Finite Group Databasebeta

← C4×D11×#120 #14912183

Subgroups — C4×D11×#120 #14912183

Order 2816.

8582 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D11C211yesmaximal, characteristic, complemented
2C2×D11×#120C211yesmaximal, characteristic
3C2×C4×D4×D11C213yesmaximal, complemented
4#13071121C213yesmaximal, complemented
5C4×#66935C213yesmaximal, complemented
6#120×Dic11C211yesmaximal, characteristic, complemented
7C4×#67006C211yesmaximal, characteristic, complemented
8#13071117C213yesmaximal, complemented
9C4×#66990C213yesmaximal, complemented
10#13071115C211yesmaximal, characteristic, complemented
11D11×#386C213yesmaximal, complemented
12D11×#385C213yesmaximal, complemented
13D11×#379C211yesmaximal, characteristic, complemented
14C4×C22⋊C4×D11C213yesmaximal, complemented
15C4×C11×#120C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic, complemented
18C24×Dic11C2211yescharacteristic, complemented
19C22×D4×D11C2213yes—
20C23×C4×D11—224no—
21C23×C4×D11C2213yes—
22C23×C4×D11C2213yes—
23C23×C4×D11C2213yescomplemented
24C23×C4×D11C2213yescomplemented
25C23×C4×D11C2211yescharacteristic, complemented
26C2×C11×#120C2211yescharacteristic
27C2×C4×D4×C11C2213yescomplemented
28C2×#67006C2211yescharacteristic
29C2×#66990C2213yes—
30C2×D4×Dic11C2213yescomplemented
31C2×C4×C22⋊D11C2213yescomplemented
32C2×C4×C22⋊D11C2213yescomplemented
33D11×#120C4116yesdirect product factor
34C4×D4×D11—224no—
35C2×#66946C2213yescomplemented
36C2×C4⋊C4×D11C2213yescomplemented
37C2×#66935C2213yes—
38C2×(C22⋊D11)⋊C4C2213yescomplemented
39C2×(C22⋊D11)⋊C4C2213yescomplemented
40C2×C22⋊C4×D11C2213yes—
41C2×C22⋊C4×D11C2213yes—
42C2×C22⋊C4×D11C2213yes—
43C2×C22⋊C4×D11C2213yescomplemented
44C2×C4×D44C2213yescomplemented
45C2×C42×D11C2213yescomplemented
46C11×#386C2213yescomplemented
47C11×#385C2213yescomplemented
48C11×#379C2211yescharacteristic, complemented
49C4×C11×C22⋊C4C2213yescomplemented
50#10622860C2211yescharacteristic, complemented
51#10622833C2213yescomplemented
52#10622826C2213yescomplemented
53#10622823C2213yescomplemented
54C4×C22⋊Dic11C2213yescomplemented
55#10622602C2216yescomplemented
56#10622571C2213yescomplemented
57#10622569C2216yescomplemented
58#10622568C2213yescomplemented
59#10622568C2213yescomplemented
60#10622563C2213yescomplemented
61#10622559C2213yescomplemented
62C22⋊C4×Dic11C2213yescomplemented
63C22⋊C4×Dic11C2213yescomplemented
64C4×(C2×D11)⋊C4C2216yescomplemented
65#10622281C2216yescomplemented
66#10622279C2216yescomplemented
67#10622278C2216yescomplemented
68D11×#95C2216yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11—212no—
71C24×D11—212no—
