Finite Group Databasebeta

← C2×#13071633 #14913303

Subgroups — C2×#13071633 #14913303

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×#66992C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13071633C2116yesmaximal, direct product factor
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622585C211yesmaximal, characteristic, complemented
8C2×#10622553C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622833C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622823C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C2×C4×D4×C11—28no—
26C2×C4×D4×C11C2218yescomplemented
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992C4116yescomplemented
36C2×#66992C2218yes—
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×Dic11⋊C4—28no—
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2218yescomplemented
51C22×C4×Dic11C2211yescharacteristic
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×(C22⋊D11)⋊C4—28no—
55C2×(C22⋊D11)⋊C4C2218yescomplemented
56#10622833C2218yescomplemented
57#10622826C2218yescomplemented
58#10622823C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622602C2218yescomplemented
66#10622585C2218yescomplemented
67#10622570C2218yescomplemented
68#10622557C2218yescomplemented
69C22⋊C4×Dic11C2218yescomplemented
70#10622553C2218yescomplemented
71C4×Dic11⋊C4C2218yescomplemented
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11C2×C418yescomplemented
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—42no—
84C23×C4×C11—42no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2314yes—
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11C2×C418yescomplemented
97C22×C22⋊D11C2×C418yescomplemented
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—24no—
103C23×Dic11—24no—
104C23×Dic11—42no—
105C23×Dic11C2×C418yescomplemented
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2314yes—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2314yes—
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—42no—
118C22×C4×D11C2314yes—
119C4×D4×C11—232no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2314yes—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4D418yescomplemented
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C42×C11—24no—
127C2×C42×C11C2314yes—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2×C418yescomplemented
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66992C2×C4164yescomplemented
137C4×C22⋊D11—232no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4C2×C418yescomplemented
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—232no—
151C2×Dic11⋊C4C2×C418yescomplemented
152C2×Dic11⋊C4D418yescomplemented
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×C4×Dic11—24no—
160C2×C4×Dic11—24no—
161C2×C4×Dic11—24no—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165(C22⋊D11)⋊C4—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×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11C22×C414yes—
184C24×C11C22×C414yes—
185C24×C11C2×D414yes—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11C22×C414yes—
197C23×D11C2412yes—
198C2×D4×C11—232no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11C22×C4116yescomplemented
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×C11—28no—
213C22×C4×C11—22no—
214C22×C4×C11—28no—
215C22×C4×C11—28no—
216C22×C4×C11—28no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—416no—
220C22×C4×C11—416no—
221C22×C4×C11C22×C414yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—232no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11C22×C4116yescomplemented
237C2×C22⋊D11C22×C4116yescomplemented
238C22×Dic11—232no—
239C22×Dic11—28no—
