Finite Group Databasebeta

← C2×#13072158 #14921249

Subgroups — C2×#13072158 #14921249

Order 2816.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4C22×D4×Dic11C211yesmaximal, characteristic, complemented
5C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13072158C2116yesmaximal, direct product factor
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622603C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×#10622823C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic, complemented
21C24×C4×C11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic, complemented
28C2×C11×#121—28no—
29C2×C11×#121C2218yescomplemented
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C22×C11×C22⋊C4C2211yescharacteristic, complemented
32C22×C11×C22⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic, complemented
36C22×C22⋊Dic11C2211yescharacteristic, complemented
37C22×C22⋊Dic11C2211yescharacteristic, complemented
38C2×#66992—28no—
39C2×#66992C2218yescomplemented
40C2×#66990—28no—
41C2×#66990—28no—
42C2×#66990C2218yescomplemented
43C2×#66990C2218yescomplemented
44C2×D4×Dic11—28no—
45C2×D4×Dic11C2218yescomplemented
46C22×(C2×D11)⋊C4—28no—
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×(C2×D11)⋊C4C2211yescharacteristic
54C22×(C2×D11)⋊C4C2211yescharacteristic
55C22×(C2×D11)⋊C4C2218yescomplemented
56C22×C4⋊Dic11C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C22×Dic11⋊C4C2211yescharacteristic, complemented
59C22×C4×Dic11C2211yescharacteristic, complemented
60#10622836C2218yescomplemented
61#10622833C2218yescomplemented
62#10622823C2218yescomplemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67#10622607C2218yescomplemented
68#10622603C2218yescomplemented
69#10622574C2218yescomplemented
70#10622572C2218yescomplemented
71#10622571C2218yescomplemented
72#10622570C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—24no—
81C24×D11—42no—
82C24×D11—42no—
83C24×D11C2311yescharacteristic
84C24×D11C2311yescharacteristic
85C24×D11C2314yes—
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—24no—
90C22×D4×C11—24no—
91C22×D4×C11—24no—
92C22×D4×C11—24no—
93C22×D4×C11—42no—
94C22×D4×C11D418yescomplemented
95C22×D4×C11C2314yes—
96C22×D4×C11C2314yes—
97C22×D4×C11C2314yescomplemented
98C23×C4×C11—24no—
99C23×C4×C11—24no—
100C23×C4×C11—42no—
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2314yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—24no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11—24no—
109C22×C22⋊D11—24no—
110C22×C22⋊D11—24no—
111C22×C22⋊D11—24no—
112C22×C22⋊D11—24no—
113C22×C22⋊D11—24no—
114C22×C22⋊D11—42no—
115C22×C22⋊D11—42no—
116C22×C22⋊D11—42no—
117C22×C22⋊D11—42no—
118C22×C22⋊D11C2314yes—
119C22×C22⋊D11C2314yes—
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2314yes—
122C23×Dic11—24no—
123C23×Dic11—24no—
124C23×Dic11—24no—
125C23×Dic11—24no—
126C23×Dic11—42no—
127C23×Dic11—42no—
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2314yes—
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2314yescomplemented
136C11×#121—232no—
137C2×C11×C4⋊C4—24no—
138C2×C11×C4⋊C4C2314yescomplemented
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4C2314yescomplemented
142C2×C11×C22⋊C4C2314yescomplemented
143C2×C22⋊Dic11—24no—
144C2×C22⋊Dic11—24no—
145C2×C22⋊Dic11—24no—
146C2×C22⋊Dic11—42no—
147C2×C22⋊Dic11D418yescomplemented
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2314yescomplemented