72C24×D11C2×C418yescomplemented
73C24×D11C2311yescharacteristic
74C24×D11C2313yes—
75C24×D11C2313yes—
76C22×D4×C11C2313yes—
77C23×C4×C11—212no—
78C23×C4×C11C2313yes—
79C23×C4×C11C2313yes—
80C23×C4×C11C2311yescharacteristic, complemented
81C22×C22⋊D11C2313yes—
82C22×C22⋊D11C2313yes—
83C23×Dic11—212no—
84C23×Dic11C2313yes—
85C23×Dic11C2313yes—
86C23×Dic11C2311yescharacteristic, complemented
87C2×D4×D11—212no—
88C2×D4×D11—212no—
89C2×D4×D11C2×C4124yescomplemented
90C22×D44C2313yes—
91C22×C4×D11—2128no—
92C22×C4×D11—212no—
93C22×C4×D11—212no—
94C22×C4×D11—212no—
95C22×C4×D11—224no—
96C22×C4×D11—224no—
97C22×C4×D11—224no—
98C22×C4×D11—224no—
99C22×C4×D11—212no—
100C22×C4×D11D4124yescomplemented
101C22×C4×D11C2313yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2316yes—
104C22×C4×D11C2313yes—
105C22×C4×D11C2313yes—
106C22×C4×D11C2313yes—
107C22×C4×D11C2313yes—
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic, complemented
110C22×C4×D11C2311yescharacteristic, complemented
111C11×#120C2×C418yescomplemented
112C4×D4×C11—212no—
113C2×C11×C4⋊C4C2313yescomplemented
114C2×C11×C22⋊C4C2313yes—
115C2×C11×C22⋊C4C2313yes—
116C2×C11×C22⋊C4C2313yes—
117C2×C11×C22⋊C4C2313yescomplemented
118C2×C42×C11C2313yescomplemented
119#67006C2×C418yescomplemented
120C2×C22⋊Dic11C2313yes—
121C2×C22⋊Dic11C2313yes—
122C2×C22⋊Dic11C2313yes—
123C2×C22⋊Dic11C2313yescomplemented
124#66990C2×C4124yescomplemented
125D4×Dic11—212no—
126C4×C22⋊D11—212no—
127C4×C22⋊D11—212no—
128C2×(C2×D11)⋊C4C2313yes—
129C2×(C2×D11)⋊C4C2313yes—
130C2×(C2×D11)⋊C4C2316yes—
131C2×(C2×D11)⋊C4C2316yes—
132C2×(C2×D11)⋊C4C2313yescomplemented
133C2×(C2×D11)⋊C4C2313yescomplemented
134C2×C4⋊Dic11C2313yescomplemented
135C2×Dic11⋊C4C2313yescomplemented
136C2×Dic11⋊C4C2313yescomplemented
137C2×C4×Dic11C2313yescomplemented
138C2×C4×Dic11C2313yescomplemented
139C2×C4×Dic11C2313yescomplemented
140#66946—212no—
141C4⋊C4×D11—212no—
142#66935C2×C4124yescomplemented
143(C22⋊D11)⋊C4—212no—
144(C22⋊D11)⋊C4—212no—
145C22⋊C4×D11—212no—
146C22⋊C4×D11—212no—
147C22⋊C4×D11—212no—
148C22⋊C4×D11C2×C4124yescomplemented
149C4×D44—212no—
150C42×D11—212no—
151C11×#95C2316yescomplemented
152C11⋊#95C2316yescomplemented
153C11⋊#95C2316yescomplemented
154C11⋊#95C2316yescomplemented
155C2×C4×#120—111nomaximal, Sylow
156C24×C11—26no—
157C24×C11—26no—
158C24×C11C22×C414yescomplemented
159C24×C11C2411yescharacteristic
160C24×C11C2413yes—
161C23×D11—232no—
162C23×D11—296no—
163C23×D11—26no—
164C23×D11—26no—
165C23×D11—296no—
166C23×D11—212no—
167C23×D11—212no—
168C23×D11—212no—
169C23×D11—212no—
170C23×D11—26no—
171C23×D11—26no—
172C23×D11C22×C4112yes—