240C22×Dic11—28no—
241C22×Dic11—28no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—28no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—44no—
259C22×Dic11—416no—
260C22×Dic11C22×C414yes—
261C22×Dic11C22×C414yes—
262C22×Dic11C22×C414yes—
263C22×Dic11C22×C4116yescomplemented
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—44no—
277C2×C4×D11—416no—
278C11×C4⋊C4—28no—
279C11×C22⋊C4—28no—
280C11×C22⋊C4C2×D4116yescomplemented
281C42×C11—28no—
282C22⋊Dic11—28no—
283C22⋊Dic11—28no—
284C22⋊Dic11—44no—
285C22⋊Dic11C22×C4116yescomplemented
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4C22×C4116yescomplemented
290Dic11⋊C4—28no—
291Dic11⋊C4—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×D4D1111yescharacteristic, complemented
303C23×C4⋊C4—111no—
304#2361—1116no—
305C2×#390—111no—
306C2×#389—111no—
307C2×#388—111no—
308C2×#388—111no—
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—28no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11C4×D4116yescomplemented
339C23×C11C23×C414yes—
340C23×C11C23×C414yes—
341C23×C11C23×C412yes—
342C23×C11C22×D412yes—
343C23×C11C22×D414yes—
344C23×C11C22×D412yes—
345C23×C11C2×#4114yes—
346C23×C11C2×#4112yes—
347C23×C11C2×#4112yes—
348C23×C11H(5,𝔽2)12yes—
349C23×C112−1+412yes—
350C23×C11C2511yescharacteristic
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11C23×C414yes—
365D4×C11—232no—
366C2×C4×C11—28no—
367C2×C4×C11—28no—
368C2×C4×C11—28no—
369C2×C4×C11—28no—
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—416no—
382C2×C4×C11—416no—
383C2×C4×C11—44no—
384C2×C4×C11C23×C414yes—
385C2×C4×C11C22×D414yes—
386C2×C4×C11C22×D414yes—
387C2×C4×C11C22×D414yes—
388C22⋊D11—232no—
389C22⋊D11—232no—
390C2×Dic11—28no—
391C2×Dic11—28no—
392C2×Dic11—28no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—232no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—416no—
410C2×Dic11—44no—
411C2×Dic11—44no—
412C2×Dic11—44no—
413C2×Dic11C4×D4116yescomplemented
414C2×Dic11C23×C414yes—
415C2×Dic11C23×C414yes—
416C2×Dic11C23×C414yes—
417C2×Dic11C22×D414yes—
418C2×Dic11C22×D414yes—
419C2×Dic11C2×#4114yes—
420C4×D11—416no—
421C23×D4—111no—
422C23×D4—111no—
423C23×D4C2×D1111yescharacteristic
424C24×C4—111no—
425C24×C4—111no—
426C24×C4—111no—
427C24×C4C2×D1111yescharacteristic
428C24×C4C2×D1111yescharacteristic
429C2×#121—118no—
430C2×#121—1116no—
431C2×C4×D4—28no—
432C2×C4×D4—118no—
433C2×C4×D4—118no—
434C2×C4×D4—228no—
435C2×C4×D4—228no—
436C2×C4×D4C2×D1118yescomplemented
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—118no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
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⋊C4—111no—
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#388—118no—
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×#95—111no—
475C2×#95—111no—
476C22×C11—232no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—24no—
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—24no—
486C22×C11—416no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C2×C4×D414yes—
492C22×C11C2×C4×D414yes—
493C22×C11C2×C4×D418yescomplemented
494C22×C11#52014yes—
495C22×C11D4214yes—
496C22×C11#54714yes—
497C22×C11#54814yes—
498C22×C11#55314yes—
499C22×C11C24×C411yescharacteristic
500C22×C11C23×D411yescharacteristic
501C22×C11C23×D411yescharacteristic
502C22×C11C22×#4111yescharacteristic
503C22×C11C22×#4111yescharacteristic
504C22×C11C2×H(5,𝔽2)11yescharacteristic
505C22×C11C2×2−1+411yescharacteristic
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—416no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C4×C11—24no—
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11—42no—
