Finite Group Databasebeta

← #14762899

Subgroups — #14762899

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13069057C214yesmaximal, complemented
4#13068918C214yesmaximal, complemented
5#13068713C212yesmaximal, complemented
6#13068559C212yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2212yescomplemented
11C2×#67006—21no—
12C22×C22⋊Dic11—21no—
13#10623322—21no—
14#10623322—21no—
15#10623322—21no—
16#10623322—21no—
17#10623322C412yescomplemented
18#10623322C412yescomplemented
19#10623322C2212yes—
20#10623322C2212yes—
21C2×#66983C411yescharacteristic, complemented
22C2×#66983C411yescharacteristic, complemented
23C2×#66982—21no—
24C2×C4×C22⋊D11—21no—
25C2×C4×C22⋊D11—21no—
26C2×#66979C2211yescharacteristic
27C2×#66977C411yescharacteristic, complemented
28C2×#66977C411yescharacteristic, complemented
29C22×C4×Dic11C2212yescomplemented
30C11×#407—21no—
31C11×#407—21no—
32C11×#407C2212yes—
33C11×#407C2212yescomplemented
34C2×C11×C22⋊C8—21no—
35C2×C11×C22⋊C8—21no—
36C4×C22⋊Dic11—21no—
37C4×C22⋊Dic11—21no—
38C4×C22⋊Dic11C2212yes—
39C4×C22⋊Dic11C2212yescomplemented
40C2×C11⋊#95—21no—
41C2×#66889C2218yescomplemented
42#10622193C2218yescomplemented
43C25×C11D411yescharacteristic
44C23×C4×C11—44no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
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⋊D11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C23×Dic11—22no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—44no—
66C2×#4339C2×C412yescomplemented
67C2×#4339C2312yes—
68C22×D44C2×C411yescharacteristic, complemented
69C22×C4×D11—21no—
70C22×Dic22C2×C411yescharacteristic, complemented
71C2×C11×M16—22no—
72C2×C11×M16—44no—
73C2×C11×M16C2314yes—
74C22×C8×C11—22no—
75#67006—22no—
76#67006—22no—
77#67006—22no—
78#67006—22no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85#66983—21no—
86#66983—21no—
87#66983—21no—
88#66983—21no—
89#66983C2×C412yes—
90#66983C2×C412yes—
91#66983C2×C412yescomplemented
92#66983C2×C412yescomplemented
93#66982—22no—
94#66982—22no—
95#66982—22no—
96#66982—22no—
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C4×C22⋊D11—22no—
104C4×C22⋊D11—22no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107#66979—21no—
108#66979—21no—
109#66979C2×C412yescomplemented
110#66979C2312yes—
111C2×C4⋊Dic11C2×C411yescharacteristic, complemented
112C2×C4⋊Dic11C2×C411yescharacteristic, complemented
113#66977—21no—
114#66977—21no—
115#66977—21no—
116#66977—21no—
117#66977C2×C412yes—
118#66977C2×C412yes—
119#66977C2×C412yescomplemented
120#66977C2×C412yescomplemented
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×C4×Dic11—21no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—44no—
126C2×C4×Dic11C2314yes—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133#66889—48no—
134#21773—111nomaximal, Sylow
135C24×C11—24no—
136C24×C11—42no—
137C24×C11—42no—
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22⋊C411yescharacteristic
141C24×C11C22⋊C411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
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×C11—42no—
159C22×C4×C11—42no—
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×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
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×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—44no—
195C2×C22⋊D11—44no—
196C2×C22⋊D11—44no—
197C22×Dic11—28no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—24no—
202C22×Dic11—44no—
