Finite Group Databasebeta

← #14792560

Subgroups — #14792560

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13071196C211yesmaximal, characteristic, complemented
4#13070001C211yesmaximal, characteristic, complemented
5#13069987C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069491C211yesmaximal, characteristic, complemented
9#13069481C211yesmaximal, characteristic, complemented
10#13069312C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13068939C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068546C211yesmaximal, characteristic, complemented
15C11×#2624C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C11×#399—21no—
23C11×#397—21no—
24C11×#394—21no—
25C11×#394—21no—
26C11×#390C2211yescharacteristic, complemented
27C11×#390C2211yescharacteristic, complemented
28C11×#389C2211yescharacteristic, complemented
29C11×#389C2211yescharacteristic, complemented
30C11×#380C2211yescharacteristic
31C2×#66896C2211yescharacteristic, complemented
32C2×#66896C2211yescharacteristic, complemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622649—24no—
36#10622613—24no—
37#10622601—21no—
38#10622601—21no—
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622568—21no—
48#10622568—21no—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622552C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66867C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C11×#121—22no—
75C11×#121—22no—
76C11×#117—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×#4323—22no—
97C2×#4323—22no—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—41no—
101C2×#4323—41no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110#66979—41no—
111#66979—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4×Dic11—21no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122#66896—41no—
123#66896—41no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)D414yes—
126#66873—22no—
127#66873—22no—
128#66873—22no—
129#66873—22no—
130#66873—41no—
131#66873—41no—
132#66872—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138#24512—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11—81no—
149C23×D11—81no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—42no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—21no—
175C22×Dic11—21no—
176C2×D44—24no—
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—21no—
186C2×D44—21no—
187C2×D44—44no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44#4112yes—
194C2×D44#4112yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—81no—
204C11×C4⋊C4—81no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C22⋊Dic11—42no—
218#4323—44no—
219#4323—44no—
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—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4×Dic11—42no—
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⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×#447—111no—
246C2×#433—111no—
247#2624D1111yescharacteristic, complemented
248#2309—111no—
249#2067—111no—
250#2065—111no—
251#2054—111no—
252#2054—111no—
253#1972—111no—
254#1970—111no—
255#1936—111no—
256#1934—111no—
257#1875—111no—
258#1854—111no—
259#1786—111no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11#12112yes—
274C23×C11C22×D411yescharacteristic
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—48no—
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—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11—84no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11#12112yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341D44—22no—
342D44—22no—
343D44—22no—
344D44—22no—
345D44—48no—
346D44—41no—
347D44—41no—
348D44—41no—
349D44—41no—
350C11⋊C8—22no—
351C11⋊C8—22no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C23×D4—111no—
355C22×D8—111no—
356C22×D8—111no—
357C2×#121C2×D1111yescharacteristic
358C2×#117—111no—
359C2×#117C2×D1111yescharacteristic
360#447—224no—
361#433—224no—
362C2×#107—111no—
363C2×#106—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
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⋊C8—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378#399—21no—
379#397—21no—
380#394—21no—
381#394—21no—
382#390—111no—
383#390—111no—
384#390—111no—
385#390—111no—
386#390—221no—
387#390—221no—
388#390C2×D1111yescharacteristic, complemented
389#390C2×D1111yescharacteristic, complemented
390#389C2×D1111yescharacteristic, complemented
391#389C2×D1111yescharacteristic, complemented
392#380C2×D1111yescharacteristic
393#379—221no—
394#379—221no—
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11C2×#12111yescharacteristic
414C22×C11#52511yescharacteristic
415C22×C11#53511yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57611yescharacteristic
418C22×C11#57611yescharacteristic
419C22×C11#57711yescharacteristic
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—816no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C4×C11—22no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—81no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11#54611yescharacteristic
444C4×C11#54611yescharacteristic
445C4×C11#55111yescharacteristic
446C4×C11#55111yescharacteristic
447Dic11—81no—
448Dic11—81no—