519Dic11—24no—
520Dic11—24no—
521Dic11—24no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11C2×C4×D418yescomplemented
526C25—111no—
527C25C22×D1111yescharacteristic
528C25C22×D1111yescharacteristic
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—118no—
532C22×D4—118no—
533C22×D4—114no—
534C22×D4—114no—
535C22×D4—224no—
536C22×D4—224no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4C4×D1118yescomplemented
540C22×D4C22×D1114yes—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—42no—
547C23×C4—111no—
548C23×C4—118no—
549C23×C4—114no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—114no—
557C23×C4—114no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—442no—
565C23×C4—442no—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1114yes—
568C23×C4C22×D1114yes—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—1164no—
574C4×D4—232no—
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—118no—
594C2×C22⋊C4—114no—
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—224no—
607C2×C22⋊C4—442no—
608C2×C22⋊C4—442no—
609C2×C22⋊C4C22⋊D1118yescomplemented
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#95—114no—
625#95—114no—
626C2×C11—28no—
627C2×C11—44no—
628C2×C11#236118yescomplemented
629C2×C11C22×C4×D411yescharacteristic
630C2×C11C22×C4×D411yescharacteristic
631C2×C11C2×#52011yescharacteristic
632C2×C11C2×D4211yescharacteristic
633C2×C11C2×#54711yescharacteristic
634C2×C11C2×#54811yescharacteristic
635C2×C11C2×#55311yescharacteristic
636D11—44no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—114no—
648C24—112no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24C2×C4×D1114yes—
656C24C2×C4×D1114yes—
657C24#433914yes—
658C24C2×C22⋊D1114yes—
659C24C23×D1112yes—
660C24C23×D1112yes—
661C24C23×D1111yescharacteristic
662C2×D4—232no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—1116no—
666C2×D4—1116no—
667C2×D4—228no—
668C2×D4—2232no—
669C2×D4—228no—
670C2×D4—2232no—
671C2×D4—228no—
672C2×D4—228no—
673C2×D4C2×C4×D11116yescomplemented
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—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—416no—
692C22×C4—416no—
693C22×C4—114no—
694C22×C4—114no—
695C22×C4—114no—
696C22×C4—112no—
697C22×C4—114no—
698C22×C4—114no—
699C22×C4—1116no—
700C22×C4—114no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—228no—
708C22×C4—228no—
709C22×C4—2232no—
710C22×C4—228no—
711C22×C4—228no—
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—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—444no—
730C22×C4—4416no—
731C22×C4—444no—
732C22×C4—4416no—
733C22×C4C2×C4×D1114yes—
734C22×C4D4×D1114yes—
735C22×C4C2×C22⋊D1114yes—
736C22×C4C2×C22⋊D1114yes—
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—1116no—
751C22⋊C4—1116no—
752C22⋊C4—228no—
753C22⋊C4—228no—
754C22⋊C4—228no—
755C22⋊C4—228no—
756C22⋊C4—444no—
757C22⋊C4—444no—
758C22⋊C4C2×C22⋊D11116yescomplemented
759C42—28no—
760C42—228no—
761C42—228no—
762C42—228no—
763C11C2×#236111yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—114no—
788C23—228no—
789C23—228no—
790C23—228no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—444no—
798C23—444no—
799C23—444no—
800C23—444no—
801C23C4×C22⋊D11116yescomplemented
802C23C22×C4×D1114yes—
803C23C22×C4×D1114yes—
804C23C22×C4×D1112yes—
805C23C2×#433914yes—
806C23C2×#433912yes—
807C23C2×D4×D1112yes—
808C23#6703712yes—
809C23#41×D1112yes—
810C23#6704312yes—
811C23C22×C22⋊D1114yes—
812C23C22×C22⋊D1112yes—
813C23C24×D1111yescharacteristic
814D4—232no—
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—416no—
833C2×C4—416no—
834C2×C4—44no—
835C2×C4—1116no—
836C2×C4—114no—
837C2×C4—114no—