173C23×D11C22×C4112yescomplemented
174C23×D11C22×C414yescomplemented
175C23×D11C2×D4112yes—
176C23×D11#41112yes—
177C23×D11C2411yescharacteristic
178C23×D11C2413yes—
179C23×D11C2411yescharacteristic
180C2×D4×C11—26no—
181C2×D4×C11—26no—
182C2×D4×C11C22×C4112yescomplemented
183C22×C4×C11—232no—
184C22×C4×C11—26no—
185C22×C4×C11—212no—
186C22×C4×C11—212no—
187C22×C4×C11—26no—
188C22×C4×C11C2×D4112yescomplemented
189C22×C4×C11C2413yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2413yes—
192C22×C4×C11C2413yes—
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—26no—
195C2×C22⋊D11—26no—
196C2×C22⋊D11—26no—
197C2×C22⋊D11—26no—
198C2×C22⋊D11C22×C4112yescomplemented
199C2×C22⋊D11C22×C4112yescomplemented
200C22×Dic11—232no—
201C22×Dic11—212no—
202C22×Dic11—212no—
203C22×Dic11—26no—
204C22×Dic11—26no—
205C22×Dic11C2×D4112yescomplemented
206C22×Dic11C2413yes—
207C22×Dic11C2411yescharacteristic
208C22×Dic11C2413yes—
209C22×Dic11C2413yes—
210C22×Dic11C2411yescharacteristic
211D4×D11—296no—
212C2×D44—26no—
213C2×D44—26no—
214C2×D44C22×C4112yescomplemented
215C2×C4×D11—296no—
216C2×C4×D11—296no—
217C2×C4×D11—296no—
218C2×C4×D11—212no—
219C2×C4×D11—212no—
220C2×C4×D11—296no—
221C2×C4×D11—26no—
222C2×C4×D11—26no—
223C2×C4×D11—212no—
224C2×C4×D11—212no—
225C2×C4×D11—26no—
226C2×C4×D11—26no—
227C2×C4×D11—26no—
228C2×C4×D11—212no—
229C2×C4×D11—212no—
230C2×C4×D11—212no—
231C2×C4×D11—26no—
232C2×C4×D11—416no—
233C2×C4×D11C22×C4112yescomplemented
234C2×C4×D11C2×D4112yes—
235C2×C4×D11C2×D4112yes—
236C2×C4×D11C2×D4112yescomplemented
237C2×C4×D11C2×D4112yescomplemented
238C11×C4⋊C4—26no—
239C11×C22⋊C4—26no—
240C11×C22⋊C4—26no—
241C11×C22⋊C4—26no—
242C11×C22⋊C4C22×C4112yescomplemented
243C42×C11—26no—
244C22⋊Dic11—26no—
245C22⋊Dic11—26no—
246C22⋊Dic11—26no—
247C22⋊Dic11C22×C4112yescomplemented
248(C2×D11)⋊C4—26no—
249(C2×D11)⋊C4—26no—
250(C2×D11)⋊C4—26no—
251(C2×D11)⋊C4—212no—
252(C2×D11)⋊C4—26no—
253(C2×D11)⋊C4C22×C4124yescomplemented
254C4⋊Dic11—26no—
255Dic11⋊C4—26no—
256Dic11⋊C4—26no—
257C4×Dic11—26no—
258C4×Dic11—26no—
259C4×Dic11—26no—
260C25×C4—111no—
261C22×#120—111no—
262C22×C4×D4—113no—
263C4×#120—113no—
264C4×#120—113no—
265C4×#120—111no—
266C4×#120—113no—
267C4×#120—111no—
268C4×#120—111no—
269C4×#120—113no—
270C4×#120D1111yescharacteristic, direct product factor
271C2×#386—113no—
272C2×#385—113no—
273C2×#379—111no—
274C2×C4×C22⋊C4—113no—
275C23×C11—28no—
276C23×C11—224no—
277C23×C11—224no—
278C23×C11—26no—
279C23×C11—26no—
280C23×C11—23no—
281C23×C11—23no—
282C23×C11C23×C416yes—
283C23×C11C23×C412yescomplemented
284C23×C11C22×D416yes—
285C23×C11C2×#4116yes—