151C2×C22⋊Dic11C2314yescomplemented
152C2×C22⋊Dic11C2314yescomplemented
153#66992—232no—
154#66990—232no—
155#66990—232no—
156D4×Dic11—232no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—24no—
159C2×(C2×D11)⋊C4—24no—
160C2×(C2×D11)⋊C4—24no—
161C2×(C2×D11)⋊C4—24no—
162C2×(C2×D11)⋊C4—24no—
163C2×(C2×D11)⋊C4—24no—
164C2×(C2×D11)⋊C4—232no—
165C2×(C2×D11)⋊C4D418yescomplemented
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×C4⋊Dic11—24no—
175C2×C4⋊Dic11C2314yescomplemented
176C2×Dic11⋊C4—24no—
177C2×Dic11⋊C4—42no—
178C2×Dic11⋊C4C2314yescomplemented
179C2×Dic11⋊C4C2314yescomplemented
180C2×C4×Dic11—24no—
181C2×C4×Dic11C2314yescomplemented
182C11⋊#95C2314yescomplemented
183C11⋊#95C2314yescomplemented
184C11⋊#95C2314yescomplemented
185C11⋊#95C2314yescomplemented
186C2×#2424—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—22no—
203C24×C11—22no—
204C24×C11C2×D414yes—
205C24×C11C2×D414yes—
206C24×C11C2×D414yes—
207C24×C11#4114yes—
208C24×C11C2412yes—
209C24×C11C2412yes—
210C24×C11C2412yes—
211C24×C11C2411yescharacteristic
212C23×D11—232no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—28no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—22no—
226C23×D11—28no—
227C23×D11—28no—
228C23×D11—28no—
229C23×D11—28no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—416no—
233C23×D11—416no—
234C23×D11—416no—
235C23×D11—416no—
236C23×D11—416no—
237C23×D11—416no—
238C23×D11C2×D414yes—
239C23×D11#4114yes—
240C23×D11C2412yes—
241C23×D11C2412yes—
242C2×D4×C11—232no—
243C2×D4×C11—28no—
244C2×D4×C11—28no—
245C2×D4×C11—28no—
246C2×D4×C11—28no—
247C2×D4×C11—28no—
248C2×D4×C11—28no—
249C2×D4×C11—28no—
250C2×D4×C11—44no—
251C2×D4×C11—416no—
252C2×D4×C11—416no—
253C2×D4×C11C2×D4116yescomplemented
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—28no—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—28no—
266C22×C4×C11—44no—
267C22×C4×C11—416no—
268C22×C4×C11C2×D414yes—
269C22×C4×C11C2×D414yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—28no—
279C2×C22⋊D11—28no—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—44no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C2×C22⋊D11—416no—
287C2×C22⋊D11—416no—
288C2×C22⋊D11—416no—
289C2×C22⋊D11—416no—
290C22×Dic11—28no—
291C22×Dic11—28no—
292C22×Dic11—28no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—28no—
301C22×Dic11—22no—
302C22×Dic11—22no—
303C22×Dic11—22no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—44no—
310C22×Dic11—44no—
311C22×Dic11—416no—
312C22×Dic11—416no—
313C22×Dic11C2×D414yes—
314C22×Dic11C2×D414yes—
315C22×Dic11C2×D414yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C11×C4⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—28no—
325C22⋊Dic11—28no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—44no—
329C22⋊Dic11C2×D4116yescomplemented
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—28no—
337(C2×D11)⋊C4C2×D4116yescomplemented
338C4⋊Dic11—28no—
339Dic11⋊C4—28no—
340Dic11⋊C4—44no—
341C4×Dic11—28no—
342C22×#121—111no—
343C22×#121D1111yescharacteristic, complemented
344C22×#120—111no—
345C22×#120—111no—
346C22×C4×D4—111no—
347C23×C22⋊C4—111no—
348#2424—1116no—
349C2×#396—111no—
350C2×#394—111no—
351C2×#394—111no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#388—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#385—111no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—28no—
