Finite Group Databasebeta

← #14719765

Subgroups — #14719765

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13066981C212yesmaximal, complemented
4#13066977C212yesmaximal, complemented
5#13066965C214yesmaximal, complemented
6#13066932C214yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C411yescharacteristic
10C22×C11×M16—21no—
11C2×#67006C412yes—
12#10623322—21no—
13#10623322—21no—
14#10623322—21no—
15#10623322—21no—
16#10623322—21no—
17#10623322—21no—
18#10623322—21no—
19#10623322—21no—
20C2×#66983C411yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66982C2212yes—
23C2×C4×C22⋊D11C412yes—
24C2×C4×C22⋊D11C2212yes—
25C2×#66979C411yescharacteristic
26C2×#66977C411yescharacteristic
27C2×#66977C2211yescharacteristic
28C23×C11⋊C8—21no—
29C11×#407—21no—
30C11×#407—21no—
31C11×#407C2212yes—
32C11×#407C2212yes—
33C2×C11×C22⋊C8—21no—
34C2×C11×C22⋊C8C2212yes—
35C2×C22⋊(C11⋊C8)—21no—
36C2×C22⋊(C11⋊C8)—21no—
37C2×C22⋊(C11⋊C8)—21no—
38C2×C22⋊(C11⋊C8)C2212yes—
39C2×C22⋊(C11⋊C8)C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622107C2218yescomplemented
42#10622106C2218yescomplemented
43C25×C11C2×C411yescharacteristic
44C23×C4×C11—44no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11C2×C412yes—
60C22×C22⋊D11C2×C412yes—
61C22×C22⋊D11C2×C412yes—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—44no—
67C22×D44C2×C411yescharacteristic
68C22×C4×D11C2×C412yes—
69C22×Dic22C2×C411yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—44no—
73C22×C8×C11—22no—
74#67006—22no—
75#67006—22no—
76#67006—22no—
77#67006—22no—
78C2×C22⋊Dic11C2×C412yes—
79C2×C22⋊Dic11C2×C412yes—
80C2×C22⋊Dic11C2×C412yes—
81#66983—21no—
82#66983—21no—
83#66983—21no—
84#66983—21no—
85#66983—21no—
86#66983—21no—
87#66983—21no—
88#66983—21no—
89#66982—22no—
90#66982—22no—
91#66982—22no—
92#66982—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C4×C22⋊D11—22no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C2×(C2×D11)⋊C4C2×C412yes—
102C2×(C2×D11)⋊C4C2312yes—
103#66979—21no—
104#66979—21no—
105#66979—21no—
106#66979—21no—
107C2×C4⋊Dic11C2×C411yescharacteristic
108C2×C4⋊Dic11C2×C411yescharacteristic
109#66977—21no—
110#66977—21no—
111#66977—21no—
112#66977—21no—
113#66977—21no—
114#66977—21no—
115#66977—21no—
116#66977—21no—
117C2×Dic11⋊C4C2×C412yes—
118C2×Dic11⋊C4C2312yes—
119C2×C4×Dic11C2×C412yes—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—44no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8C2314yes—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)C2314yes—
132#17381—111nomaximal, Sylow
133C24×C11—24no—
134C24×C11—42no—
135C24×C11—42no—
136C24×C11C22⋊C411yescharacteristic
137C24×C11C22⋊C411yescharacteristic
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C24×C11C22×C411yescharacteristic
143C23×D11C22×C412yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C22⋊C411yescharacteristic
159C22×C4×C11C22⋊C411yescharacteristic
160C22×C4×C11C22⋊C411yescharacteristic
161C22×C4×C11C22⋊C411yescharacteristic
162C22×C4×C11C22⋊C411yescharacteristic
