Finite Group Databasebeta

← C2×#13071463 #14912985

Subgroups — C2×#13071463 #14912985

Order 2816.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D11C211yesmaximal, characteristic
4#13071463C2116yesmaximal, direct product factor
5C2×#10622283C211yesmaximal, characteristic, complemented
6C2×#10622283C211yesmaximal, characteristic, complemented
7C2×#10622603C211yesmaximal, characteristic, complemented
8C2×#10622603C211yesmaximal, characteristic, complemented
9C2×#10622563C211yesmaximal, characteristic, complemented
10C2×#10622277C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C2×#10622568C211yesmaximal, characteristic
13C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4—28no—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2218yes—
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic, complemented
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×C4×Dic11C2211yescharacteristic, complemented
43C22×C4×Dic11C2211yescharacteristic, complemented
44C22×C4×Dic11C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46C2×#66945—28no—
47C2×#66945C2218yescomplemented
48C2×C22⋊C4×D11C4116yescomplemented
49C2×C22⋊C4×D11C2218yes—
50C11×#385C2218yescomplemented
51C2×C11×#95C2211yescharacteristic, complemented
52C2×C11×#95C2211yescharacteristic, complemented
53C4×C22⋊Dic11C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60#10622603C2218yescomplemented
61#10622603C2218yescomplemented
62#10622600C2218yescomplemented
63#10622568C2218yes—
64#10622563C2218yescomplemented
65C22⋊C4×Dic11C2218yescomplemented
66#10622283C2218yescomplemented
67#10622283C2218yescomplemented
68#10622279C2218yescomplemented
69#10622277C2218yescomplemented
70C25×C11C2311yescharacteristic
71C24×D11—24no—
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11C2×C418yes—
78C24×D11C2311yescharacteristic
79C24×D11C2314yes—
80C24×D11C2311yescharacteristic
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—42no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11—42no—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11C2×C418yescomplemented
106C22×C4×D11C2×C418yescomplemented
107C22×C4×D11C2314yes—
108C22×C4×D11C2314yes—
109C2×C11×C4⋊C4—24no—
110C2×C11×C4⋊C4—42no—
111C2×C11×C4⋊C4C2314yescomplemented
112C2×C11×C4⋊C4C2314yescomplemented
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4C2×C418yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11C2×C418yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—232no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4C2×C418yescomplemented
130C2×(C2×D11)⋊C4C2×C418yescomplemented
131C2×(C2×D11)⋊C4D418yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×C4⋊Dic11—24no—
143C2×C4⋊Dic11—42no—
144C2×C4⋊Dic11C2314yescomplemented
145C2×C4⋊Dic11C2314yescomplemented
146C2×C4×Dic11—24no—
147C2×C4×Dic11—24no—
148C2×C4×Dic11—42no—
149C2×C4×Dic11—42no—
150C2×C4×Dic11C2314yescomplemented
151C2×C4×Dic11C2314yescomplemented
152C2×C4×Dic11C2314yescomplemented
153C2×C4×Dic11C2314yescomplemented
154#66945—232no—
155C22⋊C4×D11C2×C4164yescomplemented
156C11×#95C2314yescomplemented
157C11×#95C2314yescomplemented
158C11⋊#95C2314yescomplemented
159C11⋊#95C2314yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162C11⋊#95C2314yescomplemented
163C11⋊#95C2314yescomplemented
164C2×#2342—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11C22×C414yes—
170C24×C11#4114yes—
171C24×C11#4114yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—232no—
179C23×D11—22no—
180C23×D11—28no—
181C23×D11—28no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—232no—
188C23×D11—28no—
189C23×D11—28no—
190C23×D11—416no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—416no—
194C23×D11—416no—
195C23×D11—416no—
196C23×D11—416no—
197C23×D11C22×C414yes—
198C23×D11C22×C4116yes—
199C23×D11C22×C414yes—
200C23×D11C2×D414yes—
201C23×D11#4114yes—
202C23×D11C2412yes—
203C23×D11C2412yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—28no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—28no—
221C22×C4×C11—44no—
222C22×C4×C11—416no—
223C22×C4×C11C22×C414yes—
224C22×C4×C11C22×C414yes—
225C22×C4×C11C2×D414yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×Dic11—28no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—28no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—44no—
250C22×Dic11—416no—
251C22×Dic11C22×C414yes—
252C22×Dic11C22×C414yes—
