Finite Group Databasebeta

← #14797600

Subgroups — #14797600

Order 2816.

1070 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×#10622650C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13071447C211yesmaximal, characteristic, complemented
4#13070155C211yesmaximal, characteristic, complemented
5#13070047C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069291C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068862C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14#13068554C211yesmaximal, characteristic, complemented
15C11×#2422C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#397—21no—
25C11×#394—21no—
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#385—21no—
29C11×#384C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622650—24no—
38C4×#4323—24no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622569—21no—
48#10622569—21no—
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622277—21no—
54D11×#95—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×Dic22C2311yescharacteristic
77C11×#123—44no—
78C11×#121—22no—
79C11×#121—41no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×#4324—22no—
99C2×#4324—22no—
100C2×#4324—41no—
101C2×#4323—22no—
102C2×#4323—22no—
103C2×#4323D414yes—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C4×D44—22no—
113C4×D44—22no—
114C4×D44—41no—
115C4×D44—41no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#66896—22no—
121#66896—41no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—41no—
129#66874—22no—
130#66874—22no—
131#66874—41no—
132#66873—22no—
133#66873—22no—
134#66873—22no—
135#66871—22no—
136#66871—41no—
137C4⋊(C11⋊C8)—41no—
138C4×C11⋊C8—22no—
139#24899—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—81no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—81no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—24no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176#4339—44no—
177#4339—44no—
178#4339—44no—
179#4339—44no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44C2×D412yes—
184C2×D44#4112yes—
185C2×D44#4112yes—
186C2×C4×D11—24no—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
194C2×C4×D11—81no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22#4112yes—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4—81no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C22⋊Dic11—81no—
222#4324—44no—
223#4323—28no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—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⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8C2×D412yes—
242C2×#449—111no—
243C2×C4×D8—111no—
244#2422D1111yescharacteristic, complemented
245#2339—111no—
246#2095—111no—
247#2076—111no—
248#2055—111no—
249#2033—111no—
250#1933—111no—
251#1923—111no—
252#1879—111no—
253#1877—111no—
254#1862—111no—
255#1802—111no—
256#1788—111no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C22×D411yescharacteristic
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279D4×C11—22no—
280D4×C11—22no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—84no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
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—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—84no—
311C2×C4×C11#13512yes—
312C2×C4×C11AGL(1,ℤ/8)12yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C22⋊D11—48no—
320C2×Dic11—22no—
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#12314yescomplemented
333C4×D11—48no—
334C4×D11—84no—
335C4×D11—84no—
336Dic22—22no—
337Dic22—22no—
338Dic22—41no—
339Dic22—41no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×#41—111no—
345C22×SD16—111no—
346C22×D8—111no—
347C2×#123—21no—
348C2×#121C2×D1111yescharacteristic
349C2×C4×D4—111no—
350C2×C4×D4—111no—
351C2×C4×D4C2×D1111yescharacteristic
352#449—224no—
353C4×D8—224no—
354C2×#107—111no—
355C2×#107—111no—
356C2×C4⋊C8—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C4×C8—111no—
368#397—21no—
369#394—21no—
370#391—111no—
371#391—111no—
372#390C2×D1111yescharacteristic
373#389C2×D1111yescharacteristic
374#386—221no—
375#386—221no—
376#385—21no—
377#384C2×D1111yescharacteristic
378#381—221no—
379#380—111no—
380#380C2×D1111yescharacteristic
381C4×C22⋊C4C2×D1111yescharacteristic
382C2×#95—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—41no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11#52511yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11C2×#13511yescharacteristic
407C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C11#57611yescharacteristic
409C22×C11#57811yescharacteristic
410C2×D11—24no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11C2×#12311yescharacteristic
426C4×C11#53811yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#55111yescharacteristic