203C22×Dic11—44no—
204#4339—28no—
205#4339—44no—
206#4339—44no—
207#4339—44no—
208C2×D44—21no—
209C2×D44—42no—
210C2×D44C22×C412yes—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—44no—
214C2×Dic22—21no—
215C2×Dic22—42no—
216C2×Dic22C22×C412yes—
217C11×M16—28no—
218C11×M16—44no—
219C2×C8×C11—24no—
220C2×C8×C11—44no—
221C22⋊Dic11—28no—
222C22⋊Dic11—28no—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—22no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11C22×C412yes—
236C4⋊Dic11C22×C412yes—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240Dic11⋊C4—22no—
241C4×Dic11—22no—
242C4×Dic11—22no—
243C4×Dic11—28no—
244C4×Dic11—44no—
245C2×#525—111no—
246C2×#407D1111yescharacteristic, complemented
247C2×C4×C22⋊C4—111no—
248#1896—114no—
249#1871—114no—
250#1826—112no—
251#1789—112no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—416no—
273C23×C11#10414yescomplemented
274C23×C11C2×C22⋊C411yescharacteristic
275C23×C11C2×C22⋊C411yescharacteristic
276C23×C11C2×C22⋊C411yescharacteristic
277C23×C11C2×C22⋊C411yescharacteristic
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C2×C22⋊C411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C22×D11—22no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
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—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
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—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C2×C22⋊C411yescharacteristic
314C2×C4×C11C2×C22⋊C411yescharacteristic
315C2×C4×C11C2×C22⋊C411yescharacteristic
316C2×C4×C11C2×C22⋊C411yescharacteristic
317C2×C4×C11C2×C22⋊C411yescharacteristic
318C2×C4×C11C23×C411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11H(5,𝔽2)14yes—
321C22⋊D11—44no—
322C22⋊D11—44no—
323C22⋊D11—44no—
324C22⋊D11—44no—
325C22⋊D11—44no—
326C22⋊D11—44no—
327C2×Dic11—28no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—416no—
333C2×Dic11—44no—
334C2×Dic11—42no—
335C2×Dic11—44no—
336C2×Dic11—42no—
337D44—24no—
338D44—42no—
339C4×D11—44no—
340C4×D11—44no—
341Dic22—24no—
342Dic22—42no—
343C8×C11—44no—
344C22×#41—111no—
345C24×C4C2×D1111yescharacteristic
346C22×M16C2×D1112yescomplemented
347#525—112no—
348#525—112no—
349#525—112no—
350#525—112no—
351#525—221no—
352#525—221no—
353#525—221no—
354#525—221no—
355C2×#123—221no—
356C2×C22⋊Q8—111no—
357C2×C22⋊Q8—111no—
358C2×#121—111no—
359C2×#121—111no—
360C2×#120—221no—
361C2×C4×D4—221no—
362C2×C4×D4—221no—
363C2×#117—111no—
364C22×C22⋊C4—221no—
365C22×C42—112no—
366C2×#104—118no—
367#407—21no—
368#407—21no—
369#407C2×D1112yes—
370#407C2×D1112yescomplemented
371C2×C22⋊C8—21no—
372C2×C22⋊C8—21no—
373C4×C22⋊C4—112no—
374C4×C22⋊C4—112no—
375C4×C22⋊C4—221no—
376C4×C22⋊C4—221no—
377C2×#95—221no—
378#339—118no—
379C22×C11—28no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
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×C11—44no—
398C22×C11—44no—
399C22×C11—44no—
400C22×C11—44no—
401C22×C11—44no—
402C22×C11C2×#10412yes—
403C22×C11C2×#10412yes—
404C22×C11C2×#10412yes—
405C22×C11#42112yes—
406C22×C11C22×C22⋊C411yescharacteristic
407C22×C11#53412yes—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—84no—
412C4×C11—21no—
413C4×C11—21no—
414C4×C11—21no—
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11#51812yes—
419C4×C11#53412yes—
420Dic11—48no—
421Dic11—42no—
422Dic11—42no—
423Dic11—42no—
424C25D4411yescharacteristic
425C2×#41—112no—
426C2×#41—112no—
427C2×#41—221no—
