Finite Group Databasebeta

← #14769645

Subgroups — #14769645

Order 2816.

1368 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic
2C2×#10622436C212yesmaximal, complemented
3#13077066C211yesmaximal, characteristic, complemented
4#13077065C211yesmaximal, characteristic, complemented
5#13069506C212yesmaximal, complemented
6#13068941C212yesmaximal, complemented
7#13068940C212yesmaximal, complemented
8#13068652C211yesmaximal, characteristic, complemented
9#13068561C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C2×#67003—28no—
15C2×#67003C411yescharacteristic, complemented
16C2×#67003C411yescharacteristic, complemented
17C2×#67003C411yescharacteristic, complemented
18C2×#67003C411yescharacteristic, complemented
19C2×#67003C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21C2×#67003C2211yescharacteristic
22C2×#67003C2211yescharacteristic
23C2×#67001C2212yescomplemented
24C22×#4326C411yescharacteristic, complemented
25C22×#4325C411yescharacteristic, complemented
26C22×#4324C411yescharacteristic, complemented
27C22×#4323C411yescharacteristic, complemented
28C23×C11⋊C8C2211yescharacteristic
29C2×#66960C2212yescomplemented
30C2×C11×#104C2212yescomplemented
31C2×C11×#104C2212yescomplemented
32C11×#407C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622847—22no—
35#10622847C2212yescomplemented
36#10622820—21no—
37#10622820C2211yescharacteristic
38C2×C22⋊(C11⋊C8)—21no—
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622742C2212yescomplemented
41C2×#66886C2212yescomplemented
42C2×#66869C2212yescomplemented
43C2×#66869C2212yescomplemented
44C2×#66867C2212yescomplemented
45#10622436—28no—
46#10622340—22no—
47#10622339—21no—
48D11×C22⋊C8—21no—
49#10622196C2212yescomplemented
50#10622162C2212yescomplemented
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—24no—
54C2×C11×#41—42no—
55C2×C11×#41C2×C411yescharacteristic
56C2×C11×#41C2×C411yescharacteristic
57C2×C11×#41C2311yescharacteristic
58C2×C11×#41C2311yescharacteristic
59C22×Q8×C11C2×C411yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—24no—
68C2×#4339—42no—
69C2×#4339C2×C411yescharacteristic
70C2×#4339C2×C411yescharacteristic
71C2×#4339C2311yescharacteristic
72C2×#4339C2311yescharacteristic
73C22×D44C2×C411yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2×C411yescharacteristic
76C2×C11×M16C2312yes—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2312yes—
79#67003—24no—
80#67003—24no—
81#67003—24no—
82#67003—24no—
83#67003—24no—
84#67003—24no—
85#67003—24no—
86#67003D418yes—
87#67001—24no—
88#67001—42no—
89C2×#4326—24no—
90C2×#4326C2×C411yescharacteristic
91C2×#4326C2×C411yescharacteristic
92C2×#4326C2×C411yescharacteristic
93C2×#4326C2×C411yescharacteristic
94C2×#4325—24no—
95C2×#4325C2×C411yescharacteristic
96C2×#4325C2×C411yescharacteristic
97C2×#4325C2×C411yescharacteristic
98C2×#4325C2×C411yescharacteristic
99C2×#4324—24no—
100C2×#4324C2×C411yescharacteristic
101C2×#4324C2×C411yescharacteristic
102C2×#4324C2×C411yescharacteristic
103C2×#4324C2×C411yescharacteristic
104C2×#4323—24no—
105C2×#4323C2×C411yescharacteristic
106C2×#4323C2×C411yescharacteristic
