Finite Group Databasebeta

← #14810832

Subgroups — #14810832

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic
3#13072319C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic11C211yesmaximal, characteristic
5#13070142C211yesmaximal, characteristic, complemented
6#13070002C211yesmaximal, characteristic, complemented
7#13070000C211yesmaximal, characteristic, complemented
8#13069750C211yesmaximal, characteristic, complemented
9#13068865C211yesmaximal, characteristic, complemented
10#13068861C211yesmaximal, characteristic, complemented
11#13068806C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068643C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C22⋊Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66941C2211yescharacteristic, complemented
23C2×#66931—21no—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30#10622860—21no—
31#10622834C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622833—21no—
34#10622833—21no—
35C2×#66896—24no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825C2211yescharacteristic
41C4×C22⋊Dic11C2211yescharacteristic
42C2×#66882C2211yescharacteristic, complemented
43C2×#66882C2211yescharacteristic, complemented
44C2×Dic11⋊C8C2211yescharacteristic, complemented
45C2×Dic11⋊C8C2211yescharacteristic, complemented
46#10622598C2211yescharacteristic, complemented
47#10622589C2211yescharacteristic, complemented
48#10622586C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622559—21no—
52#10622372—24no—
53#10622270—21no—
54#10622269—21no—
55#10622189C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, 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—41no—
67C22×D4×C11—41no—
68C22×D4×C11Q814yescomplemented
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C23×Dic11—21no—
74C23×Dic11—21no—
75C22×Dic22—21no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11D411yescharacteristic
90C2×C22⋊Dic11D411yescharacteristic
91D4×Dic11—22no—
92D4×Dic11—22no—
93D4×Dic11—41no—
94D4×Dic11—41no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—41no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—41no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114#66941—22no—
115#66941—41no—
116#66931—44no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#102—41no—
120C11×#102—41no—
121C11×C22⋊C8—22no—
122C11×#95—21no—
123#66896—22no—
124#66896—22no—
125#66896—22no—
126#66896D414yes—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66882—22no—
133#66882—41no—
134Dic11⋊C8—22no—
135Dic11⋊C8—41no—
136#66871—22no—
137#66871—41no—
138#25950—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—24no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
149C2×D4×C11—28no—
150C2×D4×C11—24no—
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—44no—
160C2×D4×C11—44no—
161C2×D4×C11—44no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11C2×D412yes—
165C2×D4×C11C2×Q812yes—
166C2×D4×C11C2×Q812yes—
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×Q812yes—
176C22×C4×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C22×Dic11—81no—
189C22×Dic11—81no—
190C22×Dic11—81no—
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C2×Dic22—42no—
196C2×Dic22—42no—
197C2×Dic22—81no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C22⋊C4—42no—
209C22⋊Dic11—22no—
210C22⋊Dic11—42no—
211C22⋊Dic11—42no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—81no—
216C22⋊Dic11—81no—
217C22⋊Dic11D814yes—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—42no—
226C4⋊Dic11—42no—
227C4⋊Dic11C2×D412yes—
228Dic11⋊C4—42no—
229Dic11⋊C4—42no—
230Dic11⋊C4—42no—
231Dic11⋊C4—81no—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—44no—
242C2×C11⋊C8C2×D412yes—
243C2×#474—111no—
244C22×#102—111no—
245#2440—111no—
246D4×C22⋊C4—111no—
247#2093—111no—
248#2067—111no—
249#2067—111no—
250#2023—111no—
251#1862—111no—
252#1862—111no—
253#1852—111no—
254#1850—111no—