428C2×#41—221no—
429C2×#41—444no—
430C22×Q8—111no—
431C22×D4—111no—
432C22×D4—221no—
433C22×D4—221no—
434C22×D4—221no—
435C23×C4—44no—
436C23×C4—222no—
437C23×C4—221no—
438C23×C4C4×D1111yescharacteristic
439C23×C4C4×D1111yescharacteristic
440C23×C4C4×D1111yescharacteristic
441C23×C4C4×D1111yescharacteristic
442C23×C4D4411yescharacteristic
443C23×C4D4411yescharacteristic
444C23×C4D4411yescharacteristic
445C23×C4C22⋊D1111yescharacteristic
446C23×C4C22⋊D1111yescharacteristic
447C23×C4C22⋊D1111yescharacteristic
448C23×C4C22⋊D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C2×M16—22no—
453C2×M16—44no—
454C2×M16C22×D1114yes—
455C22×C8—22no—
456#123—222no—
457#123—222no—
458#123—222no—
459#123—222no—
460C22⋊Q8—112no—
461C22⋊Q8—112no—
462C22⋊Q8—112no—
463C22⋊Q8—112no—
464C22⋊Q8—221no—
465C22⋊Q8—221no—
466C22⋊Q8—221no—
467C22⋊Q8—221no—
468#121—112no—
469#121—112no—
470#121—112no—
471#121—112no—
472#121—221no—
473#121—221no—
474#121—221no—
475#121—221no—
476#120—222no—
477#120—222no—
478#120—222no—
479#120—222no—
480C4×D4—222no—
481C4×D4—222no—
482C4×D4—222no—
483C4×D4—222no—
484C4×D4—222no—
485C4×D4—222no—
486C4×D4—222no—
487C4×D4—222no—
488#117—112no—
489#117—112no—
490#117—221no—
491#117—221no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C22⋊C4—228no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C42—114no—
505C2×C42—221no—
506C2×C42—222no—
507C2×C42—444no—
508#104—448no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513#95—222no—
514#95—222no—
515C2×C11—22no—
516C2×C11—22no—
517C2×C11—22no—
518C2×C11—22no—
519C2×C11—22no—
520C2×C11—41no—
521C2×C11—41no—
522C2×C11#230811yescharacteristic
523C2×C11C22×#10411yescharacteristic
524C2×C11C2×#42111yescharacteristic
525D11—82no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—221no—
530C24(C2×D11)⋊C411yescharacteristic
531C24(C2×D11)⋊C411yescharacteristic
532C24(C2×D11)⋊C411yescharacteristic
533C24(C2×D11)⋊C411yescharacteristic
534C24C2×D4411yescharacteristic
535C24C2×D4411yescharacteristic
536C24C2×D4411yescharacteristic
537#41—228no—
538#41—444no—
539#41—444no—
540#41—444no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—442no—
544C2×D4—112no—
545C2×D4—222no—
546C2×D4—222no—
547C2×D4—222no—
548C2×D4—222no—
549C2×D4—222no—
550C2×D4—222no—
551C2×D4—221no—
552C2×D4—442no—
553C2×D4—444no—
554C2×D4—444no—
555C2×D4—444no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—228no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—224no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—444no—
578C22×C4—444no—
579C22×C4—444no—
580C22×C4(C2×D11)⋊C411yescharacteristic
581C22×C4(C2×D11)⋊C411yescharacteristic
582C22×C4(C2×D11)⋊C411yescharacteristic
583C22×C4(C2×D11)⋊C411yescharacteristic
584C22×C4(C2×D11)⋊C411yescharacteristic
585C22×C4(C2×D11)⋊C411yescharacteristic
586C22×C4(C2×D11)⋊C411yescharacteristic
587C22×C4(C2×D11)⋊C411yescharacteristic
588C22×C4(C2×D11)⋊C411yescharacteristic
589C22×C4(C2×D11)⋊C411yescharacteristic
590C22×C4(C2×D11)⋊C411yescharacteristic
591C22×C4(C2×D11)⋊C411yescharacteristic
592C22×C4C2×C4×D1111yescharacteristic
593C22×C4C2×C4×D1111yescharacteristic
594C22×C4C2×C4×D1111yescharacteristic
595C22×C4C2×C4×D1111yescharacteristic
596C22×C4C2×C4×D1111yescharacteristic
597C22×C4C2×C4×D1111yescharacteristic
598C22×C4C2×D4411yescharacteristic
599C22×C4C2×D4411yescharacteristic
600C22×C4C2×D4411yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C2×C22⋊D1111yescharacteristic