286C23×C11C2511yescharacteristic
287C22×D11—224no—
288C22×D11—248no—
289C22×D11—224no—
290C22×D11—2256no—
291C22×D11—224no—
292C22×D11—26no—
293C22×D11—26no—
294C22×D11—248no—
295C22×D11—248no—
296C22×D11—224no—
297C22×D11—224no—
298C22×D11—248no—
299C22×D11—23no—
300C22×D11—23no—
301C22×D11—224no—
302C22×D11—44no—
303C22×D11—412no—
304C22×D11C4×D4148yescomplemented
305C22×D11C23×C416yes—
306C22×D11C23×C412yes—
307C22×D11C23×C412yescomplemented
308C22×D11C22×D416yes—
309C22×D11C22×D416yes—
310C22×D11C2×#4116yes—
311C22×D11C2×#4116yes—
312D4×C11—224no—
313C2×C4×C11—224no—
314C2×C4×C11—23no—
315C2×C4×C11—26no—
316C2×C4×C11—23no—
317C2×C4×C11—224no—
318C2×C4×C11—23no—
319C2×C4×C11—23no—
320C2×C4×C11—26no—
321C2×C4×C11—44no—
322C2×C4×C11C23×C416yescomplemented
323C2×C4×C11C22×D416yes—
324C2×C4×C11C22×D416yes—
325C22⋊D11—224no—
326C22⋊D11—224no—
327C2×Dic11—224no—
328C2×Dic11—23no—
329C2×Dic11—26no—
330C2×Dic11—23no—
331C2×Dic11—224no—
332C2×Dic11—23no—
333C2×Dic11—23no—
334C2×Dic11—26no—
335C2×Dic11—44no—
336C2×Dic11C23×C416yescomplemented
337C2×Dic11C22×D416yes—
338C2×Dic11C22×D416yes—
339D44—224no—
340C4×D11—248no—
341C4×D11—224no—
342C4×D11—224no—
343C4×D11—224no—
344C4×D11—224no—
345C4×D11—44no—
346C4×D11—412no—
347C4×D11—44no—
348C4×D11—44no—
349C4×D11#120116yesdirect product factor
350C26—111no—
351C23×D4—113no—
352C24×C4—113no—
353C24×C4—111no—
354C24×C4—113no—
355C24×C4—113no—
356C24×C4—113no—
357C24×C4—111no—
358C24×C4—2224no—
359C24×C4C2×D1111yescharacteristic, complemented
360C2×#120—111no—
361C2×#120—113no—
362C2×#120—1116no—
363C2×#120—113no—
364C2×#120C2×D1111yescharacteristic
365C2×C4×D4—113no—
366C2×C4×D4—113no—
367C2×C4×D4—113no—
368C2×C4×D4—113no—
369C2×C4×D4—113no—
370C2×C4×D4—113no—
371C2×C4×D4—113no—
372C2×C4×D4—2224no—
373C2×C4×D4C2×D1113yescomplemented
374C22×C4⋊C4—113no—
375C22×C22⋊C4—113no—
376C22×C22⋊C4—113no—
377C22×C22⋊C4—113no—
378C22×C22⋊C4—113no—
379C22×C42—113no—
380#386—113no—
381#386—113no—
382#386—113no—
383#386—116no—
384#386—116no—
385#386C2×D1113yescomplemented
386#385—113no—
387#385—116no—
388#385—113no—
389#385—113no—
390#385—116no—
391#385C2×D1113yescomplemented
392#379—111no—
393#379—113no—
394#379—113no—
395#379C2×D1111yescharacteristic, complemented
396C4×C22⋊C4—113no—
397C4×C22⋊C4—113no—
398C4×C22⋊C4—113no—
399C4×C22⋊C4—116no—
400C4×C22⋊C4—116no—
401C4×C22⋊C4C2×D1113yescomplemented
402C2×#95—116no—
403C22×C11—232no—
404C22×C11—212no—
405C22×C11—26no—
406C22×C11—26no—
407C22×C11—212no—
408C22×C11—26no—
409C22×C11—41no—
410C22×C11—43no—
411C22×C11C2×C4×D4112yescomplemented
412C22×C11C24×C411yescharacteristic
413C22×C11C23×D413yes—