107C2×#4323C2×C411yescharacteristic
108C2×#4323C2×C411yescharacteristic
109C2×#4318—22no—
110C2×#4318C2312yes—
111C22×C11⋊C8—24no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8C2×C411yescharacteristic
114C22×C11⋊C8C2×C411yescharacteristic
115C22×C11⋊C8C2×C411yescharacteristic
116C22×C11⋊C8C2×C411yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2312yes—
119C22×C11⋊C8C2311yescharacteristic
120#66960—24no—
121#66960—42no—
122C2×#4313—22no—
123C2×C8×D11—22no—
124C11×#104—24no—
125C11×#104—42no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8—21no—
128C11×#95—21no—
129C22⋊(C11⋊C8)—21no—
130C22⋊(C11⋊C8)—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)D411yescharacteristic
134C22⋊(C11⋊C8)D411yescharacteristic
135C22⋊(C11⋊C8)D412yes—
136#66886—24no—
137(C2×D11)⋊C8—22no—
138(C2×D11)⋊C8—22no—
139#66869—24no—
140#66869—42no—
141#66867—24no—
142#22452—111nomaximal, Sylow
143C24×C11—21no—
144C24×C11#4111yescharacteristic
145C23×D11—21no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—44no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—44no—
155C11×#41C2×D414yes—
156C2×Q8×C11—21no—
157C2×Q8×C11—22no—
158C2×Q8×C11—41no—
159C2×Q8×C11C22×C411yescharacteristic
160C2×Q8×C11C22×C411yescharacteristic
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—41no—
168C2×D4×C11—44no—
169C2×D4×C11C22×C411yescharacteristic
170C2×D4×C11C22×C411yescharacteristic
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—44no—
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—21no—
187C2×C22⋊D11—21no—
188C2×C22⋊D11—21no—
189C2×C22⋊D11—21no—
190C2×C22⋊D11—44no—
191C22×Dic11—21no—
192#4339—22no—
193#4339—22no—
194#4339—22no—
195#4339—22no—
196#4339—22no—
197#4339—41no—
198#4339—41no—
199#4339—44no—
200#4339—44no—
201#4339C2×D414yes—
202C2×D44—22no—
203C2×D44—21no—
204C2×D44—41no—
205C2×D44C22×C411yescharacteristic
206C2×D44C22×C411yescharacteristic
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—44no—
212C2×Dic22—22no—
213C2×Dic22—21no—
214C2×Dic22—41no—
215C2×Dic22C22×C411yescharacteristic
216C2×Dic22C22×C411yescharacteristic
217C11×M16—22no—
218C11×M16—22no—
219C2×C8×C11—22no—
220C11×C22⋊C4—42no—
221C42×C11—22no—
222C42×C11—22no—
223#4326—22no—
224#4326—22no—
225#4326—22no—
226#4326C22⋊C414yescomplemented
227#4325—22no—
228#4325—22no—
229#4325—22no—
230#4325C22⋊C414yescomplemented
231#4324—22no—
232#4324—22no—
233#4324—22no—
234#4324C22⋊C414yescomplemented
235#4323—22no—
236#4323—22no—
237#4323—22no—
238#4323C22⋊C414yescomplemented
239#4318—22no—
240#4318—22no—
241#4318—44no—
242C2×C11⋊C8—22no—
243C2×C11⋊C8—22no—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8—44no—
251C2×C11⋊C8C22×C411yescharacteristic
252C2×C11⋊C8C22×C411yescharacteristic
253C2×C11⋊C8C22×C411yescharacteristic
254C2×C11⋊C8C22×C411yescharacteristic
255C2×C11⋊C8C2×D412yes—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D414yes—
258#4313—44no—
259C8×D11—44no—
260C22×#135—111no—
261C2×#444—112no—
262#2880—111no—
263#2880—111no—
264#1975—112no—
265#1876—112no—
266#1876—112no—
267#1810—111no—
268#1789—111no—
269#1789D1111yescharacteristic, complemented
270#1752—111no—