361C23×C11—28no—
362C23×C11—28no—
363C23×C11—28no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—28no—
369C23×C11—28no—
370C23×C11—28no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—44no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—44no—
388C23×C11—44no—
389C23×C11—44no—
390C23×C11—44no—
391C23×C11—44no—
392C23×C11—44no—
393C23×C11—44no—
394C23×C11—44no—
395C23×C11#121116yescomplemented
396C23×C11C22×D414yes—
397C23×C11C22×D412yes—
398C23×C11C22×D412yes—
399C23×C11C22×D414yes—
400C23×C11C22×D414yes—
401C23×C11C22×D412yes—
402C23×C11C2×#4114yes—
403C23×C11C2×#4112yes—
404C23×C11C2×#4112yes—
405C23×C11H(5,𝔽2)12yes—
406C23×C11H(5,𝔽2)12yes—
407C23×C11C2511yescharacteristic
408C22×D11—232no—
409C22×D11—28no—
410C22×D11—28no—
411C22×D11—28no—
412C22×D11—28no—
413C22×D11—28no—
414C22×D11—28no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—416no—
428C22×D11—416no—
429C22×D11—416no—
430C22×D11—416no—
431C22×D11—4128no—
432C22×D11—416no—
433C22×D11—44no—
434C22×D11—44no—
435C22×D11—416no—
436C22×D11—44no—
437C22×D11—44no—
438C22×D11—44no—
439C22×D11—44no—
440C22×D11—44no—
441C22×D11—44no—
442C22×D11C22×D414yes—
443C22×D11C2×#4114yes—
444D4×C11—232no—
445D4×C11—416no—
446D4×C11—416no—
447C2×C4×C11—28no—
448C2×C4×C11—28no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—416no—
460C2×C4×C11—44no—
461C2×C4×C11—44no—
462C2×C4×C11C22×D414yes—
463C2×C4×C11C22×D414yes—
464C22⋊D11—416no—
465C22⋊D11—416no—
466C22⋊D11—416no—
467C22⋊D11—416no—
468C2×Dic11—28no—
469C2×Dic11—28no—
470C2×Dic11—28no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—416no—
487C2×Dic11—416no—
488C2×Dic11—44no—
489C2×Dic11—44no—
490C2×Dic11—44no—
491C2×Dic11C22×D414yes—
492C2×Dic11C22×D414yes—
493C2×Dic11C22×D414yes—
494C26—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4C2×D1111yescharacteristic
500C23×D4C2×D1111yescharacteristic
501C23×D4C2×D1111yescharacteristic, complemented
502C24×C4—111no—
503C24×C4—111no—
504C24×C4C2×D1111yescharacteristic
505C2×#121—28no—
506C2×#121—118no—
507C2×#121—228no—
508C2×#121C2×D1118yescomplemented
509C2×#120—118no—
510C2×#120—118no—
511C2×#120—228no—
512C2×#120—228no—
513C2×C4×D4—118no—
514C2×C4×D4—228no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C4⋊C4C2×D1111yescharacteristic, complemented
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—118no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—228no—
534C22×C22⋊C4C2×D1111yescharacteristic, complemented
535C22×C22⋊C4C2×D1111yescharacteristic, complemented
536C22×C42—111no—
537#396—118no—
538#394—118no—
539#394—118no—
540#392—118no—
541#390—118no—
542#388—118no—
543#386—118no—
544#386—118no—
545#385—118no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C22×C11—24no—
551C22×C11—232no—
552C22×C11—24no—
553C22×C11—24no—
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—24no—
559C22×C11—24no—
560C22×C11—42no—
561C22×C11—416no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—88no—
573C22×C11C2×#12114yes—
574C22×C11C2×#12118yescomplemented
575C22×C11#52514yes—
576C22×C11#53814yes—
577C22×C11D4214yes—
578C22×C11D4214yes—
579C22×C11#54614yes—
580C22×C11#54614yes—
581C22×C11C23×D411yescharacteristic
582C22×C11C23×D411yescharacteristic
583C22×C11C23×D411yescharacteristic
584C22×C11C22×#4111yescharacteristic
585C22×C11C22×#4111yescharacteristic
586C22×C11C2×H(5,𝔽2)11yescharacteristic
