Finite Group Databasebeta

← C2×#13071629 #14913299

Subgroups — C2×#13071629 #14913299

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
6#13071629C2116yesmaximal, direct product factor
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622260C211yesmaximal, characteristic, complemented
9C2×#10622283C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622563C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×C4⋊C4×D11—28no—
47C2×C4⋊C4×D11C2218yescomplemented
48C2×#66937C4116yescomplemented
49C2×#66937C2218yes—
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4—28no—
52C2×(C22⋊D11)⋊C4C2218yescomplemented
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C2×C4×D44—28no—
55C2×C4×D44C2218yescomplemented
56C11×#388C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63#10622602C2218yescomplemented
64#10622570C2218yescomplemented
65#10622569C2218yescomplemented
66#10622563C2218yescomplemented
67C4×Dic11⋊C4C2218yescomplemented
68#10622283C2218yescomplemented
69#10622279C2218yescomplemented
70#10622278C2218yescomplemented
71#10622260C2218yescomplemented
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11C2×C418yescomplemented
86C22×C22⋊D11C2×C418yescomplemented
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11—24no—
90C23×Dic11—24no—
91C23×Dic11—42no—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C22×D44—24no—
100C22×D44—24no—
101C22×D44C2×C418yescomplemented
102C22×D44C2314yes—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—42no—
112C22×C4×D11—42no—
113C22×C4×D11—42no—
114C22×C4×D11C2×C418yescomplemented
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C22×C4×D11C2314yes—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4C2314yes—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4C2×C418yescomplemented
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C42×C11—24no—
128C2×C42×C11C2314yes—
129C2×C22⋊Dic11—42no—
130C2×C22⋊Dic11C2314yes—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4C2×C418yescomplemented
136C2×(C2×D11)⋊C4D418yescomplemented
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×C4⋊Dic11—24no—
144C2×C4⋊Dic11—24no—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4C2×C418yescomplemented
150C2×Dic11⋊C4D418yescomplemented
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11—24no—
157C2×C4×Dic11—24no—
158C2×C4×Dic11C2314yes—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2314yes—
161C4⋊C4×D11—232no—
162#66937C2×C4164yescomplemented
163(C22⋊D11)⋊C4—232no—
164(C22⋊D11)⋊C4—232no—
165C4×D44—232no—
166C11×#95C2314yes—
167C11×#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2361—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11C22×C414yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11C22×C414yes—
193C23×D11C22×C414yes—
194C23×D11C2×D414yes—
195C23×D11#4114yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
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×C11C22×C414yes—
213C22×C4×C11C22×C414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C2×C22⋊D11—232no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—232no—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11C22×C4116yescomplemented
229C2×C22⋊D11C22×C4116yescomplemented
230C22×Dic11—28no—
231C22×Dic11—28no—
232C22×Dic11—22no—
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—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—44no—
245C22×Dic11—416no—
246C22×Dic11C22×C414yes—
247C22×Dic11C22×C414yes—
248C22×Dic11C2×D414yes—
249C22×Dic11C2×D414yes—
250C22×Dic11C2×D414yes—
251C22×Dic11#4114yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×D44—232no—
259C2×D44—28no—
260C2×D44—28no—
261C2×D44C22×C4116yescomplemented
262C2×C4×D11—232no—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—416no—
275C2×C4×D11—416no—
276C2×C4×D11—416no—
277C2×C4×D11C22×C4116yescomplemented