429Dic11—42no—
430Dic11—81no—
431Dic11—81no—
432C2×#41—222no—
433C2×#41—222no—
434C2×#41—222no—
435C2×#41—222no—
436C2×#41—441no—
437C2×#41—441no—
438C22×Q8—111no—
439C22×D4—21no—
440C22×D4—111no—
441C22×D4—221no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—221no—
445C23×C4—221no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C2×SD16—222no—
449C2×SD16—222no—
450C2×SD16—441no—
451C2×D8—114no—
452C2×D8—222no—
453C2×D8—222no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458#123—44no—
459#121—22no—
460#121—41no—
461C4×D4—22no—
462C4×D4—41no—
463C4×D4—222no—
464C4×D4—222no—
465C4×D4—441no—
466C4×D4—441no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4C22⋊D1111yescharacteristic
484C2×C22⋊C4C22⋊D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
486C2×C42C22×D1111yescharacteristic
487#107—222no—
488#107—441no—
489C4⋊C8—441no—
490#103—222no—
491#103—222no—
492#103—441no—
493#102—222no—
494#102—222no—
495#102—222no—
496#102—222no—
497#102—441no—
498C22⋊C8—222no—
499C22⋊C8—441no—
500C4×C8—222no—
501#95—21no—
502#95—21no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95C22⋊D1111yescharacteristic
509#95C22⋊D1111yescharacteristic
510C2×C11—81no—
511C2×C11—82no—
512C2×C11#241811yescharacteristic
513C2×C11#310611yescharacteristic
514C2×C11#312411yescharacteristic
515C2×C11#326411yescharacteristic
516C2×C11#328311yescharacteristic
517C2×C11#329711yescharacteristic
518C2×C11#333011yescharacteristic
519D11—44no—
520C24—21no—
521C24—221no—
522C24C2×C22⋊D1111yescharacteristic
523#41—444no—
524#41—444no—
525#41—444no—
526#41—444no—
527C2×Q8—112no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—81no—
541C2×D4—112no—
542C2×D4—112no—
543C2×D4—112no—
544C2×D4—224no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—442no—
549C2×D4—442no—
550C2×D4D4×D1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—224no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4—881no—
574C22×C4—881no—
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C23×D1111yescharacteristic
581SD16—444no—
582D8—228no—
583C2×C8—112no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—81no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—881no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C11#2489911yescharacteristic, complemented, Sylow
623C23—21no—
624C23—22no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23C22×C22⋊D1111yescharacteristic
645Q8—222no—
646Q8—222no—
647Q8—441no—
648Q8—441no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—114no—
655D4—222no—
656D4—222no—
657D4—222no—
658D4—448no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—222no—
687C2×C4—448no—
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—884no—
697C2×C4—884no—
698C2×C4#6698512yes—
699C2×C4#6700312yes—
700C2×C4C2×D4×D1111yescharacteristic
701C2×C4#6703711yescharacteristic
702C2×C4#41×D1111yescharacteristic
703C2×C4#41×D1111yescharacteristic
704C2×C4#41×D1111yescharacteristic
705C2×C4#6704211yescharacteristic
706C8—222no—
707C8—441no—
708C8—441no—
709C8—441no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—224no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22C2×#6698511yescharacteristic
732C22D4×C22⋊D1111yescharacteristic
733C22C2×#6700311yescharacteristic
734C22#1062335911yescharacteristic
735C22#1062336011yescharacteristic
736C22#1062336611yescharacteristic
737C22#1062336911yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—442no—
747C4—881no—
748C4—881no—
749C4D11×#12311yescharacteristic
750C4#1062318511yescharacteristic
751C4#1062318811yescharacteristic
752C4#1062319011yescharacteristic
753C2—81no—
754C2—82no—
755C2—444no—
756C2#1307207511yescharacteristic
757C2#1307867011yescharacteristic
758C2#1307887211yescharacteristic
759C2#1308009211yescharacteristic
760C2#1308033411yescharacteristic
761C2#1308046011yescharacteristic
762C2#1308091511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2422C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
hypercenter#2422D11
hypocenterC11#24899
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2422

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4323C2semidirect
3. #13071447C2semidirect
4. #13070155C2semidirect
5. #13070047C2semidirect
6. #13069933C2semidirect
7. #13069795C2semidirect
8. #13069291C2semidirect
9. #13069224C2semidirect
10. #13068967C2semidirect
11. #13068950C2semidirect
12. #13068862C2semidirect
13. #13068613C2semidirect
14. #13068554C2semidirect
15. C11×#2422C2semidirect
244. #2422D11semidirect
332. D44#123semidirect
622. C11#24899semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
C2×C4×#43232
#130714472
#130701552
#130700472
#130699332
#130697952
#130692912
#130692242
#130689672
#130689502
#130688622
#130686132
#130685542
C11×#24222
#2489911