Finite Group Databasebeta

← C2×#13071651 #14913323

Subgroups — C2×#13071651 #14913323

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3C22×#66930C211yesmaximal, characteristic, complemented
4#13071651C2116yesmaximal, direct product factor
5C2×#10622570C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622585C211yesmaximal, characteristic, complemented
8C2×#10622603C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622833C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992C4116yescomplemented
34C2×#66992C2218yes—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2218yescomplemented
50C2×#66930—28no—
51C2×#66930C2218yescomplemented
52C11×#390C2218yescomplemented
53#10622833C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622603C2218yescomplemented
61#10622585C2218yescomplemented
62#10622570C2218yescomplemented
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622557C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67C22⋊C4×Dic11C2218yescomplemented
68C4×(C2×D11)⋊C4C2218yescomplemented
69C4×Dic11⋊C4C2218yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2×C418yescomplemented
76C22×D4×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11C2×C418yes—
87C22×C22⋊D11C2×C418yescomplemented
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C23×Dic11—24no—
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—42no—
95C23×Dic11C2×C418yescomplemented
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C2×C11×C4⋊C4—42no—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C42×C11—42no—
120C2×C42×C11C2314yes—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11C2×C418yescomplemented
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129#66992C2×C4164yescomplemented
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4C2×C418yescomplemented
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—42no—
140C2×Dic11⋊C4C2×C418yescomplemented
141C2×Dic11⋊C4D418yescomplemented
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11—24no—
148C2×C4×Dic11—24no—
149C2×C4×Dic11—24no—
150C2×C4×Dic11—42no—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156(C22⋊D11)⋊C4—232no—
157#66930—232no—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2363—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11C22×C414yes—
178C24×C11C22×C414yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C22×C414yes—
189C23×D11C2412yes—
190C2×D4×C11—416no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11C22×C4116yescomplemented
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
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×C11C22×C414yes—
207C22×C4×C11C2×D414yes—
208C22×C4×C11#4114yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—232no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—416no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11C22×C4116yes—
221C2×C22⋊D11C22×C4116yescomplemented
222C22×Dic11—232no—
223C22×Dic11—28no—
224C22×Dic11—28no—
225C22×Dic11—28no—
226C22×Dic11—28no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
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—44no—
242C22×Dic11—416no—
243C22×Dic11C22×C414yes—
244C22×Dic11C22×C414yes—
245C22×Dic11C22×C414yes—
246C22×Dic11C22×C4116yescomplemented
247C22×Dic11C2×D414yes—
248C22×Dic11C2×D414yes—
249C22×Dic11#4114yes—
250C22×Dic11#4114yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—416no—
262C11×C4⋊C4—44no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C42×C11—44no—
268C22⋊Dic11—28no—
269C22⋊Dic11—28no—
270C22⋊Dic11—44no—
271C22⋊Dic11C22×C4116yescomplemented
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—44no—
275(C2×D11)⋊C4C22×C4116yescomplemented
276Dic11⋊C4—28no—
277Dic11⋊C4—44no—
278Dic11⋊C4C22×C4116yescomplemented
279Dic11⋊C4C2×D4116yescomplemented
280C4×Dic11—28no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—28no—
284C4×Dic11—44no—
285C22×#121—111no—
286C22×C4×D4—111no—
287C22×#117—111no—
288#2363—1116no—
289C2×#390—111no—
290C2×#390—111no—
291C2×#390D1111yescharacteristic, complemented
292C2×#389—111no—
293C2×#388—111no—
294C2×#388—111no—
295C2×#386—111no—
296C2×#386—111no—
297C2×C4×C4⋊C4—111no—
298C2×C4×C22⋊C4—111no—
299C2×C4×C22⋊C4—111no—
300C2×C4×C22⋊C4—111no—
301C23×C11—28no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11C23×C414yes—
328C23×C11C23×C414yes—
329C23×C11C23×C412yes—
330C23×C11C22×D412yes—
331C23×C11C2×#4112yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C11H(5,𝔽2)12yes—
336C23×C11C2511yescharacteristic
337C22×D11—28no—
338C22×D11—28no—
339C22×D11—28no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11C23×C414yes—