163C22×C4×C11C22⋊C411yescharacteristic
164C22×C4×C11C22⋊C411yescharacteristic
165C22×C4×C11C22⋊C411yescharacteristic
166C22×C4×C11C22⋊C411yescharacteristic
167C22×C4×C11C22⋊C411yescharacteristic
168C22×C4×C11C22⋊C411yescharacteristic
169C22×C4×C11C22⋊C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—22no—
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—28no—
193C2×C22⋊D11—44no—
194C2×C22⋊D11—44no—
195C22×Dic11C22×C412yes—
196C22×Dic11C22×C412yes—
197C22×Dic11C22×C412yes—
198#4339—44no—
199#4339—44no—
200#4339—44no—
201#4339—44no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—42no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—44no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—42no—
211C11×M16—44no—
212C11×M16—44no—
213C2×C8×C11—24no—
214C2×C8×C11—44no—
215C22⋊Dic11—22no—
216C22⋊Dic11—22no—
217C22⋊Dic11—22no—
218C22⋊Dic11—22no—
219C22⋊Dic11—22no—
220C22⋊Dic11—22no—
221(C2×D11)⋊C4—22no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—22no—
224(C2×D11)⋊C4—22no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229Dic11⋊C4—22no—
230Dic11⋊C4—22no—
231Dic11⋊C4—22no—
232Dic11⋊C4—22no—
233C4×Dic11—22no—
234C4×Dic11—22no—
235C2×C11⋊C8—24no—
236C2×C11⋊C8—44no—
237C2×C11⋊C8—44no—
238C2×C11⋊C8—44no—
239C2×#525—111no—
240C2×#407D1111yescharacteristic, complemented
241C22×C22⋊C8—111no—
242#1472—112no—
243#1471—112no—
244#1468—114no—
245#1459—114no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—416no—
267C23×C11C2×C22⋊C411yescharacteristic
268C23×C11C2×C22⋊C411yescharacteristic
269C23×C11C2×C22⋊C411yescharacteristic
270C23×C11C2×C22⋊C411yescharacteristic
271C23×C11C2×C22⋊C411yescharacteristic
272C23×C11C2×C22⋊C411yescharacteristic
273C23×C11#13114yes—
274C23×C11C23×C411yescharacteristic
275C22×D11—22no—
276C22×D11—24no—
277C22×D11—42no—
278C22×D11—42no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11#9914yes—
307C2×C4×C11C2×C22⋊C411yescharacteristic
308C2×C4×C11C2×C22⋊C411yescharacteristic
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C22⋊D11—44no—
316C22⋊D11—44no—
317C22⋊D11—44no—
318C22⋊D11—44no—
319C22⋊D11—44no—
320C22⋊D11—44no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327D44—42no—
328D44—42no—
329C4×D11—44no—
330C4×D11—44no—
331Dic22—42no—
332Dic22—42no—
333C8×C11—44no—
334C11⋊C8—44no—
335C22×#41—111no—
336C24×C4C2×D1111yescharacteristic
337C22×M16—21no—
338C23×C8—221no—
339#525—221no—
340#525—221no—
341#525—221no—
342#525—221no—
343#525—221no—
344#525—221no—
345#525—221no—
346#525—221no—
347C2×#123—112no—
348C2×C22⋊Q8—111no—
349C2×C22⋊Q8—111no—
350C2×#121—111no—
351C2×#121—111no—
352C2×#120—112no—
353C2×C4×D4—112no—
354C2×C4×D4—112no—
355C2×#117—111no—
356#407—21no—
357#407—21no—
358#407C2×D1112yes—
359#407C2×D1112yes—
360C2×C22⋊C8—21no—
361C2×C22⋊C8—112no—
362C2×C22⋊C8—112no—
363C2×C22⋊C8—112no—
364C2×C22⋊C8—221no—
365C2×C22⋊C8—221no—
366C2×C22⋊C8—221no—
367C2×C22⋊C8C2×D1112yes—
368#324—118no—
369#323—118no—
370C22×C11—28no—
371C22×C11—21no—