587C22×C11C2×H(5,𝔽2)11yescharacteristic
588C2×D11—24no—
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
593C2×D11—24no—
594C2×D11—464no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—416no—
598C2×D11—416no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C4×C11—24no—
606C4×C11—24no—
607C4×C11—42no—
608C4×C11—42no—
609Dic11—24no—
610Dic11—24no—
611Dic11—24no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615C25—111no—
616C25—111no—
617C25—114no—
618C25—224no—
619C25—224no—
620C25—224no—
621C25—224no—
622C25—224no—
623C25—442no—
624C25—442no—
625C25C22×D1111yescharacteristic
626C25C22×D1111yescharacteristic
627C25C22×D1111yescharacteristic
628C22×D4—24no—
629C22×D4—24no—
630C22×D4—24no—
631C22×D4—24no—
632C22×D4—24no—
633C22×D4—24no—
634C22×D4—24no—
635C22×D4—42no—
636C22×D4—114no—
637C22×D4—114no—
638C22×D4—114no—
639C22×D4—114no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—224no—
643C22×D4—224no—
644C22×D4—224no—
645C22×D4—224no—
646C22×D4—224no—
647C22×D4—224no—
648C22×D4—442no—
649C22×D4—442no—
650C22×D4—442no—
651C22×D4—442no—
652C22×D4C22⋊D1118yescomplemented
653C22×D4C22×D1114yes—
654C22×D4C22×D1114yes—
655C22×D4C22×D1114yescomplemented
656C23×C4—24no—
657C23×C4—24no—
658C23×C4—42no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—111no—
665C23×C4—114no—
666C23×C4—114no—
667C23×C4—224no—
668C23×C4—224no—
669C23×C4—224no—
670C23×C4—224no—
671C23×C4—442no—
672C23×C4—442no—
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1114yes—
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678#121—232no—
679#121—2232no—
680#120—2232no—
681#120—2232no—
682C4×D4—2232no—
683C2×C4⋊C4—24no—
684C2×C4⋊C4—114no—
685C2×C4⋊C4—114no—
686C2×C4⋊C4—114no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—442no—
690C2×C4⋊C4C22×D1114yescomplemented
691C2×C22⋊C4—24no—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—118no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—118no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—114no—
708C2×C22⋊C4—2232no—
709C2×C22⋊C4—224no—
710C2×C22⋊C4—224no—
711C2×C22⋊C4—224no—
712C2×C22⋊C4—224no—
713C2×C22⋊C4—224no—
714C2×C22⋊C4—224no—
715C2×C22⋊C4—224no—
716C2×C22⋊C4—224no—
717C2×C22⋊C4—224no—
718C2×C22⋊C4—224no—
719C2×C22⋊C4—442no—
720C2×C22⋊C4C22×D1114yescomplemented
721C2×C22⋊C4C22×D1114yescomplemented
722C2×C42—114no—
723C2×C42—224no—
724#95—114no—
725#95—114no—
726#95—114no—
727#95—114no—
728C2×C11—28no—
729C2×C11—44no—
730C2×C11—82no—
731C2×C11#242418yescomplemented
732C2×C11C22×#12111yescharacteristic
733C2×C11C2×#52511yescharacteristic
734C2×C11C2×#53811yescharacteristic
735C2×C11C2×D4211yescharacteristic
736C2×C11C2×D4211yescharacteristic
737C2×C11C2×#54611yescharacteristic
738C2×C11C2×#54611yescharacteristic
739D11—44no—
740D11—44no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—22no—
758C24—114no—
759C24—114no—
760C24—112no—
761C24—112no—
762C24—228no—
763C24—228no—
764C24—2232no—
765C24—222no—
766C24—222no—
767C24—222no—
768C24—228no—
769C24—222no—
770C24—222no—
771C24—222no—
772C24—222no—
773C24—222no—
774C24—222no—
775C24—222no—
776C24—222no—
777C24—222no—
778C24—228no—
779C24—228no—
780C24—444no—
781C24—444no—
782C24—4416no—
783C24—4416no—
784C24—4416no—
785C24—4416no—
786C24—4416no—
787C24—4416no—
788C24D4×D1114yes—
789C24#434114yes—
790C24C2×C22⋊D1114yes—
791C24C2×C22⋊D1114yes—
792C24C23×D1112yes—
793C24C23×D1112yes—
