Finite Group Databasebeta

← #14661682

Subgroups — #14661682

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic
2C2×#10622589C211yesmaximal, characteristic
3C2×#10622189C211yesmaximal, characteristic
4C2×#10622167C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622188C211yesmaximal, characteristic
7C2×C11×#340C211yesmaximal, characteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C22×Dic11⋊C4—21no—
16C22×C4×Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×C11⋊#95—21no—
19#10622598—22no—
20#10622598C414yescomplemented
21#10622589—22no—
22#10622589—22no—
23C11×#340—22no—
24#10622189—22no—
25#10622188—22no—
26#10622167—22no—
27#10622167—22no—
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C23×Dic11D411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C22×C8×C11Q812yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4Q812yes—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—24no—
65C2×C4⋊Dic11—42no—
66C2×C4⋊Dic11—42no—
67C2×C4⋊Dic11C2×C412yes—
68C2×C4⋊Dic11D412yes—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—42no—
72C2×Dic11⋊C4—42no—
73C2×Dic11⋊C4—42no—
74C2×Dic11⋊C4—42no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11C2×C412yes—
80C2×C4×Dic11D412yes—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8Q812yes—
88C11⋊#95—24no—
89#11207—111nomaximal, Sylow
90C24×C11C2×D411yescharacteristic
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×Q811yescharacteristic
111C22×C4×C11C2×Q811yescharacteristic
112C22×C4×C11C2×Q811yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×Dic11—22no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11C22⋊C412yes—
142C22×Dic11C22⋊C412yes—
143C22×Dic11D812yes—
144C22×Dic11SD1612yes—
145C22×Dic11SD1612yes—
146C22×Dic11Q1612yes—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—41no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4C4⋊C414yescomplemented
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—48no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171Dic11⋊C4—48no—
172Dic11⋊C4—48no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—41no—
181C2×C11⋊C8—41no—
182C2×C11⋊C8—41no—
183C2×C11⋊C8—41no—
184C2×#389—111no—
185C2×#384—111no—
186C2×#340—111no—
187C2×#340—111no—
188C2×#340—111no—
189C2×#340D1111yescharacteristic
190C2×#336—111no—
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11#12011yescharacteristic
193C23×C11#12111yescharacteristic
194C23×C11C22⋊Q811yescharacteristic
195C23×C11#12311yescharacteristic
196C23×C11#12411yescharacteristic
197C23×C11C4⋊Q811yescharacteristic
198C23×C11C2×D811yescharacteristic
199C23×C11C2×SD1611yescharacteristic
200C23×C11C2×SD1611yescharacteristic
201C23×C11C2×Q1611yescharacteristic
202C23×C11AGL(1,ℤ/8)11yescharacteristic
203C23×C11AGL(1,ℤ/8)11yescharacteristic
204C23×C11#13711yescharacteristic
205C23×C11#13711yescharacteristic
206C2×C4×C11—24no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—81no—
217C2×C4×C11—81no—
218C2×C4×C11—81no—
219C2×C4×C11—81no—
220C2×C4×C11C2×C4⋊C411yescharacteristic
221C2×C4×C11#11711yescharacteristic
222C2×C4×C11C4×D411yescharacteristic
223C2×C4×C11C4×D411yescharacteristic
224C2×C4×C11C4×Q811yescharacteristic
225C2×C4×C11C4×Q811yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11C22⋊Q811yescharacteristic
232C2×C4×C11C22⋊Q811yescharacteristic
233C2×C4×C11C22⋊Q811yescharacteristic
234C2×C4×C11C22⋊Q811yescharacteristic
235C2×C4×C11C22⋊Q811yescharacteristic
236C2×C4×C11C22⋊Q811yescharacteristic
237C2×C4×C11C22⋊Q811yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12511yescharacteristic
241C2×C4×C11#12511yescharacteristic
242C2×C4×C11#12511yescharacteristic
243C2×C4×C11#12511yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C2×C4×C11#12611yescharacteristic
246C2×C4×C11C4⋊Q811yescharacteristic
247C2×C4×C11C4⋊Q811yescharacteristic
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—81no—
267C2×Dic11—81no—
268C2×Dic11—81no—
269C2×Dic11—81no—
270C2×Dic11—81no—
271C2×Dic11—81no—
272C2×Dic11—81no—
273C2×Dic11—81no—
274C2×Dic11#10214yes—
275C2×Dic11#10314yes—
276C8×C11—42no—
277C11⋊C8—42no—
278C23×C8—111no—