255#1808—111no—
256#1802—111no—
257#1786D1111yescharacteristic
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—48no—
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—41no—
276C23×C11—41no—
277C23×C11—48no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11—84no—
282C23×C11—84no—
283C23×C11C22⋊Q812yes—
284C23×C11C2×D812yes—
285C23×C11#13712yes—
286C23×C11C22×D411yescharacteristic
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—48no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11C22⋊Q814yescomplemented
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
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×C11C22⋊Q812yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×Q811yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
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—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—84no—
338C2×Dic11—84no—
339C2×Dic11—84no—
340C2×Dic11C2×D812yes—
341C2×Dic11C2×D812yes—
342Dic22—84no—
343C8×C11—41no—
344C8×C11—41no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C23×D4C2×D1111yescharacteristic
348C23×C8—111no—
349C2×C4⋊Q8—111no—
350C2×C22⋊Q8—221no—
351C2×C4×D4—111no—
352C2×C4×D4—111no—
353C22×C4⋊C4—111no—
354C22×C22⋊C4—221no—
355#474—224no—
356C2×#107—111no—
357C2×#107—111no—
358C2×#107—111no—
359C2×#107—111no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—224no—
367C2×#102C2×D1111yescharacteristic
368C2×#102C2×D1111yescharacteristic
369C2×#102C2×D1111yescharacteristic
370C2×#102C2×D1111yescharacteristic
371C2×C22⋊C8C2×D1111yescharacteristic
372#398—221no—
373#395—221no—
374#390—111no—
375#390—111no—
376#389—111no—
377#389—111no—
378#386—221no—
379#386—221no—
380#385—221no—
381#384—111no—
382#380—111no—
383#380C2×D1111yescharacteristic
384#379—221no—
385C4×C22⋊C4—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390#336—111no—
391#336—111no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—24no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—816no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11#47414yescomplemented
414C22×C11C2×C22⋊Q811yescharacteristic
415C22×C11D4211yescharacteristic
416C22×C11#54611yescharacteristic
417C22×C11C22×D811yescharacteristic
418C22×C11C2×#13711yescharacteristic
419C22×C11#57611yescharacteristic
420C22×C11#57711yescharacteristic
421C4×C11—22no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11C2×C22⋊Q811yescharacteristic
425C4×C11#54311yescharacteristic
426C4×C11#54611yescharacteristic
427C4×C11#55111yescharacteristic
428Dic11—22no—
429Dic11—22no—
430Dic11—41no—
431Dic11—42no—
432Dic11—41no—
433Dic11—81no—
434Dic11—81no—
435Dic11—81no—
436C25—21no—
437C22×Q8—221no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—22no—
442C22×D4—41no—
443C22×D4—41no—
444C22×D4Dic2214yescomplemented
445C22×D4C22×D1111yescharacteristic
446C22×D4C22×D1111yescharacteristic
447C23×C4—221no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—222no—
454C22×C8—222no—
455C22×C8—441no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C4⋊Q8—222no—
459C4⋊Q8—441no—
460C22⋊Q8—444no—
461C4×D4—222no—
462C4×D4—222no—
463C4×D4—441no—
464C4×D4—441no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—441no—
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
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—444no—
490C2×C42—111no—
491C2×C42—111no—
492#107—222no—
493#107—222no—
494#107—441no—
495#107—441no—
496C4⋊C8—222no—
497C4⋊C8—441no—
498#102—22no—
499#102—22no—
500#102—41no—
501#102—41no—
502#102—114no—
503#102—222no—
504#102—222no—
505#102—222no—
506C22⋊C8—22no—
507#95—21no—
508#95—111no—
509#95—111no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—24no—
514C2×C11—44no—
515C2×C11—82no—
516C2×C11#243711yescharacteristic
517C2×C11C2×#47411yescharacteristic
518C2×C11#308111yescharacteristic
519C2×C11#326611yescharacteristic
520C2×C11D4×D811yescharacteristic
