Finite Group Databasebeta

← #14675349

Subgroups — #14675349

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic
5C2×C4×Dic11⋊C4C212yesmaximal
6#13066849C212yesmaximal
7#13066847C212yesmaximal
8#13066845C211yesmaximal, characteristic
9#13066842C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic
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⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C4×C11×C4⋊C4—24no—
25C2×C11×#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C4⋊C4×Dic11—24no—
37C4⋊C4×Dic11C418yescomplemented
38#10622586C418yescomplemented
39C4×Dic11⋊C4—28no—
40#10622541C418yescomplemented
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
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⋊Dic11C2×C414yes—
67C2×C4⋊Dic11C2×C414yes—
68C2×C4⋊Dic11C2×C414yes—
69C2×C4⋊Dic11C2×C414yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4C2×C418yes—
75C2×Dic11⋊C4C2×C418yes—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—42no—
85C2×C4×Dic11C2×C414yes—
86C2×C4×Dic11C2×C418yes—
87C2×C4×Dic11C2×C414yes—
88C11×#95—24no—
89C11⋊#95—24no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—42no—
95C11⋊#95C2×C418yes—
96C11⋊#95C2×C418yes—
97C11⋊#95C2×C418yes—
98C11⋊#95D414yes—
99#13821—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×Q814yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C412yes—
168C22×Dic11C22×C414yes—
169C22×Dic11C22×C414yes—
170C22×Dic11C22×C414yes—
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C412yes—
174C22×Dic11C2×D412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11#4112yes—
177C22×Dic11#4112yes—
178C11×C4⋊C4—28no—
179C11×C4⋊C4C4⋊C4116yescomplemented
180C42×C11—28no—
181C42×C11—48no—
182C4⋊Dic11—28no—
183C4⋊Dic11C42116yescomplemented
184Dic11⋊C4—216no—
185Dic11⋊C4—216no—
186C4×Dic11—216no—
187C4×Dic11—28no—
188C4×Dic11—28no—
189C4×Dic11—48no—
190C2×#389—111no—
191C2×#389—111no—
192C2×C4×C4⋊C4—112no—
193C2×C4×C4⋊C4—111no—
194C2×C4×C4⋊C4—111no—
195C2×C4×C4⋊C4D1111yescharacteristic
196#1436—112no—
197#1436—112no—
198C4⋊#95—111no—
199#1434—112no—
200C4×#95—111no—
201C23×C11C23×C411yescharacteristic
202C23×C11C23×C411yescharacteristic
203C23×C11C23×C411yescharacteristic
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×Q811yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4111yescharacteristic
212C23×C11H(5,𝔽2)11yescharacteristic
213C23×C112−1+411yescharacteristic
214C23×C112−1+411yescharacteristic
215C23×C112−1+411yescharacteristic
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11C2×C4214yes—
243C2×C4×C11C2×C4⋊C418yes—
244C2×C4×C11C2×C4⋊C414yes—
245C2×C4×C11#11714yes—
246C2×C4×C11C4×D414yes—
247C2×C4×C11C4×D414yes—
248C2×C4×C11C4×D414yes—
249C2×C4×C11C4×Q814yes—
250C2×C4×C11C4×Q814yes—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
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—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11C2×C4218yes—
291C2×Dic11C4×D414yes—
292C2×Dic11C4×D414yes—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295C22×C4⋊C4—112no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C4⋊C4C2×D1111yescharacteristic
299C22×C42—111no—
300C22×C42—111no—
301C22×C42—112no—
302C22×C42—112no—
303C22×C42C2×D1112yes—
304C22×C42C2×D1111yescharacteristic
305#389—118no—
306#389—118no—
307C4×C4⋊C4—24no—
308C4×C4⋊C4—118no—
309C4×C4⋊C4—228no—
310C4×C4⋊C4—224no—
311C2×#95—111no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—111no—