279C23×C8C2×D1111yescharacteristic
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—221no—
283C22×C4⋊C4—221no—
284C22×C4⋊C4—221no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C4⋊C4C2×D1111yescharacteristic
287C22×C42—111no—
288#389—114no—
289#389—222no—
290#384—222no—
291#384—222no—
292C2×#95—221no—
293#340—22no—
294#340—222no—
295#340—222no—
296#340—222no—
297#336—222no—
298C22×C11#38011yescharacteristic
299C22×C11#38611yescharacteristic
300C22×C11#39111yescharacteristic
301C22×C11#39411yescharacteristic
302C22×C11#39511yescharacteristic
303C22×C11#39811yescharacteristic
304C22×C11#40011yescharacteristic
305C22×C11C2×#10211yescharacteristic
306C22×C11C2×#10311yescharacteristic
307C22×C11#41711yescharacteristic
308C22×C11#41711yescharacteristic
309C22×C11#44711yescharacteristic
310C22×C11#44811yescharacteristic
311C22×C11#45011yescharacteristic
312C22×C11#45111yescharacteristic
313C22×C11#45911yescharacteristic
314C22×C11#46011yescharacteristic
315C22×C11#46111yescharacteristic
316C22×C11#46211yescharacteristic
317C22×C11#47411yescharacteristic
318C22×C11#47511yescharacteristic
319C22×C11#47611yescharacteristic
320C22×C11#47711yescharacteristic
321C22×C11#48011yescharacteristic
322C22×C11#48111yescharacteristic
323C22×C11#48311yescharacteristic
324C22×C11#48411yescharacteristic
325C22×C11#48611yescharacteristic
326C22×C11#48711yescharacteristic
327C22×C11#49011yescharacteristic
328C22×C11#49111yescharacteristic
329C22×C11#49811yescharacteristic
330C22×C11#50011yescharacteristic
331C22×C11#50111yescharacteristic
332C22×C11#50111yescharacteristic
333C4×C11—44no—
334C4×C11—82no—
335C4×C11#38711yescharacteristic
336C4×C11#38711yescharacteristic
337C4×C11#38911yescharacteristic
338C4×C11#38911yescharacteristic
339C4×C11#39611yescharacteristic
340C4×C11#39611yescharacteristic
341C4×C11#39811yescharacteristic
342C4×C11#39811yescharacteristic
343Dic11—24no—
344Dic11—24no—
345Dic11—82no—
346Dic11—82no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—221no—
352C23×C4—221no—
353C23×C4C22×D1111yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—112no—
361C22×C8—221no—
362C22×C8—221no—
363C22×C8—221no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8Dic2212yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—442no—
392C2×C4⋊C4—442no—
393C2×C4⋊C4—442no—
394C2×C4⋊C4—442no—
395C2×C4⋊C4—442no—
396C2×C4⋊C4—442no—
397C2×C4⋊C4Dic2212yes—
398C2×C4⋊C4C4×D1112yes—
399C2×C4⋊C4D4412yes—
400C2×C4⋊C4C22⋊D1112yes—
401C2×C42—112no—
402C2×C42—112no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407#95—224no—
408C2×C11#144111yescharacteristic
409C2×C11#180211yescharacteristic
410C2×C11#180311yescharacteristic
411C2×C11#187211yescharacteristic
412C2×C11#187411yescharacteristic
413C2×C11#199011yescharacteristic
414C2×C11#199211yescharacteristic
415C2×C11#204111yescharacteristic
416C2×C11#204311yescharacteristic
417C2×C11#205711yescharacteristic
418C2×C11#205811yescharacteristic
419C2×C11#208311yescharacteristic
420C2×C11#208411yescharacteristic
421C2×C11#209911yescharacteristic
422C2×C11#210011yescharacteristic
423C24D4×D1111yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4C2×Dic2211yescharacteristic
467C22×C4C2×Dic2211yescharacteristic
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4#433911yescharacteristic
471C22×C4#433911yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4#434111yescharacteristic
475C22×C4#434111yescharacteristic
476C22×C4#434111yescharacteristic
477C22×C4Q8×D1111yescharacteristic
478C22×C4#434311yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—222no—
488C2×C8—222no—
489C2×C8—222no—
490C2×C8—441no—
491C2×C8—441no—
492C2×C8—441no—
493C2×C8—441no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—448no—
506C4⋊C4—448no—
507C4⋊C4—448no—
508C4⋊C4—441no—
509C4⋊C4—441no—
510C4⋊C4—441no—
511C4⋊C4—441no—
512C4⋊C4Dic11⋊C414yescomplemented
513C42—222no—
514C42—222no—
515C42—222no—
516C42—222no—
517C11#1120711yescharacteristic, complemented, Sylow
518C23#6693111yescharacteristic
519C23C22⋊C4×D1111yescharacteristic
520C23#6693511yescharacteristic
521C23#6693811yescharacteristic