838C2×C4—114no—
839C2×C4—114no—
840C2×C4—114no—
841C2×C4—114no—
842C2×C4—2232no—
843C2×C4—228no—
844C2×C4—228no—
845C2×C4—228no—
846C2×C4—222no—
847C2×C4—222no—
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—222no—
861C2×C4—4416no—
862C2×C4—4416no—
863C2×C4—444no—
864C2×C4—444no—
865C2×C4—444no—
866C2×C4C22×C4×D1114yes—
867C2×C4C2×D4×D1114yes—
868C2×C4C22×C22⋊D1114yes—
869C2×C4C22×C22⋊D1114yes—
870C22—232no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—416no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—224no—
886C22—224no—
887C22—224no—
888C22—4416no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22#1062307114yes—
894C22C4×D4×D1114yes—
895C22#1062307714yes—
896C22#1062308314yes—
897C22C2×C4×C22⋊D1114yes—
898C22C2×C4×C22⋊D1118yescomplemented
899C22D4×C22⋊D1114yes—
900C22#1062335514yes—
901C22C23×C4×D1111yescharacteristic
902C22C22×#433911yescharacteristic
903C22C22×D4×D1111yescharacteristic
904C22C2×#6703711yescharacteristic
905C22C2×#41×D1111yescharacteristic
906C22C2×#6704311yescharacteristic
907C22C23×C22⋊D1111yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—118no—
914C4—224no—
915C4—224no—
916C4—224no—
917C4—442no—
918C4—442no—
919C4—442no—
920C2—28no—
921C2—44no—
922C2—444no—
923C2#1307163318yesdirect product factor
924C2C2×C4×D4×D1111yescharacteristic
925C2C22×C4×C22⋊D1111yescharacteristic
926C2C2×#1062307711yescharacteristic
927C2C2×D4×C22⋊D1111yescharacteristic
928C2C2×#1062335511yescharacteristic
929C2C2×#1062308311yescharacteristic
930C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C23×Dic11⋊C4C2semidirect
5. #13071633C2direct (N × H)
6. C2×#10622570C2semidirect
7. C2×#10622585C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622823C2semidirect
13. C2×#10622602C2semidirect
14. C2×C4×Dic11⋊C4C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C22×C4×D4×C11C2semidirect
26. C2×C4×D4×C11C22semidirect
35. C2×#66992C4semidirect
38. C2×C4×C22⋊D11C22semidirect
50. C22×Dic11⋊C4C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. #10622833C22semidirect
57. #10622826C22semidirect
58. #10622823C22semidirect
65. #10622602C22semidirect
66. #10622585C22semidirect
67. #10622570C22semidirect
68. #10622557C22semidirect
69. C22⋊C4×Dic11C22semidirect
70. #10622553C22semidirect
71. C4×Dic11⋊C4C22semidirect
77. C22×D4×C11C2×C4semidirect
96. C22×C22⋊D11C2×C4semidirect
97. C22×C22⋊D11C2×C4semidirect
105. C23×Dic11C2×C4semidirect
123. C2×C11×C22⋊C4D4semidirect
131. C2×C22⋊Dic11C2×C4semidirect
136. #66992C2×C4semidirect
141. C2×(C2×D11)⋊C4C2×C4semidirect
151. C2×Dic11⋊C4C2×C4semidirect
152. C2×Dic11⋊C4D4semidirect
201. C2×D4×C11C22×C4semidirect
236. C2×C22⋊D11C22×C4semidirect
237. C2×C22⋊D11C22×C4semidirect
263. C22×Dic11C22×C4semidirect
280. C11×C22⋊C4C2×D4semidirect
285. C22⋊Dic11C22×C4semidirect
289. (C2×D11)⋊C4C22×C4semidirect
294. Dic11⋊C4C22×C4semidirect
295. Dic11⋊C4C2×D4semidirect
302. C22×C4×D4D11semidirect
338. C23×C11C4×D4semidirect
413. C2×Dic11C4×D4semidirect
436. C2×C4×D4C2×D11semidirect
493. C22×C11C2×C4×D4semidirect
525. Dic11C2×C4×D4semidirect
539. C22×D4C4×D11semidirect
609. C2×C22⋊C4C22⋊D11semidirect
628. C2×C11#2361semidirect
673. C2×D4C2×C4×D11semidirect
758. C22⋊C4C2×C22⋊D11semidirect
763. C11C2×#2361semidirect
801. C23C4×C22⋊D11semidirect
898. C22C2×C4×C22⋊D11semidirect
923. C2#13071633direct (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×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
#130716332
C2×#106225702
C2×#106225852
C2×#106225532
C2×#106225572
C2×#106228332
C2×#106228262
C2×#106228232
C2×#106226022
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
C22×C4×D4×C112
C2×#236111