Finite Group Databasebeta

← #14810834

Subgroups — #14810834

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×#10622620C211yesmaximal, characteristic, complemented
2C2×D11×#102C211yesmaximal, characteristic
3#13072320C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13070141C211yesmaximal, characteristic, complemented
6#13070005C211yesmaximal, characteristic, complemented
7#13070001C211yesmaximal, characteristic, complemented
8#13069753C211yesmaximal, characteristic, complemented
9#13068861C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068644C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic
15C11×#1862C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×(C2×D11)⋊C4—21no—
20C22×C8×D11C2211yescharacteristic
21C2×#66949—21no—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66922C2211yescharacteristic, complemented
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#389C2211yescharacteristic, complemented
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622826—21no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic, complemented
35#10622620—24no—
36#10622601C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622592—21no—
40#10622589C2211yescharacteristic, complemented
41#10622586C2211yescharacteristic, complemented
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622571—21no—
48#10622568—21no—
49#10622552C2211yescharacteristic
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52D11×#102—24no—
53#10622281—21no—
54#10622270—21no—
55C11×#340C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×D4×D11—22no—
67C2×D4×D11—22no—
68C2×D4×D11—22no—
69C2×D4×D11—41no—
70C2×D4×D11—41no—
71C2×D4×D11Q814yescomplemented
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—21no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87D4×Dic11—22no—
88D4×Dic11—41no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×(C2×D11)⋊C4D411yescharacteristic
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×C8×D11—22no—
110C2×C8×D11—22no—
111C2×C8×D11—41no—
112#66949—44no—
113C4⋊C4×D11—22no—
114C4⋊C4×D11—41no—
115#66922—22no—
116#66922—41no—
117C11×#107—41no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#95—21no—
121#66896—22no—
122#66896D414yes—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66885—22no—
129#66885—41no—
130(C2×D11)⋊C8—22no—
131Dic11⋊C8—41no—
132#66873—22no—
133#66873—41no—
134#66871—22no—
135#66871—22no—
136#66871—41no—
137C4⋊(C11⋊C8)—22no—
138#25950—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C23×D11—24no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×Q812yes—
154C2×D4×C11#4112yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—81no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—24no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—81no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176D4×D11—28no—
177D4×D11—44no—
178D4×D11—44no—
179D4×D11—44no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44C2×Q812yes—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—81no—
193C2×C4×D11C2×Q812yes—
194C2×C4×D11#4112yes—
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×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C22⋊C4—42no—
212C42×C11—21no—
213C42×C11—21no—
214C22⋊Dic11—42no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—42no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4D814yes—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4⋊Dic11C2×D412yes—
230Dic11⋊C4—42no—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—81no—
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⋊C8C2×D412yes—
242C8×D11—44no—
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#1862D1111yescharacteristic, complemented
253#1852—111no—
254#1850—111no—
255#1808—111no—
256#1802—111no—
257#1786—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11C22×D411yescharacteristic
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—22no—
271C22×D11—48no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—48no—
279C22×D11—84no—
280C22×D11—84no—
281C22×D11—84no—
282C22×D11—84no—
283C22×D11—84no—
284C22×D11C22⋊Q812yes—
285C22×D11C2×D812yes—
286C22×D11#13712yes—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11C22⋊Q814yescomplemented
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—41no—
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—84no—
306C2×C4×C11C2×D812yes—
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×Q811yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C22⋊D11—48no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—84no—
331C2×Dic11C22⋊Q812yes—
332C2×Dic11C2×D812yes—
333D44—22no—
334D44—22no—
335D44—41no—
336D44—41no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—84no—
342Dic22—84no—
343C8×C11—41no—
344C8×C11—41no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C23×D4—111no—
348C23×C8—111no—
349C2×C4⋊Q8—111no—
350C2×C22⋊Q8—221no—
351C2×C4×D4—111no—
352C2×C4×D4C2×D1111yescharacteristic
353C22×C4⋊C4—111no—
354C22×C22⋊C4—221no—
355#474—224no—
356C2×#107—111no—
357C2×#107—111no—
358C2×#107—111no—
359C2×#107C2×D1111yescharacteristic, complemented
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—224no—
369C2×#102C2×D1111yescharacteristic
370C2×#102C2×D1111yescharacteristic
371C2×C22⋊C8—111no—
372#398—221no—
373#395—221no—
374#390—111no—
375#390—111no—
376#389—111no—
377#389C2×D1111yescharacteristic, complemented
378#386—221no—
379#386—221no—
380#385—221no—
381#384—111no—
382#380—111no—
383#380—111no—
384#379—221no—
385C4×C22⋊C4—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340C2×D1111yescharacteristic, complemented
390#336—111no—
391#336C2×D1111yescharacteristic, complemented
392C22×C11—24no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11C2×C22⋊Q811yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11C22×D811yescharacteristic
403C22×C11C2×#13711yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57711yescharacteristic