278C11×C4⋊C4—28no—
279C11×C22⋊C4—28no—
280C11×C22⋊C4—28no—
281C11×C22⋊C4C22×C4116yescomplemented
282C42×C11—28no—
283C22⋊Dic11—44no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4C22×C4116yescomplemented
289(C2×D11)⋊C4C2×D4116yescomplemented
290C4⋊Dic11—28no—
291C4⋊Dic11—28no—
292Dic11⋊C4—28no—
293Dic11⋊C4—28no—
294Dic11⋊C4C22×C4116yescomplemented
295Dic11⋊C4C2×D4116yescomplemented
296C4×Dic11—28no—
297C4×Dic11—28no—
298C4×Dic11—28no—
299C22×#121—111no—
300C22×C4×D4—111no—
301C22×C4×D4—111no—
302C22×C4×D4—111no—
303C23×C4⋊C4—111no—
304#2361—1116no—
305C2×#390—111no—
306C2×#389—111no—
307C2×#388—111no—
308C2×#388D1111yescharacteristic, complemented
309C2×#386—111no—
310C2×#386—111no—
311C2×#385—111no—
312C2×#385—111no—
313C2×C4×C4⋊C4—111no—
314C2×C4×C22⋊C4—111no—
315C23×C11—28no—
316C23×C11—28no—
317C23×C11—28no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11C23×C414yes—
329C23×C11C23×C412yes—
330C23×C11C22×D412yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C112−1+412yes—
336C23×C11C2511yescharacteristic
337C22×D11—28no—
338C22×D11—28no—
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11C4×D4116yescomplemented
361C22×D11C23×C414yes—
362C22×D11C23×C414yes—
363C22×D11C22×D414yes—
364C22×D11C2×#4114yes—
365C2×C4×C11—28no—
366C2×C4×C11—28no—
367C2×C4×C11—28no—
368C2×C4×C11—28no—
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—22no—
383C2×C4×C11—44no—
384C2×C4×C11—44no—
385C2×C4×C11C23×C414yes—
386C2×C4×C11C23×C414yes—
387C2×C4×C11C22×D414yes—
388C2×C4×C11C22×D414yes—
389C22⋊D11—232no—
390C22⋊D11—232no—
391C2×Dic11—28no—
392C2×Dic11—28no—
393C2×Dic11—28no—
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—416no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409C2×Dic11C4×D4116yescomplemented
410C2×Dic11C23×C414yes—
411C2×Dic11C23×C414yes—
412C2×Dic11C22×D414yes—
413C2×Dic11C22×D414yes—
414C2×Dic11C22×D414yes—
415C2×Dic11C2×#4114yes—
416D44—232no—
417C4×D11—232no—
418C4×D11—416no—
419C4×D11—416no—
420C4×D11—416no—
421C23×D4—111no—
422C23×D4—111no—
423C23×D4—111no—
424C24×C4—111no—
425C24×C4—111no—
426C24×C4—111no—
427C24×C4—111no—
428C24×C4—111no—
429C2×#121—118no—
430C2×#121—1116no—
431C2×C4×D4—118no—
432C2×C4×D4—118no—
433C2×C4×D4—118no—
434C2×C4×D4—228no—
435C2×C4×D4—228no—
436C2×C4×D4—228no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—118no—
444C22×C4⋊C4—228no—
445C22×C4⋊C4C2×D1111yescharacteristic
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456C22×C42—111no—
457C22×C42—111no—
458C22×C42—111no—
459C22×C42C2×D1111yescharacteristic
460#390—118no—
461#389—118no—
462#388—118no—
463#388C2×D1118yescomplemented
464#386—118no—
465#386—118no—
466#385—118no—
467#385—118no—
468C4×C4⋊C4—118no—
469C4×C22⋊C4—118no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—416no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11C2×C4×D414yes—
485C22×C11C2×C4×D414yes—
486C22×C11#52014yes—
487C22×C11D4214yes—
488C22×C11#54714yes—
489C22×C11#54814yes—
490C22×C11#55314yes—
491C22×C11C24×C411yescharacteristic
492C22×C11C23×D411yescharacteristic
493C22×C11C23×D411yescharacteristic
494C22×C11C22×#4111yescharacteristic
495C22×C11C22×#4111yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11C2×2−1+411yescharacteristic
498C2×D11—232no—
499C2×D11—24no—
500C2×D11—24no—
501C2×D11—24no—
502C2×D11—24no—
503C2×D11—24no—
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—416no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11C2×C4×D418yescomplemented
514C4×C11—24no—
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11—42no—
519C4×C11—42no—
520Dic11—24no—
521Dic11—24no—
522Dic11—24no—
523Dic11—42no—
524Dic11—42no—
525Dic11C2×C4×D418yescomplemented
526C25—111no—
527C25—111no—
528C25C22×D1111yescharacteristic
529C22×D4—118no—
530C22×D4—118no—
531C22×D4—114no—
532C22×D4—114no—