794C24C23×D1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—232no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—416no—
806C2×D4—416no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C2×D4—444no—
816C2×D4—444no—
817C2×D4—444no—
818C2×D4—444no—
819C2×D4—4416no—
820C2×D4—4416no—
821C2×D4—4416no—
822C2×D4—4416no—
823C2×D4C2×C22⋊D11116yescomplemented
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—28no—
835C22×C4—28no—
836C22×C4—44no—
837C22×C4—416no—
838C22×C4—114no—
839C22×C4—114no—
840C22×C4—114no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—228no—
848C22×C4—228no—
849C22×C4—228no—
850C22×C4—222no—
851C22×C4—222no—
852C22×C4—222no—
853C22×C4—222no—
854C22×C4—222no—
855C22×C4—222no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—228no—
860C22×C4—222no—
861C22×C4—222no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—222no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—4416no—
869C22×C4—4416no—
870C22×C4D4×D1114yes—
871C22×C4C2×C22⋊D1114yes—
872C22×C4C23×D1112yes—
873C22×C4C23×D1112yes—
874C22×C4C23×D1112yes—
875C22×C4C23×D1112yes—
876C4⋊C4—28no—
877C4⋊C4—228no—
878C4⋊C4—228no—
879C4⋊C4—444no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—1116no—
883C22⋊C4—1116no—
884C22⋊C4—228no—
885C22⋊C4—228no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—228no—
894C22⋊C4—444no—
895C42—228no—
896C11C2×#242411yescharacteristic, complemented, Sylow
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—28no—
908C23—28no—
909C23—28no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—44no—
924C23—44no—
925C23—44no—
926C23—44no—
927C23—44no—
928C23—44no—
929C23—44no—
930C23—44no—
931C23—44no—
932C23—44no—
933C23—44no—
934C23—114no—
935C23—114no—
936C23—2232no—
937C23—228no—
938C23—228no—
939C23—228no—
940C23—228no—
941C23—228no—
942C23—228no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—4416no—
956C23—4416no—
957C23—4416no—
958C23—4416no—
959C23—44128no—
960C23—4416no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—4416no—
965C23—444no—
966C23—444no—
967C23—444no—
968C23—444no—
969C23—444no—
970C23#66992116yescomplemented
971C23C2×D4×D1114yes—
972C23C2×D4×D1112yes—
973C23C2×D4×D1112yes—
974C23C2×#434114yes—
975C23C2×#434112yes—
976C23#6703712yes—
977C23#41×D1112yes—
978C23#6704212yes—
979C23C22×C22⋊D1114yes—
980C23C22×C22⋊D1114yes—
981C23C22×C22⋊D1112yes—
982C23C24×D1111yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—4416no—
987D4—4416no—
988D4—4416no—
989D4—4416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—416no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—114no—
1008C2×C4—228no—
1009C2×C4—228no—
1010C2×C4—228no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—4416no—
1027C2×C4—4416no—
1028C2×C4—444no—
1029C2×C4—444no—
1030C2×C4—444no—
1031C2×C4C2×D4×D1114yes—
1032C2×C4C22×C22⋊D1114yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—42no—
1044C22—416no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—88no—
1056C22—224no—
1057C22—224no—
1058C22—224no—
1059C22—224no—
1060C22—224no—
1061C22—224no—
1062C22—4464no—
1063C22—4416no—
1064C22—4416no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22#1062313714yes—
1074C22#1062314014yes—
1075C22#1062314114yes—
1076C22#1062314814yes—
1077C22D4×C22⋊D1114yes—
1078C22C2×#6699214yes—
1079C22C2×#6699218yescomplemented
1080C22#1062336014yes—
1081C22C22×D4×D1111yescharacteristic
