Finite Group Databasebeta

← D11×#1472 #14719741

Subgroups — D11×#1472 #14719741

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic
3C2×D11×C22⋊C8C211yesmaximal, characteristic
4#13066981C211yesmaximal, characteristic, complemented
5#13066980C211yesmaximal, characteristic, complemented
6#13066979C211yesmaximal, characteristic, complemented
7#13066978C214yesmaximal, complemented
8D11×#324C214yesmaximal, complemented
9C11×#1472C211yesmaximal, characteristic, complemented
10C22×Q8×D11C411yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×#66999C411yescharacteristic
14C2×#66977C2211yescharacteristic
15C2×M16×D11—21no—
16C22×C8×D11—21no—
17D11×C22⋊Q8—21no—
18D11×C22⋊Q8—21no—
19D11×C22⋊Q8—21no—
20D11×C22⋊Q8—21no—
21D11×C22⋊Q8—21no—
22D11×C22⋊Q8—21no—
23D11×C22⋊Q8—21no—
24D11×C22⋊Q8—21no—
25C2×#66950C411yescharacteristic
26C2×#66949C2212yes—
27C2×C4⋊C4×D11C411yescharacteristic
28C2×C4⋊C4×D11C2212yes—
29C2×C22⋊C4×D11C412yes—
30C2×#66931C412yes—
31C11×#407C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33#10622820C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622739—21no—
36C2×(C2×D11)⋊C8—21no—
37#10622339—21no—
38#10622339C2212yes—
39D11×C22⋊C8—21no—
40D11×C22⋊C8—21no—
41D11×C22⋊C8—21no—
42D11×C22⋊C8C2212yes—
43D11×C22⋊C8C2212yes—
44D11×C22⋊C8C2212yes—
45C11×#324C2214yescomplemented
46#10622166C2214yescomplemented
47#10622107C2214yescomplemented
48#10622107C2214yescomplemented
49C24×D11C2×C411yescharacteristic
50C22×Q8×C11C2×C411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2×C411yescharacteristic
53C2×Q8×D11—21no—
54C2×Q8×D11—21no—
55C2×Q8×D11—21no—
56C2×Q8×D11—21no—
57C2×Q8×D11—44no—
58C22×C4×D11—44no—
59C22×C4×D11C2×C412yes—
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2×C412yes—
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11D411yescharacteristic
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×Dic22C2×C412yes—
74C22×Dic22C2×C411yescharacteristic
75C2×C11×M16—21no—
76C22×C8×C11—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4C2×C412yes—
84C2×C22⋊Dic11C2×C412yes—
85#66999—21no—
86#66999—21no—
87#66999—21no—
88#66999—21no—
89C2×(C2×D11)⋊C4C2×C412yes—
90C2×(C2×D11)⋊C4C2×C412yes—
91C2×C4⋊Dic11C2×C412yes—
92C2×C4⋊Dic11C2×C411yescharacteristic
93#66977—21no—
94#66977—21no—
95#66977—21no—
96#66977—21no—
97C2×Dic11⋊C4C2×C412yes—
98C2×Dic11⋊C4C2×C412yes—
99C2×Dic11⋊C4C2312yes—
100C2×#4318—21no—
101C22×C11⋊C8—21no—
102M16×D11—44no—
103C2×#4313—22no—
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—22no—
107C2×C8×D11—44no—
108#66950—21no—
109#66950—21no—
110#66950—21no—
111#66950—21no—
112#66949—22no—
113#66949—22no—
114#66949—22no—
115#66949—22no—
116C4⋊C4×D11—21no—
117C4⋊C4×D11—21no—
118C4⋊C4×D11—21no—
119C4⋊C4×D11—21no—
120C4⋊C4×D11—22no—
121C4⋊C4×D11—22no—
122C4⋊C4×D11—22no—
123C4⋊C4×D11—22no—
124C22⋊C4×D11—22no—
125C22⋊C4×D11—22no—
126C22⋊C4×D11—22no—
127C22⋊C4×D11—22no—
128#66931—22no—
129#66931—22no—
130#66931—22no—
131#66931—22no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8C2312yes—
135C11×C22⋊C8C2312yes—
136C22⋊(C11⋊C8)—21no—
137C22⋊(C11⋊C8)—21no—
138C22⋊(C11⋊C8)C2312yes—
139C22⋊(C11⋊C8)C2312yes—
140(C2×D11)⋊C8—22no—
141(C2×D11)⋊C8—22no—
142(C2×D11)⋊C8—22no—
143(C2×D11)⋊C8—22no—
144C2×#1472—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11C22⋊C411yescharacteristic
150C23×D11C22⋊C411yescharacteristic
