Finite Group Databasebeta

← #14765112

Subgroups — #14765112

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622345C211yesmaximal, characteristic
2#13071305C211yesmaximal, characteristic, complemented
3#13071196C211yesmaximal, characteristic, complemented
4#13069490C211yesmaximal, characteristic, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069311C211yesmaximal, characteristic, complemented
7#13069297C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic, complemented
9#13069235C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×D88C2211yescharacteristic
22C2×#66946C2211yescharacteristic, complemented
23C2×C11×#107C2211yescharacteristic, complemented
24C2×C11×#106C2211yescharacteristic, complemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2211yescharacteristic, complemented
31C2×C8×Dic11C2211yescharacteristic, complemented
32#10622601C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622601C2211yescharacteristic, complemented
37C4⋊C4×Dic11C2211yescharacteristic, complemented
38#10622586C2211yescharacteristic, complemented
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic, complemented
45#10622570—21no—
46#10622569—21no—
47#10622568—21no—
48#10622568—21no—
49#10622552—21no—
50#10622552—21no—
51#10622345C418yescomplemented
52#10622283—21no—
53#10622281—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60C24×D11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44—21no—
64C22×D44—22no—
65C22×D44—41no—
66C22×D44—41no—
67C22×D44—41no—
68C22×D44—41no—
69C22×D44C2×C414yescomplemented
70C22×D44C2311yescharacteristic
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C22⋊Dic11D411yescharacteristic
86C2×C22⋊Dic11D411yescharacteristic
87#66983—22no—
88#66983C2×C414yes—
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—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101#66979—41no—
102#66979—41no—
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11D411yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×D88—41no—
113C2×D88—41no—
114C2×D88—41no—
115C2×D88—41no—
116C2×D88C2×C414yes—
117C2×D88C2×C414yes—
118#66946—41no—
119#66946—41no—
120C11×#107—41no—
121C11×#106—41no—
122C11×C22⋊C8C2×C414yescomplemented
123C11×#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127#66885C2×C414yescomplemented
128#66885C2×C414yescomplemented
129#66879—41no—
130C8×Dic11—41no—
131#66873—41no—
132#66873—41no—
133#66873—41no—
134#66873—41no—
135#66873—41no—
136#66873—41no—
137#22056—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—81no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11—81no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—81no—
163C2×C22⋊D11—81no—
164C22×Dic11—21no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×D44—24no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—42no—
188C2×D44—42no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44C22×C412yes—
192C2×D44C22×C412yes—
193C2×D44C22×C412yes—
194C2×C4×D11—42no—
195C2×C4×D11—81no—
196C2×C4×D11—81no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11C22×C412yes—
202C2×C8×C11C22×C412yes—
203C11×C4⋊C4—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—21no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C42×C11—42no—
214C22⋊Dic11—41no—
215C22⋊Dic11—41no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—81no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4—81no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—41no—
230C4⋊Dic11—41no—
231C4⋊Dic11C22×C412yes—
232Dic11⋊C4—81no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—81no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244D88—44no—
245D88—44no—
246C2×#447—111no—
247#2324—111no—
248#2309—111no—
249#1972—111no—
250#1970—111no—
251#1936—111no—
252#1934—111no—
253#1926—111no—
254#1925—111no—
255#1879—111no—
256#1879—111no—
257#1875—111no—
258#1854D1111yescharacteristic, complemented
259#1786—111no—