372C22×C11—21no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11#40812yes—
394C22×C11#40812yes—
395C22×C11C2×#9912yes—
396C22×C11#41312yes—
397C22×C11C22×C22⋊C411yescharacteristic
398C22×C11C2×#13112yes—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—84no—
403C4×C11—21no—
404C4×C11—21no—
405C4×C11—21no—
406C4×C11—21no—
407C4×C11—21no—
408C4×C11—21no—
409C4×C11C2×#9912yes—
410C4×C11C2×#9912yes—
411Dic11—42no—
412Dic11—42no—
413Dic11—42no—
414C25C4×D1111yescharacteristic
415C2×#41—221no—
416C2×#41—221no—
417C2×#41—221no—
418C2×#41—221no—
419C2×#41—444no—
420C22×Q8—111no—
421C22×D4—112no—
422C22×D4—112no—
423C22×D4—112no—
424C22×D4—111no—
425C23×C4—44no—
426C23×C4—112no—
427C23×C4C4×D1111yescharacteristic
428C23×C4C4×D1111yescharacteristic
429C23×C4C4×D1111yescharacteristic
430C23×C4D4411yescharacteristic
431C23×C4D4411yescharacteristic
432C23×C4D4411yescharacteristic
433C23×C4D4411yescharacteristic
434C23×C4C22⋊D1111yescharacteristic
435C23×C4C22⋊D1111yescharacteristic
436C23×C4C22⋊D1111yescharacteristic
437C23×C4C22⋊D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C2×M16—22no—
442C2×M16—22no—
443C2×M16—44no—
444C22×C8—22no—
445C22×C8—222no—
446C22×C8—222no—
447C22×C8—222no—
448C22×C8—444no—
449#123—222no—
450#123—222no—
451#123—222no—
452#123—222no—
453C22⋊Q8—221no—
454C22⋊Q8—221no—
455C22⋊Q8—221no—
456C22⋊Q8—221no—
457C22⋊Q8—221no—
458C22⋊Q8—221no—
459C22⋊Q8—221no—
460C22⋊Q8—221no—
461#121—221no—
462#121—221no—
463#121—221no—
464#121—221no—
465#121—221no—
466#121—221no—
467#121—221no—
468#121—221no—
469#120—222no—
470#120—222no—
471#120—222no—
472#120—222no—
473C4×D4—222no—
474C4×D4—222no—
475C4×D4—222no—
476C4×D4—222no—
477C4×D4—222no—
478C4×D4—222no—
479C4×D4—222no—
480C4×D4—222no—
481#117—221no—
482#117—221no—
483#117—221no—
484#117—221no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C42—112no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—114no—
499C22⋊C8—222no—
500C22⋊C8—222no—
501C22⋊C8—222no—
502C22⋊C8C22×D1114yes—
503C2×C11—22no—
504C2×C11—22no—
505C2×C11—22no—
506C2×C11—22no—
507C2×C11—22no—
508C2×C11—41no—
509C2×C11—41no—
510C2×C11C2×#40811yescharacteristic
511C2×C11C22×#9911yescharacteristic
512C2×C11C2×#41311yescharacteristic
513D11—82no—
514C24—24no—
515C24—42no—
516C24—42no—
517C24—112no—
518C24(C2×D11)⋊C411yescharacteristic
519C24(C2×D11)⋊C411yescharacteristic
520C24(C2×D11)⋊C411yescharacteristic
521C24(C2×D11)⋊C411yescharacteristic
522C24C2×C4×D1111yescharacteristic
523C24C2×C4×D1111yescharacteristic
524C24C2×C4×D1111yescharacteristic
525#41—444no—
526#41—444no—
527#41—444no—
528#41—444no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—442no—
532C2×D4—228no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—442no—
542C2×D4—444no—
543C2×D4—444no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—444no—
564C22×C4(C2×D11)⋊C411yescharacteristic
565C22×C4(C2×D11)⋊C411yescharacteristic
566C22×C4(C2×D11)⋊C411yescharacteristic
567C22×C4(C2×D11)⋊C411yescharacteristic
568C22×C4(C2×D11)⋊C411yescharacteristic