151C23×D11C22⋊C411yescharacteristic
152C23×D11C22⋊C411yescharacteristic
153C23×D11C22×C411yescharacteristic
154C23×D11C22×C411yescharacteristic
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—42no—
168C22×Dic11C22⋊C411yescharacteristic
169C22×Dic11C22⋊C411yescharacteristic
170C22×Dic11C22⋊C411yescharacteristic
171C22×Dic11C22⋊C411yescharacteristic
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C412yes—
175C22×Dic11C22×C411yescharacteristic
176Q8×D11—44no—
177Q8×D11—44no—
178Q8×D11—44no—
179Q8×D11—44no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—28no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—44no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—42no—
198C2×C4×D11C22⋊C411yescharacteristic
199C2×C4×D11C22⋊C411yescharacteristic
200C2×C4×D11C22⋊C411yescharacteristic
201C2×C4×D11C22⋊C411yescharacteristic
202C2×C4×D11C22⋊C411yescharacteristic
203C2×C4×D11C22⋊C411yescharacteristic
204C2×C4×D11C22⋊C411yescharacteristic
205C2×C4×D11C22⋊C411yescharacteristic
206C2×C4×D11C2×D411yescharacteristic
207C2×C4×D11C2×D411yescharacteristic
208C2×C4×D11C2×D411yescharacteristic
209C2×C4×D11C2×D411yescharacteristic
210C2×C4×D11C2×D411yescharacteristic
211C2×C4×D11C2×D411yescharacteristic
212C2×C4×D11C2×D411yescharacteristic
213C2×C4×D11C2×D411yescharacteristic
214C2×Dic22—22no—
215C2×Dic22—22no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—42no—
219C2×Dic22—44no—
220C11×M16—42no—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—42no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—22no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240Dic11⋊C4—22no—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4—22no—
246#4318—42no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—42no—
250#4313—44no—
251C8×D11—44no—
252C8×D11—44no—
253C8×D11—44no—
254C22×C22⋊Q8—111no—
255C2×#407—111no—
256C22×C22⋊C8—111no—
257#1472—111no—
258#1472—111no—
259#1472—114no—
260#1472—111no—
261#1472D1111yescharacteristic, direct product factor
262C2×#324—114no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—41no—
266C23×C11C2×C22⋊C411yescharacteristic
267C23×C11C2×C22⋊C411yescharacteristic
268C23×C11C23×C411yescharacteristic
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—416no—
286C22×D11#10114yes—
287C22×D11C2×C22⋊C411yescharacteristic
288C22×D11C2×C22⋊C411yescharacteristic
289C22×D11C2×C22⋊C411yescharacteristic
290C22×D11C2×C22⋊C411yescharacteristic
291C22×D11#13114yes—
292Q8×C11—42no—
293Q8×C11—42no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—42no—
304C2×C4×C11C2×C22⋊C411yescharacteristic
305C2×C4×C11C2×C22⋊C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—42no—
318C2×Dic11C2×C22⋊C411yescharacteristic
319C2×Dic11C2×C22⋊C411yescharacteristic
320C2×Dic11C2×C22⋊C411yescharacteristic
321C2×Dic11C2×C22⋊C411yescharacteristic
322C4×D11—22no—
323C4×D11—22no—
324C4×D11—22no—
325C4×D11—22no—
326C4×D11—22no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—41no—
332C4×D11—41no—
333C4×D11—41no—
334C4×D11—41no—
335C4×D11—41no—
336C4×D11—41no—
337C4×D11—44no—
338C4×D11—44no—
339C4×D11—44no—
340C4×D11—44no—
341C4×D11#9914yes—
342Dic22—44no—
343Dic22—42no—
344Dic22—42no—
345Dic22—44no—
346C8×C11—42no—
347C8×C11—42no—
348C11⋊C8—42no—
349C11⋊C8—42no—
350C23×Q8—111no—
351C24×C4—111no—
352C22×M16—221no—
353C23×C8—221no—
354C2×C22⋊Q8—111no—
355C2×C22⋊Q8—111no—
356C2×C22⋊Q8—112no—