260#1750—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11C4×D412yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—48no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11—84no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
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—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11C4×D412yes—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—84no—
323C2×Dic11—22no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338D44—22no—
339D44—22no—
340D44—22no—
341D44—22no—
342D44—22no—
343D44—22no—
344D44—48no—
345D44—41no—
346D44—41no—
347D44—41no—
348D44—41no—
349D44—41no—
350D44—41no—
351C4×D11—84no—
352C8×C11—22no—
353C8×C11—22no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C23×D4—111no—
357C22×D8—111no—
358C22×D8—111no—
359C2×#121—111no—
360C2×C4×D4—111no—
361C2×#117—111no—
362C2×#117C2×D1111yescharacteristic
363#447—118no—
364C2×#107C2×D1111yescharacteristic, complemented
365C2×#106C2×D1111yescharacteristic, complemented
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8C2×D1111yescharacteristic
376C2×#97—111no—
377C2×C4×C8—111no—
378#390—111no—
379#390—111no—
380#390—111no—
381#390—111no—
382#390—111no—
383#390—221no—
384#390—221no—
385#390—221no—
386#389—111no—
387#388—221no—
388#386—221no—
389#385—221no—
390#380C2×D1111yescharacteristic
391#379—221no—
392#379—221no—
393C4×C4⋊C4—111no—
394#340—111no—
395#340—111no—
396#340C2×D1111yescharacteristic, complemented
397#340C2×D1111yescharacteristic, complemented
398#336—111no—
399#336—111no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11C2×C4×D411yescharacteristic
408C22×C11#53411yescharacteristic
409C22×C11#53511yescharacteristic
410C22×C11#57611yescharacteristic
411C22×C11#57611yescharacteristic
412C22×C11#57611yescharacteristic
413C22×C11#57711yescharacteristic
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—816no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—22no—
437C4×C11—81no—
438C4×C11—81no—
439C4×C11—81no—
440C4×C11—81no—
441C4×C11#51811yescharacteristic
442C4×C11#51811yescharacteristic
443C4×C11#53811yescharacteristic
444C4×C11#53811yescharacteristic
445Dic11—41no—
446Dic11—41no—
447Dic11—41no—
448Dic11—41no—
449Dic11—42no—
450C25—221no—
451C22×D4—114no—
452C22×D4—111no—
453C22×D4—111no—
454C22×D4—111no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4—222no—
458C22×D4—441no—
459C22×D4—441no—
460C22×D4—441no—
461C22×D4—441no—
462C23×C4—221no—
463C23×C4C22×D1111yescharacteristic
464C2×D8—114no—
465C2×D8—114no—
466C2×D8—441no—
467C2×D8—441no—
468C2×D8—441no—
469C2×D8—441no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8C22×D1111yescharacteristic
473C22×C8C22×D1111yescharacteristic
474#121—114no—
475#121—222no—
476C4×D4—441no—
477C4×D4—441no—
478#117—41no—
479#117—41no—
480#117—441no—
481#117—441no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C42—21no—
507C2×C42—111no—
508C2×C42—111no—
509C2×C42—221no—
510#107—41no—
511#106—41no—
512#102—114no—
513#102—114no—
514#102—441no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519#102—441no—
520C22⋊C8—222no—
521C22⋊C8C4×D1114yescomplemented
522#97—441no—
523C4×C8—441no—
524#95—21no—
525#95—221no—
526#95—221no—
527C2×C11—42no—
528C2×C11#232111yescharacteristic
529C2×C11#294611yescharacteristic
530C2×C11#294811yescharacteristic
531C2×C11#319811yescharacteristic
532C2×C11#319911yescharacteristic
533C2×C11#322011yescharacteristic
534C2×C11#322411yescharacteristic
535D11—82no—
536D11—82no—
537D11—82no—
538C24—221no—
539C24—221no—
540C24—221no—
541C24—224no—
542C24—442no—
543C24—442no—
544C24—881no—
545C24—881no—
546C24—881no—
547C24—881no—
548C24D4×D1111yescharacteristic
549C2×D4—112no—
550C2×D4—112no—
551C2×D4—112no—
552C2×D4—224no—
553C2×D4—224no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—442no—
572C2×D4—442no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—881no—
576C2×D4—881no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—221no—
