Finite Group Databasebeta

← #14786730

Subgroups — #14786730

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3#13072913C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic, complemented
6#13069802C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068884C211yesmaximal, characteristic, complemented
11#13068870C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#550C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#550—24no—
19C11×#550—24no—
20C2×C11×#127—21no—
21C2×C11×#127C2211yescharacteristic
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C23×C11⋊C8C2211yescharacteristic
31#10622846—24no—
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622835—21no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45#10622825C2211yescharacteristic
46#10622825C2211yescharacteristic
47#10622825C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622648—24no—
52#10622591—21no—
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622565—21no—
56#10622557—21no—
57#10622541C2211yescharacteristic
58#10622541C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41D414yes—
75C22×Q8×C11C2311yescharacteristic
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C11×#127—28no—
90C11×#127—22no—
91C11×#127—22no—
92C11×#121—28no—
93C11×#121—28no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121D414yes—
98C4×Q8×C11—22no—
99C4×Q8×C11—22no—
100C4×D4×C11—28no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66979—22no—
117#66979—22no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132#66899—22no—
133#66899—22no—
134#66899—22no—
135#66899—22no—
136#66896—22no—
137#66896—22no—
138#66896—22no—
139#66896—22no—
140#66896—41no—
141#66896—41no—
142#66896—41no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C22⋊(C11⋊C8)—22no—
150C22⋊(C11⋊C8)—41no—
151C22⋊(C11⋊C8)—41no—
152#66872—22no—
153#66871—22no—
154#24034—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C11×#41—44no—
164C11×#41—44no—
165C11×#41—44no—
166C11×#41—44no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11C2×D412yes—
171C2×Q8×C11#4112yes—
172C2×Q8×C11#4112yes—
173C2×D4×C11—24no—
174C2×D4×C11—24no—
175C2×D4×C11—22no—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—24no—
180C2×D4×C11—22no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—41no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—81no—
199C2×D4×C11—81no—
200C2×D4×C11—81no—
201C2×D4×C11—81no—
202C2×D4×C11—81no—
203C2×D4×C11—81no—
204C2×D4×C11C2×D412yes—
205C2×D4×C11C2×D412yes—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—24no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4C2×D412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—22no—
243C42×C11—24no—
244C42×C11—21no—
245C42×C11—21no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—81no—
249C22⋊Dic11—81no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258Dic11⋊C4—42no—
259Dic11⋊C4—81no—
260C4×Dic11—42no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—44no—
274C2×#550D1111yescharacteristic
275C2×#482—111no—
276C2×#416—111no—
277#2485—111no—
278#2041—111no—
279#2041—111no—
280#2034—111no—
281#2033—111no—
282#1893—111no—
283#1869—111no—
284#1865—111no—
285#1863—111no—
286#1788—111no—
287#1788—111no—
288#1788—111no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11#12012yes—
317C23×C11C22×D411yescharacteristic
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11#12314yes—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—22no—
326D4×C11—44no—
327D4×C11—48no—
328D4×C11—48no—
329D4×C11—48no—
330D4×C11—41no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—84no—
335D4×C11—84no—
336D4×C11—84no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—48no—
356C2×C4×C11—48no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11#12012yes—
364C2×C4×C11#13512yes—
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C2×#4111yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×C4×C11H(5,𝔽2)11yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C11⋊C8—41no—
384C11⋊C8—41no—
385C11⋊C8—41no—
386C11⋊C8—41no—
387C22×#41C2×D1111yescharacteristic
388C22×#41C2×D1111yescharacteristic
389C23×C8—111no—
390#550—24no—
391#550—24no—
392C2×#127—21no—
393C2×#127C2×D1111yescharacteristic
394C2×#121—21no—
395C2×#121—21no—
396C2×#121C2×D1111yescharacteristic
397C2×#121C2×D1111yescharacteristic
398C2×C4×Q8C2×D1111yescharacteristic
399C2×C4×D4—21no—
400C2×C4×D4C2×D1111yescharacteristic
401C2×#117—111no—
402#482—224no—
403C2×#107—111no—
404C2×#106—111no—
405#416—224no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421#397—221no—
422#394—221no—
423#389—111no—
424#389—111no—
425#388—221no—
426#387—221no—
427#380—111no—
428#380—111no—
429#380—111no—
430#340—111no—
431#340—111no—
432#336—111no—
433#336—111no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11C2×#12011yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11C2×#13511yescharacteristic
466C22×C11#57511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C4×C11—22no—
470C4×C11—24no—
471C4×C11—22no—
