋊C4×D1112yes—
1293C22C2×C22⋊C4×D1111yescharacteristic
1294C22C2×C22⋊C4×D1112yes—
1295C22C2×C22⋊C4×D1111yescharacteristic
1296C22C22×D4×D1111yescharacteristic
1297C4—24no—
1298C4—44no—
1299C4—112no—
1300C4—112no—
1301C4—112no—
1302C4—112no—
1303C4—224no—
1304C4—444no—
1305C4C2×C22⋊C4×D1112yes—
1306C4C2×C22⋊C4×D1111yescharacteristic
1307C4C2×C22⋊C4×D1111yescharacteristic
1308C4C2×C22⋊C4×D1112yes—
1309C4C23×C4×D1111yescharacteristic
1310C4C22×D4×D1111yescharacteristic
1311C2—21no—
1312C2—22no—
1313C2—21no—
1314C2—22no—
1315C2—44no—
1316C2—114no—
1317C2—222no—
1318C2—222no—
1319C2—222no—
1320C2—444no—
1321C2D11×#42112yesdirect product factor
1322C2C22×C22⋊C4×D1111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#421C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#41×D11C2
cosocleC2×C4×C11C25
hypercenterC2×#421D11
hypocenterC11C22×#421
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C22×M16×D11C2semidirect
3. C2×D11×#117C2semidirect
4. C2×#10622618C2semidirect
5. C2×#10622849C2semidirect
6. C2×#10622752C2semidirect
7. C2×#10622434C2semidirect
8. D11×#421C2direct (N × H)
9. C2×D11×#104C2semidirect
10. C2×C11×#421C2semidirect
18. C2×#41×D11C4semidirect
19. C2×#41×D11C4semidirect
20. C2×#41×D11C4semidirect
24. C22×#4343C4semidirect
25. C22×Q8×D11C4semidirect
27. C22×#4341C4semidirect
29. C22×D4×D11C4semidirect
34. C22×C11×M16C22semidirect
35. C2×C11×#117C22semidirect
36. C2×#66979C22semidirect
37. C22×#4318C22semidirect
41. C2×M16×D11C22semidirect
42. C2×M16×D11C22semidirect
43. C2×M16×D11C22semidirect
47. D11×#117C22semidirect
52. C2×#66925C22semidirect
53. C2×C42×D11C22semidirect
54. C11×#421C22semidirect
55. C2×C11×#104C22semidirect
56. #10622849C22semidirect
57. C2×#66901C22semidirect
58. #10622752C22semidirect
59. C2×#66889C22semidirect
60. #10622618C22semidirect
61. C2×#66869C22semidirect
62. #10622434C22semidirect
63. D11×#104C22semidirect
70. C2×C11×#41C2×C4semidirect
71. C2×C11×#41C2×C4semidirect
74. C22×Q8×C11C2×C4semidirect
76. C22×D4×C11C2×C4semidirect
99. #41×D11C2×C4semidirect
100. #41×D11C2×C4semidirect
101. #41×D11C2×C4semidirect
108. C2×#4343C2×C4semidirect
109. C2×#4343C2×C4semidirect
114. C2×Q8×D11C2×C4semidirect
115. C2×Q8×D11C2×C4semidirect
126. C2×#4341C2×C4semidirect
127. C2×#4341C2×C4semidirect
138. C2×D4×D11C2×C4semidirect
139. C2×D4×D11C2×C4semidirect
150. C2×#4339C2×C4semidirect
151. C2×#4339C2×C4semidirect
155. C22×D44C2×C4semidirect
183. C22×Dic22C2×C4semidirect
186. C2×C11×M16C23semidirect
187. C2×C11×M16C23semidirect
190. C11×#117C23semidirect
193. C2×C42×C11C23semidirect
197. #66979C23semidirect
201. C2×C4×Dic11C23semidirect
204. C2×#4318C23semidirect
205. C2×#4318C23semidirect
211. M16×D11C23semidirect
212. M16×D11C23semidirect
224. #66925C23semidirect
226. C42×D11C23semidirect
227. C11×#104C23semidirect
228. #66901C23semidirect
229. #66889C23semidirect
230. #66869C23semidirect
256. C11×#41C22×C4semidirect
261. C2×Q8×C11C22×C4semidirect
269. C2×D4×C11C22×C4semidirect
314. #4343C22×C4semidirect
320. Q8×D11C22×C4semidirect
332. #4341C22×C4semidirect
344. D4×D11C22×C4semidirect
359. #4339C22×C4semidirect
367. C2×D44C22×C4semidirect
436. C2×Dic22C22×C4semidirect
439. C11×M16C24semidirect
445. C42×C11C24semidirect
452. C4×Dic11C24semidirect
455. #4318C24semidirect
470. C2×#421D11direct (N × H)
643. C22×M16C2×D11semidirect
651. C2×#117C2×D11semidirect
659. #421C2×D11direct (N × H)
664. C2×#104C2×D11semidirect
694. C2×D11#421direct (N × H)
771. C2×#41C4×D11semidirect
772. C2×#41C4×D11semidirect
783. C22×Q8C4×D11semidirect
802. C22×D4C4×D11semidirect
848. C2×M16C22×D11semidirect
849. C2×M16C22×D11semidirect
862. #117C22×D11semidirect
875. C2×C42C22×D11semidirect
879. #104C22×D11semidirect
885. C2×C11C2×#421semidirect
891. D11C2×#421direct (N × H)
950. #41C2×C4×D11semidirect
968. C2×Q8C2×C4×D11semidirect
1005. C2×D4C2×C4×D11semidirect
1104. M16C23×D11semidirect
1121. C42C23×D11semidirect
1122. C11C22×#421semidirect
1321. C2D11×#421direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D112
C22×M16×D112
C2×D11×#1172
C2×#106226182
C2×#106228492
C2×#106227522
C2×#106224342
D11×#4212
C2×D11×#1042
C2×C11×#4212
C22×#42111