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—816no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11#47414yescomplemented
421C4×C11—22no—
422C4×C11—41no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11C2×C22⋊Q811yescharacteristic
427C4×C11#54311yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430Dic11—22no—
431Dic11—22no—
432Dic11—42no—
433Dic11—41no—
434Dic11—81no—
435Dic11—81no—
436C25—221no—
437C22×Q8—221no—
438C22×D4—114no—
439C22×D4—111no—
440C22×D4—222no—
441C22×D4—221no—
442C22×D4—222no—
443C22×D4—222no—
444C22×D4—441no—
445C22×D4—441no—
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—111no—
449C23×C4—221no—
450C23×C4—221no—
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—22no—
462C4×D4—41no—
463C4×D4—222no—
464C4×D4—441no—
465C2×C4⋊C4—21no—
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—441no—
476C2×C4⋊C4C22×D1111yescharacteristic
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×C42C22×D1111yescharacteristic
492#107—41no—
493#107—222no—
494#107—222no—
495#107—441no—
496C4⋊C8—222no—
497C4⋊C8—441no—
498#102—22no—
499#102—22no—
500#102—114no—
501#102—222no—
502#102—222no—
503#102—222no—
504#102—441no—
505#102—441no—
506C22⋊C8—222no—
507#95—21no—
508#95—111no—
509#95—111no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—44no—
514C2×C11#243711yescharacteristic
515C2×C11C2×#47411yescharacteristic
516C2×C11#308111yescharacteristic
517C2×C11#326611yescharacteristic
518C2×C11D4×D811yescharacteristic
519C2×C11#329411yescharacteristic
520C2×C11#331411yescharacteristic
521D11—24no—
522D11—82no—
523C24—21no—
524C24—111no—
525C24—224no—
526C24—221no—
527C24—442no—
528C24—442no—
529C24—442no—
530C24—442no—
531C24—881no—
532C24—881no—
533C2×Q8—442no—
534C2×Q8—442no—
535C2×Q8—881no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—112no—
540C2×D4—224no—
541C2×D4—228no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—444no—
548C2×D4—444no—
549C2×D4—444no—
550C2×D4—442no—
551C2×D4—442no—
552C2×D4#433912yes—
553C2×D4D4×D1112yes—
554C2×D4Q8×D1112yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—111no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—881no—
578C22×C4—881no—
579C22×C4D4×D1111yescharacteristic
580C22×C4D4×D1111yescharacteristic
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—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—112no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
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—21no—
624C42—21no—
625C42—221no—
626C42—221no—
627C11#2595011yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—112no—
636C23—112no—
637C23—112no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—222no—
643C23—448no—
644C23—448no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—884no—
652C23—884no—
653C23—884no—
654C23—884no—
655C23—884no—
656C23C2×D4×D1111yescharacteristic
657Q8—884no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—222no—
662D4—222no—
663D4—448no—
664D4—441no—
665D4—441no—
666D4#6694914yescomplemented
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—84no—
682C2×C4—112no—
683C2×C4—112no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—222no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—884no—
705C2×C4—884no—
706C2×C4D8×D1112yes—
707C2×C4C2×#433911yescharacteristic
708C2×C4C2×D4×D1111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4C2×Q8×D1111yescharacteristic
711C2×C4#41×D1111yescharacteristic
712C2×C4#6704211yescharacteristic
713C8—41no—
714C8—41no—
715C8—222no—
716C8—441no—
717C22—24no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—114no—
725C22—222no—
726C22—222no—
727C22—222no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—8816no—
735C22—881no—
736C22—881no—
737C22—881no—
738C22—881no—
739C22#1062308111yescharacteristic
740C22#1062312111yescharacteristic
741C22D11×C22⋊Q811yescharacteristic
742C22C2×D8×D1111yescharacteristic
743C22#1062330111yescharacteristic
744C22#1062330511yescharacteristic
745C22D11×#13711yescharacteristic
746C4—22no—
747C4—41no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—222no—
752C4—222no—
753C4—441no—
754C4—442no—
755C4—881no—
756C4—881no—
757C4C2×#6694911yescharacteristic
758C4#1062308711yescharacteristic
759C4#1062316511yescharacteristic
760C4#1062318511yescharacteristic
761C2—44no—
762C2—224no—
763C2—882no—
764C2#1307228111yescharacteristic
765C2D11×#47411yescharacteristic
766C2#1307844611yescharacteristic
767C2#1308012411yescharacteristic
768C2#1308028611yescharacteristic
769C2#1308043111yescharacteristic
770C2#1308070211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#1862D11
hypocenterC11#25950
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. C2×#10622620C2semidirect
3. #13072320C2semidirect
5. #13070141C2semidirect
6. #13070005C2semidirect
7. #13070001C2semidirect
8. #13069753C2semidirect
9. #13068861C2semidirect
10. #13068802C2semidirect
11. #13068795C2semidirect
12. #13068644C2semidirect
13. #13068614C2semidirect
15. C11×#1862C2semidirect
23. C2×#66922C22semidirect
24. C2×C11×#107C22semidirect
27. C11×#389C22semidirect
34. C2×Dic11⋊C8C22semidirect
40. #10622589C22semidirect
41. #10622586C22semidirect
44. C2×#66871C22semidirect
45. C2×#66871C22semidirect
46. C2×#66871C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
55. C11×#340C22semidirect
56. C11×#336C22semidirect
57. #10622189C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
71. C2×D4×D11Q8semidirect
252. #1862D11semidirect
290. D4×C11C22⋊Q8semidirect
359. C2×#107C2×D11semidirect
377. #389C2×D11semidirect
389. #340C2×D11semidirect
391. #336C2×D11semidirect
420. C2×D11#474semidirect
627. C11#25950semidirect
666. D4#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
C2×D11×#1022
#130723202
D4×(C2×D11)⋊C42
#130701412
#130700052
#130700012
#130697532
#130688612
#130688022
#130687952
#130686442
#130686142
#130685452
C11×#18622
#2595011