317C2×#95—111no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95C2×D1112yes—
322C22×C11C22×C4211yescharacteristic
323C22×C11C22×C4⋊C411yescharacteristic
324C22×C11C2×#11711yescharacteristic
325C22×C11C2×C4×D411yescharacteristic
326C22×C11C2×C4×D411yescharacteristic
327C22×C11C2×C4×D411yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11C2×C4×D411yescharacteristic
330C22×C11C2×C4×Q811yescharacteristic
331C22×C11C2×C4×Q811yescharacteristic
332C22×C11C4×#4111yescharacteristic
333C22×C11C4×#4111yescharacteristic
334C22×C11C4×#4111yescharacteristic
335C22×C11#51911yescharacteristic
336C22×C11#51911yescharacteristic
337C22×C11#51911yescharacteristic
338C22×C11#52011yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11#52011yescharacteristic
341C22×C11D4211yescharacteristic
342C22×C11#54711yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11#54711yescharacteristic
345C22×C11#54811yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11D4×Q811yescharacteristic
348C22×C11#55211yescharacteristic
349C22×C11#55211yescharacteristic
350C22×C11#55311yescharacteristic
351C22×C11#55311yescharacteristic
352C22×C11#55411yescharacteristic
353C22×C11#55611yescharacteristic
354C22×C11#55611yescharacteristic
355C22×C11#55711yescharacteristic
356C22×C11#55711yescharacteristic
357C4×C11—28no—
358C4×C11—24no—
359C4×C11—44no—
360C4×C11—42no—
361C4×C11C4×C4⋊C418yescomplemented
362Dic11—24no—
363Dic11—24no—
364Dic11—28no—
365Dic11—42no—
366Dic11—44no—
367Dic11—42no—
368C23×C4—112no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—112no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—118no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4Dic2214yes—
394C2×C4⋊C4C4×D1114yes—
395C2×C4⋊C4C4×D1114yes—
396C2×C4⋊C4C22⋊D1114yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—118no—
403C2×C42—114no—
404C2×C42—114no—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42—222no—
408C2×C42—222no—
409C2×C42—222no—
410C2×C42—222no—
411C2×C42—224no—
412C2×C42—224no—
413C2×C42—442no—
414C2×C42C4×D1114yes—
415#95—24no—
416#95—118no—
417#95—118no—
418#95—118no—
419#95—114no—
420#95—222no—
421#95—222no—
422#95—224no—
423#95—222no—
424#95—224no—
425#95—442no—
426C2×C11C2×C4×C4⋊C411yescharacteristic
427C2×C11C42×D411yescharacteristic
428C2×C11#227611yescharacteristic
429C2×C11#234411yescharacteristic
430C2×C11#234711yescharacteristic
431C2×C11D4×C4⋊C411yescharacteristic
432C2×C11#235111yescharacteristic
433C2×C11#236111yescharacteristic
434C2×C11#236111yescharacteristic
435C2×C11#236211yescharacteristic
436C2×C11#236211yescharacteristic
437C2×C11#236511yescharacteristic
438C2×C11#236511yescharacteristic
439C2×C11#237011yescharacteristic
440C2×C11#237011yescharacteristic
441C24C23×D1111yescharacteristic
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4C2×Dic2214yes—
505C22×C4C2×Dic2212yes—
506C22×C4C2×C4×D1112yes—
507C22×C4C2×C4×D1114yes—
508C22×C4C2×C4×D1112yes—
509C22×C4C2×C4×D1114yes—
510C22×C4C2×C4×D1112yes—
511C22×C4C2×C4×D1112yes—
512C22×C4C2×C4×D1112yes—
513C22×C4#433912yes—
514C22×C4#433912yes—
515C22×C4D4×D1112yes—
516C22×C4#434312yes—
517C22×C4C2×C22⋊D1114yes—
518C22×C4C2×C22⋊D1112yes—
519C4⋊C4—28no—
520C4⋊C4—1116no—
521C4⋊C4—2216no—
522C4⋊C4—2216no—
523C4⋊C4—228no—
524C4⋊C4Dic11⋊C4116yescomplemented
525C42—28no—
526C42—48no—
527C42—2216no—
528C42—228no—
529C42—228no—
530C42—448no—
531C11#1382111yescharacteristic, complemented, Sylow