357C2×C22⋊Q8—111no—
358C2×C22⋊Q8—112no—
359C2×C22⋊Q8—221no—
360C2×C22⋊Q8—221no—
361C2×C22⋊Q8—221no—
362C2×C22⋊Q8—221no—
363C2×C22⋊Q8—221no—
364C2×C22⋊Q8—221no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8—221no—
367C2×C22⋊Q8C2×D1111yescharacteristic
368C22×C4⋊C4—112no—
369C22×C4⋊C4—111no—
370C22×C22⋊C4—112no—
371#407—111no—
372#407—112no—
373#407—221no—
374#407—221no—
375#407C2×D1111yescharacteristic
376C2×C22⋊C8—111no—
377C2×C22⋊C8—112no—
378C2×C22⋊C8—112no—
379C2×C22⋊C8—112no—
380C2×C22⋊C8—221no—
381C2×C22⋊C8—221no—
382C2×C22⋊C8—221no—
383C2×C22⋊C8—221no—
384C2×C22⋊C8C2×D1111yescharacteristic
385#324—114no—
386#324—114no—
387#324—114no—
388#324C2×D1114yescomplemented
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—44no—
397C22×C11C2×#10112yes—
398C22×C11C22×C22⋊C411yescharacteristic
399C22×C11C2×#13112yes—
400C2×D11—21no—
401C2×D11—21no—
402C2×D11—21no—
403C2×D11—21no—
404C2×D11—28no—
405C2×D11—28no—
406C2×D11—21no—
407C2×D11—21no—
408C2×D11—21no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11#40812yes—
414C2×D11#40812yes—
415C2×D11C2×#9912yes—
416C2×D11C2×#10112yes—
417C2×D11C2×#10112yes—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11C2×#9912yes—
424Dic11—21no—
425Dic11—21no—
426Dic11—21no—
427Dic11—42no—
428Dic11—42no—
429Dic11C2×#9912yes—
430C25—111no—
431C22×Q8—112no—
432C22×Q8—111no—
433C22×Q8—221no—
434C22×Q8—221no—
435C22×Q8—221no—
436C22×Q8—221no—
437C22×Q8—444no—
438C22×Q8C4×D1111yescharacteristic
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—112no—
453C23×C4—112no—
454C23×C4—444no—
455C23×C4C22×D1111yescharacteristic
456C2×M16—21no—
457C2×M16—222no—
458C2×M16—221no—
459C2×M16—444no—
460C22×C8—21no—
461C22×C8—222no—
462C22×C8—222no—
463C22×C8—222no—
464C22×C8—221no—
465C22×C8—444no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—222no—
471C22⋊Q8—222no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474C22⋊Q8—222no—
475C22⋊Q8—222no—
476C22⋊Q8—222no—
477C22⋊Q8—222no—
478C22⋊Q8—221no—
479C22⋊Q8—221no—
480C22⋊Q8—221no—
481C22⋊Q8—221no—
482C22⋊Q8—221no—
483C22⋊Q8—221no—
484C22⋊Q8—221no—
485C22⋊Q8—221no—
486C22⋊Q8—221no—
487C22⋊Q8—221no—
488C22⋊Q8—221no—
489C22⋊Q8—221no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4C4×D1111yescharacteristic
504C2×C4⋊C4C22×D1112yes—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—222no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4—222no—
511C2×C22⋊C4—222no—
512C2×C22⋊C4C4×D1112yes—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—112no—
516C22⋊C8—112no—
517C22⋊C8—222no—
518C22⋊C8—222no—
519C22⋊C8—222no—
520C22⋊C8—222no—
521C22⋊C8—221no—
522C22⋊C8—221no—
523C22⋊C8C22×D1112yes—
524C22⋊C8C22×D1112yes—
525C2×C11—22no—
526C2×C11—22no—
527C2×C11—41no—
528C2×C11C2×#40811yescharacteristic
529C2×C11C22×#9911yescharacteristic
530C2×C11C22×#10111yescharacteristic
531D11—22no—
532D11—22no—
533D11—41no—
534D11#147214yesdirect product factor
535C24—111no—
536C24—111no—
537C24—111no—
538C24—111no—
539C24—111no—
540C24—111no—
541C24—224no—
542C24—224no—
543C24—442no—
544C24C2×C4×D1111yescharacteristic
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—42no—
548C2×Q8—222no—
549C2×Q8—222no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—442no—
553C2×Q8—444no—
554C2×Q8—444no—
555C2×Q8—444no—
556C2×Q8—444no—
557C2×Q8—444no—