472C4×C11—41no—
473C4×C11—41no—
474C4×C11—42no—
475C4×C11C2×#12311yescharacteristic
476C4×C11#53411yescharacteristic
477C4×C11#54611yescharacteristic
478C4×C11#54611yescharacteristic
479Dic11—81no—
480Dic11—81no—
481Dic11—81no—
482Dic11—81no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41C22⋊D1114yes—
495C22×Q8C22×D1111yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C22⋊D1111yescharacteristic
503C22×D4C22×D1111yescharacteristic
504C22×D4C22×D1111yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512C22×C8—111no—
513C22×C8—222no—
514C22×C8—441no—
515C22×C8—441no—
516#127—28no—
517#127—22no—
518#127—22no—
519#121—28no—
520#121—28no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121C22⋊D1114yes—
525C4×Q8—22no—
526C4×Q8—22no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530#117—222no—
531#117—222no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4C22⋊D1111yescharacteristic
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4C22⋊D1111yescharacteristic
548C2×C22⋊C4C22⋊D1111yescharacteristic
549C2×C42—21no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552#107—222no—
553#106—222no—
554#103—222no—
555#103—222no—
556#103—222no—
557#103—222no—
558#102—222no—
559#102—222no—
560#102—222no—
561#102—222no—
562#102—441no—
563#102—441no—
564#102—441no—
565#102—441no—
566C22⋊C8—222no—
567C22⋊C8—441no—
568C22⋊C8—441no—
569#95—221no—
570#95—221no—
571#95—221no—
572#95—221no—
573#95—221no—
574C2×C11—42no—
575C2×C11—81no—
576C2×C11—82no—
577C2×C11—82no—
578C2×C11#240511yescharacteristic
579C2×C11#300211yescharacteristic
580C2×C11#301211yescharacteristic
581C2×C11#330411yescharacteristic
582C2×C11#330511yescharacteristic
583C2×C11#330911yescharacteristic
584C2×C11#331711yescharacteristic
585C24—21no—
586C24—21no—
587C24C2×C22⋊D1111yescharacteristic
588C24C2×C22⋊D1111yescharacteristic
589#41—28no—
590#41—44no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8#434112yes—
601C2×Q8#434112yes—
602C2×Q8C2×C22⋊D1112yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—41no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4C2×C22⋊D1112yes—
635C2×D4C2×C22⋊D1112yes—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4C2×C22⋊D1111yescharacteristic
659C22×C4C2×C22⋊D1111yescharacteristic
660C22×C4C2×C22⋊D1111yescharacteristic
661C22×C4C2×C22⋊D1111yescharacteristic
662C22×C4C2×C22⋊D1112yes—
663C22×C4C2×C22⋊D1112yes—
664C22×C4C23×D1111yescharacteristic
665C2×C8—221no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—444no—
678C4⋊C4—24no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—221no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4—221no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—442no—
690C4⋊C4—881no—
691C4⋊C4C2×C22⋊D1112yes—
692C22⋊C4—24no—
693C22⋊C4—22no—
694C22⋊C4—24no—
695C22⋊C4—22no—
696C22⋊C4—442no—
697C22⋊C4—442no—
698C22⋊C4—881no—
699C22⋊C4—881no—
700C42—24no—
701C42—21no—
702C42—21no—
703C42—442no—
704C11#2403411yescharacteristic, complemented, Sylow
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#6700612yes—
733C23C22×C22⋊D1111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#6698814yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—441no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4#6700312yes—
792C2×C4#6700612yes—
793C2×C4C2×#434111yescharacteristic
794C2×C4C2×#434111yescharacteristic
795C2×C4#6703711yescharacteristic
796C2×C4#6703711yescharacteristic
797C2×C4C22×C22⋊D1111yescharacteristic
798C2×C4C22×C22⋊D1111yescharacteristic
799C8—441no—
800C8—441no—
801C8—441no—
802C8—441no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22#1062333711yescharacteristic
832C22#1062333711yescharacteristic
833C22C2×#6700311yescharacteristic
834C22#1062335311yescharacteristic
835C22#1062336611yescharacteristic
836C22#1062336711yescharacteristic
837C22C2×#6700611yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—881no—
845C4—881no—
846C4—881no—
847C4—881no—
848C4C2×#6698811yescharacteristic
849C4#1062333511yescharacteristic
850C4#1062333711yescharacteristic
851C4#1062333711yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2#1307193911yescharacteristic
857C2#1307783411yescharacteristic
858C2#1307792011yescharacteristic
859C2#1308055511yescharacteristic
860C2#1308056611yescharacteristic
861C2#1308062211yescharacteristic
862C2#1308074211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#24034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622648C2semidirect
2. C2×#10622846C2semidirect
3. #13072913C2semidirect
4. #13069847C2semidirect
5. #13069847C2semidirect
6. #13069802C2semidirect
7. #13069795C2semidirect
8. #13069045C2semidirect
9. #13068909C2semidirect
10. #13068884C2semidirect
11. #13068870C2semidirect
12. #13068556C2semidirect
13. #13068556C2semidirect
14. #13068556C2semidirect
704. C11#24034semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
C2×#106228462
#130729132
#130698472
#130698022
#130697952
#130690452
#130689092
#130688842
#130688702
#130685562
C2×C11×#5502
#2403411