533C22×D4—118no—
534C22×D4—114no—
535C22×D4—224no—
536C22×D4—224no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4—224no—
540C22×D4—224no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—118no—
546C23×C4—114no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—114no—
550C23×C4—114no—
551C23×C4—114no—
552C23×C4—114no—
553C23×C4—224no—
554C23×C4—224no—
555C23×C4—224no—
556C23×C4—224no—
557C23×C4—224no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—442no—
564C23×C4—442no—
565C23×C4—442no—
566C23×C4—442no—
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—1164no—
574C4×D4—2232no—
575C4×D4—2232no—
576C4×D4—2232no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—118no—
579C2×C4⋊C4—118no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—2232no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—224no—
590C2×C4⋊C4—224no—
591C2×C4⋊C4C22×D1114yes—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—118no—
595C2×C22⋊C4—118no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—224no—
604C2×C22⋊C4—224no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—442no—
607C2×C22⋊C4—442no—
608C2×C22⋊C4C4×D1118yescomplemented
609C2×C22⋊C4C22×D1114yes—
610C2×C22⋊C4C22×D1114yes—
611C2×C22⋊C4C22×D1114yes—
612C2×C42—24no—
613C2×C42—114no—
614C2×C42—114no—
615C2×C42—114no—
616C2×C42—224no—
617C2×C42—224no—
618C2×C42—224no—
619C2×C42C22×D1114yes—
620#95—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95C22×D1114yes—
625#95C22×D1114yes—
626C2×C11—44no—
627C2×C11#236118yescomplemented
628C2×C11C22×C4×D411yescharacteristic
629C2×C11C22×C4×D411yescharacteristic
630C2×C11C2×#52011yescharacteristic
631C2×C11C2×D4211yescharacteristic
632C2×C11C2×#54711yescharacteristic
633C2×C11C2×#54811yescharacteristic
634C2×C11C2×#55311yescharacteristic
635D11—28no—
636D11—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—114no—
644C24—114no—
645C24—114no—
646C24—112no—
647C24—114no—
648C24—112no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24C2×C4×D1114yes—
660C24C23×D1112yes—
661C24C23×D1111yescharacteristic
662C2×D4—1116no—
663C2×D4—1116no—
664C2×D4—1116no—
665C2×D4—228no—
666C2×D4—2232no—
667C2×D4—228no—
668C2×D4—228no—
669C2×D4—2232no—
670C2×D4—228no—
671C2×D4—228no—
672C2×D4—2232no—
673C2×D4—228no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—114no—
689C22×C4—114no—
690C22×C4—114no—
691C22×C4—112no—
692C22×C4—114no—
693C22×C4—114no—
694C22×C4—114no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—1116no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—228no—
702C22×C4—2232no—
703C22×C4—228no—
704C22×C4—228no—
705C22×C4—228no—
706C22×C4—228no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—228no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4—444no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4—4416no—
728C22×C4—4416no—
729C22×C4—4416no—
730C22×C4—444no—
731C22×C4—4416no—
732C22×C4C2×C4×D1114yes—
733C22×C4C2×C4×D1114yes—
734C22×C4D4×D1114yes—
735C22×C4D4×D1114yes—
736C22×C4C23×D1112yes—
737C22×C4C23×D1112yes—
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C4⋊C4—28no—
743C4⋊C4—1116no—
744C4⋊C4—1116no—
745C4⋊C4—228no—
746C4⋊C4—228no—
747C4⋊C4—228no—
748C4⋊C4—228no—
749C22⋊C4—28no—
750C22⋊C4—28no—
751C22⋊C4—1116no—
752C22⋊C4—1116no—
753C22⋊C4—228no—
754C22⋊C4—228no—
755C22⋊C4—228no—
756C22⋊C4—444no—
757C22⋊C4—444no—
758C22⋊C4C2×C4×D11116yescomplemented
759C42—28no—
760C42—228no—
761C42—228no—
762C42—228no—
763C11C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—1116no—
778C23—114no—
779C23—114no—
780C23—114no—
781C23—114no—
782C23—228no—
783C23—228no—
784C23—228no—
785C23—228no—
786C23—228no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—228no—
792C23—228no—
793C23—228no—
794C23—228no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—444no—
802C23—444no—
803C23—444no—