522C23#6694111yescharacteristic
523C23#6694711yescharacteristic
524C23D8×D1111yescharacteristic
525C23#6696411yescharacteristic
526C23SD16×D1111yescharacteristic
527C23SD16×D1111yescharacteristic
528C23#6696711yescharacteristic
529C23#6696811yescharacteristic
530C23Q16×D1111yescharacteristic
531C23#6697111yescharacteristic
532C23#6699211yescharacteristic
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—114no—
548C2×C4—114no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—881no—
568C2×C4—881no—
569C2×C4—881no—
570C2×C4—881no—
571C2×C4—881no—
572C2×C4—881no—
573C2×C4—881no—
574C2×C4—881no—
575C2×C4C4×Dic2211yescharacteristic
576C2×C4#6692211yescharacteristic
577C2×C4#6692311yescharacteristic
578C2×C4C4×D4411yescharacteristic
579C2×C4#6693011yescharacteristic
580C2×C4#6693111yescharacteristic
581C2×C4#6693111yescharacteristic
582C2×C4#6693111yescharacteristic
583C2×C4#6693211yescharacteristic
584C2×C4#6693611yescharacteristic
585C2×C4#6693711yescharacteristic
586C2×C4#6693911yescharacteristic
587C2×C4#6694011yescharacteristic
588C2×C4#6694111yescharacteristic
589C2×C4#6694211yescharacteristic
590C2×C4#6694311yescharacteristic
591C2×C4#6694311yescharacteristic
592C2×C4#6694611yescharacteristic
593C2×C4#6694811yescharacteristic
594C2×C4#6694911yescharacteristic
595C2×C4#6695011yescharacteristic
596C2×C4#6695111yescharacteristic
597C2×C4C2×Dic11⋊C411yescharacteristic
598C2×C4#6697711yescharacteristic
599C2×C4#6698311yescharacteristic
600C2×C4#6699111yescharacteristic
601C2×C4#6699211yescharacteristic
602C2×C4#6699911yescharacteristic
603C8—42no—
604C8—442no—
605C22#1062225911yescharacteristic
606C22#1062226911yescharacteristic
607C22#1062227311yescharacteristic
608C22#1062227811yescharacteristic
609C22#1062237211yescharacteristic
610C22#1062237311yescharacteristic
611C22#1062237411yescharacteristic
612C22#1062237711yescharacteristic
613C22D11×#10211yescharacteristic
614C22#1062238411yescharacteristic
615C22#1062238611yescharacteristic
616C22#1062238911yescharacteristic
617C22#1062240411yescharacteristic
618C22#1062240511yescharacteristic
619C22#1062240711yescharacteristic
620C22#1062241011yescharacteristic
621C22D11×#10311yescharacteristic
622C22#1062241611yescharacteristic
623C22#1062241911yescharacteristic
624C22#1062242111yescharacteristic
625C22#1062246811yescharacteristic
626C22#1062246911yescharacteristic
627C22#1062247511yescharacteristic
628C22#1062247611yescharacteristic
629C22#1062248711yescharacteristic
630C22#1062248911yescharacteristic
631C22#1062249511yescharacteristic
632C22#1062249711yescharacteristic
633C22#1062255511yescharacteristic
634C22#1062257411yescharacteristic
635C22#1062259711yescharacteristic
636C22#1062276311yescharacteristic
637C22#1062277511yescharacteristic
638C22#1062277611yescharacteristic
639C22#1062279511yescharacteristic
640C4—44no—
641C4—82no—
642C4—224no—
643C4—224no—
644C4—882no—
645C4—882no—
646C4#1062226611yescharacteristic
647C4#1062226711yescharacteristic
648C4#1062227011yescharacteristic
649C4#1062227411yescharacteristic
650C4#1062254111yescharacteristic
651C4#1062256111yescharacteristic
652C4#1062258611yescharacteristic
653C4#1062260711yescharacteristic
654C2#1306686811yescharacteristic
655C2#1306861411yescharacteristic
656C2#1306861911yescharacteristic
657C2#1306892211yescharacteristic
658C2#1306893211yescharacteristic
659C2#1306957511yescharacteristic
660C2#1306958311yescharacteristic
661C2#1306984911yescharacteristic
662C2#1306986111yescharacteristic
663C2#1306994311yescharacteristic
664C2#1306994811yescharacteristic
665C2#1307009011yescharacteristic
666C2#1307009511yescharacteristic
667C2#1307017711yescharacteristic
668C2#1307018211yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#340C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#340D11
hypocenterC11#11207
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
20. #10622598C4semidirect
161. C11×C4⋊C4C4⋊C4semidirect
512. C4⋊C4Dic11⋊C4semidirect
517. C11#11207semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225892
C2×#106221892
C2×#106221672
C2×#106221882
C2×C11×#3402
#1120711