271C23×C11—21no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—21no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—81no—
279C23×C11C4×D411yescharacteristic
280C23×C11C4×D411yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—81no—
287Q8×C11—21no—
288Q8×C11—21no—
289Q8×C11—21no—
290Q8×C11—42no—
291Q8×C11C2×C22⋊C412yes—
292D4×C11—24no—
293D4×C11—21no—
294D4×C11—21no—
295D4×C11—21no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11C2×C22⋊C412yes—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C4×D411yescharacteristic
319C2×C4×C11C4×D411yescharacteristic
320C2×C4×C11C23×C411yescharacteristic
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11H(5,𝔽2)12yes—
324C22⋊D11—24no—
325C22⋊D11—42no—
326C22⋊D11—42no—
327C22⋊D11—42no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—42no—
331D44—21no—
332D44—21no—
333D44—21no—
334D44—42no—
335D44C2×C22⋊C412yes—
336C4×D11—24no—
337C4×D11—42no—
338C4×D11—42no—
339C4×D11—42no—
340Dic22—21no—
341Dic22—21no—
342Dic22—21no—
343Dic22—42no—
344Dic22C2×C22⋊C412yes—
345C8×C11—42no—
346C11⋊C8—21no—
347C11⋊C8—21no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—42no—
351C11⋊C8C2×C22⋊C412yes—
352C11⋊C8C2×C22⋊C412yes—
353C22×#41—111no—
354C22×#41C2×D1111yescharacteristic
355C2×#135—111no—
356C2×#135—111no—
357C2×#135—111no—
358C2×#135—111no—
359C2×#135—111no—
360C2×#135—111no—
361C2×#135—111no—
362C2×#135—111no—
363C2×#135—228no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×D8—111no—
368C2×#131—112no—
369C2×#131—112no—
370C23×C8—111no—
371#444—228no—
372C2×#108—112no—
373C2×#104—112no—
374C2×#104—112no—
375C2×#104C2×D1112yescomplemented
376C2×#104C2×D1112yescomplemented
377#408—112no—
378#408—112no—
379#408—222no—
380#408—222no—
381#407—111no—
382#407—221no—
383#407—221no—
384#407C2×D1111yescharacteristic
385C2×C22⋊C8—111no—
386C2×C22⋊C8—221no—
387C2×C22⋊C8—221no—
388C2×#97—112no—
389C4×C22⋊C4C2×D1111yescharacteristic
390#341—112no—
391#336—112no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—22no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—44no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—84no—
407C22×C11#44412yescomplemented
408C22×C11C2×C4×D411yescharacteristic
409C22×C11#54612yes—
410C2×D11—22no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—84no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—22no—
420C4×C11—41no—
421C4×C11—82no—
422C4×C11C22×C22⋊C411yescharacteristic
423C4×C11#51811yescharacteristic
424C4×C11D4212yes—
425Dic11—22no—
426Dic11—41no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—24no—
430C2×#41—42no—
431C2×#41—111no—
432C2×#41—111no—
433C2×#41—111no—
434C2×#41—111no—
435C2×#41—224no—
436C2×#41—221no—
437C2×#41—221no—
438C2×#41—442no—
439C2×#41C4×D1111yescharacteristic
440C2×#41C4×D1111yescharacteristic
441C2×#41C22×D1111yescharacteristic
442C2×#41C22×D1111yescharacteristic
443C22×Q8—111no—
444C22×Q8C4×D1111yescharacteristic
445C22×D4—21no—
446C22×D4—111no—
447C22×D4—221no—
448C22×D4C4×D1111yescharacteristic
449C23×C4—21no—
450C23×C4—221no—
451C23×C4C22×D1111yescharacteristic
452#135—118no—
453#135—224no—
454#135—224no—
455#135—224no—
