Finite Group Databasebeta

← #14792618

Subgroups — #14792618

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622831C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13074413C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic, complemented
5#13069990C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069496C211yesmaximal, characteristic, complemented
9#13069469C211yesmaximal, characteristic, complemented
10#13069316C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic, complemented
12#13068928C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic
15C11×#2309C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C11×#390—21no—
23C11×#390—21no—
24C11×#390C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#379—21no—
29C11×#379—21no—
30#10622831—24no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622613—24no—
41#10622595—21no—
42#10622593—21no—
43C2×#66874C2211yescharacteristic, complemented
44C2×#66874C2211yescharacteristic, complemented
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622565—21no—
48#10622565—21no—
49#10622542C2211yescharacteristic, complemented
50#10622542C2211yescharacteristic, complemented
51#10622541C2211yescharacteristic, complemented
52#10622541C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66867C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—41no—
76C11×#117—41no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×#4324—22no—
98C2×#4324—22no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—41no—
102C2×#4324—41no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106#66977—22no—
107#66977—22no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115#66896—22no—
116#66896—22no—
117#66896—22no—
118#66896—22no—
119#66896—41no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)D414yes—
130#66874—41no—
131#66874—41no—
132#66872—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138#24516—111nomaximal, Sylow
139C24×C11—24no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—44no—
161C2×D4×C11—44no—
162C2×D4×C11—44no—
163C2×D4×C11—44no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11#4112yes—
167C2×D4×C11#4112yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4112yes—
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—81no—
202C11×C22⋊C4—81no—
203C11×C22⋊C4—81no—
204C11×C22⋊C4—81no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—81no—
216#4324—44no—
217#4324—44no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224Dic11⋊C4—42no—
225Dic11⋊C4—81no—
226Dic11⋊C4—81no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8C2×D412yes—
238C2×C11⋊C8C2×D412yes—
239C2×#450—111no—
240C2×#433—111no—
241#2625—111no—
242#2309D1111yescharacteristic
243#2067—111no—
244#2065—111no—
245#2055—111no—
246#2055—111no—
247#1973—111no—
248#1968—111no—
249#1936—111no—
250#1934—111no—
251#1873—111no—
252#1854—111no—
253#1786—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—48no—
263C23×C11—41no—
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—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11#12112yes—
282C23×C11C22×D411yescharacteristic
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11#12112yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335Dic22—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C23×D4C2×D1111yescharacteristic
344C22×SD16—111no—
345C22×SD16—111no—
346C2×C22⋊Q8—111no—
347C2×#117C2×D1111yescharacteristic
348C2×#117C2×D1111yescharacteristic
349#450—224no—
350#433—224no—
351C2×#107—111no—
352C2×#106—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×#97—111no—
366C2×C4×C8—111no—
367#400—221no—
368#398—221no—
369#397—221no—
370#397—221no—
371#391—111no—
372#391—111no—
373#390—21no—
374#390—21no—
375#390C2×D1111yescharacteristic
376#390C2×D1111yescharacteristic
377#390C2×D1111yescharacteristic
378#390C2×D1111yescharacteristic
379#389—111no—
380#389—111no—
381#380—111no—
382#379—21no—
383#379—21no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—816no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11C2×#12111yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C22×C11#57711yescharacteristic
417C4×C11—22no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11#54611yescharacteristic
425C4×C11#54611yescharacteristic
426C4×C11#55111yescharacteristic
427C4×C11#55111yescharacteristic
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432C25—21no—
433C22×Q8—111no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—21no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4C22×D1111yescharacteristic
442C22×D4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×SD16—222no—
445C2×SD16—222no—
446C2×SD16—222no—
447C2×SD16—222no—
448C2×SD16—441no—
449C2×SD16—441no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22⋊Q8—222no—
455C22⋊Q8—222no—
456#117—22no—
457#117—22no—
458#117—41no—
459#117—41no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4C22⋊D1111yescharacteristic
467C2×C4⋊C4C22⋊D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4C22⋊D1111yescharacteristic
482C2×C22⋊C4C22⋊D1111yescharacteristic
483C2×C42—21no—
484C2×C42C22×D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
486#107—441no—
487#106—441no—
488C4⋊C8—222no—
489C4⋊C8—222no—
490#103—441no—
491#103—441no—
492#102—222no—
493#102—222no—
494#102—222no—
495#102—222no—
496#102—441no—
497#102—441no—
498C22⋊C8—114no—
499C22⋊C8—222no—
500#97—222no—
501C4×C8—222no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509C2×C11—42no—
510C2×C11—82no—
511C2×C11—82no—
512C2×C11#241111yescharacteristic
513C2×C11#305711yescharacteristic
514C2×C11#306211yescharacteristic
515C2×C11#311811yescharacteristic
516C2×C11#312311yescharacteristic
517C2×C11#322211yescharacteristic
518C2×C11#322411yescharacteristic
519C24—24no—
520C24—21no—
521C24—21no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24C2×C22⋊D1111yescharacteristic
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8—221no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4#433912yes—
553C2×D4#433912yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4D4×D1112yes—
565C22×C4#434112yes—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572SD16—444no—
573SD16—444no—
574C2×C8—112no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—442no—
599C4⋊C4—881no—
600C4⋊C4—881no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—442no—
613C22⋊C4—881no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C11#2451611yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23#6699212yes—
648C23C22×C22⋊D1111yescharacteristic
649Q8—441no—
650Q8—441no—
651Q8—441no—
652Q8—441no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4#6699212yes—
699C2×C4C2×#433911yescharacteristic
700C2×C4C2×#433911yescharacteristic
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4C2×#434111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#6703711yescharacteristic
705C8—222no—
706C8—222no—
707C8—441no—
708C8—441no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22#1062332211yescharacteristic
732C22C2×#6699211yescharacteristic
733C22#1062333611yescharacteristic
734C22#1062336611yescharacteristic
735C22#1062336711yescharacteristic
736C22#1062336711yescharacteristic
737C22#1062336711yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—881no—
746C4—881no—
747C4—881no—
748C4—881no—
749C4#1062302111yescharacteristic
750C4#1062302111yescharacteristic
751C4#1062302611yescharacteristic
752C4#1062302611yescharacteristic
753C2—42no—
754C2—82no—
755C2—82no—
756C2#1307200111yescharacteristic
757C2#1307825211yescharacteristic
758C2#1307829211yescharacteristic
759C2#1307880011yescharacteristic
760C2#1307886811yescharacteristic
761C2#1307968811yescharacteristic
762C2#1307971011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2309C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenter#2309D11
hypocenterC11#24516
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
3. #13074413C2semidirect
4. #13070004C2semidirect
5. #13069990C2semidirect
6. #13069933C2semidirect
7. #13069933C2semidirect
8. #13069496C2semidirect
9. #13069469C2semidirect
10. #13069316C2semidirect
11. #13069302C2semidirect
12. #13068928C2semidirect
13. #13068815C2semidirect
43. C2×#66874C22semidirect
44. C2×#66874C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
49. #10622542C22semidirect
50. #10622542C22semidirect
51. #10622541C22semidirect
52. #10622541C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
55. C2×#66867C22semidirect
56. C2×C4×C11⋊C8C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
619. C11#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#106228312
C2×#106226132
#130744132
#130700042
#130699902
#130699332
#130694962
#130694692
#130693162
#130693022
#130689282
#130688152
#130685472
C11×#23092
#2451611