253C22×Dic11C2×D414yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×C4×D11—232no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—416no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11C22×C4116yescomplemented
267C2×C4×D11C22×C4116yescomplemented
268C11×C4⋊C4—28no—
269C11×C4⋊C4—44no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4C22×C4116yes—
272C22⋊Dic11—28no—
273C22⋊Dic11C22×C4116yes—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4C22×C4116yescomplemented
282(C2×D11)⋊C4C22×C4116yescomplemented
283(C2×D11)⋊C4C2×D4116yes—
284C4⋊Dic11—28no—
285C4⋊Dic11—44no—
286C4×Dic11—28no—
287C4×Dic11—28no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C22×#117—111no—
291C23×C22⋊C4—111no—
292C23×C22⋊C4—111no—
293#2342—1116no—
294C2×#388—111no—
295C2×#388—111no—
296C2×#388—111no—
297C2×#388—111no—
298C2×#385—111no—
299C2×#385D1111yescharacteristic, complemented
300C2×#381—111no—
301C2×#380—111no—
302C2×#379—111no—
303C2×C4×C22⋊C4—111no—
304C2×C4×C22⋊C4—111no—
305C2×C4×C22⋊C4—111no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—28no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11#117116yescomplemented
317C23×C11C23×C414yes—
318C23×C11C23×C412yes—
319C23×C11C22×D412yes—
320C23×C11C2×#4114yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4114yes—
323C23×C11C2×#4112yes—
324C23×C11C2×#4112yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11C2511yescharacteristic
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—28no—
331C22×D11—28no—
332C22×D11—28no—
333C22×D11—28no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—28no—
339C22×D11—232no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—232no—
349C22×D11—416no—
350C22×D11—4128no—
351C22×D11—416no—
352C22×D11—416no—
353C22×D11—416no—
354C22×D11—416no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11C4×D4116yes—
360C22×D11C23×C414yes—
361C22×D11C23×C414yes—
362C22×D11C22×D414yes—
363C22×D11C2×#4114yes—
364C2×C4×C11—28no—
365C2×C4×C11—28no—
366C2×C4×C11—28no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—416no—
383C2×C4×C11—44no—
384C2×C4×C11—44no—
385C2×C4×C11—44no—
386C2×C4×C11C23×C414yes—
387C2×C4×C11C23×C414yes—
388C2×C4×C11C22×D414yes—
389C2×Dic11—28no—
390C2×Dic11—28no—
391C2×Dic11—28no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—416no—
408C2×Dic11—44no—
409C2×Dic11—44no—
410C2×Dic11—44no—
411C2×Dic11C23×C414yes—
412C2×Dic11C23×C414yes—
413C2×Dic11C22×D414yes—
414C4×D11—232no—
415C4×D11—416no—
416C26—111no—
417C24×C4—111no—
418C24×C4—111no—
419C24×C4—111no—
420C24×C4C2×D1111yescharacteristic
421C2×#117—118no—
422C2×#117—228no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4C2×D1111yescharacteristic, complemented
426C22×C4⋊C4C2×D1111yescharacteristic, complemented
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—118no—
432C22×C22⋊C4—1116no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—118no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—228no—
443C22×C22⋊C4C2×D1111yescharacteristic
444C22×C22⋊C4C2×D1111yescharacteristic
445C22×C42—111no—
446C22×C42—111no—
447C22×C42—111no—
448C22×C42—111no—
449#388—118no—
450#388—118no—
451#388—118no—
452#388—118no—
453#385—118no—
454#385C2×D1118yescomplemented
455#381—118no—
456#380—118no—
457#379—118no—
458C4×C22⋊C4—118no—
459C4×C22⋊C4—118no—
460C4×C22⋊C4—118no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95C2×D1111yescharacteristic, complemented
468C2×#95C2×D1111yescharacteristic, complemented
469C22×C11—232no—
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—24no—
474C22×C11—24no—
475C22×C11—24no—
476C22×C11C2×#11714yes—
477C22×C11C2×#11718yescomplemented
478C22×C11C2×C4×D414yes—
479C22×C11#51814yes—
480C22×C11#54614yes—
481C22×C11#54614yes—
482C22×C11#55114yes—
483C22×C11#55114yes—
484C22×C11C24×C411yescharacteristic
485C22×C11C23×D411yescharacteristic
486C22×C11C22×#4111yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×H(5,𝔽2)11yescharacteristic
491C2×D11—232no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—24no—
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—24no—
499C2×D11—24no—
500C2×D11—24no—
501C2×D11—464no—
502C2×D11—416no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11C2×C4×D418yes—
508C4×C11—24no—
509C4×C11—24no—
510C4×C11—24no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514Dic11—24no—
515Dic11—24no—
516Dic11—24no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520C25—111no—
