Finite Group Databasebeta

← #14788607

Subgroups — #14788607

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic, complemented
4#13069859C211yesmaximal, characteristic, complemented
5#13069852C211yesmaximal, characteristic, complemented
6#13069699C211yesmaximal, characteristic, complemented
7#13069693C211yesmaximal, characteristic
8#13069553C211yesmaximal, characteristic, complemented
9#13069428C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068631C211yesmaximal, characteristic, complemented
15C2×C11×#556C211yesmaximal, characteristic, complemented
16C11×#556—24no—
17C11×#556—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C11×#126—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×C22⋊Q8—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117—21no—
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33#10622844—21no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622670—24no—
44C4×#4325—24no—
45#10622605—21no—
46#10622602—21no—
47#10622602—21no—
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622549C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×#126—28no—
73C11×#126—28no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124D414yes—
78C11×C22⋊Q8—28no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11D414yes—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C11×#117—28no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—22no—
111C2×#4325—41no—
112C2×#4323—22no—
113C2×#4323—22no—
114C2×#4323—41no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C4×D44—22no—
130C4×D44—22no—
131#66899—22no—
132#66899—22no—
133#66899—22no—
134#66899—41no—
135#66899—41no—
136#66899—41no—
137#66896—22no—
138#66896—22no—
139#66896—41no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66873—22no—
145#66872—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24193—111nomaximal, Sylow
149C24×C11—21no—
150C23×D11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—41no—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11C2×D412yes—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11C2×D412yes—
172C22×C4×C11—24no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44#4112yes—
194C2×C4×D11—42no—
195C2×C4×D11—81no—
196C2×C4×D11—81no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C2×D412yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C42×C11—24no—
212C42×C11—24no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11C2×D412yes—
218C42×C11C2×D412yes—
219#4325—28no—
220#4325—44no—
221#4323—44no—
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—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233Dic11⋊C4—81no—
234Dic11⋊C4—81no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8#4112yes—
247C2×#556D1111yescharacteristic, complemented
248C2×#463—111no—
249C2×C4×SD16—111no—
250#2580—111no—
251#2043—111no—
252#2042—111no—
253#2013—111no—
254#2012—111no—
255#1984—111no—
256#1958—111no—
257#1880—111no—
258#1879—111no—
259#1865—111no—
260#1864—111no—
261#1805—111no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—44no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—41no—
289D4×C11—41no—
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—22no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
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—48no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11#12012yes—
316C2×C4×C11#12012yes—
317C2×C4×C11#13512yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
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—
333D44—22no—
334D44—22no—
335D44—41no—
336D44—41no—
337C4×D11—84no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C22×SD16—111no—
343C22×SD16—111no—
344C22×D8—111no—
345#556—24no—
346#556—24no—
347C2×C4⋊Q8C2×D1111yescharacteristic
348C2×#126—21no—
349C2×#126—21no—
350C2×#124C2×D1111yescharacteristic
351C2×#124C2×D1111yescharacteristic
352C2×C22⋊Q8—21no—
353C2×C4×Q8C2×D1111yescharacteristic
354C2×C4×Q8C2×D1111yescharacteristic
355C2×C4×Q8C2×D1111yescharacteristic
356C2×C4×D4—111no—
357C2×C4×D4C2×D1111yescharacteristic
358C2×#117—21no—
359#463—224no—
360C4×SD16—224no—
361C2×#106—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×C4×C8—111no—
374#399—221no—
375#393—221no—
376#390—111no—
377#390—111no—
378#389—111no—
379#389—111no—
380#385—221no—
381#385—221no—
382#382—111no—
383#340—111no—
384#340—111no—
385#336—111no—
386#336—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×#12011yescharacteristic
397C22×C11#54811yescharacteristic
398C22×C11#55011yescharacteristic
399C22×C11C2×#13511yescharacteristic
400C22×C11#57511yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57711yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11#52511yescharacteristic