456#135—224no—
457#135—224no—
458#135—224no—
459#135—224no—
460C2×Q16—111no—
461C2×Q16—111no—
462C2×Q16—111no—
463C2×Q16—111no—
464C2×Q16—224no—
465C2×SD16—111no—
466C2×SD16—111no—
467C2×SD16—111no—
468C2×SD16—111no—
469C2×SD16—111no—
470C2×SD16—111no—
471C2×SD16—111no—
472C2×SD16—111no—
473C2×SD16—224no—
474C2×SD16—224no—
475C2×D8—111no—
476C2×D8—111no—
477C2×D8—111no—
478C2×D8—111no—
479C2×D8—224no—
480#131—224no—
481#131—224no—
482#131—442no—
483#131—442no—
484C2×M16—112no—
485C2×M16—222no—
486C2×M16—222no—
487C2×M16C22×D1112yes—
488C22×C8—111no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—112no—
495C22×C8—222no—
496C22×C8—224no—
497C22×C8—222no—
498C2×C22⋊C4—21no—
499C2×C42C22×D1112yes—
500#108—224no—
501#104—24no—
502#104—42no—
503#104—224no—
504#104—442no—
505C22⋊C8—21no—
506C22⋊C8—21no—
507C22⋊C8—111no—
508C22⋊C8—111no—
509C22⋊C8—112no—
510C22⋊C8—222no—
511C22⋊C8—222no—
512C22⋊C8—222no—
513C22⋊C8—222no—
514C22⋊C8—221no—
515C22⋊C8—221no—
516#97—224no—
517#95—21no—
518C2×C11—22no—
519C2×C11—22no—
520C2×C11—41no—
521C2×C11—42no—
522C2×C11—81no—
523C2×C11D4×C22⋊C411yescharacteristic
524C2×C11C2×#44411yescharacteristic
525C2×C11#295711yescharacteristic
526D11—42no—
527D11—81no—
528C24—21no—
529C24—221no—
530C24#434111yescharacteristic
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—44no—
537#41—41no—
538#41—41no—
539#41—44no—
540#41—114no—
541#41—222no—
542#41—222no—
543#41—222no—
544#41—222no—
545#41—222no—
546#41—444no—
547#41—441no—
548#41—441no—
549#41—444no—
550#41D4×D1114yes—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—41no—
554C2×Q8—111no—
555C2×Q8—111no—
556C2×Q8—222no—
557C2×Q8—221no—
558C2×Q8—441no—
559C2×Q8C2×C4×D1111yescharacteristic
560C2×Q8C2×C4×D1111yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—41no—
568C2×D4—44no—
569C2×D4—111no—
570C2×D4—111no—
571C2×D4—222no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—441no—
578C2×D4—444no—
579C2×D4C2×C4×D1111yescharacteristic
580C2×D4C2×C4×D1111yescharacteristic
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—44no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—444no—
596C22×C4C2×C4×D1111yescharacteristic
597C22×C4C2×C4×D1111yescharacteristic
598C22×C4D4×D1111yescharacteristic
599C22×C4D4×D1111yescharacteristic
600C22×C4#434111yescharacteristic
601C22×C4C23×D1111yescharacteristic
602Q16—114no—
603Q16—222no—
604Q16—222no—
605Q16—222no—
606SD16—114no—
607SD16—114no—
608SD16—222no—
609SD16—222no—
610SD16—222no—
611SD16—222no—
612SD16—222no—
613SD16—222no—
614D8—114no—
615D8—222no—
616D8—222no—
617D8—222no—
618M16—22no—
619M16—22no—
620M16—222no—
621M16—222no—
622M16—444no—
623M16—444no—
624C2×C8—22no—
625C2×C8—111no—
626C2×C8—111no—
627C2×C8—114no—
628C2×C8—111no—
629C2×C8—111no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—222no—
633C2×C8—222no—
634C2×C8—222no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8—222no—
639C2×C8—222no—
640C2×C8—444no—
641C2×C8—444no—
642C22⋊C4—42no—
643C42—22no—
644C42—22no—
645C11#2245211yescharacteristic, complemented, Sylow
646C23—21no—
647C23—22no—
648C23—22no—
649C23—21no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—81no—
