Finite Group Databasebeta

← C4⋊C4×Dic11⋊C4 #14675210

Subgroups — C4⋊C4×Dic11⋊C4 #14675210

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622589C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4C2×C4×Dic11⋊C4C212yesmaximal
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic
6#13066849C212yesmaximal
7#13066847C212yesmaximal
8#13066846C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic
10Dic11⋊#95C212yesmaximal
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C4×C11×C4⋊C4—24no—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622589C418yescomplemented
37C4⋊C4×Dic11—24no—
38C4⋊C4×Dic11C418yescomplemented
39C4×Dic11⋊C4—28no—
40C4×Dic11⋊C4C418yescomplemented
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4D414yes—
57C2×C11×C4⋊C4Q814yes—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—24no—
61C2×C42×C11—24no—
62C2×C42×C11—42no—
63C2×C42×C11C2×C414yes—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2×C414yes—
69C2×C4⋊Dic11C2×C414yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—42no—
75C2×Dic11⋊C4—42no—
76C2×Dic11⋊C4C2×C414yes—
77C2×Dic11⋊C4C2×C418yes—
78C2×Dic11⋊C4C2×C418yes—
79C2×Dic11⋊C4C2×C414yes—
80C2×Dic11⋊C4D414yes—
81C2×Dic11⋊C4Q814yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11C2×C414yes—
90C2×C4×Dic11C2×C418yes—
91C2×C4×Dic11C2×C414yes—
92C2×C4×Dic11C2×C414yes—
93C2×C4×Dic11C2×C414yes—
94C11×#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95C2×C414yes—
101C11⋊#95C2×C414yes—
102C11⋊#95C2×C418yes—
103C4⋊C42—111nomaximal, Sylow
104C24×C11C2411yescharacteristic
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×Q814yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C414yes—
168C22×Dic11C22×C414yes—
169C22×Dic11C22×C412yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C412yes—
174C22×Dic11C22×C412yes—
175C22×Dic11C22×C412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11C2×Q812yes—
179C22×Dic11C2×Q812yes—
180C22×Dic11#4112yes—
181C22×Dic11#4112yes—
182C11×C4⋊C4—28no—
183C11×C4⋊C4C4⋊C4116yescomplemented
184C42×C11—28no—
185C42×C11—48no—
186C4⋊Dic11—28no—
187C4⋊Dic11—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—216no—
190Dic11⋊C4—48no—
191Dic11⋊C4C4⋊C4116yesdirect product factor
192C4×Dic11—216no—
193C4×Dic11—28no—
194C4×Dic11—48no—
195C4×Dic11C42116yescomplemented
196C2×#384—111no—
197C2×C4×C4⋊C4—111no—
198C2×C4×C4⋊C4—112no—
199C2×C4×C4⋊C4—111no—
200C2×C4×C4⋊C4—111no—
201C2×C4×C4⋊C4D1111yescharacteristic
202#1436—112no—
203#1436—112no—
204C4⋊#95—111no—
205C4⋊#95—112no—
206C4⋊#95—111no—
207C23×C11C23×C411yescharacteristic
208C23×C11C23×C411yescharacteristic
209C23×C11C23×C411yescharacteristic
210C23×C11C22×D411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×Q811yescharacteristic
213C23×C11C22×Q811yescharacteristic
214C23×C11C2×#4111yescharacteristic
215C23×C11C2×#4111yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11H(5,𝔽2)11yescharacteristic
219C23×C11H(5,𝔽2)11yescharacteristic
220C23×C112−1+411yescharacteristic
221C23×C112−1+411yescharacteristic
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C4214yes—
249C2×C4×C11C2×C4⋊C414yes—
250C2×C4×C11C2×C4⋊C418yes—
251C2×C4×C11C2×C4⋊C414yes—
252C2×C4×C11#11714yes—
253C2×C4×C11C4×D414yes—
254C2×C4×C11C4×D414yes—
255C2×C4×C11C4×Q814yes—
256C2×C4×C11C4×Q814yes—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—42no—
287C2×Dic11—41no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11C2×C4214yes—
291C2×Dic11C2×C4214yes—
292C2×Dic11C2×C4⋊C414yes—
293C2×Dic11C2×C4⋊C414yes—
294C2×Dic11#11714yes—
295C2×Dic11C4×D414yes—
296C2×Dic11C4×D414yes—
297C2×Dic11C4×Q814yes—
298C2×Dic11C4×Q814yes—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—112no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C42—111no—