420C4×C11#53711yescharacteristic
421C4×C11#54611yescharacteristic
422C4×C11#54711yescharacteristic
423Dic11—81no—
424Dic11—81no—
425Dic11—81no—
426C22×Q8C22⋊D1111yescharacteristic
427C22×Q8C22×D1111yescharacteristic
428C22×Q8C22×D1111yescharacteristic
429C22×D4—111no—
430C22×D4C22×D1111yescharacteristic
431C23×C4—21no—
432C23×C4—221no—
433C2×SD16—222no—
434C2×SD16—222no—
435C2×SD16—222no—
436C2×SD16—222no—
437C2×SD16—222no—
438C2×SD16—441no—
439C2×D8—222no—
440C2×D8—222no—
441C2×D8—441no—
442C22×C8—111no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446C4⋊Q8—22no—
447C4⋊Q8—22no—
448#126—28no—
449#126—28no—
450#124—22no—
451#124—22no—
452#124—22no—
453#124C22⋊D1114yes—
454C22⋊Q8—28no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8C22⋊D1114yes—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—222no—
464C4×D4—222no—
465#117—28no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4C22⋊D1111yescharacteristic
476C2×C4⋊C4C22⋊D1111yescharacteristic
477C2×C4⋊C4C22⋊D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42C22×D1111yescharacteristic
492C2×C42C22×D1111yescharacteristic
493C2×C42C22×D1111yescharacteristic
494#106—222no—
495C4⋊C8—222no—
496#103—222no—
497#103—222no—
498#103—222no—
499#103—441no—
500#103—441no—
501#103—441no—
502#102—222no—
503#102—222no—
504#102—222no—
505#102—441no—
506C4×C8—222no—
507#95—221no—
508#95—221no—
509#95—221no—
510#95—221no—
511C2×C11—82no—
512C2×C11#240711yescharacteristic
513C2×C11#300211yescharacteristic
514C2×C11#301011yescharacteristic
515C2×C11#336011yescharacteristic
516C2×C11#337611yescharacteristic
517C2×C11#339411yescharacteristic
518C2×C11#340111yescharacteristic
519D11—82no—
520C24—21no—
521C24—221no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—41no—
535C2×Q8C2×C22⋊D1112yes—
536C2×Q8C2×C22⋊D1112yes—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—112no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4C2×C22⋊D1112yes—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—442no—
559C22×C4—881no—
560C22×C4—881no—
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C23×D1111yescharacteristic
568SD16—228no—
569SD16—444no—
570D8—444no—
571C2×C8—112no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—881no—
598C4⋊C4—881no—
599C4⋊C4C2×C22⋊D1112yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—442no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—881no—
609C22⋊C4—881no—
610C42—24no—
611C42—24no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42C2×C22⋊D1112yes—
617C42C2×C22⋊D1112yes—
618C11#2419311yescharacteristic, complemented, Sylow
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—222no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23C22×C22⋊D1111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—222no—
648D4—222no—
649D4—441no—
650D4—441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—884no—
686C2×C4#6700312yes—
687C2×C4#6700612yes—
688C2×C4#6700612yes—
689C2×C4#41×D1111yescharacteristic
690C2×C4#41×D1111yescharacteristic
691C2×C4#6704211yescharacteristic
692C2×C4#6704311yescharacteristic
693C2×C4C22×C22⋊D1111yescharacteristic
694C2×C4C22×C22⋊D1111yescharacteristic
695C8—222no—
696C8—441no—
697C8—441no—
698C8—441no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—442no—
707C22—442no—
708C22—442no—
709C22—881no—
710C22—881no—
711C22—881no—
712C22—881no—
713C22C2×#6700311yescharacteristic
714C22#1062335311yescharacteristic
715C22#1062336211yescharacteristic
716C22#1062336511yescharacteristic
717C22#1062336811yescharacteristic
718C22#1062336811yescharacteristic
719C22C2×#6700611yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—881no—
730C4—881no—
731C4—881no—
732C4#1062335511yescharacteristic
733C4#1062335911yescharacteristic
734C4#1062336011yescharacteristic
735C4#1062336411yescharacteristic
736C2—82no—
737C2—882no—
738C2#1307195511yescharacteristic
739C2#1307783411yescharacteristic
740C2#1307790211yescharacteristic
741C2#1308126111yescharacteristic
742C2#1308143711yescharacteristic
743C2#1308161211yescharacteristic
744C2#1308168211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11#24193
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. #13073974C2semidirect
4. #13069859C2semidirect
5. #13069852C2semidirect
6. #13069699C2semidirect
8. #13069553C2semidirect
9. #13069428C2semidirect
10. #13068971C2semidirect
12. #13068884C2semidirect
13. #13068877C2semidirect
14. #13068631C2semidirect
15. C2×C11×#556C2semidirect
247. C2×#556D11semidirect
618. C11#24193semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×C4×#43252
#130739742
#130698592
#130698522
#130696992
#130696932
#130695532
#130694282
#130689712
#130689642
#130688842
#130688772
#130686312
C2×C11×#5562
#2419311