449C25—221no—
450C22×D4—21no—
451C22×D4—111no—
452C22×D4—111no—
453C22×D4—222no—
454C22×D4—222no—
455C22×D4—222no—
456C22×D4—222no—
457C22×D4—221no—
458C22×D4—441no—
459C22×D4—441no—
460C22×D4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C2×D8—222no—
463C2×D8—222no—
464C2×D8—222no—
465C2×D8—222no—
466C2×D8—441no—
467C2×D8—441no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472#121—22no—
473#121—22no—
474#117—22no—
475#117—22no—
476#117—441no—
477#117—441no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4C22⋊D1111yescharacteristic
483C2×C4⋊C4C22⋊D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—221no—
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⋊C4C22⋊D1111yescharacteristic
503C2×C22⋊C4C22⋊D1111yescharacteristic
504C2×C42—221no—
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1111yescharacteristic
507#107—441no—
508#106—441no—
509C4⋊C8—222no—
510C4⋊C8—222no—
511#102—222no—
512#102—222no—
513#102—222no—
514#102—222no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519C22⋊C8—114no—
520C22⋊C8—222no—
521#97—222no—
522C4×C8—222no—
523#95—21no—
524#95—21no—
525#95—21no—
526C2×C11—42no—
527C2×C11—161no—
528C2×C11#241111yescharacteristic
529C2×C11#305811yescharacteristic
530C2×C11#306211yescharacteristic
531C2×C11#311811yescharacteristic
532C2×C11#312211yescharacteristic
533C2×C11#322011yescharacteristic
534C2×C11#322411yescharacteristic
535D11—82no—
536D11—82no—
537C24—21no—
538C24—224no—
539C24—221no—
540C24—221no—
541C24—442no—
542C24—442no—
543C24—881no—
544C24—881no—
545C24—881no—
546C24—881no—
547C24C2×C22⋊D1111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—112no—
558C2×D4—112no—
559C2×D4—224no—
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—221no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—444no—
574C2×D4—442no—
575C2×D4—442no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4D4×D1112yes—
586C22×C4#434112yes—
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C23×D1111yescharacteristic
593D8—444no—
594D8—444no—
595C2×C8—112no—
596C2×C8—112no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—81no—
616C4⋊C4—81no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—442no—
630C22⋊C4—881no—
631C22⋊C4—881no—
632C22⋊C4—881no—
633C22⋊C4—881no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C22⋊C4—881no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—442no—
643C11#2451211yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—222no—
658C23—222no—
659C23—448no—
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—884no—
673C23—884no—
674C23—884no—
675C23—884no—
676C23—884no—
677C23—884no—
678C23#6699212yes—
679C23C22×C22⋊D1111yescharacteristic
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—222no—
686D4—222no—
687D4—222no—
688D4—222no—
689D4—448no—
690D4—441no—
691D4—441no—
692D4—441no—
693D4—441no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4#6699212yes—
728C2×C4C2×D4×D1111yescharacteristic
729C2×C4C2×#434111yescharacteristic
730C2×C4#41×D1111yescharacteristic
731C2×C4#41×D1111yescharacteristic
732C2×C4#6704211yescharacteristic
733C2×C4#6704211yescharacteristic
734C8—222no—
735C8—222no—
736C8—441no—
737C8—441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
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—
767C22C2×#6699211yescharacteristic
768C22#1062335911yescharacteristic
769C22#1062336111yescharacteristic
770C22#1062336611yescharacteristic
771C22#1062336611yescharacteristic
772C22#1062336611yescharacteristic
773C22#1062336811yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—881no—
783C4—881no—
784C4#1062318511yescharacteristic
785C4#1062318511yescharacteristic
786C4#1062318911yescharacteristic
787C4#1062318911yescharacteristic
788C2—42no—
789C2—161no—
790C2—882no—
791C2—882no—
792C2#1307200211yescharacteristic
793C2#1307826111yescharacteristic
794C2#1307829811yescharacteristic
795C2#1307879411yescharacteristic
796C2#1307885411yescharacteristic
797C2#1307966011yescharacteristic
798C2#1307970411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2624C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenter#2624D11
hypocenterC11#24512
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
3. #13071196C2semidirect
4. #13070001C2semidirect
5. #13069987C2semidirect
6. #13069926C2semidirect
7. #13069926C2semidirect
8. #13069491C2semidirect
9. #13069481C2semidirect
10. #13069312C2semidirect
11. #13069298C2semidirect
12. #13068939C2semidirect
13. #13068813C2semidirect
14. #13068546C2semidirect
15. C11×#2624C2semidirect
26. C11×#390C22semidirect
27. C11×#390C22semidirect
28. C11×#389C22semidirect
29. C11×#389C22semidirect
31. C2×#66896C22semidirect
32. C2×#66896C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
55. C2×#66867C22semidirect
56. C2×C4×C11⋊C8C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
247. #2624D11semidirect
388. #390C2×D11semidirect
389. #390C2×D11semidirect
390. #389C2×D11semidirect
391. #389C2×D11semidirect
643. C11#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106226132
#130711962
#130700012
#130699872
#130699262
#130694912
#130694812
#130693122
#130692982
#130689392
#130688132
#130685462
C11×#26242
#2451211