414C22×C11C22×#4113yes—
415C2×D11—296no—
416C2×D11—212no—
417C2×D11—26no—
418C2×D11—26no—
419C2×D11—212no—
420C2×D11—296no—
421C2×D11—26no—
422C2×D11—41no—
423C2×D11—43no—
424C2×D11—416no—
425C2×D11C2×C4×D4112yes—
426C2×D11C2×C4×D4112yescomplemented
427C2×D11C2×#12014yes—
428C2×D11#525112yes—
429C4×C11—26no—
430C4×C11—26no—
431C4×C11—41no—
432C4×C11—43no—
433C4×C11C2×#12014yescomplemented
434Dic11—26no—
435Dic11—26no—
436Dic11—41no—
437Dic11—43no—
438Dic11C2×#12014yescomplemented
439C25—113no—
440C25—118no—
441C25—111no—
442C25—113no—
443C25—2212no—
444C25—2212no—
445C25C22×D1111yescharacteristic
446C22×D4—113no—
447C22×D4—113no—
448C22×D4—1124no—
449C22×D4—113no—
450C22×D4—2212no—
451C22×D4—2212no—
452C22×D4C22×D1113yes—
453C23×C4—212no—
454C23×C4—111no—
455C23×C4—113no—
456C23×C4—1124no—
457C23×C4—113no—
458C23×C4—113no—
459C23×C4—113no—
460C23×C4—113no—
461C23×C4—111no—
462C23×C4—113no—
463C23×C4—113no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—116no—
467C23×C4—111no—
468C23×C4—2212no—
469C23×C4—2224no—
470C23×C4—2224no—
471C23×C4—2224no—
472C23×C4—2224no—
473C23×C4—2212no—
474C23×C4—2212no—
475C23×C4—22128no—
476C23×C4—2212no—
477C23×C4—2212no—
478C23×C4C22×D1113yes—
479C23×C4C22×D1113yes—
480C23×C4C22×D1111yescharacteristic, complemented
481#120—118no—
482#120—1124no—
483#120—1124no—
484#120C4×D1118yesdirect product factor
485C4×D4—212no—
486C4×D4—2212no—
487C4×D4—2212no—
488C4×D4—2212no—
489C4×D4—2212no—
490C4×D4—2212no—
491C4×D4—2212no—
492C4×D4—2212no—
493C2×C4⋊C4—113no—
494C2×C4⋊C4—113no—
495C2×C4⋊C4—113no—
496C2×C4⋊C4—2212no—
497C2×C4⋊C4C22×D1113yescomplemented
498C2×C22⋊C4—113no—
499C2×C22⋊C4—116no—
500C2×C22⋊C4—1124no—
501C2×C22⋊C4—113no—
502C2×C22⋊C4—113no—
503C2×C22⋊C4—113no—
504C2×C22⋊C4—113no—
505C2×C22⋊C4—113no—
506C2×C22⋊C4—113no—
507C2×C22⋊C4—113no—
508C2×C22⋊C4—116no—
509C2×C22⋊C4—2212no—
510C2×C22⋊C4—2212no—
511C2×C22⋊C4—2212no—
512C2×C22⋊C4C22×D1113yes—
513C2×C22⋊C4C22×D1113yes—
514C2×C22⋊C4C22×D1113yes—
515C2×C22⋊C4C22×D1113yescomplemented
516C2×C42—113no—
517C2×C42—113no—
518C2×C42—113no—
519C2×C42—2212no—
520C2×C42C22×D1113yescomplemented
521#95—116no—
522#95—116no—
523#95—116no—
524#95C22×D1116yescomplemented
525C2×C11—212no—
526C2×C11—42no—
527C2×C11C22×C4×D413yes—
528C2×C11C22×#12011yescharacteristic
529C2×C11C2×#52513yes—
530D11—212no—
531D11—42no—
532D11C4×#12018yesdirect product factor
533C24—26no—
534C24—26no—
535C24—111no—
536C24—1112no—
537C24—1112no—
538C24—1112no—
539C24—113no—
540C24—1112no—
541C24—114no—
542C24—111no—
543C24—2212no—
544C24—2212no—
545C24—2296no—
546C24—2212no—
547C24—2212no—
548C24—226no—