605C22×C4C2×C22⋊D1111yescharacteristic
606C22×C4C2×C22⋊D1111yescharacteristic
607C22×C4C23×D1111yescharacteristic
608M16—28no—
609M16—44no—
610C2×C8—24no—
611C2×C8—44no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—222no—
617C4⋊C4—222no—
618C4⋊C4—222no—
619C4⋊C4—222no—
620C22⋊C4—228no—
621C22⋊C4—228no—
622C22⋊C4—222no—
623C22⋊C4—222no—
624C22⋊C4—222no—
625C22⋊C4—222no—
626C22⋊C4—222no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—222no—
630C22⋊C4—222no—
631C22⋊C4—222no—
632C42—222no—
633C42—222no—
634C42—228no—
635C42—444no—
636C11#2177311yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—416no—
658C23—222no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23#6688914yescomplemented
663C23C2×(C2×D11)⋊C411yescharacteristic
664C23C2×(C2×D11)⋊C411yescharacteristic
665C23C2×(C2×D11)⋊C411yescharacteristic
666C23C2×(C2×D11)⋊C411yescharacteristic
667C23C2×(C2×D11)⋊C411yescharacteristic
668C23C2×(C2×D11)⋊C411yescharacteristic
669C23C22×D4411yescharacteristic
670Q8—224no—
671Q8—442no—
672D4—224no—
673D4—442no—
674D4—444no—
675D4—444no—
676D4—444no—
677D4—444no—
678D4—444no—
679D4—444no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—228no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—444no—
712C2×C4—442no—
713C2×C4—4416no—
714C2×C4—444no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—444no—
718C2×C4—444no—
719C2×C4C2×(C2×D11)⋊C411yescharacteristic
720C2×C4C2×(C2×D11)⋊C411yescharacteristic
721C2×C4C2×(C2×D11)⋊C411yescharacteristic
722C2×C4C2×(C2×D11)⋊C411yescharacteristic
723C2×C4C2×(C2×D11)⋊C411yescharacteristic
724C2×C4C2×(C2×D11)⋊C411yescharacteristic
725C2×C4C22×C4×D1111yescharacteristic
726C2×C4#6703714yes—
727C2×C4C22×C22⋊D1111yescharacteristic
728C8—44no—
729C22—28no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—884no—
756C22C2×#6688912yes—
757C22C2×#6688912yes—
758C22C2×#6688912yes—
759C22#1062275212yes—
760C22#1062302412yes—
761C22C22×(C2×D11)⋊C411yescharacteristic
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—448no—
769C4—442no—
770C4—442no—
771C4—442no—
772C4#1062301712yes—
773C4#1062333512yes—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—22no—
778C2—22no—
779C2—41no—
780C2—41no—
781C2—882no—
782C2#1307119111yescharacteristic
783C2C22×#6688911yescharacteristic
784C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21773
LCSG ▷ C2×C4×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. C2×C4×C22⋊Dic11C2semidirect
3. #13069057C2semidirect
4. #13068918C2semidirect
5. #13068713C2semidirect
6. #13068559C2semidirect
7. C2×C11×#407C2semidirect
10. C22×C11×M16C22semidirect
17. #10623322C4semidirect
18. #10623322C4semidirect
21. C2×#66983C4semidirect
22. C2×#66983C4semidirect
27. C2×#66977C4semidirect
28. C2×#66977C4semidirect
29. C22×C4×Dic11C22semidirect
33. C11×#407C22semidirect
39. C4×C22⋊Dic11C22semidirect
41. C2×#66889C22semidirect
42. #10622193C22semidirect
66. C2×#4339C2×C4semidirect
68. C22×D44C2×C4semidirect
70. C22×Dic22C2×C4semidirect
91. #66983C2×C4semidirect
92. #66983C2×C4semidirect
109. #66979C2×C4semidirect
111. C2×C4⋊Dic11C2×C4semidirect
112. C2×C4⋊Dic11C2×C4semidirect
119. #66977C2×C4semidirect
120. #66977C2×C4semidirect
246. C2×#407D11semidirect
273. C23×C11#104semidirect
346. C22×M16C2×D11semidirect
370. #407C2×D11semidirect
636. C11#21773semidirect
662. C23#66889semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×C4×C22⋊Dic112
#130690572
#130689182
#130687132
#130685592
C2×C11×#4072
#2177311