521C25—111no—
522C25—118no—
523C25—114no—
524C25—224no—
525C25—224no—
526C25—224no—
527C25—224no—
528C25—442no—
529C25—442no—
530C25C22×D1111yescharacteristic
531C23×C4—24no—
532C23×C4—24no—
533C23×C4—42no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—118no—
538C23×C4—114no—
539C23×C4—118no—
540C23×C4—114no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—114no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—224no—
548C23×C4—224no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4—442no—
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1114yes—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559#117—2232no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—42no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—442no—
566C2×C4⋊C4C22×D1114yescomplemented
567C2×C4⋊C4C22×D1114yescomplemented
568C2×C22⋊C4—24no—
569C2×C22⋊C4—118no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—118no—
572C2×C22⋊C4—118no—
573C2×C22⋊C4—118no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—1164no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—2232no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—442no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4C4×D1118yes—
596C2×C22⋊C4C22×D1114yes—
597C2×C22⋊C4C22×D1114yes—
598C2×C42—114no—
599C2×C42—114no—
600C2×C42—114no—
601C2×C42—114no—
602C2×C42—224no—
603C2×C42—224no—
604C2×C42—442no—
605C2×C42—442no—
606#95—114no—
607#95—114no—
608#95—114no—
609#95—114no—
610#95—114no—
611#95—114no—
612#95C22×D1114yescomplemented
613#95C22×D1114yescomplemented
614C2×C11—28no—
615C2×C11#234218yescomplemented
616C2×C11C22×#11711yescharacteristic
617C2×C11C22×C4×D411yescharacteristic
618C2×C11C2×#51811yescharacteristic
619C2×C11C2×#54611yescharacteristic
620C2×C11C2×#54611yescharacteristic
621C2×C11C2×#55111yescharacteristic
622C2×C11C2×#55111yescharacteristic
623D11—28no—
624D11—44no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—114no—
630C24—114no—
631C24—114no—
632C24—112no—
633C24—114no—
634C24—112no—
635C24—1116no—
636C24—228no—
637C24—2232no—
638C24—228no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—2232no—
644C24—222no—
645C24—228no—
646C24—222no—
647C24—222no—
648C24—228no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—4416no—
653C24—444no—
654C24—444no—
655C24—4416no—
656C24—4416no—
657C24—4416no—
658C24—4416no—
659C24C2×C4×D1114yes—
660C24#434114yes—
661C24#434314yes—
662C24C23×D1112yes—
663C24C23×D1111yescharacteristic
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—44no—
682C22×C4—416no—
683C22×C4—114no—
684C22×C4—114no—
685C22×C4—114no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—1116no—
690C22×C4—1116no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—228no—
695C22×C4—2232no—
696C22×C4—228no—
697C22×C4—228no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—228no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—4416no—
715C22×C4—444no—
716C22×C4—444no—
717C22×C4—444no—
718C22×C4—4416no—
719C22×C4C2×C4×D1114yes—
720C22×C4C2×C4×D1114yes—
721C22×C4D4×D1114yes—
722C22×C4C23×D1112yes—
723C22×C4C23×D1112yes—
724C22×C4C23×D1112yes—
725C22×C4C23×D1112yes—
726C22×C4C23×D1112yes—
727C22×C4C23×D1112yes—
728C4⋊C4—28no—
729C4⋊C4—44no—
730C4⋊C4—228no—
731C4⋊C4—444no—
732C22⋊C4—28no—
733C22⋊C4—1116no—
734C22⋊C4—1116no—
735C22⋊C4—1116no—
736C22⋊C4—1116no—
737C22⋊C4—228no—
738C22⋊C4—228no—
739C22⋊C4—228no—
740C22⋊C4—228no—
741C22⋊C4—228no—
742C22⋊C4—228no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C22⋊C4C2×C4×D11116yes—
746C42—228no—
747C42—228no—
748C42—444no—
749C42—444no—
750C11C2×#234211yescharacteristic, complemented, Sylow
751C23—28no—
752C23—28no—
753C23—28no—
754C23—28no—
755C23—28no—
756C23—22no—
757C23—28no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—1116no—
762C23—114no—
763C23—114no—
764C23—114no—
765C23—114no—
766C23—2232no—
767C23—228no—
768C23—228no—
769C23—228no—
770C23—228no—
771C23—228no—
772C23—228no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—228no—
778C23—2232no—
779C23—228no—
780C23—228no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—4416no—
788C23—4416no—
789C23—44128no—
790C23—4416no—
791C23—4416no—
792C23—4416no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23—444no—
797C23#66945116yescomplemented
798C23C22×C4×D1114yes—
799C23C22×C4×D1112yes—
800C23C2×D4×D1112yes—
801C23C2×#434114yes—
802C23C2×#434112yes—