549C24—226no—
550C24—2232no—
551C24—2296no—
552C24—226no—
553C24—226no—
554C24C2×C4×D1114yescomplemented
555C24C23×D1111yescharacteristic
556C24C23×D1113yes—
557C2×D4—26no—
558C2×D4—26no—
559C2×D4—1112no—
560C2×D4—1112no—
561C2×D4—1112no—
562C2×D4—226no—
563C2×D4—226no—
564C2×D4—2296no—
565C2×D4—226no—
566C2×D4—226no—
567C2×D4—226no—
568C2×D4—226no—
569C2×D4C2×C4×D11112yescomplemented
570C22×C4—232no—
571C22×C4—26no—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—26no—
575C22×C4—111no—
576C22×C4—1112no—
577C22×C4—1112no—
578C22×C4—113no—
579C22×C4—113no—
580C22×C4—1112no—
581C22×C4—1112no—
582C22×C4—1112no—
583C22×C4—1112no—
584C22×C4—113no—
585C22×C4—111no—
586C22×C4—2212no—
587C22×C4—2212no—
588C22×C4—2296no—
589C22×C4—226no—
590C22×C4—226no—
591C22×C4—2212no—
592C22×C4—2212no—
593C22×C4—226no—
594C22×C4—2296no—
595C22×C4—2296no—
596C22×C4—2296no—
597C22×C4—226no—
598C22×C4—226no—
599C22×C4—2212no—
600C22×C4—2212no—
601C22×C4—2212no—
602C22×C4—226no—
603C22×C4—2232no—
604C22×C4—226no—
605C22×C4—2212no—
606C22×C4—2212no—
607C22×C4—226no—
608C22×C4—4416no—
609C22×C4D4×D11112yescomplemented
610C22×C4C23×D1113yes—
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1113yes—
613C22×C4C23×D1113yes—
614C22×C4C23×D1111yescharacteristic
615C4⋊C4—26no—
616C4⋊C4—226no—
617C4⋊C4—226no—
618C4⋊C4—226no—
619C22⋊C4—26no—
620C22⋊C4—26no—
621C22⋊C4—26no—
622C22⋊C4—1112no—
623C22⋊C4—1124no—
624C22⋊C4—226no—
625C22⋊C4—226no—
626C22⋊C4—226no—
627C22⋊C4—2212no—
628C22⋊C4—226no—
629C22⋊C4—226no—
630C22⋊C4—226no—
631C22⋊C4—226no—
632C22⋊C4C2×C4×D11112yescomplemented
633C42—26no—
634C42—226no—
635C42—226no—
636C42—226no—
637C11C2×C4×#12011yescharacteristic, complemented, Sylow
638C23—28no—
639C23—224no—
640C23—224no—
641C23—26no—
642C23—26no—
643C23—23no—
644C23—23no—
645C23—112no—
646C23—116no—
647C23—116no—
648C23—1148no—
649C23—116no—
650C23—116no—
651C23—116no—
652C23—112no—
653C23—2224no—
654C23—2248no—
655C23—2248no—
656C23—2224no—
657C23—2248no—
658C23—2224no—
659C23—2224no—
660C23—22256no—
661C23—2224no—
662C23—2248no—
663C23—2224no—
664C23—226no—
665C23—226no—
666C23—223no—
667C23—223no—
668C23—444no—
669C23—4412no—
670C23C22×C4×D1116yes—
671C23C22×C4×D1112yescomplemented
672C23C2×D4×D1116yes—
673C23#41×D1116yes—
674C23C24×D1111yescharacteristic
675D4—224no—
676D4—2224no—
677D4—2224no—
678D4—2224no—
679C2×C4—224no—
680C2×C4—23no—
681C2×C4—26no—
682C2×C4—23no—
683C2×C4—224no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—26no—
687C2×C4—44no—
688C2×C4—116no—
689C2×C4—1116no—
690C2×C4—116no—
691C2×C4—116no—
692C2×C4—2224no—
693C2×C4—2224no—
694C2×C4—2224no—
