Finite Group Databasebeta

← #14676918

Subgroups — #14676918

Order 2816.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622552C211yesmaximal, characteristic, complemented
4C2×#10622570C212yesmaximal, complemented
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622825C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×D44C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×#66983—24no—
21C2×#66983—24no—
22C2×#66983C418yescomplemented
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2212yes—
33C4×C11×C22⋊C4—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622825—24no—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622570—28no—
41#10622552—24no—
42#10622552—24no—
43C4×C4⋊Dic11—24no—
44#10622541—24no—
45C25×C11C2311yescharacteristic
46C24×D11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11C2×C414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—42no—
65C22×C22⋊D11—42no—
66C22×C22⋊D11C2×C418yes—
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44C2×C414yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D414yescomplemented
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11D414yescomplemented
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—42no—
92#66983—232no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—42no—
104C2×(C2×D11)⋊C4—42no—
105C2×(C2×D11)⋊C4—42no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4C2×C418yes—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11C2×C414yes—
114C2×C4⋊Dic11D414yes—
115C2×C4⋊Dic11D414yes—
116C2×C4⋊Dic11D414yescomplemented
117C2×Dic11⋊C4—24no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—42no—
120C2×C4×Dic11—24no—
121C2×C4×Dic11—24no—
122C2×C4×Dic11—42no—
123C11×#95—22no—
124C11×#95—22no—
125C11⋊#95—24no—
126C11⋊#95—24no—
127C11⋊#95—24no—
128#13998—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C22×C412yes—
142C24×C11C2×D412yes—
143C24×C11#4112yes—
144C24×C11C2411yescharacteristic
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11C22×C414yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—28no—
189C22×C4×C11—28no—
190C22×C4×C11—28no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11#4112yes—
206C22×C4×C11#4112yes—
207C22×C4×C11#4112yes—
208C22×C4×C11#4112yes—
209C2×C22⋊D11—216no—
210C2×C22⋊D11—216no—
211C2×C22⋊D11—48no—
212C2×C22⋊D11—48no—
213C2×C22⋊D11—48no—
214C2×C22⋊D11—48no—
215C2×C22⋊D11—48no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11C22×C414yes—
234C22×Dic11C2×D414yes—
235C22×Dic11C2×D414yes—
236C22×Dic11C2×D414yes—
237C2×D44—28no—
238C2×D44—28no—
239C2×D44—28no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—44no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—28no—
246C42×C11—28no—
247C42×C11—44no—
248C22⋊Dic11—48no—
249(C2×D11)⋊C4—216no—
250(C2×D11)⋊C4—48no—
251(C2×D11)⋊C4—48no—
252(C2×D11)⋊C4—48no—
253(C2×D11)⋊C4—48no—
254C4⋊Dic11—28no—
255C4⋊Dic11—44no—
256C4⋊Dic11C22⋊C4116yescomplemented
257Dic11⋊C4—48no—
258C4×Dic11—48no—
259C22×#121—111no—
260C2×#390—111no—
261C2×#390—111no—
262C2×#390—112no—
263C2×#389—111no—
264C2×#380—111no—
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4D1111yescharacteristic, complemented
267#1439—112no—
268#1438—112no—
269#1437—112no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11C4×D414yes—
305C23×C11C23×C411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×D411yescharacteristic
310C23×C11C22×D411yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
320C22×D11—24no—
321C22×D11—24no—
322C22×D11—24no—
323C22×D11—24no—
324C22×D11—24no—
325C22×D11—24no—
326C22×D11—24no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
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—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—416no—
390C2×C4×C11C2×C22⋊C414yes—
391C2×C4×C11C4×D414yes—
392C2×C4×C11C4×D414yes—
393C2×C4×C11#12114yes—
394C2×C4×C11#12114yes—
395C2×C4×C11#12114yescomplemented
396C2×C4×C11#12414yes—
397C2×C4×C11#12714yes—
398C22⋊D11—432no—
399C2×Dic11—24no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—24no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—24no—
406C2×Dic11—24no—
407C2×Dic11—24no—
408C2×Dic11—42no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—42no—
419C2×Dic11C2×C22⋊C418yes—
420D44—416no—
421C23×D4—112no—
422C23×D4—111no—
423C24×C4C2×D1111yescharacteristic
424C2×#121—118no—
425C2×#121—224no—
426C2×#121—224no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—112no—
431C22×C22⋊C4—112no—
432C22×C22⋊C4—112no—
433C22×C22⋊C4—112no—
434C22×C22⋊C4—112no—
435C22×C22⋊C4—112no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4C2×D1111yescharacteristic
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C42—112no—