1082C22C22×D4×D1111yescharacteristic
1083C22C22×#434111yescharacteristic
1084C22C2×#6703711yescharacteristic
1085C22C2×#41×D1111yescharacteristic
1086C22C2×#6704211yescharacteristic
1087C22C23×C22⋊D1111yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—42no—
1091C4—42no—
1092C4—224no—
1093C4—224no—
1094C4—224no—
1095C4—442no—
1096C4—442no—
1097C4—442no—
1098C2—28no—
1099C2—44no—
1100C2—82no—
1101C2—444no—
1102C2—444no—
1103C2#1307215818yesdirect product factor
1104C2C22×#6699211yescharacteristic
1105C2C2×#1062313711yescharacteristic
1106C2C2×#1062314811yescharacteristic
1107C2C2×D4×C22⋊D1111yescharacteristic
1108C2C2×#1062314011yescharacteristic
1109C2C2×#1062336011yescharacteristic
1110C2C2×#1062314111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#66990C2semidirect
3. C22×#66990C2semidirect
4. C22×D4×Dic11C2semidirect
5. C23×(C2×D11)⋊C4C2semidirect
6. #13072158C2direct (N × H)
7. C2×#10622607C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622603C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622571C2semidirect
15. C2×#10622823C2semidirect
16. C22×C11×#121C2semidirect
20. C23×D4×C11C22semidirect
27. C24×Dic11C22semidirect
29. C2×C11×#121C22semidirect
30. C22×C11×C4⋊C4C22semidirect
31. C22×C11×C22⋊C4C22semidirect
32. C22×C11×C22⋊C4C22semidirect
35. C22×C22⋊Dic11C22semidirect
36. C22×C22⋊Dic11C22semidirect
37. C22×C22⋊Dic11C22semidirect
39. C2×#66992C22semidirect
42. C2×#66990C22semidirect
43. C2×#66990C22semidirect
45. C2×D4×Dic11C22semidirect
55. C22×(C2×D11)⋊C4C22semidirect
56. C22×C4⋊Dic11C22semidirect
57. C22×Dic11⋊C4C22semidirect
58. C22×Dic11⋊C4C22semidirect
59. C22×C4×Dic11C22semidirect
60. #10622836C22semidirect
61. #10622833C22semidirect
62. #10622823C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. #10622607C22semidirect
68. #10622603C22semidirect
69. #10622574C22semidirect
70. #10622572C22semidirect
71. #10622571C22semidirect
72. #10622570C22semidirect
94. C22×D4×C11D4semidirect
97. C22×D4×C11C23semidirect
135. C23×Dic11C23semidirect
138. C2×C11×C4⋊C4C23semidirect
141. C2×C11×C22⋊C4C23semidirect
142. C2×C11×C22⋊C4C23semidirect
147. C2×C22⋊Dic11D4semidirect
150. C2×C22⋊Dic11C23semidirect
151. C2×C22⋊Dic11C23semidirect
152. C2×C22⋊Dic11C23semidirect
165. C2×(C2×D11)⋊C4D4semidirect
175. C2×C4⋊Dic11C23semidirect
178. C2×Dic11⋊C4C23semidirect
179. C2×Dic11⋊C4C23semidirect
181. C2×C4×Dic11C23semidirect
182. C11⋊#95C23semidirect
183. C11⋊#95C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
253. C2×D4×C11C2×D4semidirect
329. C22⋊Dic11C2×D4semidirect
337. (C2×D11)⋊C4C2×D4semidirect
343. C22×#121D11semidirect
395. C23×C11#121semidirect
501. C23×D4C2×D11semidirect
508. C2×#121C2×D11semidirect
518. C22×C4⋊C4C2×D11semidirect
534. C22×C22⋊C4C2×D11semidirect
535. C22×C22⋊C4C2×D11semidirect
574. C22×C11C2×#121semidirect
652. C22×D4C22⋊D11semidirect
655. C22×D4C22×D11semidirect
690. C2×C4⋊C4C22×D11semidirect
720. C2×C22⋊C4C22×D11semidirect
721. C2×C22⋊C4C22×D11semidirect
731. C2×C11#2424semidirect
823. C2×D4C2×C22⋊D11semidirect
896. C11C2×#2424semidirect
970. C23#66992semidirect
1079. C22C2×#66992semidirect
1103. C2#13072158direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×#669902
C22×D4×Dic112
C23×(C2×D11)⋊C42
#130721582
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106228362
C2×#106225702
C2×#106226032
C2×#106228332
C2×#106225712
C2×#106228232
C22×C11×#1212
C2×#242411