308C22×C42—112no—
309C22×C42—111no—
310C22×C42—112no—
311C22×C42C2×D1112yes—
312C22×C42C2×D1111yescharacteristic
313#384—118no—
314C4×C4⋊C4—24no—
315C4×C4⋊C4—118no—
316C4×C4⋊C4—118no—
317C4×C4⋊C4—228no—
318C4×C4⋊C4—224no—
319C2×#95—111no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95C2×D1112yes—
328C22×C11C22×C4211yescharacteristic
329C22×C11C22×C4⋊C411yescharacteristic
330C22×C11C22×C4⋊C411yescharacteristic
331C22×C11C2×#11711yescharacteristic
332C22×C11C2×#11711yescharacteristic
333C22×C11C2×C4×D411yescharacteristic
334C22×C11C2×C4×D411yescharacteristic
335C22×C11C2×C4×D411yescharacteristic
336C22×C11C2×C4×D411yescharacteristic
337C22×C11C2×C4×Q811yescharacteristic
338C22×C11C2×C4×Q811yescharacteristic
339C22×C11C2×C4×Q811yescharacteristic
340C22×C11C2×C4×Q811yescharacteristic
341C22×C11#51811yescharacteristic
342C22×C11#51911yescharacteristic
343C22×C11#52011yescharacteristic
344C22×C11#52011yescharacteristic
345C22×C11#52011yescharacteristic
346C22×C11#52011yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11#54711yescharacteristic
349C22×C11#54711yescharacteristic
350C22×C11D4×Q811yescharacteristic
351C22×C11D4×Q811yescharacteristic
352C22×C11#55011yescharacteristic
353C22×C11#55011yescharacteristic
354C22×C11#55411yescharacteristic
355C22×C11#55411yescharacteristic
356C22×C11#55511yescharacteristic
357C22×C11#55611yescharacteristic
358C22×C11#55611yescharacteristic
359C22×C11#55711yescharacteristic
360C22×C11#55711yescharacteristic
361C22×C11Q8211yescharacteristic
362C22×C11#55911yescharacteristic
363C4×C11—28no—
364C4×C11—24no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11C4×C4⋊C418yescomplemented
368Dic11—24no—
369Dic11—24no—
370Dic11—44no—
371Dic11—42no—
372Dic11—44no—
373Dic11C4×C4⋊C418yescomplemented
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4C22×D1112yes—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—118no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—118no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—224no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—442no—
404C2×C4⋊C4—442no—
405C2×C4⋊C4Dic2214yes—
406C2×C4⋊C4C4×D1114yes—
407C2×C4⋊C4C4×D1114yes—
408C2×C4⋊C4C22⋊D1114yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42—114no—
415C2×C42—114no—
416C2×C42—114no—
417C2×C42—118no—
418C2×C42—114no—
419C2×C42—224no—
420C2×C42—224no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—224no—
424C2×C42—224no—
425C2×C42—442no—
426C2×C42C4×D1114yes—
427#95—24no—
428#95—114no—
429#95—114no—
430#95—118no—
431#95—224no—
432#95—224no—
433#95—224no—
434#95—442no—
435#95—442no—
436C2×C11C2×C4×C4⋊C411yescharacteristic
437C2×C11C2×C4×C4⋊C411yescharacteristic
438C2×C11#227411yescharacteristic
439C2×C11D4×C4⋊C411yescharacteristic
440C2×C11D4×C4⋊C411yescharacteristic
441C2×C11Q8×C4⋊C411yescharacteristic
442C2×C11Q8×C4⋊C411yescharacteristic
443C2×C11#235411yescharacteristic
444C2×C11#235411yescharacteristic
445C2×C11#235511yescharacteristic
446C2×C11#235511yescharacteristic
447C2×C11#236511yescharacteristic
448C2×C11#236511yescharacteristic
449C2×C11#236611yescharacteristic
450C2×C11#236911yescharacteristic
451C24C23×D1111yescharacteristic
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4C2×Dic2214yes—
515C22×C4C2×Dic2212yes—
516C22×C4C2×C4×D1112yes—
517C22×C4C2×C4×D1114yes—
518C22×C4C2×C4×D1112yes—
519C22×C4C2×C4×D1114yes—
520C22×C4C2×C4×D1112yes—
521C22×C4C2×C4×D1112yes—
522C22×C4C2×C4×D1112yes—
523C22×C4#433912yes—
524C22×C4#433912yes—
525C22×C4D4×D1112yes—
526C22×C4Q8×D1112yes—
527C22×C4C2×C22⋊D1114yes—
528C22×C4C2×C22⋊D1112yes—
529C4⋊C4—28no—
530C4⋊C4—1116no—
531C4⋊C4—228no—
532C4⋊C4—2216no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—448no—