803C23#6703712yes—
804C23C2×#434314yes—
805C23C2×#434312yes—
806C23#41×D1112yes—
807C23#6704212yes—
808C23C24×D1111yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—416no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—114no—
832C2×C4—114no—
833C2×C4—114no—
834C2×C4—2232no—
835C2×C4—228no—
836C2×C4—228no—
837C2×C4—228no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—4416no—
854C2×C4—4416no—
855C2×C4—444no—
856C2×C4—444no—
857C2×C4—444no—
858C2×C4C22×C4×D1114yes—
859C2×C4C22×C4×D1114yes—
860C2×C4C2×D4×D1114yes—
861C22—24no—
862C22—232no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—118no—
869C22—224no—
870C22—2232no—
871C22—224no—
872C22—224no—
873C22—224no—
874C22—224no—
875C22—224no—
876C22—224no—
877C22—224no—
878C22—224no—
879C22—4464no—
880C22—442no—
881C22—4416no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22C2×#6694514yes—
886C22C2×#6694518yescomplemented
887C22C4×D4×D1114yes—
888C22#1062307614yes—
889C22#1062312214yes—
890C22#1062316114yes—
891C22#1062316814yes—
892C22#1062318914yes—
893C22C23×C4×D1111yescharacteristic
894C22C22×D4×D1111yescharacteristic
895C22C22×#434111yescharacteristic
896C22C2×#6703711yescharacteristic
897C22C22×#434311yescharacteristic
898C22C2×#41×D1111yescharacteristic
899C22C2×#6704211yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—224no—
907C4—224no—
908C4—224no—
909C4—442no—
910C4—442no—
911C4—442no—
912C2—28no—
913C2—228no—
914C2—444no—
915C2#1307146318yesdirect product factor
916C2C22×#6694511yescharacteristic
917C2C2×C4×D4×D1111yescharacteristic
918C2C2×#1062307611yescharacteristic
919C2C2×#1062312211yescharacteristic
920C2C2×#1062316111yescharacteristic
921C2C2×#1062318911yescharacteristic
922C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×D11C22
cosocleC23×C11C25
hypercenterC2×#385D11
hypocenterC11C2×#2342
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66945C2semidirect
4. #13071463C2direct (N × H)
5. C2×#10622283C2semidirect
6. C2×#10622283C2semidirect
7. C2×#10622603C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622277C2semidirect
11. C2×#10622600C2semidirect
13. C2×C22⋊C4×Dic11C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#385C2semidirect
22. C22×C11×C4⋊C4C22semidirect
23. C22×C11×C4⋊C4C22semidirect
40. C22×C4⋊Dic11C22semidirect
41. C22×C4⋊Dic11C22semidirect
42. C22×C4×Dic11C22semidirect
43. C22×C4×Dic11C22semidirect
44. C22×C4×Dic11C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66945C22semidirect
48. C2×C22⋊C4×D11C4semidirect
50. C11×#385C22semidirect
51. C2×C11×#95C22semidirect
52. C2×C11×#95C22semidirect
53. C4×C22⋊Dic11C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. #10622603C22semidirect
61. #10622603C22semidirect
62. #10622600C22semidirect
64. #10622563C22semidirect
65. C22⋊C4×Dic11C22semidirect
66. #10622283C22semidirect
67. #10622283C22semidirect
68. #10622279C22semidirect
69. #10622277C22semidirect
105. C22×C4×D11C2×C4semidirect
106. C22×C4×D11C2×C4semidirect
111. C2×C11×C4⋊C4C23semidirect
112. C2×C11×C4⋊C4C23semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
144. C2×C4⋊Dic11C23semidirect
145. C2×C4⋊Dic11C23semidirect
150. C2×C4×Dic11C23semidirect
151. C2×C4×Dic11C23semidirect
152. C2×C4×Dic11C23semidirect
153. C2×C4×Dic11C23semidirect
155. C22⋊C4×D11C2×C4semidirect
156. C11×#95C23semidirect
157. C11×#95C23semidirect
158. C11⋊#95C23semidirect
159. C11⋊#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
162. C11⋊#95C23semidirect
163. C11⋊#95C23semidirect
266. C2×C4×D11C22×C4semidirect
267. C2×C4×D11C22×C4semidirect
281. (C2×D11)⋊C4C22×C4semidirect
282. (C2×D11)⋊C4C22×C4semidirect
299. C2×#385D11semidirect
316. C23×C11#117semidirect
425. C22×C4⋊C4C2×D11semidirect
426. C22×C4⋊C4C2×D11semidirect
454. #385C2×D11semidirect
467. C2×#95C2×D11semidirect
468. C2×#95C2×D11semidirect
477. C22×C11C2×#117semidirect
566. C2×C4⋊C4C22×D11semidirect
567. C2×C4⋊C4C22×D11semidirect
612. #95C22×D11semidirect
613. #95C22×D11semidirect
615. C2×C11#2342semidirect
750. C11C2×#2342semidirect
797. C23#66945semidirect
886. C22C2×#66945semidirect
915. C2#13071463direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669452
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
#130714632
C2×#106222832
C2×#106226032
C2×#106225632
C2×#106222772
C2×#106226002
C2×#106225682
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×#106222792
C2×C11×#3852
C2×#234211