532C23C22×Dic2211yescharacteristic
533C23C22×C4×D1111yescharacteristic
534C23C22×C4×D1111yescharacteristic
535C23C22×C4×D1111yescharacteristic
536C23C2×#433911yescharacteristic
537C23C2×#433911yescharacteristic
538C23C2×D4×D1111yescharacteristic
539C23#6703711yescharacteristic
540C23C2×#434311yescharacteristic
541C23#6704011yescharacteristic
542C23#41×D1111yescharacteristic
543C23#41×D1111yescharacteristic
544C23#6704311yescharacteristic
545C23#6704311yescharacteristic
546C23C22×C22⋊D1111yescharacteristic
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—118no—
574C2×C4—114no—
575C2×C4—114no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—442no—
608C2×C4—441no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4C4×Dic2214yes—
616C2×C4C4×Dic2214yes—
617C2×C4C42×D1114yes—
618C2×C4#6692514yes—
619C2×C4#6694614yes—
620C2×C4C2×Dic11⋊C418yes—
621C2×C4C2×Dic11⋊C414yes—
622C2×C4C4×C22⋊D1114yes—
623C2×C4C4×C22⋊D1114yes—
624C22C2×C4×Dic2211yescharacteristic
625C22C2×C4×Dic2211yescharacteristic
626C22C2×C42×D1111yescharacteristic
627C22C2×#6692511yescharacteristic
628C22C2×#6694611yescharacteristic
629C22#1062303511yescharacteristic
630C22#1062303811yescharacteristic
631C22#1062304511yescharacteristic
632C22#1062304711yescharacteristic
633C22#1062305311yescharacteristic
634C22#1062306011yescharacteristic
635C22#1062306411yescharacteristic
636C22D4×Dic2211yescharacteristic
637C22#1062307011yescharacteristic
638C22C4×D4×D1111yescharacteristic
639C22C4×D4×D1111yescharacteristic
640C22#1062307711yescharacteristic
641C22#1062307711yescharacteristic
642C22#1062308211yescharacteristic
643C22#1062308911yescharacteristic
644C22#1062310011yescharacteristic
645C22#1062310111yescharacteristic
646C22#1062310311yescharacteristic
647C22#1062310311yescharacteristic
648C22C4×#434311yescharacteristic
649C22C4×#434311yescharacteristic
650C22#1062311211yescharacteristic
651C22#1062311511yescharacteristic
652C22C22×Dic11⋊C411yescharacteristic
653C22C2×C4×C22⋊D1111yescharacteristic
654C22C2×C4×C22⋊D1111yescharacteristic
655C22D4×C22⋊D1111yescharacteristic
656C22#1062334811yescharacteristic
657C22#1062335511yescharacteristic
658C22#1062336211yescharacteristic
659C4—24no—
660C4—28no—
661C4—44no—
662C4—42no—
663C4—224no—
664C4—228no—
665C4—224no—
666C4—444no—
667C4—442no—
668C4—442no—
669C4C4×Dic11⋊C418yescomplemented
670C2C2×C4×Dic11⋊C411yescharacteristic
671C2C4×#6694611yescharacteristic
672C2#1307098011yescharacteristic
673C2#1307148111yescharacteristic
674C2#1307150511yescharacteristic
675C2D4×Dic11⋊C411yescharacteristic
676C2#1307153411yescharacteristic
677C2#1307162811yescharacteristic
678C2#1307163211yescharacteristic
679C2#1307163911yescharacteristic
680C2#1307164311yescharacteristic
681C2#1307167211yescharacteristic
682C2#1307167511yescharacteristic
683C2#1307170811yescharacteristic
684C2#1307171211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13821
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C4⋊C4×Dic11C4semidirect
38. #10622586C4semidirect
40. #10622541C4semidirect
179. C11×C4⋊C4C4⋊C4semidirect
183. C4⋊Dic11C42semidirect
361. C4×C11C4×C4⋊C4semidirect
524. C4⋊C4Dic11⋊C4semidirect
531. C11#13821semidirect
669. C4C4×Dic11⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106225862
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
#130668492
#130668472
#130668452
#130668422
C4×C11⋊#952
C2×C4×C11×C4⋊C42
#1382111