440C22×C42C2×D1111yescharacteristic
441C22×C42C2×D1111yescharacteristic
442#390—224no—
443#390—228no—
444#390—224no—
445#389—224no—
446#380—224no—
447C4×C4⋊C4—224no—
448C4×C22⋊C4—24no—
449C2×#95—112no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95C2×D1111yescharacteristic
453C2×#95C2×D1111yescharacteristic
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11C22×C22⋊C411yescharacteristic
470C22×C11C2×C4×D411yescharacteristic
471C22×C11C2×C4×D411yescharacteristic
472C22×C11C2×C4×D411yescharacteristic
473C22×C11C4×#4111yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11C2×#12111yescharacteristic
477C22×C11C2×#12111yescharacteristic
478C22×C11C2×#12111yescharacteristic
479C22×C11#52511yescharacteristic
480C22×C11C2×#12411yescharacteristic
481C22×C11#52911yescharacteristic
482C22×C11C2×#12711yescharacteristic
483C22×C11#53211yescharacteristic
484C22×C11#53511yescharacteristic
485C22×C11#53711yescharacteristic
486C22×C11#54011yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11D4211yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11D4211yescharacteristic
491C22×C11#54611yescharacteristic
492C22×C11#54611yescharacteristic
493C22×C11#54611yescharacteristic
494C22×C11#54711yescharacteristic
495C22×C11#54811yescharacteristic
496C22×C11#54811yescharacteristic
497C22×C11#54811yescharacteristic
498C22×C11#55011yescharacteristic
499C22×C11#55011yescharacteristic
500C22×C11#55011yescharacteristic
501C22×C11#55311yescharacteristic
502C22×C11#55311yescharacteristic
503C22×C11#55511yescharacteristic
504C2×D11—44no—
505C2×D11—44no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—44no—
509C2×D11—44no—
510C2×D11—44no—
511C2×D11—82no—
512C2×D11—82no—
513C2×D11—82no—
514C2×D11—82no—
515C2×D11—82no—
516C2×D11—82no—
517C2×D11—82no—
518C2×D11—82no—
519C4×C11—24no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11#39018yescomplemented
525Dic11—28no—
526Dic11—44no—
527Dic11—82no—
528C25—112no—
529C25C22×D1111yescharacteristic
530C22×D4—118no—
531C22×D4—114no—
532C22×D4—224no—
533C22×D4—224no—
534C22×D4—224no—
535C22×D4—224no—
536C22×D4—222no—
537C22×D4—222no—
538C22×D4—222no—
539C22×D4—222no—
540C22×D4—222no—
541C22×D4—222no—
542C22×D4—442no—
543C22×D4—442no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—112no—
551C23×C4—112no—
552C23×C4—112no—
553C23×C4C4×D1114yes—
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560#121—2232no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—442no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—118no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4—442no—
593C2×C22⋊C4—442no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4D4414yescomplemented
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—224no—
603C2×C42—224no—
604C2×C42—442no—
605C2×C42C22⋊D1114yescomplemented
606#95—22no—
607#95—22no—
608#95—224no—
609#95—224no—
610#95—224no—
611C2×C11—44no—
612C2×C11C2×#39011yescharacteristic
613C2×C11C4×#12111yescharacteristic
614C2×C11#232411yescharacteristic
615C2×C11D4×C22⋊C411yescharacteristic
616C2×C11#234111yescharacteristic
617C2×C11#236111yescharacteristic
618C2×C11#236311yescharacteristic
619C2×C11#241411yescharacteristic
620C2×C11#241611yescharacteristic
621C2×C11#242611yescharacteristic
622C2×C11#242811yescharacteristic
623C2×C11#249011yescharacteristic
624C2×C11#249111yescharacteristic
625C2×C11#254011yescharacteristic
626C2×C11#254111yescharacteristic
627D11—84no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—114no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24—222no—
648C24—222no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24C2×C4×D1112yes—
656C24C2×D4412yes—
657C24#433912yes—
658C24C23×D1111yescharacteristic
659C2×D4—2216no—
660C2×D4—2216no—
661C2×D4—228no—
662C2×D4—228no—
663C2×D4—228no—
664C2×D4—448no—
665C2×D4—448no—
666C2×D4—448no—
667C2×D4—448no—
668C2×D4—448no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—444no—
672C2×D4—444no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—114no—
711C22×C4—114no—
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—222no—
728C22×C4—222no—
729C22×C4C2×C4×D1112yes—
730C22×C4C2×C4×D1112yes—
731C22×C4C2×D4412yes—
732C22×C4C2×D4412yes—
733C22×C4#433912yes—
734C22×C4#433912yes—
735C22×C4#433912yes—
736C22×C4D4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4D4×D1112yes—
739C22×C4#434112yes—
740C22×C4C2×C22⋊D1112yes—
741C22×C4C2×C22⋊D1112yes—
742C22×C4C2×C22⋊D1112yes—
743C4⋊C4—1116no—
744C4⋊C4—228no—
745C4⋊C4—448no—
746C4⋊C4—444no—
747C22⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—2216no—
750C22⋊C4—448no—
751C22⋊C4—448no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—28no—
