Finite Group Databasebeta

← C2×#13079379 #15624305

Subgroups — C2×#13079379 #15624305

Order 2816.

2718 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079379C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622648C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622770C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C22×D4×D11—21no—
19C22×D4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×D8C2211yescharacteristic, complemented
23C2×C11×#121C2211yescharacteristic
24#10623359—24no—
25#10623359C2218yescomplemented
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic, complemented
29C2×#66992—21no—
30C2×#66991C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic, complemented
33C2×#66990—21no—
34C2×#66988—21no—
35C22×#4323C2211yescharacteristic, complemented
36C2×#66983C2211yescharacteristic
37C2×C4×C22⋊D11—21no—
38C2×C4×C22⋊D11—21no—
39C2×#66979C2211yescharacteristic, complemented
40C22×C8×D11C2211yescharacteristic, complemented
41C22×C8×D11C2211yescharacteristic, complemented
42D11×#121—24no—
43D11×#121C2218yescomplemented
44C2×#66948C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937—21no—
47C2×C22⋊C4×D11—21no—
48C11×#449C2218yescomplemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic, complemented
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
58#10622784C2218yescomplemented
59#10622782C2218yescomplemented
60#10622770C2218yescomplemented
61#10622769C2218yescomplemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66885C2211yescharacteristic, complemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66882C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68#10622648C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622422C2218yescomplemented
72#10622420C2218yescomplemented
73#10622390C2218yescomplemented
74#10622388C2218yescomplemented
75#10622350C2218yescomplemented
76D11×C22⋊C8C2218yescomplemented
77C24×D11—21no—
78C24×D11D411yescharacteristic
79C2×C11×#41—22no—
80C2×C11×#41—42no—
81C2×C11×#41—42no—
82C2×C11×#41C2314yescomplemented
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C23×Dic11D411yescharacteristic
96C2×D4×D11—28no—
97C2×D4×D11—22no—
98C2×D4×D11—42no—
99C2×D4×D11—42no—
100C2×D4×D11—48no—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11—42no—
106C22×C4×D11—42no—
107C22×C4×D11D411yescharacteristic
108C22×C4×D11D411yescharacteristic
109C22×C4×D11D414yes—
110C22×C4×D11C2311yescharacteristic
111C22×C4×D11C2311yescharacteristic
112C22×C4×D11C2314yes—
113C2×C11×SD16—42no—
114C2×C11×SD16C2314yescomplemented
115C2×C11×D8—42no—
116C2×C11×D8C2314yescomplemented
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2311yescharacteristic
119C11×#121—22no—
120C11×#121C2314yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127#66999—22no—
128#66999—22no—
129#66999C2314yes—
130#66999C2314yescomplemented
131C2×#4325—42no—
132C2×#4325C2314yescomplemented
133#66992—28no—
134#66991—22no—
135#66991—22no—
136#66991—22no—
137#66991C2314yes—
138#66991C2314yes—
139#66991C2314yescomplemented
140#66990—28no—
141#66988—28no—
142C2×#4323—42no—
143C2×#4323C2314yescomplemented
144#66983—22no—
145#66983C2314yes—
146C4×C22⋊D11—28no—
147C4×C22⋊D11—28no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152#66979—22no—
153#66979C2314yescomplemented
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×Dic11⋊C4—21no—
160C2×C4×Dic11—21no—
161C22×C11⋊C8C2311yescharacteristic
162C22×C11⋊C8C2311yescharacteristic
163C2×C8×D11—42no—
164C2×C8×D11—42no—
165C2×C8×D11C2314yescomplemented
166C2×C8×D11C2314yescomplemented
167#66948—22no—
168#66948C2314yes—
169C4⋊C4×D11—22no—
170C4⋊C4×D11C2314yes—