804C23—444no—
805C23C22×C4×D1114yes—
806C23C22×C4×D1112yes—
807C23C2×D4×D1112yes—
808C23C2×D4×D1112yes—
809C23#41×D1112yes—
810C23#41×D1112yes—
811C23#6704212yes—
812C23#6704312yes—
813C23C24×D1111yescharacteristic
814D4—2232no—
815D4—2232no—
816D4—2232no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—1116no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—114no—
842C2×C4—114no—
843C2×C4—114no—
844C2×C4—2232no—
845C2×C4—228no—
846C2×C4—228no—
847C2×C4—228no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—4416no—
861C2×C4—4416no—
862C2×C4—4416no—
863C2×C4—4416no—
864C2×C4—444no—
865C2×C4—444no—
866C2×C4C22×C4×D1114yes—
867C2×C4C22×C4×D1114yes—
868C2×C4C2×D4×D1114yes—
869C2×C4C2×D4×D1114yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—416no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—118no—
879C22—2232no—
880C22—224no—
881C22—224no—
882C22—224no—
883C22—224no—
884C22—224no—
885C22—224no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—4416no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22#1062305414yes—
895C22C4×D4×D1114yes—
896C22C4×D4×D1114yes—
897C22#1062314014yes—
898C22#1062318614yes—
899C22#1062320814yes—
900C22#1062324014yes—
901C22C23×C4×D1111yescharacteristic
902C22C22×D4×D1111yescharacteristic
903C22C22×D4×D1111yescharacteristic
904C22C2×#41×D1111yescharacteristic
905C22C2×#41×D1111yescharacteristic
906C22C2×#6704211yescharacteristic
907C22C2×#6704311yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—42no—
914C4—118no—
915C4—224no—
916C4—224no—
917C4—224no—
918C4—442no—
919C4—442no—
920C2—44no—
921C2—228no—
922C2—444no—
923C2#1307162918yesdirect product factor
924C2C2×C4×D4×D1111yescharacteristic
925C2C2×C4×D4×D1111yescharacteristic
926C2C2×#1062305411yescharacteristic
927C2C2×#1062314011yescharacteristic
928C2C2×#1062318611yescharacteristic
929C2C2×#1062320811yescharacteristic
930C2C2×#1062324011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. C22×C4⋊C4×D11C2semidirect
6. #13071629C2direct (N × H)
7. C2×#10622570C2semidirect
8. C2×#10622260C2semidirect
9. C2×#10622283C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622563C2semidirect
13. C2×#10622602C2semidirect
14. C2×C4×Dic11⋊C4C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#388C2semidirect
47. C2×C4⋊C4×D11C22semidirect
48. C2×#66937C4semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×C4×D44C22semidirect
56. C11×#388C22semidirect
63. #10622602C22semidirect
64. #10622570C22semidirect
65. #10622569C22semidirect
66. #10622563C22semidirect
67. C4×Dic11⋊C4C22semidirect
68. #10622283C22semidirect
69. #10622279C22semidirect
70. #10622278C22semidirect
71. #10622260C22semidirect
85. C22×C22⋊D11C2×C4semidirect
86. C22×C22⋊D11C2×C4semidirect
101. C22×D44C2×C4semidirect
114. C22×C4×D11C2×C4semidirect
123. C2×C11×C22⋊C4C2×C4semidirect
135. C2×(C2×D11)⋊C4C2×C4semidirect
136. C2×(C2×D11)⋊C4D4semidirect
149. C2×Dic11⋊C4C2×C4semidirect
150. C2×Dic11⋊C4D4semidirect
162. #66937C2×C4semidirect
228. C2×C22⋊D11C22×C4semidirect
229. C2×C22⋊D11C22×C4semidirect
261. C2×D44C22×C4semidirect
277. C2×C4×D11C22×C4semidirect
281. C11×C22⋊C4C22×C4semidirect
288. (C2×D11)⋊C4C22×C4semidirect
289. (C2×D11)⋊C4C2×D4semidirect
294. Dic11⋊C4C22×C4semidirect
295. Dic11⋊C4C2×D4semidirect
308. C2×#388D11semidirect
360. C22×D11C4×D4semidirect
409. C2×Dic11C4×D4semidirect
463. #388C2×D11semidirect
513. C2×D11C2×C4×D4semidirect
525. Dic11C2×C4×D4semidirect
608. C2×C22⋊C4C4×D11semidirect
627. C2×C11#2361semidirect
758. C22⋊C4C2×C4×D11semidirect
763. C11C2×#2361semidirect
923. C2#13071629direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×D442
C22×(C22⋊D11)⋊C42
C22×C4⋊C4×D112
#130716292
C2×#106225702
C2×#106222602
C2×#106222832
C2×#106222782
C2×#106225692
C2×#106225632
C2×#106226022
C2×C4×Dic11⋊C42
C2×#106222792
C2×C11×#3882
C2×#236111