756C42—44no—
757C42—448no—
758C11#1399811yescharacteristic, complemented, Sylow
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—224no—
794C23—224no—
795C23—224no—
796C23—224no—
797C23—224no—
798C23—224no—
799C23—224no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—442no—
805C23—442no—
806C23—442no—
807C23—442no—
808C23—442no—
809C23—442no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23—442no—
816C23—442no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—442no—
823C23—442no—
824C23—442no—
825C23—442no—
826C23—442no—
827C23—442no—
828C23C4×D4414yes—
829C23C22×C4×D1111yescharacteristic
830C23C22×D4411yescharacteristic
831C23C2×#433911yescharacteristic
832C23C2×#433911yescharacteristic
833C23C2×#433911yescharacteristic
834C23C2×#433911yescharacteristic
835C23C2×D4×D1111yescharacteristic
836C23C2×D4×D1111yescharacteristic
837C23C2×D4×D1111yescharacteristic
838C23C2×#434111yescharacteristic
839C23#6704211yescharacteristic
840C23#6704211yescharacteristic
841C23#6704211yescharacteristic
842C23#6704311yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—4432no—
845D4—4416no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—416no—
881C2×C4—118no—
882C2×C4—224no—
883C2×C4—224no—
884C2×C4—224no—
885C2×C4—224no—
886C2×C4—224no—
887C2×C4—224no—
888C2×C4—224no—
889C2×C4—224no—
890C2×C4—224no—
891C2×C4—442no—
892C2×C4—442no—
893C2×C4—442no—
894C2×C4—442no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4—442no—
899C2×C4—442no—
900C2×C4—442no—
901C2×C4—442no—
902C2×C4C22⋊C4×D1114yes—
903C2×C4(C22⋊D11)⋊C414yes—
904C2×C4#6693714yes—
905C2×C4#6693814yes—
906C2×C4C4×C22⋊D1114yes—
907C2×C4#6698314yescomplemented
908C2×C4#6699214yes—
909C2×C4#6699314yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—444no—
926C22—444no—
927C22—444no—
928C22—444no—
929C22—444no—
930C22—444no—
931C22—444no—
932C22—882no—
933C22—882no—
934C22—882no—
935C22—882no—
936C22—882no—
937C22—882no—
938C22—882no—
939C22—882no—
940C22C2×C4×D4411yescharacteristic
941C22C4×#433911yescharacteristic
942C22#1062300811yescharacteristic
943C22#1062301011yescharacteristic
944C22C2×C22⋊C4×D1111yescharacteristic
945C22C2×(C22⋊D11)⋊C411yescharacteristic
946C22C2×#6693711yescharacteristic
947C22C2×#6693811yescharacteristic
948C22#1062305211yescharacteristic
949C22#1062305411yescharacteristic
950C22#1062306511yescharacteristic
951C22#1062306611yescharacteristic
952C22D4×D4411yescharacteristic
953C22D4×D4411yescharacteristic
954C22D4×D4411yescharacteristic
955C22#1062308111yescharacteristic
956C22#1062308111yescharacteristic
957C22#1062308111yescharacteristic
958C22#1062308311yescharacteristic
959C22#1062308311yescharacteristic
960C22#1062308311yescharacteristic
961C22#1062308411yescharacteristic
962C22#1062308411yescharacteristic
963C22#1062308411yescharacteristic
964C22#1062308611yescharacteristic
965C22#1062309411yescharacteristic
966C22#1062309611yescharacteristic
967C22#1062309611yescharacteristic
968C22C2×C4×C22⋊D1111yescharacteristic
969C22C2×#6698311yescharacteristic
970C22#1062332211yescharacteristic
971C22C2×#6699211yescharacteristic
972C22C2×#6699311yescharacteristic
973C22#1062336111yescharacteristic
974C22#1062336411yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—228no—
981C4—444no—
982C4—882no—
983C4#1062257018yescomplemented
984C2—44no—
985C2—884no—
986C2C2×#1062257011yescharacteristic
987C2C4×#6698311yescharacteristic
988C2#1307130911yescharacteristic
989C2C22⋊C4×D4411yescharacteristic
990C2#1307145611yescharacteristic
991C2#1307163011yescharacteristic
992C2#1307165211yescharacteristic
993C2#1307203411yescharacteristic
994C2#1307205611yescharacteristic
995C2#1307218211yescharacteristic
996C2#1307220411yescharacteristic
997C2#1307296811yescharacteristic
998C2#1307297911yescharacteristic
999C2#1307355511yescharacteristic
1000C2#1307356211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622552C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622825C2semidirect
7. C2×C4×C4⋊Dic11C2semidirect
8. #13066860C2semidirect
9. #13066855C2semidirect
10. #13066852C2semidirect
11. C2×C4×C11×C22⋊C4C2semidirect
22. C2×#66983C4semidirect
82. C2×C11×C22⋊C4D4semidirect
88. C2×C42×C11D4semidirect
116. C2×C4⋊Dic11D4semidirect
256. C4⋊Dic11C22⋊C4semidirect
266. C2×C4×C22⋊C4D11semidirect
395. C2×C4×C11#121semidirect
524. C4×C11#390semidirect
596. C2×C22⋊C4D44semidirect
605. C2×C42C22⋊D11semidirect
758. C11#13998semidirect
907. C2×C4#66983semidirect
983. C4#10622570semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106225522
C2×#106225702
C2×#106225412
C2×#106228252
C2×C4×C4⋊Dic112
#130668602
#130668552
#130668522
C2×C4×C11×C22⋊C42
#1399811