171#66937—28no—
172C22⋊C4×D11—28no—
173C11×#103C2314yescomplemented
174C11×#102C2314yescomplemented
175C11×C22⋊C8C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yescomplemented
178#66896C2314yescomplemented
179#66896C2314yescomplemented
180C22⋊(C11⋊C8)C2314yescomplemented
181#66885C2314yescomplemented
182#66885C2314yescomplemented
183(C2×D11)⋊C8C2314yes—
184(C2×D11)⋊C8C2314yes—
185#66882C2314yescomplemented
186#66881C2314yescomplemented
187#66872C2314yescomplemented
188#66871C2314yescomplemented
189C2×#3188—111nomaximal, Sylow
190C24×C11—21no—
191C24×C11—21no—
192C24×C11C2×D411yescharacteristic
193C23×D11—24no—
194C23×D11—24no—
195C23×D11—21no—
196C23×D11—24no—
197C23×D11—42no—
198C23×D11—44no—
199C23×D11—44no—
200C23×D11—44no—
201C23×D11C2×D414yes—
202C23×D11C2×D411yescharacteristic
203C23×D11C2×D411yescharacteristic
204C11×#41—44no—
205C11×#41—44no—
206C11×#41—48no—
207C2×Q8×C11—21no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11C2412yes—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—21no—
214C2×D4×C11—21no—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11C2412yes—
222C2×D4×C11C2412yes—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—24no—
228C22×C4×C11—44no—
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2411yescharacteristic
233C2×C22⋊D11—24no—
234C2×C22⋊D11—24no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—42no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249C22×Dic11C2×D414yes—
250D4×D11—44no—
251D4×D11—44no—
252D4×D11—432no—
253D4×D11—48no—
254C2×D44—24no—
255C2×D44—21no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—44no—
259C2×D44C2412yes—
260C2×C4×D11—24no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—42no—
266C2×C4×D11—42no—
267C2×C4×D11—48no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2×D412yes—
273C2×C4×D11C2×D414yes—
274C2×C4×D11C2×D414yes—
275C2×C4×D11C2412yes—
276C2×C4×D11C2412yes—
277C11×SD16—44no—
278C11×D8—44no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2412yes—
285C11×C22⋊C4—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11—24no—
289C22⋊Dic11—24no—
290#4325—44no—
291#4323—44no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296C4⋊Dic11—21no—
297C4⋊Dic11—21no—
298C4⋊Dic11—21no—
299C4⋊Dic11C2412yes—
300C4⋊Dic11C2412yes—
301C4⋊Dic11C2412yes—
302Dic11⋊C4—24no—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305C4×Dic11—24no—
306C2×C11⋊C8—22no—
307C2×C11⋊C8—22no—
308C2×C11⋊C8C2412yes—
309C2×C11⋊C8C2412yes—
310C8×D11—44no—
311C8×D11—44no—
312C2×#525—111no—
313C22×#121—111no—
314#3188—1116no—
315C2×#484—111no—
316C2×#481—111no—
317C2×#482—111no—
318C2×#482—111no—
319C2×#466—111no—
320C2×#466—111no—
321C2×#465—111no—
322C2×#465—111no—
323C2×#449—111no—
324C2×#449D1111yescharacteristic, complemented
325C2×#450—111no—
326C2×#447—111no—
327C22×C22⋊C8—111no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11C22×D412yes—
340C23×C11C22×D411yescharacteristic
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—416no—
350C22×D11—48no—
351C22×D11—48no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—48no—
356C22×D11—816no—
357C22×D11#13514yes—
358C22×D11AGL(1,ℤ/8)14yes—
359C22×D11C22×D412yes—
360C22×D11C22×D412yes—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—42no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—48no—
369D4×C11—48no—
370D4×C11—42no—
371D4×C11—42no—
372C2×C4×C11—22no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—48no—
379C2×C4×C11—42no—
380C2×C4×C11—42no—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11H(5,𝔽2)12yes—
384C2×C4×C11H(5,𝔽2)12yes—
385C2×C4×C11C2511yescharacteristic
386C22⋊D11—48no—