521C2×C11#329411yescharacteristic
522C2×C11#331411yescharacteristic
523C24—21no—
524C24—21no—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—81no—
531C24—81no—
532C24D4×D1111yescharacteristic
533C2×Q8—442no—
534C2×Q8—442no—
535C2×Q8—881no—
536C2×D4—28no—
537C2×D4—24no—
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—42no—
550C2×D4—42no—
551C2×D4C2×Dic2212yes—
552C2×D4C2×Dic2212yes—
553C2×D4D4×D1112yes—
554C2×D4#434112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—881no—
576C22×C4—881no—
577C22×C4—881no—
578C22×C4C2×Dic2212yes—
579C22×C4D4×D1111yescharacteristic
580C22×C4#434112yes—
581C22×C4C23×D1111yescharacteristic
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—444no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—112no—
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—442no—
610C4⋊C4—442no—
611C4⋊C4—442no—
612C4⋊C4—881no—
613C22⋊C4—42no—
614C22⋊C4—114no—
615C22⋊C4—222no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—881no—
622C22⋊C4—881no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—221no—
627C11#2595011yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—48no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#6693112yes—
654C23D8×D1112yes—
655C23#6696812yes—
656C23C2×D4×D1111yescharacteristic
657Q8—884no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#6693114yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—222no—
691C2×C4—221no—
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—884no—
704C2×C4—884no—
705C2×C4—884no—
706C2×C4#6693112yes—
707C2×C4C22×Dic2211yescharacteristic
708C2×C4C2×D4×D1111yescharacteristic
709C2×C4C2×#434111yescharacteristic
710C2×C4C2×#434111yescharacteristic
711C2×C4#6703711yescharacteristic
712C2×C4#6703711yescharacteristic
713C8—41no—
714C8—41no—
715C8—222no—
716C8—441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1062237214yescomplemented
739C22C2×#6693111yescharacteristic
740C22#1062312111yescharacteristic
741C22#1062312211yescharacteristic
742C22C2×D8×D1111yescharacteristic
743C22C2×#6696811yescharacteristic
744C22#1062330511yescharacteristic
745C22#1062330611yescharacteristic
746C4—22no—
747C4—81no—
748C4—81no—
749C4—222no—
750C4—222no—
751C4—441no—
752C4—441no—
753C4—442no—
754C4—881no—
755C4—881no—
756C4—881no—
757C4C2×#6693111yescharacteristic
758C4#1062301411yescharacteristic
759C4#1062311811yescharacteristic
760C4#1062312211yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1307228211yescharacteristic
765C2C2×#1062237211yescharacteristic
766C2#1307844911yescharacteristic
767C2#1308013011yescharacteristic
768C2#1308028611yescharacteristic
769C2#1308042211yescharacteristic
770C2#1308070111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenter#1786D11
hypocenterC11#25950
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#10622372C2semidirect
3. #13072319C2semidirect
5. #13070142C2semidirect
6. #13070002C2semidirect
7. #13070000C2semidirect
8. #13069750C2semidirect
9. #13068865C2semidirect
10. #13068861C2semidirect
11. #13068806C2semidirect
12. #13068793C2semidirect
13. #13068643C2semidirect
14. #13068614C2semidirect
22. C2×#66941C22semidirect
42. C2×#66882C22semidirect
43. C2×#66882C22semidirect
44. C2×Dic11⋊C8C22semidirect
45. C2×Dic11⋊C8C22semidirect
46. #10622598C22semidirect
47. #10622589C22semidirect
48. #10622586C22semidirect
49. C2×#66871C22semidirect
50. C2×#66871C22semidirect
55. #10622189C22semidirect
56. #10622189C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
68. C22×D4×C11Q8semidirect
295. D4×C11C22⋊Q8semidirect
413. C22×C11#474semidirect
444. C22×D4Dic22semidirect
627. C11#25950semidirect
666. D4#66931semidirect
738. C22#10622372semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C22×#668962
#130723192
D4×C22⋊Dic112
#130701422
#130700022
#130700002
#130697502
#130688652
#130688612
#130688062
#130687932
#130686432
#130686142
C11×#17862
#2595011