536C4⋊C4Dic11⋊C4116yesdirect product factor
537C42—28no—
538C42—48no—
539C42—1116no—
540C42—2216no—
541C42—228no—
542C42—448no—
543C11C4⋊C4211yescharacteristic, complemented, Sylow
544C23C22×Dic2211yescharacteristic
545C23C22×C4×D1111yescharacteristic
546C23C22×C4×D1111yescharacteristic
547C23C22×C4×D1111yescharacteristic
548C23C2×#433911yescharacteristic
549C23C2×#433911yescharacteristic
550C23C2×D4×D1111yescharacteristic
551C23#6703711yescharacteristic
552C23C2×Q8×D1111yescharacteristic
553C23#6704011yescharacteristic
554C23#41×D1111yescharacteristic
555C23#41×D1111yescharacteristic
556C23#6704211yescharacteristic
557C23#6704311yescharacteristic
558C23C22×C22⋊D1111yescharacteristic
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—114no—
588C2×C4—114no—
589C2×C4—114no—
590C2×C4—114no—
591C2×C4—114no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—441no—
625C2×C4—442no—
626C2×C4—441no—
627C2×C4C4×Dic2214yes—
628C2×C4C4×Dic2214yes—
629C2×C4C42×D1114yes—
630C2×C4#6692514yes—
631C2×C4C4⋊C4×D1114yes—
632C2×C4C2×Dic11⋊C418yes—
633C2×C4C2×Dic11⋊C414yes—
634C2×C4C4×C22⋊D1114yes—
635C2×C4C4×C22⋊D1114yes—
636C22C2×C4×Dic2211yescharacteristic
637C22C2×C4×Dic2211yescharacteristic
638C22C2×C42×D1111yescharacteristic
639C22C2×#6692511yescharacteristic
640C22C2×C4⋊C4×D1111yescharacteristic
641C22#1062303511yescharacteristic
642C22#1062303811yescharacteristic
643C22#1062304211yescharacteristic
644C22D11×#11711yescharacteristic
645C22#1062305411yescharacteristic
646C22#1062306311yescharacteristic
647C22#1062306411yescharacteristic
648C22D4×Dic2211yescharacteristic
649C22#1062307011yescharacteristic
650C22C4×D4×D1111yescharacteristic
651C22C4×D4×D1111yescharacteristic
652C22#1062307611yescharacteristic
653C22#1062307711yescharacteristic
654C22#1062308411yescharacteristic
655C22#1062309011yescharacteristic
656C22Q8×Dic2211yescharacteristic
657C22#1062309811yescharacteristic
658C22#1062309911yescharacteristic
659C22#1062310011yescharacteristic
660C22C4×Q8×D1111yescharacteristic
661C22C4×Q8×D1111yescharacteristic
662C22#1062310311yescharacteristic
663C22#1062310511yescharacteristic
664C22C22×Dic11⋊C411yescharacteristic
665C22C2×C4×C22⋊D1111yescharacteristic
666C22C2×C4×C22⋊D1111yescharacteristic
667C22D4×C22⋊D1111yescharacteristic
668C22Q8×C22⋊D1111yescharacteristic
669C22#1062335511yescharacteristic
670C22#1062336511yescharacteristic
671C4—28no—
672C4—24no—
673C4—44no—
674C4—42no—
675C4—118no—
676C4—224no—
677C4—224no—
678C4—444no—
679C4—444no—
680C4—442no—
681C4C4×Dic11⋊C418yescomplemented
682C2C4×C4⋊C4×D1111yescharacteristic
683C2C2×C4×Dic11⋊C411yescharacteristic
684C2#1307097011yescharacteristic
685C2D4×Dic11⋊C411yescharacteristic
686C2C4⋊C4×C22⋊D1111yescharacteristic
687C2Q8×Dic11⋊C411yescharacteristic
688C2C4⋊C4×Dic2211yescharacteristic
689C2#1307156111yescharacteristic
690C2#1307156611yescharacteristic
691C2#1307156911yescharacteristic
692C2#1307157411yescharacteristic
693C2#1307167011yescharacteristic
694C2#1307167511yescharacteristic
695C2#1307167811yescharacteristic
696C2#1307170311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4⋊C42
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. #10622589C4semidirect
38. C4⋊C4×Dic11C4semidirect
40. C4×Dic11⋊C4C4semidirect
183. C11×C4⋊C4C4⋊C4semidirect
191. Dic11⋊C4C4⋊C4direct (N × H)
195. C4×Dic11C42semidirect
367. C4×C11C4×C4⋊C4semidirect
373. Dic11C4×C4⋊C4semidirect
536. C4⋊C4Dic11⋊C4direct (N × H)
543. C11C4⋊C42semidirect
681. C4C4×Dic11⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106225892
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
#130668492
#130668472
#130668462
#130668452
Dic11⋊#952
C2×C4×C11×C4⋊C42
C4⋊C4211