387C22⋊D11—48no—
388C22⋊D11—48no—
389C22⋊D11—48no—
390C22⋊D11—48no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—44no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402D44—22no—
403D44—22no—
404D44—48no—
405D44—42no—
406C4×D11—24no—
407C4×D11—24no—
408C4×D11—22no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—22no—
412C4×D11—44no—
413C4×D11—44no—
414C4×D11—48no—
415C8×C11—22no—
416C8×C11—22no—
417C11⋊C8—22no—
418C11⋊C8—22no—
419C22×#41C2×D1111yescharacteristic, complemented
420C23×D4—111no—
421C23×D4—221no—
422C24×C4—111no—
423C22×SD16—111no—
424C22×SD16C2×D1111yescharacteristic, complemented
425C22×D8—111no—
426C22×D8C2×D1111yescharacteristic, complemented
427C23×C8—111no—
428C23×C8—111no—
429#525—118no—
430#525—224no—
431C2×#123—221no—
432C2×C22⋊Q8—111no—
433C2×C22⋊Q8—111no—
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—111no—
437C2×#121—111no—
438C2×#121—118no—
439C2×#121—111no—
440C2×#121—221no—
441C2×#121—224no—
442C2×#121—221no—
443C2×#121C2×D1111yescharacteristic
444C2×#120—221no—
445C2×C4×D4—221no—
446C2×C4×D4—221no—
447C2×#117—111no—
448C22×C4⋊C4—111no—
449C22×C22⋊C4—221no—
450#484—118no—
451#482—118no—
452#482—118no—
453#481—118no—
454#466—118no—
455#466—118no—
456#465—118no—
457#465—118no—
458#450—118no—
459#449—118no—
460#449C2×D1118yescomplemented
461#447—118no—
462C2×#107—111no—
463C2×#107—111no—
464C2×#106—111no—
465C2×#106—111no—
466C2×#103—111no—
467C2×#103C2×D1111yescharacteristic, complemented
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102—111no—
472C2×#102—111no—
473C2×#102C2×D1111yescharacteristic, complemented
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8—111no—
477C2×C22⋊C8—118no—
478C2×C22⋊C8C2×D1111yescharacteristic, complemented
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—44no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—84no—
490C22×C11—84no—
491C22×C11#53412yes—
492C22×C11C2×#13512yes—
493C22×C11C2×AGL(1,ℤ/8)12yes—
494C22×C11C23×D411yescharacteristic
495C2×D11—28no—
496C2×D11—28no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—22no—
501C2×D11—416no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—816no—
506C2×D11—84no—
507C2×D11C2×#13514yes—
508C2×D11C2×AGL(1,ℤ/8)14yes—
509C4×C11—22no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11#53412yes—
513C4×C11C2×H(5,𝔽2)11yescharacteristic
514C4×C11C2×H(5,𝔽2)11yescharacteristic
515Dic11—22no—
516Dic11—22no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520C25—111no—
521C25—221no—
522C2×#41—22no—
523C2×#41—42no—
524C2×#41—42no—
525C2×#41C22×D1114yescomplemented
526C22×Q8C22×D1111yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—114no—
530C22×D4—111no—
531C22×D4—221no—
532C22×D4—222no—
533C22×D4—221no—
534C22×D4—228no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4—221no—
539C22×D4—442no—
540C22×D4—442no—
541C22×D4—448no—
542C22×D4C22×D1111yescharacteristic
543C22×D4C22×D1111yescharacteristic
544C23×C4—21no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—114no—
551C23×C4—114no—
552C23×C4—221no—
553C23×C4—442no—
554C23×C4—442no—
555C23×C4C22×D1111yescharacteristic
556C2×SD16—42no—
557C2×SD16—114no—
558C2×SD16—442no—
559C2×SD16C22×D1114yescomplemented
560C2×D8—42no—
561C2×D8—114no—
562C2×D8—442no—
563C2×D8C22×D1114yescomplemented
564C22×C8—111no—
565C22×C8—111no—
566C22×C8—114no—
567C22×C8—114no—
568C22×C8—442no—
569C22×C8—442no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#123—228no—
573C22⋊Q8—114no—
574C22⋊Q8—114no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577#121—22no—
578#121—114no—
579#121—114no—
580#121—114no—
581#121—114no—
582#121—114no—
