Finite Group Databasebeta

← #14774044

Subgroups — #14774044

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622783C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic, complemented
3C2×D11×#103C211yesmaximal, characteristic, complemented
4#13071637C211yesmaximal, characteristic
5#13071450C211yesmaximal, characteristic, complemented
6#13069303C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic
9#13068974C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068867C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13#13068447C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C11×#1973C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#390C2211yescharacteristic
32#10622843C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622783C418yescomplemented
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622569—21no—
46#10622559—21no—
47#10622557—21no—
48C4×(C2×D11)⋊C4C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50D11×#103—24no—
51#10622370—24no—
52#10622280—21no—
53#10622279—21no—
54#10622259—21no—
55#10622259—21no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—41no—
70C2×Q8×D11—41no—
71C2×Q8×D11C2×C414yescomplemented
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—21no—
76C22×Dic22C2311yescharacteristic
77C2×C11×SD16—41no—
78C2×C11×SD16—41no—
79C2×C11×SD16C2×C414yescomplemented
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#66991—22no—
90#66991C2×C414yes—
91D4×Dic11—22no—
92D4×Dic11—41no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324C2×C414yescomplemented
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4D411yescharacteristic
98C2×(C2×D11)⋊C4D411yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×C8×D11—22no—
113C2×C8×D11—22no—
114C2×C8×D11—41no—
115C4⋊C4×D11—22no—
116C4⋊C4×D11—41no—
117#66940—22no—
118#66940—41no—
119(C22⋊D11)⋊C4—44no—
120C4×Dic22—22no—
121C4×Dic22—41no—
122C11×#107—41no—
123C11×#103—22no—
124C11×#102—22no—
125C11×#97—41no—
126C11×#95—21no—
127C11×#95—21no—
128#66899—22no—
129#66899C2×C414yescomplemented
130#66896—41no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95D411yescharacteristic
137C11⋊#95D411yescharacteristic
138(C2×D11)⋊C8C2×C414yescomplemented
139#66880C2×C414yescomplemented
140#66880D414yescomplemented
141#66879—22no—
142#66874—22no—
143#66871—22no—
144#22855—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C22×C412yes—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11C22×C412yes—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11—42no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—81no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178Q8×D11—28no—
179Q8×D11—44no—
180Q8×D11—44no—
181Q8×D11—44no—
182C2×C4×D11—24no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—81no—
192C2×C4×D11C22×C412yes—
193C2×C4×D11#4112yes—
194C2×Dic22—24no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—42no—
199C2×Dic22—42no—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C11×SD16—44no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11C22×C412yes—
209C2×C8×C11C2×D412yes—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C42×C11—21no—
217C42×C11—21no—
218C22⋊Dic11—24no—
219C22⋊Dic11—42no—
220#4324—28no—
221(C2×D11)⋊C4—22no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—42no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11C22×C412yes—
229C4⋊Dic11C2×D412yes—
230Dic11⋊C4—42no—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—42no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245C8×D11—44no—
246C2×#448—111no—
247C2×#440—111no—
248C22×#103—111no—
249#2361—111no—
250Q8×C22⋊C4—111no—
251#1973D1111yescharacteristic, complemented
252#1935—111no—
253#1928—111no—
254#1893—111no—
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752—111no—
261C23×C11—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C22×D411yescharacteristic
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11C4×D412yes—
274C22×D11AGL(1,ℤ/8)12yes—
275C22×D11#13712yes—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—41no—
279Q8×C11—41no—
280D4×C11—22no—
281D4×C11—22no—
282D4×C11—41no—
283D4×C11—41no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C22⋊D11—48no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—21no—
311C2×Dic11—22no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—84no—
327C2×Dic11C4×D412yes—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—48no—
333C4×D11—84no—
334Dic22—22no—
335Dic22—22no—
336Dic22—22no—
337Dic22—48no—
338Dic22C4×D414yescomplemented
339C8×C11—22no—
340C8×C11—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C23×Q8—111no—
344C22×SD16—111no—
345C22×SD16C2×D1111yescharacteristic
346C23×C8—111no—
347C2×#121—111no—
348C2×C4×Q8—111no—
349C2×C4×Q8—111no—
350C2×C4×D4—111no—
351C2×C4×D4—221no—
352C22×C4⋊C4—111no—
353#448—118no—
354#440—224no—
355C2×#107—111no—
356C2×#107C2×D1111yescharacteristic
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#103—111no—
361C2×#103—111no—
362C2×#103—224no—
363C2×#103C2×D1111yescharacteristic
364C2×#102—111no—
365C2×#102C2×D1111yescharacteristic
366C2×C22⋊C8—111no—
367C2×#97—111no—
368C2×#97C2×D1111yescharacteristic
369#391—111no—
370#391—221no—
371#391—221no—
372#391C2×D1111yescharacteristic
373#390C2×D1111yescharacteristic
374#389—111no—
375#388—221no—
376#386—221no—
377#385—221no—
378#380—111no—
379#380—221no—
380C4×C4⋊C4—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11C2×C4×D411yescharacteristic
397C22×C11D4211yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57811yescharacteristic
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11#44014yescomplemented
410C4×C11—42no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11C2×C4×D411yescharacteristic
416C4×C11#51811yescharacteristic
417C4×C11#54611yescharacteristic
418C4×C11#55111yescharacteristic
419Dic11—24no—