558C22×C4—42no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—228no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4—442no—
595C22×C4—442no—
596C22×C4—442no—
597C22×C4—442no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4—444no—
601C22×C4—442no—
602C22×C4C2×C4×D1112yes—
603C22×C4C2×C4×D1111yescharacteristic
604C22×C4C2×C4×D1112yes—
605C22×C4D4×D1111yescharacteristic
606C22×C4D4×D1111yescharacteristic
607C22×C4D4×D1111yescharacteristic
608C22×C4D4×D1111yescharacteristic
609C22×C4C23×D1111yescharacteristic
610M16—42no—
611M16—444no—
612M16—442no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—42no—
616C2×C8—222no—
617C2×C8—222no—
618C2×C8—444no—
619C2×C8—444no—
620C2×C8—444no—
621C2×C8—442no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—222no—
627C4⋊C4—222no—
628C4⋊C4—222no—
629C4⋊C4—222no—
630C4⋊C4—222no—
631C4⋊C4—222no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—222no—
635C4⋊C4—222no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—222no—
639C22⋊C4—222no—
640C22⋊C4—222no—
641C22⋊C4—222no—
642C22⋊C4—222no—
643C22⋊C4—222no—
644C11C2×#147211yescharacteristic, complemented, Sylow
645C23—22no—
646C23—22no—
647C23—41no—
648C23—111no—
649C23—111no—
650C23—111no—
651C23—114no—
652C23—114no—
653C23—111no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—4416no—
671C23C22⋊C4×D1111yescharacteristic
672C23C22⋊C4×D1111yescharacteristic
673C23C22×C4×D1111yescharacteristic
674Q8—42no—
675Q8—42no—
676Q8—442no—
677Q8—444no—
678Q8—444no—
679Q8—442no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—111no—
691C2×C4—114no—
692C2×C4—111no—
693C2×C4—111no—
694C2×C4—111no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—444no—
717C2×C4—444no—
718C2×C4—444no—
719C2×C4—444no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—442no—
724C2×C4C22⋊C4×D1111yescharacteristic
725C2×C4C22⋊C4×D1111yescharacteristic
726C2×C4C2×D4×D1111yescharacteristic
727C2×C4C2×D4×D1111yescharacteristic
728C8—42no—
729C8—42no—
730C8—442no—
731C8—442no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—112no—
741C22—112no—
742C22—112no—
743C22—112no—
744C22—112no—
745C22—228no—
746C22—228no—
747C22—221no—
748C22—221no—
749C22—221no—
750C22—221no—
751C22—221no—
752C22—221no—
753C22—221no—
754C22—444no—
755C22—444no—
756C22—444no—
757C22—444no—
758C22D11×#10112yes—
759C22C2×C22⋊C4×D1111yescharacteristic
760C22D11×#13112yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—42no—
765C4—42no—
766C4—112no—
767C4—221no—
768C4—221no—
769C4—221no—
770C4—442no—
771C4—442no—
772C4D11×#9912yes—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—114no—
777C2—222no—
778C2—222no—
779C2—441no—
780C2D11×#40811yescharacteristic
781C2C2×D11×#9911yescharacteristic
782C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1472C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1472D11
hypocenterC11C2×#1472
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
4. #13066981C2semidirect
5. #13066980C2semidirect
6. #13066979C2semidirect
7. #13066978C2semidirect
8. D11×#324C2semidirect
9. C11×#1472C2semidirect
45. C11×#324C22semidirect
46. #10622166C22semidirect
47. #10622107C22semidirect
48. #10622107C22semidirect
261. #1472D11direct (N × H)
388. #324C2×D11semidirect
534. D11#1472direct (N × H)
644. C11C2×#1472semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
D11×#4072
C2×D11×C22⋊C82
#130669812
#130669802
#130669792
#130669782
D11×#3242
C11×#14722
C2×#147211