583#121—228no—
584#121—222no—
585#121—222no—
586#121—228no—
587#121—222no—
588#121—222no—
589#121—222no—
590#121C22×D1114yes—
591#120—228no—
592C4×D4—228no—
593C4×D4—228no—
594#117—114no—
595#117—222no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—228no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C42—221no—
616#107—114no—
617#107—114no—
618#106—114no—
619#106—114no—
620#103—114no—
621#103C22×D1114yescomplemented
622#102—114no—
623#102—114no—
624#102—114no—
625#102—114no—
626#102—114no—
627#102C22×D1114yescomplemented
628C22⋊C8—114no—
629C22⋊C8—114no—
630C22⋊C8—114no—
631C22⋊C8C22×D1114yescomplemented
632C2×C11—42no—
633C2×C11—82no—
634C2×C11—82no—
635C2×C11#318814yescomplemented
636C2×C11C2×#53411yescharacteristic
637C2×C11C22×#13511yescharacteristic
638C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
639D11—24no—
640D11—24no—
641D11—82no—
642C24—21no—
643C24—21no—
644C24—111no—
645C24—111no—
646C24—114no—
647C24—224no—
648C24—224no—
649C24—224no—
650C24—221no—
651C24—442no—
652C24—444no—
653C24—444no—
654C24—444no—
655C24D4×D1111yescharacteristic
656#41—44no—
657#41—44no—
658#41—48no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8C23×D1112yes—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—112no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—221no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—448no—
687C2×D4—444no—
688C2×D4—4432no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4C23×D1112yes—
694C2×D4C23×D1112yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—24no—
700C22×C4—44no—
701C22×C4—111no—
702C22×C4—111no—
703C22×C4—114no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—224no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—448no—
719C22×C4—444no—
720C22×C4—444no—
721C22×C4—442no—
722C22×C4—442no—
723C22×C4—444no—
724C22×C4—442no—
725C22×C4D4×D1112yes—
726C22×C4D4×D1111yescharacteristic
727C22×C4C23×D1112yes—
728C22×C4C23×D1111yescharacteristic
729SD16—44no—
730SD16—444no—
731D8—44no—
732D8—444no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—112no—
736C2×C8—112no—
737C2×C8—222no—
738C2×C8—222no—
739C2×C8—444no—
740C2×C8—444no—
741C2×C8C23×D1112yes—
742C2×C8C23×D1112yes—
743C4⋊C4—21no—
744C4⋊C4—112no—
745C4⋊C4—112no—
746C4⋊C4—112no—
747C4⋊C4—224no—
748C4⋊C4—224no—
749C4⋊C4—224no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4C23×D1112yes—
754C22⋊C4—24no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C42—224no—
764C11C2×#318811yescharacteristic, complemented, Sylow
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—114no—
777C23—114no—
778C23—112no—
779C23—112no—
780C23—228no—
781C23—228no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—444no—
788C23—448no—
789C23—4416no—
790C23—448no—
791C23—448no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—8816no—
796C23C2×D4×D1112yes—
797C23C2×D4×D1111yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—42no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—48no—
806D4—48no—
807D4—42no—
808D4—42no—
809D4—222no—
810D4—222no—
811D4—448no—
812D4—448no—
813D4—448no—
814D4—448no—
815D4—448no—
816D4—448no—
817D4—442no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—48no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—112no—
828C2×C4—112no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—224no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—448no—
843C2×C4—444no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4C2×D4×D1112yes—
848C2×C4C2×D4×D1111yescharacteristic
849C2×C4#6703712yes—
850C2×C4#6703712yes—
851C2×C4C24×D1111yescharacteristic
852C8—22no—
853C8—22no—
854C8—222no—
