Finite Group Databasebeta

← #14774080

Subgroups — #14774080

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622347C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4#13071652C211yesmaximal, characteristic, complemented
5#13071456C211yesmaximal, characteristic, complemented
6#13069492C211yesmaximal, characteristic, complemented
7#13069313C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068887C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622726—24no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41#10622570—21no—
42#10622570—21no—
43#10622570—21no—
44#10622569—21no—
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622347C418yescomplemented
51#10622323—24no—
52#10622282—21no—
53#10622280—21no—
54#10622279—21no—
55#10622279—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339C2×C414yescomplemented
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#66983—22no—
90#66983C2×C414yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99#66979—22no—
100#66979—41no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×D88—41no—
114C2×D88—41no—
115C2×D88C2×C414yes—
116C2×#4314—22no—
117C2×#4314—22no—
118C2×#4314C2×C414yes—
119C4×D44—22no—
120C4×D44—41no—
121C4×Dic22—22no—
122C4×Dic22—22no—
123C4×Dic22—41no—
124C4×Dic22—41no—
125C11×C22⋊C8C2×C414yescomplemented
126C11×#97—22no—
127C11×#97—41no—
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133#66885—22no—
134#66885—22no—
135#66885—22no—
136#66885—41no—
137#66885C2×C414yescomplemented
138#66882—22no—
139#66881—41no—
140#66880—22no—
141#66880C2×C414yescomplemented
142#66880D414yescomplemented
143#22857—111nomaximal, Sylow
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C23×D11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—42no—
163C2×C22⋊D11—81no—
164C2×C22⋊D11—81no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171#4339—28no—
172#4339—44no—
173#4339—44no—
174#4339—44no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44C22×C412yes—
186C2×D44C22×C412yes—
187C2×C4×D11—24no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—81no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22C22×C412yes—
197C2×Dic22C2×D412yes—
198C2×Dic22#4112yes—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
209C2×C8×C11C22×C412yes—
210C2×C8×C11C22×C412yes—
211C2×C8×C11C2×D412yes—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C22⋊Dic11—42no—
219C22⋊Dic11—81no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—81no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11C22×C412yes—
237C4⋊Dic11C2×D412yes—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240Dic11⋊C4—81no—
241C4×Dic11—42no—
242C4×Dic11—42no—
243C4×Dic11—42no—
244C4×Dic11—81no—
245D88—44no—
246#4314—28no—
247C2×#449—111no—
248C2×#440—111no—
249C2×#416—111no—
250#2363—111no—
251#2341—111no—
252#1972—111no—
253#1936—111no—
254#1925—111no—
255#1893—111no—
256#1880—111no—
257#1879—111no—
258#1865—111no—
259#1854—111no—
260#1763—111no—
261#1752D1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11C4×D412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11C4×D412yes—
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C22⋊D11—48no—
310C22⋊D11—84no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329D44—22no—
330D44—22no—
331D44—22no—
332D44—22no—
333D44—41no—
334D44—41no—
335D44—41no—
336D44—41no—
337C4×D11—48no—
338C4×D11—84no—
339Dic22—22no—
340Dic22—22no—
341Dic22—22no—
342Dic22C4×D414yes—
343C8×C11—22no—
344C8×C11—22no—
345C8×C11—22no—
346C8×C11—41no—
347C22×#41—111no—
348C22×SD16—111no—
349C22×D8—111no—
350C23×C8C2×D1111yescharacteristic
351C2×#121—111no—
352C2×C4×Q8—111no—
353C2×C4×Q8—111no—
354C2×C4×D4—111no—
355C2×#117—111no—
356#449—118no—
357#440—224no—
358C2×#107—111no—
359C2×#106—111no—
360#416—224no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×C22⋊C8C2×D1111yescharacteristic
370C2×#97C2×D1111yescharacteristic
371C2×#97C2×D1111yescharacteristic
372#390—111no—
373#390—111no—
374#390—111no—
375#390—221no—
376#390—221no—
377#390—221no—
378#389—111no—
379#388—221no—
380#386—221no—
381#380—111no—
382#380—221no—
383C4×C4⋊C4—111no—
384C4×C22⋊C4—221no—
385C4×C22⋊C4—221no—
386C4×C22⋊C4C2×D1111yescharacteristic
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#336C2×D1111yescharacteristic
392#336C2×D1111yescharacteristic
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11C2×C4×D411yescharacteristic
401C22×C11D4211yescharacteristic
402C22×C11#54611yescharacteristic
403C22×C11#57511yescharacteristic
404C22×C11#57511yescharacteristic
405C22×C11#57611yescharacteristic
406C22×C11#57711yescharacteristic
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C4×C11—22no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11C2×C4×D411yescharacteristic
427C4×C11#51811yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430Dic11—24no—
431Dic11—42no—
432Dic11—42no—
433Dic11—81no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—114no—
437C2×#41—222no—
438C2×#41—222no—
439C2×#41—222no—
440C2×#41—441no—
441C2×#41—441no—
442C22×Q8—111no—
443C22×D4—111no—
444C22×D4—111no—
445C22×D4—221no—
446C22×D4—221no—
447C23×C4—221no—