351D4×C11—416no—
352C2×C4×C11—28no—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—44no—
368C2×C4×C11—44no—
369C2×C4×C11C23×C414yes—
370C2×C4×C11C22×D414yes—
371C2×C4×C11C2×#4114yes—
372C22⋊D11—232no—
373C22⋊D11—416no—
374C2×Dic11—28no—
375C2×Dic11—28no—
376C2×Dic11—28no—
377C2×Dic11—28no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—232no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—416no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11C4×D4116yes—
397C2×Dic11C23×C414yes—
398C2×Dic11C23×C414yes—
399C2×Dic11C23×C414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C2×#4114yes—
403C2×Dic11C2×#4114yes—
404C4×D11—416no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4C2×D1111yescharacteristic
408C24×C4—111no—
409C24×C4—111no—
410C24×C4—111no—
411C2×#121—118no—
412C2×#121—1116no—
413C2×C4×D4—118no—
414C2×C4×D4—228no—
415C2×#117—118no—
416C2×#117—228no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4C2×D1111yescharacteristic
431C22×C22⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C42—111no—
435C22×C42—111no—
436C22×C42—111no—
437C22×C42—111no—
438C22×C42—111no—
439C22×C42C2×D1111yescharacteristic
440#390—118no—
441#390—118no—
442#390C2×D1118yescomplemented
443#389—118no—
444#388—118no—
445#388—118no—
446#386—118no—
447#386—118no—
448C4×C4⋊C4—118no—
449C4×C22⋊C4—118no—
450C4×C22⋊C4—118no—
451C4×C22⋊C4—118no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—416no—
465C22×C11—416no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11C2×C4×D414yes—
475C22×C11C4×#4114yes—
476C22×C11#51814yes—
477C22×C11#54614yes—
478C22×C11#55014yes—
479C22×C11#55314yes—
480C22×C11#55514yes—
481C22×C11C24×C411yescharacteristic
482C22×C11C23×D411yescharacteristic
483C22×C11C22×#4111yescharacteristic
484C22×C11C22×#4111yescharacteristic
485C22×C11C22×#4111yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C22×C11C2×H(5,𝔽2)11yescharacteristic
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—416no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C4×C11—24no—
497C4×C11—24no—
498C4×C11—24no—
499C4×C11—42no—
500C4×C11—42no—
501Dic11—24no—
502Dic11—24no—
503Dic11—24no—
504Dic11—24no—
505Dic11—42no—
506Dic11—42no—
507Dic11C2×C4×D418yes—
508C25—111no—
509C25C22×D1111yescharacteristic
510C25C22×D1111yescharacteristic
511C22×D4—42no—
512C22×D4—42no—
513C22×D4—118no—
514C22×D4—114no—
515C22×D4—118no—
516C22×D4—114no—
517C22×D4—224no—
518C22×D4—224no—
519C22×D4—442no—
520C22×D4—442no—
521C22×D4C4×D1118yescomplemented
522C22×D4C22×D1114yes—
523C23×C4—111no—
524C23×C4—118no—
525C23×C4—114no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—114no—
533C23×C4—114no—
534C23×C4—224no—
535C23×C4—224no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—442no—
541C23×C4—442no—
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547#121—1164no—
548C4×D4—2232no—
549#117—2232no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—118no—
552C2×C4⋊C4—118no—
553C2×C4⋊C4—114no—
554C2×C4⋊C4—114no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—224no—
558C2×C4⋊C4—442no—
559C2×C4⋊C4C22×D1114yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—118no—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—118no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—224no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—224no—
577C2×C22⋊C4—224no—
578C2×C22⋊C4—442no—
579C2×C22⋊C4—442no—
580C2×C22⋊C4C22×D1114yes—
581C2×C22⋊C4C22×D1114yes—
582C2×C22⋊C4C22×D1114yes—
583C2×C22⋊C4C22×D1114yes—
584C2×C42—42no—
585C2×C42—114no—
586C2×C42—114no—
587C2×C42—114no—
588C2×C42—114no—
589C2×C42—114no—
590C2×C42—224no—
591C2×C42—224no—
592C2×C42—224no—
593C2×C42—224no—
594C2×C42—442no—
595C2×C42C22×D1114yes—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602C2×C11—44no—
603C2×C11—44no—
604C2×C11#236318yescomplemented
605C2×C11C22×C4×D411yescharacteristic
606C2×C11C2×C4×#4111yescharacteristic
607C2×C11C2×#51811yescharacteristic
608C2×C11C2×#54611yescharacteristic
609C2×C11C2×#55011yescharacteristic
610C2×C11C2×#55311yescharacteristic
611C2×C11C2×#55511yescharacteristic
612D11—44no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—114no—
626C24—112no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24C2×C4×D1114yes—
634C24C2×C4×D1114yes—
635C24C23×D1112yes—
636C24C23×D1112yes—
637C24C23×D1111yescharacteristic
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—416no—
641C2×D4—1116no—
642C2×D4—1116no—
643C2×D4—228no—
644C2×D4—2232no—
645C2×D4—228no—
646C2×D4—4416no—
647C2×D4—444no—
648C2×D4—444no—
649C2×D4C2×C4×D11116yescomplemented
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—114no—