855C8—222no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—84no—
867C22—84no—
868C22—114no—
869C22—114no—
870C22—222no—
871C22—222no—
872C22—228no—
873C22—228no—
874C22—222no—
875C22—222no—
876C22—4416no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—8816no—
881C22—884no—
882C22#1062312012yes—
883C22D11×#13512yes—
884C22D11×AGL(1,ℤ/8)12yes—
885C22C22×D4×D1111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—222no—
890C4—222no—
891C4—442no—
892C4—442no—
893C4—442no—
894C4#1062312012yes—
895C4C2×#6703711yescharacteristic
896C4C2×#6703711yescharacteristic
897C2—42no—
898C2—82no—
899C2—82no—
900C2—224no—
901C2—224no—
902C2—882no—
903C2#1307937914yesdirect product factor
904C2C2×#1062312011yescharacteristic
905C2C2×D11×#13511yescharacteristic
906C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3188
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623359C2semidirect
2. C2×D11×#121C2semidirect
3. #13079379C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622648C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622770C2semidirect
10. C2×#10622420C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622769C2semidirect
15. C2×D11×C22⋊C8C2semidirect
16. C2×C11×#449C2semidirect
17. C22×C11×#41C22semidirect
21. C22×C11×SD16C22semidirect
22. C22×C11×D8C22semidirect
25. #10623359C22semidirect
27. C2×#66999C22semidirect
28. C22×#4325C22semidirect
32. C2×#66991C22semidirect
35. C22×#4323C22semidirect
39. C2×#66979C22semidirect
40. C22×C8×D11C22semidirect
41. C22×C8×D11C22semidirect
43. D11×#121C22semidirect
48. C11×#449C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×C22⋊C8C22semidirect
52. #10622851C22semidirect
53. C2×#66899C22semidirect
54. C2×#66896C22semidirect
55. C2×#66896C22semidirect
56. C2×#66896C22semidirect
57. C2×C22⋊(C11⋊C8)C22semidirect
58. #10622784C22semidirect
59. #10622782C22semidirect
60. #10622770C22semidirect
61. #10622769C22semidirect
62. C2×#66885C22semidirect
63. C2×#66885C22semidirect
66. C2×#66882C22semidirect
67. C2×#66881C22semidirect
68. #10622648C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622422C22semidirect
72. #10622420C22semidirect
73. #10622390C22semidirect
74. #10622388C22semidirect
75. #10622350C22semidirect
76. D11×C22⋊C8C22semidirect
82. C2×C11×#41C23semidirect
114. C2×C11×SD16C23semidirect
116. C2×C11×D8C23semidirect
130. #66999C23semidirect
132. C2×#4325C23semidirect
139. #66991C23semidirect
143. C2×#4323C23semidirect
153. #66979C23semidirect
165. C2×C8×D11C23semidirect
166. C2×C8×D11C23semidirect
173. C11×#103C23semidirect
174. C11×#102C23semidirect
175. C11×C22⋊C8C23semidirect
176. #66899C23semidirect
177. #66896C23semidirect
178. #66896C23semidirect
179. #66896C23semidirect
180. C22⋊(C11⋊C8)C23semidirect
181. #66885C23semidirect
182. #66885C23semidirect
185. #66882C23semidirect
186. #66881C23semidirect
187. #66872C23semidirect
188. #66871C23semidirect
324. C2×#449D11semidirect
419. C22×#41C2×D11semidirect
424. C22×SD16C2×D11semidirect
426. C22×D8C2×D11semidirect
460. #449C2×D11semidirect
467. C2×#103C2×D11semidirect
473. C2×#102C2×D11semidirect
478. C2×C22⋊C8C2×D11semidirect
525. C2×#41C22×D11semidirect
559. C2×SD16C22×D11semidirect
563. C2×D8C22×D11semidirect
621. #103C22×D11semidirect
627. #102C22×D11semidirect
631. C22⋊C8C22×D11semidirect
635. C2×C11#3188semidirect
764. C11C2×#3188semidirect
903. C2#13079379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×D11×#1212
#130793792
C2×#106224222
C2×#106223902
C2×#106223502
C2×#106226482
C2×#106223882
C2×#106227702
C2×#106224202
C2×#106227842
C2×#106228512
C2×#106227822
C2×#106227692
C2×D11×C22⋊C82
C2×C11×#4492
C2×#318811