448C23×C4—221no—
449C23×C4C22×D1111yescharacteristic
450C2×SD16—114no—
451C2×SD16—222no—
452C2×SD16—222no—
453C2×D8—114no—
454C2×D8—441no—
455C2×D8—441no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#121—114no—
464#121—222no—
465C4×Q8—222no—
466C4×Q8—222no—
467C4×Q8—441no—
468C4×Q8—441no—
469C4×D4—222no—
470C4×D4—441no—
471#117—222no—
472#117—441no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4D4411yescharacteristic
492C2×C22⋊C4D4411yescharacteristic
493C2×C42—221no—
494C2×C42—221no—
495C2×C42—221no—
496C2×C42—221no—
497C2×C42C22×D1111yescharacteristic
498C2×C42C22×D1111yescharacteristic
499#107—222no—
500#106—441no—
501#103—114no—
502#103—114no—
503#103—222no—
504#102—114no—
505#102—222no—
506#102—222no—
507#102—222no—
508#102—441no—
509C22⋊C8C4×D1114yescomplemented
510#97—22no—
511#97—41no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95D4411yescharacteristic
516#95D4411yescharacteristic
517C2×C11—42no—
518C2×C11#235811yescharacteristic
519C2×C11#294311yescharacteristic
520C2×C11#294611yescharacteristic
521C2×C11#326811yescharacteristic
522C2×C11#327111yescharacteristic
523C2×C11#330911yescharacteristic
524C2×C11#332111yescharacteristic
525D11—82no—
526D11—82no—
527C24—221no—
528C24—221no—
529C24C2×D4411yescharacteristic
530#41—228no—
531#41—444no—
532#41—444no—
533#41—444no—
534C2×Q8—112no—
535C2×Q8—112no—
536C2×Q8—112no—
537C2×Q8—221no—
538C2×Q8—221no—
539C2×Q8—221no—
540C2×D4—112no—
541C2×D4—112no—
542C2×D4—224no—
543C2×D4—224no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—442no—
555C2×D4—442no—
556C2×D4—881no—
557C2×D4—881no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—224no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4—881no—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×D4411yescharacteristic
576C22×C4C2×D4411yescharacteristic
577C22×C4C2×D4411yescharacteristic
578C22×C4C2×D4411yescharacteristic
579C22×C4C2×D4411yescharacteristic
580C22×C4#433912yes—
581C22×C4C23×D1111yescharacteristic
582SD16—228no—
583D8—444no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—44no—
594C2×C8C2×C4×D1112yes—
595C2×C8C2×C4×D1112yes—
596C2×C8D4×D1112yes—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4—881no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—224no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—881no—
619C22⋊C4—881no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—442no—
627C42—442no—
628C42—442no—
629C42—881no—
630C11#2285711yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—222no—
638C23—222no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23C4×D4412yes—
652C23C22×D4411yescharacteristic
653Q8—114no—
654Q8—222no—
655Q8—222no—
656Q8—222no—
657D4—222no—
658D4—222no—
659D4—222no—
660D4—222no—
661D4—448no—
662D4—441no—
663D4—441no—
664D4—441no—
665D4—441no—
666D4—884no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—448no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—884no—
705C2×C4C4×D4412yes—
706C2×C4C22×C4×D1111yescharacteristic
707C2×C4C2×#433911yescharacteristic
708C2×C4C2×D4×D1111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#41×D1111yescharacteristic
711C2×C4#6704211yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—41no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—442no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—881no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22—881no—
734C22—881no—
735C22—881no—
736C22—881no—
737C22C2×C4×D4411yescharacteristic
738C22D4×D4411yescharacteristic
739C22#1062308511yescharacteristic
740C22#1062327911yescharacteristic
741C22#1062327911yescharacteristic
742C22#1062328211yescharacteristic
743C22#1062328311yescharacteristic
744C4—22no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—224no—
750C4—442no—
751C4—442no—
752C4—881no—
753C4—881no—
754C4—881no—
755C4#1062302111yescharacteristic
756C4#1062305811yescharacteristic
757C4C4×D4×D1111yescharacteristic
758C4#1062307611yescharacteristic
759C2—42no—
760C2—882no—
761C2—882no—
762C2#1307159811yescharacteristic
763C2#1307741811yescharacteristic
764C2#1307745011yescharacteristic
765C2#1308016111yescharacteristic
766C2#1308020611yescharacteristic
767C2#1308062411yescharacteristic
768C2#1308080411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22857
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
3. C2×#10622726C2semidirect
4. #13071652C2semidirect
5. #13071456C2semidirect
6. #13069492C2semidirect
7. #13069313C2semidirect
8. #13069237C2semidirect
9. #13069044C2semidirect
10. #13068970C2semidirect
11. #13068963C2semidirect
12. #13068887C2semidirect
13. #13068817C2semidirect
14. #13068447C2semidirect
15. C11×#1752C2semidirect
50. #10622347C4semidirect
70. C2×#4339C2×C4semidirect
125. C11×C22⋊C8C2×C4semidirect
137. #66885C2×C4semidirect
141. #66880C2×C4semidirect
142. #66880D4semidirect
261. #1752D11semidirect
509. C22⋊C8C4×D11semidirect
630. C11#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#106223472
C2×#106223232
C2×#106227262
#130716522
#130714562
#130694922
#130693132
#130692372
#130690442
#130689702
#130689632
#130688872
#130688172
#130684472
C11×#17522
#2285711