420Dic11—22no—
421Dic11—42no—
422Dic11—42no—
423Dic11—41no—
424Dic11—41no—
425Dic11—81no—
426C22×Q8—114no—
427C22×Q8—111no—
428C22×Q8—221no—
429C22×Q8—222no—
430C22×Q8—222no—
431C22×Q8—222no—
432C22×Q8—441no—
433C22×Q8—441no—
434C22×Q8C22×D1111yescharacteristic
435C22×D4—221no—
436C22×D4C22×D1111yescharacteristic
437C23×C4—111no—
438C23×C4—221no—
439C23×C4—221no—
440C23×C4—221no—
441C2×SD16—41no—
442C2×SD16—41no—
443C2×SD16—114no—
444C2×SD16—222no—
445C2×SD16—222no—
446C2×SD16C4×D1114yescomplemented
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—222no—
450C22×C8—222no—
451C22×C8—441no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#121—114no—
455#121—222no—
456C4×Q8—222no—
457C4×Q8—222no—
458C4×Q8—441no—
459C4×Q8—441no—
460C4×D4—222no—
461C4×D4—441no—
462C4×D4—444no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—441no—
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—221no—
483C2×C42—221no—
484C2×C42—221no—
485C2×C42C22×D1111yescharacteristic
486#107—41no—
487#107—222no—
488#103—22no—
489#103—114no—
490#103—114no—
491#103—114no—
492#103—222no—
493#103—222no—
494#102—22no—
495#102—441no—
496C22⋊C8—114no—
497#97—41no—
498#97—222no—
499#95—21no—
500#95—21no—
501#95—111no—
502#95—111no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—82no—
509C2×C11#235811yescharacteristic
510C2×C11C2×#44011yescharacteristic
511C2×C11#294711yescharacteristic
512C2×C11#326511yescharacteristic
513C2×C11#327011yescharacteristic
514C2×C11#330811yescharacteristic
515C2×C11#332011yescharacteristic
516D11—24no—
517C24—21no—
518C24—111no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—112no—
525C2×Q8—112no—
526C2×Q8—112no—
527C2×Q8—224no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—228no—
532C2×Q8—442no—
533C2×Q8—442no—
534C2×Q8—444no—
535C2×Q8—444no—
536C2×Q8—444no—
537C2×Q8C2×C4×D1112yes—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—224no—
544C2×D4—442no—
545C2×D4—442no—
546C2×D4C2×C4×D1112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—111no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—111no—
554C22×C4—111no—
555C22×C4—224no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—442no—
565C22×C4—442no—
566C22×C4—442no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—881no—
571C22×C4—881no—
572C22×C4D4×D1111yescharacteristic
573C22×C4D4×D1111yescharacteristic
574C22×C4C23×D1111yescharacteristic
575SD16—44no—
576SD16—228no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—112no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—444no—
588C2×C8C2×C4×D1112yes—
589C2×C8D4×D1112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—112no—
595C4⋊C4—112no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—224no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C42—21no—
612C42—21no—
613C42—221no—
614C42—221no—
615C42—442no—
616C42—442no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—112no—
627C23—112no—
628C23—112no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23C2×D4×D1111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—41no—
637Q8—41no—
638Q8—114no—
639Q8—222no—
640Q8—222no—
641Q8—222no—
642Q8—448no—
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—448no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—112no—
664C2×C4—222no—
665C2×C4—221no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—221no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—222no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—222no—
681C2×C4—448no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—884no—
690C2×C4—884no—
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4#6703711yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C2×C4#41×D1111yescharacteristic
697C8—22no—
698C8—22no—
699C8—222no—
700C8—441no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—114no—
709C22—222no—
710C22—222no—
711C22—222no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22C4×D4×D1111yescharacteristic
716C22#1062314111yescharacteristic
717C22#1062324811yescharacteristic
718C22D11×AGL(1,ℤ/8)11yescharacteristic
719C22#1062330611yescharacteristic
720C22D11×#13711yescharacteristic
721C22#1062331011yescharacteristic
722C4—41no—
723C4—41no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—222no—
728C4—224no—
729C4—441no—
730C4—442no—
731C4—441no—
732C4—442no—
733C4—881no—
734C4#1062301711yescharacteristic
735C4C4×D4×D1111yescharacteristic
736C4#1062314111yescharacteristic
737C4#1062321011yescharacteristic
738C2—82no—
739C2—224no—
740C2#1307159711yescharacteristic
741C2D11×#44011yescharacteristic
742C2#1307745611yescharacteristic
743C2#1308011011yescharacteristic
744C2#1308018511yescharacteristic
745C2#1308060211yescharacteristic
746C2#1308078211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1973C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1973D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. C2×#10622370C2semidirect
3. C2×D11×#103C2semidirect
5. #13071450C2semidirect
6. #13069303C2semidirect
7. #13069254C2semidirect
9. #13068974C2semidirect
10. #13068952C2semidirect
11. #13068867C2semidirect
12. #13068802C2semidirect
13. #13068447C2semidirect
14. #13068393C2semidirect
15. C11×#1973C2semidirect
36. #10622783C4semidirect
71. C2×Q8×D11C2×C4semidirect
79. C2×C11×SD16C2×C4semidirect
95. C2×#4324C2×C4semidirect
129. #66899C2×C4semidirect
138. (C2×D11)⋊C8C2×C4semidirect
139. #66880C2×C4semidirect
140. #66880D4semidirect
251. #1973D11semidirect
338. Dic22C4×D4semidirect
409. C2×D11#440semidirect
446. C2×SD16C4×D11semidirect
618. C11#22855semidirect

Maximal subgroups

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

subgroupindex
C2×#106227832
C2×#106223702
C2×D11×#1032
#130716372
#130714502
#130693032
#130692542
#130690412
#130689742
#130689522
#130688672
#130688022
#130684472
#130683932
C11×#19732
#2285511