695C2×C4—2248no—
696C2×C4—2224no—
697C2×C4—2224no—
698C2×C4—223no—
699C2×C4—226no—
700C2×C4—223no—
701C2×C4—2224no—
702C2×C4—223no—
703C2×C4—223no—
704C2×C4—226no—
705C2×C4—444no—
706C2×C4—444no—
707C2×C4—4412no—
708C2×C4—444no—
709C2×C4—444no—
710C2×C4C22×C4×D1116yescomplemented
711C2×C4C2×D4×D1116yes—
712C2×C4C2×D4×D1116yes—
713C22—232no—
714C22—212no—
715C22—26no—
716C22—26no—
717C22—212no—
718C22—26no—
719C22—41no—
720C22—43no—
721C22—1112no—
722C22—114no—
723C22—1112no—
724C22—1112no—
725C22—2296no—
726C22—2296no—
727C22—2212no—
728C22—226no—
729C22—226no—
730C22—2212no—
731C22—226no—
732C22—4416no—
733C22—441no—
734C22—443no—
735C22C4×D4×D11112yescomplemented
736C22C23×C4×D1111yescharacteristic
737C22C22×D4×D1113yes—
738C22C2×#41×D1113yes—
739C4—26no—
740C4—26no—
741C4—41no—
742C4—43no—
743C4—114no—
744C4—226no—
745C4—226no—
746C4—441no—
747C4—443no—
748C4D11×#12014yesdirect product factor
749C2—212no—
750C2—42no—
751C2—118no—
752C2—2212no—
753C2—442no—
754C2C2×C4×D4×D1113yes—
755C2C2×D11×#12011yescharacteristic
756C2D11×#52513yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#120C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#120C2
hypercenterC4×#120D11
hypocenterC11C2×C4×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C24×C4×D11C2semidirect
3. C2×C4×D4×D11C2semidirect
4. #13071121C2semidirect
5. C4×#66935C2semidirect
6. #120×Dic11C2semidirect
7. C4×#67006C2semidirect
8. #13071117C2semidirect
9. C4×#66990C2semidirect
10. #13071115C2semidirect
11. D11×#386C2semidirect
12. D11×#385C2semidirect
13. D11×#379C2semidirect
14. C4×C22⋊C4×D11C2semidirect
15. C4×C11×#120C2semidirect
17. C24×C4×C11C22semidirect
18. C24×Dic11C22semidirect
23. C23×C4×D11C22semidirect
24. C23×C4×D11C22semidirect
25. C23×C4×D11C22semidirect
27. C2×C4×D4×C11C22semidirect
30. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
32. C2×C4×C22⋊D11C22semidirect
33. D11×#120C4direct (N × H)
35. C2×#66946C22semidirect
36. C2×C4⋊C4×D11C22semidirect
38. C2×(C22⋊D11)⋊C4C22semidirect
39. C2×(C22⋊D11)⋊C4C22semidirect
43. C2×C22⋊C4×D11C22semidirect
44. C2×C4×D44C22semidirect
45. C2×C42×D11C22semidirect
46. C11×#386C22semidirect
47. C11×#385C22semidirect
48. C11×#379C22semidirect
49. C4×C11×C22⋊C4C22semidirect
50. #10622860C22semidirect
51. #10622833C22semidirect
52. #10622826C22semidirect
53. #10622823C22semidirect
54. C4×C22⋊Dic11C22semidirect
55. #10622602C22semidirect
56. #10622571C22semidirect
57. #10622569C22semidirect
58. #10622568C22semidirect
59. #10622568C22semidirect
60. #10622563C22semidirect
61. #10622559C22semidirect
62. C22⋊C4×Dic11C22semidirect