663C22×C4—114no—
664C22×C4—114no—
665C22×C4—112no—
666C22×C4—114no—
667C22×C4—114no—
668C22×C4—1116no—
669C22×C4—114no—
670C22×C4—114no—
671C22×C4—112no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—228no—
678C22×C4—228no—
679C22×C4—2232no—
680C22×C4—228no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—228no—
698C22×C4—444no—
699C22×C4—4416no—
700C22×C4—444no—
701C22×C4—4416no—
702C22×C4C2×C4×D1114yes—
703C22×C4D4×D1114yes—
704C22×C4#434114yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C4⋊C4—44no—
711C4⋊C4—1116no—
712C4⋊C4—1116no—
713C4⋊C4—228no—
714C4⋊C4—444no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—1116no—
720C22⋊C4—1116no—
721C22⋊C4—228no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
725C22⋊C4—444no—
726C22⋊C4—444no—
727C42—44no—
728C42—228no—
729C42—228no—
730C42—228no—
731C42—228no—
732C42—444no—
733C11C2×#236311yescharacteristic, complemented, Sylow
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—114no—
761C23—228no—
762C23—228no—
763C23—228no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23C22×C4×D1114yes—
775C23C22×C4×D1114yes—
776C23C22×C4×D1112yes—
777C23C2×D4×D1112yes—
778C23C2×#434112yes—
779C23#6703712yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#41×D1112yes—
783C23C24×D1111yescharacteristic
784D4—416no—
785D4—2232no—
786D4—4416no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—1116no—
805C2×C4—114no—
806C2×C4—114no—
807C2×C4—114no—
808C2×C4—114no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—2232no—
813C2×C4—228no—
814C2×C4—228no—
815C2×C4—228no—
816C2×C4—228no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—4416no—
832C2×C4—4416no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4C22×C4×D1114yes—
836C2×C4C2×D4×D1114yes—
837C2×C4C2×#434114yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—416no—
847C22—416no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—442no—
858C22—4416no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22#1062301714yes—
863C22C4×#434114yes—
864C22C4×D4×D1114yes—
865C22#1062313214yes—
866C22#1062314114yes—
867C22#1062320114yes—
868C22#1062324914yes—
869C22C23×C4×D1111yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C22×#434111yescharacteristic
872C22C2×#6703711yescharacteristic
873C22C2×#6703711yescharacteristic
874C22C2×#41×D1111yescharacteristic
875C22C2×#41×D1111yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—118no—
882C4—224no—
883C4—224no—
884C4—224no—
885C4—224no—
886C4—442no—
887C4—442no—
888C2—44no—
889C2—44no—
890C2—444no—
891C2#1307165118yesdirect product factor
892C2C2×C4×D4×D1111yescharacteristic
893C2C2×C4×#434111yescharacteristic
894C2C2×#1062301711yescharacteristic
895C2C2×#1062314111yescharacteristic
896C2C2×#1062324911yescharacteristic
897C2C2×#1062313211yescharacteristic
898C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC2×#390D11
hypocenterC11C2×#2363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. C22×#66930C2semidirect
4. #13071651C2direct (N × H)
5. C2×#10622570C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622585C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622569C2semidirect
12. C2×C4×Dic11⋊C4C2semidirect
13. C2×C22⋊C4×Dic11C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#390C2semidirect
33. C2×#66992C4semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66930C22semidirect
52. C11×#390C22semidirect
53. #10622833C22semidirect
60. #10622603C22semidirect
61. #10622585C22semidirect
62. #10622570C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622557C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. C22⋊C4×Dic11C22semidirect
68. C4×(C2×D11)⋊C4C22semidirect
69. C4×Dic11⋊C4C22semidirect
75. C22×D4×C11C2×C4semidirect
87. C22×C22⋊D11C2×C4semidirect
95. C23×Dic11C2×C4semidirect
124. C2×C22⋊Dic11C2×C4semidirect
129. #66992C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×Dic11⋊C4C2×C4semidirect
141. C2×Dic11⋊C4D4semidirect
193. C2×D4×C11C22×C4semidirect
221. C2×C22⋊D11C22×C4semidirect
246. C22×Dic11C22×C4semidirect
271. C22⋊Dic11C22×C4semidirect
275. (C2×D11)⋊C4C22×C4semidirect
278. Dic11⋊C4C22×C4semidirect
279. Dic11⋊C4C2×D4semidirect
291. C2×#390D11semidirect
442. #390C2×D11semidirect
521. C22×D4C4×D11semidirect
604. C2×C11#2363semidirect
649. C2×D4C2×C4×D11semidirect
733. C11C2×#2363semidirect
891. C2#13071651direct (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×(C22⋊D11)⋊C42
C22×#669302
#130716512
C2×#106225702
C2×#106225852
C2×#106226032
C2×#106225572
C2×#106228332
C2×#106225692
C2×C4×Dic11⋊C42
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3902
C2×#236311