590C22×C4—442no—
591C22×C4—881no—
592C22×C4—881no—
593C22×C4C2×C4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4#434312yes—
596C22×C4C23×D1111yescharacteristic
597D8—444no—
598D8—444no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8C2×C4×D1112yes—
610C2×C8C2×C4×D1112yes—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—112no—
620C4⋊C4—221no—
621C4⋊C4—441no—
622C4⋊C4—441no—
623C4⋊C4—881no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—224no—
627C22⋊C4—442no—
628C22⋊C4—441no—
629C22⋊C4—441no—
630C22⋊C4—881no—
631C22⋊C4—881no—
632C22⋊C4—881no—
633C22⋊C4—881no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C22⋊C4—881no—
638C22⋊C4—881no—
639C22⋊C4—881no—
640C42—42no—
641C42—221no—
642C42—221no—
643C42—221no—
644C42—221no—
645C42—881no—
646C11#2205611yescharacteristic, complemented, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—222no—
654C23—222no—
655C23—222no—
656C23—448no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—884no—
676C23—884no—
677C23—884no—
678C23—884no—
679C23—884no—
680C23—884no—
681C23#6694612yes—
682C23C2×D4×D1111yescharacteristic
683D4—222no—
684D4—222no—
685D4—222no—
686D4—222no—
687D4—222no—
688D4—222no—
689D4—448no—
690D4—441no—
691D4—441no—
692D4—441no—
693D4—441no—
694D4—441no—
695D4—441no—
696D4—884no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—222no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—884no—
731C2×C4#6694612yes—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4#6703711yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4C2×#434311yescharacteristic
736C2×C4#6704211yescharacteristic
737C2×C4#6704211yescharacteristic
738C8—22no—
739C8—22no—
740C8—441no—
741C8—441no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—442no—
758C22—8816no—
759C22—881no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22C2×#6694611yescharacteristic
772C22#1062312311yescharacteristic
773C22#1062318411yescharacteristic
774C22#1062330011yescharacteristic
775C22#1062330011yescharacteristic
776C22#1062330511yescharacteristic
777C22#1062330911yescharacteristic
778C4—22no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—441no—
784C4—441no—
785C4—441no—
786C4—441no—
787C4—442no—
788C4#1062307611yescharacteristic
789C4#1062307611yescharacteristic
790C4#1062317511yescharacteristic
791C4#1062317511yescharacteristic
792C2—42no—
793C2—882no—
794C2—882no—
795C2—882no—
796C2#1307127311yescharacteristic
797C2#1307744611yescharacteristic
798C2#1307746711yescharacteristic
799C2#1307947411yescharacteristic
800C2#1307948011yescharacteristic
801C2#1307966411yescharacteristic
802C2#1307971611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. #13071305C2semidirect
3. #13071196C2semidirect
4. #13069490C2semidirect
5. #13069480C2semidirect
6. #13069311C2semidirect
7. #13069297C2semidirect
8. #13069242C2semidirect
9. #13069235C2semidirect
10. #13068965C2semidirect
11. #13068965C2semidirect
12. #13068938C2semidirect
13. #13068546C2semidirect
14. #13068384C2semidirect
15. C11×#1854C2semidirect
22. C2×#66946C22semidirect
23. C2×C11×#107C22semidirect
24. C2×C11×#106C22semidirect
30. C2×#66879C22semidirect
31. C2×C8×Dic11C22semidirect
36. #10622601C22semidirect
37. C4⋊C4×Dic11C22semidirect
38. #10622586C22semidirect
43. C2×#66873C22semidirect
44. C2×#66873C22semidirect
51. #10622345C4semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
69. C22×D44C2×C4semidirect
122. C11×C22⋊C8C2×C4semidirect
127. #66885C2×C4semidirect
128. #66885C2×C4semidirect
258. #1854D11semidirect
364. C2×#107C2×D11semidirect
365. C2×#106C2×D11semidirect
396. #340C2×D11semidirect
397. #340C2×D11semidirect
521. C22⋊C8C4×D11semidirect
646. C11#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#106223452
#130713052
#130711962
#130694902
#130694802
#130693112
#130692972
#130692422
#130692352
#130689652
#130689382
#130685462
#130683842
C11×#18542
#2205611