63. C22⋊C4×Dic11C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622281C22semidirect
66. #10622279C22semidirect
67. #10622278C22semidirect
68. D11×#95C22semidirect
72. C24×D11C2×C4semidirect
80. C23×C4×C11C23semidirect
86. C23×Dic11C23semidirect
89. C2×D4×D11C2×C4semidirect
100. C22×C4×D11D4semidirect
109. C22×C4×D11C23semidirect
110. C22×C4×D11C23semidirect
111. C11×#120C2×C4semidirect
113. C2×C11×C4⋊C4C23semidirect
117. C2×C11×C22⋊C4C23semidirect
118. C2×C42×C11C23semidirect
119. #67006C2×C4semidirect
123. C2×C22⋊Dic11C23semidirect
124. #66990C2×C4semidirect
132. C2×(C2×D11)⋊C4C23semidirect
133. C2×(C2×D11)⋊C4C23semidirect
134. C2×C4⋊Dic11C23semidirect
135. C2×Dic11⋊C4C23semidirect
136. C2×Dic11⋊C4C23semidirect
137. C2×C4×Dic11C23semidirect
138. C2×C4×Dic11C23semidirect
139. C2×C4×Dic11C23semidirect
142. #66935C2×C4semidirect
148. C22⋊C4×D11C2×C4semidirect
151. C11×#95C23semidirect
152. C11⋊#95C23semidirect
153. C11⋊#95C23semidirect
154. C11⋊#95C23semidirect
158. C24×C11C22×C4semidirect
173. C23×D11C22×C4semidirect
174. C23×D11C22×C4semidirect
182. C2×D4×C11C22×C4semidirect
188. C22×C4×C11C2×D4semidirect
198. C2×C22⋊D11C22×C4semidirect
199. C2×C22⋊D11C22×C4semidirect
205. C22×Dic11C2×D4semidirect
214. C2×D44C22×C4semidirect
233. C2×C4×D11C22×C4semidirect
236. C2×C4×D11C2×D4semidirect
237. C2×C4×D11C2×D4semidirect
242. C11×C22⋊C4C22×C4semidirect
247. C22⋊Dic11C22×C4semidirect
253. (C2×D11)⋊C4C22×C4semidirect
270. C4×#120D11direct (N × H)
283. C23×C11C23×C4semidirect
304. C22×D11C4×D4semidirect
307. C22×D11C23×C4semidirect
322. C2×C4×C11C23×C4semidirect
336. C2×Dic11C23×C4semidirect
349. C4×D11#120direct (N × H)
359. C24×C4C2×D11semidirect
373. C2×C4×D4C2×D11semidirect
385. #386C2×D11semidirect
391. #385C2×D11semidirect
395. #379C2×D11semidirect
401. C4×C22⋊C4C2×D11semidirect
411. C22×C11C2×C4×D4semidirect
426. C2×D11C2×C4×D4semidirect
433. C4×C11C2×#120semidirect
438. Dic11C2×#120semidirect
480. C23×C4C22×D11semidirect
484. #120C4×D11direct (N × H)
497. C2×C4⋊C4C22×D11semidirect
515. C2×C22⋊C4C22×D11semidirect
520. C2×C42C22×D11semidirect
524. #95C22×D11semidirect
532. D11C4×#120direct (N × H)
554. C24C2×C4×D11semidirect
569. C2×D4C2×C4×D11semidirect
609. C22×C4D4×D11semidirect
632. C22⋊C4C2×C4×D11semidirect
637. C11C2×C4×#120semidirect
671. C23C22×C4×D11semidirect
710. C2×C4C22×C4×D11semidirect
735. C22C4×D4×D11semidirect
748. C4D11×#120direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D112
C2×D11×#1202
C2×C4×D4×D112
#130711212
C4×#669352
#120×Dic112
C4×#670062
#130711172
C4×#669902
#130711152
D11×#3862
D11×#3852
D11×#3792
C4×C22⋊C4×D112
C4×C11×#1202
C2×C4×#12011