654C23—221no—
655C23—221no—
656C23—442no—
657C23—442no—
658C23—881no—
659C23(C22⋊D11)⋊C411yescharacteristic
660C23(C22⋊D11)⋊C411yescharacteristic
661C23C2×#434111yescharacteristic
662Q8—21no—
663Q8—21no—
664Q8—21no—
665Q8—42no—
666Q8—112no—
667Q8—221no—
668Q8—221no—
669Q8—221no—
670Q8—442no—
671Q8C22⋊C4×D1112yes—
672D4—24no—
673D4—21no—
674D4—21no—
675D4—21no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—112no—
681D4—224no—
682D4—221no—
683D4—221no—
684D4—221no—
685D4—442no—
686D4—442no—
687D4—442no—
688D4—442no—
689D4C22⋊C4×D1112yes—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—221no—
708C2×C4—224no—
709C2×C4—221no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4(C22⋊D11)⋊C411yescharacteristic
715C2×C4(C22⋊D11)⋊C411yescharacteristic
716C2×C4C22×C4×D1111yescharacteristic
717C2×C4C2×D4×D1112yes—
718C2×C4C2×D4×D1111yescharacteristic
719C2×C4#6703712yes—
720C8—42no—
721C8—112no—
722C8—112no—
723C8—221no—
724C8—221no—
725C8—222no—
726C8—222no—
727C8—442no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—22no—
736C22—44no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—84no—
743C22—222no—
744C22—441no—
745C22—441no—
746C22—441no—
747C22—441no—
748C22—441no—
749C22—884no—
750C22#1062243612yescomplemented
751C22C2×(C22⋊D11)⋊C411yescharacteristic
752C22#1062312212yes—
753C4—21no—
754C4—21no—
755C4—22no—
756C4—41no—
757C4—82no—
758C4—222no—
759C4—441no—
760C4C2×C22⋊C4×D1111yescharacteristic
761C4#1062301711yescharacteristic
762C4#1062312112yes—
763C2—22no—
764C2—22no—
765C2—41no—
766C2—42no—
767C2—81no—
768C2—442no—
769C2—881no—
770C2#1307143211yescharacteristic
771C2C2×#1062243611yescharacteristic
772C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C2×C4×D4
prime radicalC22×#67003C2
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#22452
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. C2×#10622436C2semidirect
3. #13077066C2semidirect
4. #13077065C2semidirect
5. #13069506C2semidirect
6. #13068941C2semidirect
7. #13068940C2semidirect
8. #13068652C2semidirect
9. #13068561C2semidirect
10. #13068394C2semidirect
11. C11×#1789C2semidirect
15. C2×#67003C4semidirect
16. C2×#67003C4semidirect
17. C2×#67003C4semidirect
18. C2×#67003C4semidirect
23. C2×#67001C22semidirect
24. C22×#4326C4semidirect
25. C22×#4325C4semidirect
26. C22×#4324C4semidirect
27. C22×#4323C4semidirect
29. C2×#66960C22semidirect
30. C2×C11×#104C22semidirect
31. C2×C11×#104C22semidirect
35. #10622847C22semidirect
40. #10622742C22semidirect
41. C2×#66886C22semidirect
42. C2×#66869C22semidirect
43. C2×#66869C22semidirect
44. C2×#66867C22semidirect
49. #10622196C22semidirect
50. #10622162C22semidirect
226. #4326C22⋊C4semidirect
230. #4325C22⋊C4semidirect
234. #4324C22⋊C4semidirect
238. #4323C22⋊C4semidirect
269. #1789D11semidirect
375. C2×#104C2×D11semidirect
376. C2×#104C2×D11semidirect
407. C22×C11#444semidirect
645. C11#22452semidirect
750. C22#10622436semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106224362
#130770662
#130770652
#130695062
#130689412
#130689402
#130686522
#130685612
#130683942
C11×#17892
#2245211