569C22×C4(C2×D11)⋊C411yescharacteristic
570C22×C4(C2×D11)⋊C411yescharacteristic
571C22×C4(C2×D11)⋊C411yescharacteristic
572C22×C4(C2×D11)⋊C411yescharacteristic
573C22×C4(C2×D11)⋊C411yescharacteristic
574C22×C4(C2×D11)⋊C411yescharacteristic
575C22×C4(C2×D11)⋊C411yescharacteristic
576C22×C4C2×C4×D1111yescharacteristic
577C22×C4C2×C4×D1111yescharacteristic
578C22×C4C2×C4×D1111yescharacteristic
579C22×C4C2×D4411yescharacteristic
580C22×C4C2×D4411yescharacteristic
581C22×C4C2×D4411yescharacteristic
582C22×C4C2×D4411yescharacteristic
583C22×C4C2×D4411yescharacteristic
584C22×C4C2×D4411yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C23×D1111yescharacteristic
592M16—44no—
593M16—44no—
594C2×C8—24no—
595C2×C8—44no—
596C2×C8—224no—
597C2×C8—444no—
598C2×C8—444no—
599C2×C8—444no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—222no—
605C4⋊C4—222no—
606C4⋊C4—222no—
607C4⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C42—222no—
619C42—222no—
620C11#1738111yescharacteristic, complemented, Sylow
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—416no—
642C23—222no—
643C23—224no—
644C23—442no—
645C23—442no—
646C23#6696014yes—
647C23C2×(C2×D11)⋊C411yescharacteristic
648C23C2×(C2×D11)⋊C411yescharacteristic
649C23C2×(C2×D11)⋊C411yescharacteristic
650C23C2×(C2×D11)⋊C411yescharacteristic
651C23C2×(C2×D11)⋊C411yescharacteristic
652C23C2×(C2×D11)⋊C411yescharacteristic
653C23C22×C4×D1111yescharacteristic
654Q8—442no—
655Q8—442no—
656D4—442no—
657D4—444no—
658D4—444no—
659D4—444no—
660D4—444no—
661D4—444no—
662D4—444no—
663D4—442no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—224no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4#6687014yes—
700C2×C4C2×(C2×D11)⋊C411yescharacteristic
701C2×C4C2×(C2×D11)⋊C411yescharacteristic
702C2×C4C2×(C2×D11)⋊C411yescharacteristic
703C2×C4C2×(C2×D11)⋊C411yescharacteristic
704C2×C4C2×(C2×D11)⋊C411yescharacteristic
705C2×C4C2×(C2×D11)⋊C411yescharacteristic
706C2×C4C22×D4411yescharacteristic
707C2×C4C22×C22⋊D1111yescharacteristic
708C8—44no—
709C8—444no—
710C22—28no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—884no—
737C22C2×#6687012yes—
738C22#1062274212yes—
739C22#1062274212yes—
740C22#1062274512yes—
741C22C2×#6696012yes—
742C22C22×(C2×D11)⋊C411yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—442no—
750C4—442no—
751C4—442no—
752C4C2×#6687012yes—
753C4C2×#6687012yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—41no—
760C2—41no—
761C2—882no—
762C2C2×#1062274211yescharacteristic
763C2C22×#6687011yescharacteristic
764C2C2×#1062274511yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#17381
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13066981C2semidirect
4. #13066977C2semidirect
5. #13066965C2semidirect
6. #13066932C2semidirect
7. C2×C11×#407C2semidirect
41. #10622107C22semidirect
42. #10622106C22semidirect
240. C2×#407D11semidirect
620. C11#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×C22⋊(C11⋊C8)2
#130669812
#130669772
#130669652
#130669322
C2×C11×#4072
#1738111