Finite Group Databasebeta

← #14676914

Subgroups — #14676914

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×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622601C211yesmaximal, characteristic, complemented
4C2×#10622570C212yesmaximal, complemented
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×D44C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C11×#380—24no—
34C2×C11×#95C2212yes—
35C4×C22⋊Dic11—24no—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622601—24no—
41#10622601—24no—
42C4⋊C4×Dic11—24no—
43#10622586—24no—
44#10622570—28no—
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×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—42no—
63C22×C22⋊D11—42no—
64C22×C22⋊D11C2×C418yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44C2×C414yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D414yescomplemented
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—42no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11D414yescomplemented
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⋊Dic11C2×C414yes—
109C2×C4⋊Dic11D414yes—
110C2×C4⋊Dic11D414yes—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—42no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—24no—
120C2×C4×Dic11—24no—
121C2×C4×Dic11—42no—
122C2×C4×Dic11D414yescomplemented
123C11×#95—24no—
124C11⋊#95—22no—
125C11⋊#95—22no—
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—22no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—28no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—44no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11#4112yes—
194C22×C4×C11#4112yes—
195C2×C22⋊D11—216no—
196C2×C22⋊D11—216no—
197C2×C22⋊D11—48no—
198C2×C22⋊D11—48no—
199C2×C22⋊D11—48no—
200C2×C22⋊D11—48no—
201C2×C22⋊D11—48no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11C22×C414yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D414yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D412yes—
234C22×Dic11C2×D412yes—
235C22×Dic11#4112yes—
236C22×Dic11#4112yes—
237C2×D44—28no—
238C2×D44—28no—
239C2×D44—28no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—44no—
244C11×C4⋊C4—28no—
245C11×C4⋊C4—44no—
246C11×C22⋊C4—48no—
247C22⋊Dic11—28no—
248C22⋊Dic11—28no—
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⋊Dic11C22⋊C4116yescomplemented
255Dic11⋊C4—48no—
256C4×Dic11—28no—
257C4×Dic11—48no—
258C4×Dic11—44no—
259C22×#121—111no—
260C2×#390—111no—
261C2×#390—111no—
262C2×#390—112no—
263C2×#389—111no—
264C2×#380D1111yescharacteristic, complemented
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4—111no—
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—24no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—416no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11C2×C22⋊C414yes—
378C2×C4×C11C4×D414yes—
379C2×C4×C11C4×D414yes—
380C2×C4×C11#12114yes—
381C2×C4×C11#12114yes—
382C2×C4×C11#12414yes—
383C2×C4×C11#12714yes—
384C22⋊D11—432no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11C2×C22⋊C418yes—
419C2×Dic11#12114yescomplemented
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—112no—
429C22×C4⋊C4C2×D1111yescharacteristic
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C22⋊C4—111no—
432C22×C22⋊C4—112no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—112no—
435C22×C22⋊C4—112no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4—112no—
438C22×C22⋊C4C2×D1112yes—
439C22×C42—111no—
440C22×C42—111no—
441C22×C42—112no—
442#390—224no—
443#390—228no—
444#390—224no—
445#389—224no—
446#380—24no—
447C4×C4⋊C4—224no—
448C4×C22⋊C4—224no—
449C2×#95—111no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95—111no—
453C2×#95C2×D1112yes—
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—44no—
520C4×C11—42no—
521C4×C11—82no—
522C4×C11#39018yescomplemented
523Dic11—28no—
524Dic11—24no—
525Dic11—42no—
526Dic11—42no—
527Dic11—42no—
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—111no—
551C23×C4—112no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4C4×D1114yes—
556C23×C4C22×D1112yes—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560#121—2232no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—114no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—442no—
572C2×C4⋊C4C22⋊D1114yescomplemented
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—118no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
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—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—442no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4—442no—
597C2×C42—114no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—224no—
601C2×C42—224no—
602C2×C42—222no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—442no—
606#95—24no—
607#95—222no—
608#95—222no—
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—
656C24D4×D1112yes—
657C24#434312yes—
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—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—114no—
700C22×C4—112no—
701C22×C4—114no—
702C22×C4—114no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4C2×C4×D1112yes—
735C22×C4C2×C4×D1112yes—
736C22×C4#433912yes—
737C22×C4D4×D1112yes—
738C22×C4D4×D1112yes—
739C22×C4D4×D1112yes—
740C22×C4#434112yes—
741C22×C4C2×C22⋊D1114yes—
742C22×C4C2×C22⋊D1112yes—
743C4⋊C4—28no—
744C4⋊C4—44no—
745C4⋊C4—1116no—
746C4⋊C4—448no—
747C22⋊C4—48no—
748C22⋊C4—2216no—
749C22⋊C4—228no—
750C22⋊C4—228no—
751C22⋊C4—448no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—228no—
756C42—448no—
757C42—444no—
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—
828C23#6694614yes—
829C23C22×C4×D1111yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23C2×D4×D1111yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×#434111yescharacteristic
836C23#6703711yescharacteristic
837C23C2×#434311yescharacteristic
838C23#6704011yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#6704211yescharacteristic
842C23#6704211yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—4432no—
845D4—4416no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—416no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—118no—
869C2×C4—114no—
870C2×C4—222no—
871C2×C4—224no—
872C2×C4—222no—
873C2×C4—224no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—224no—
877C2×C4—224no—
878C2×C4—222no—
879C2×C4—224no—
880C2×C4—224no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4C22⋊C4×D1114yes—
904C2×C4(C22⋊D11)⋊C414yes—
905C2×C4#6693714yes—
906C2×C4#6693814yes—
907C2×C4C4×C22⋊D1114yes—
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×C22⋊C4×D1111yescharacteristic
941C22C2×(C22⋊D11)⋊C411yescharacteristic
942C22C2×#6693711yescharacteristic
943C22C2×#6693811yescharacteristic
944C22C2×#6694611yescharacteristic
945C22#1062303511yescharacteristic
946C22#1062303811yescharacteristic
947C22#1062304511yescharacteristic
948C22#1062305211yescharacteristic
949C22#1062305311yescharacteristic
950C22#1062306111yescharacteristic
951C22#1062306311yescharacteristic
952C22#1062312711yescharacteristic
953C22#1062313011yescharacteristic
954C22#1062313011yescharacteristic
955C22D11×#12111yescharacteristic
956C22#1062313811yescharacteristic
957C22#1062314011yescharacteristic
958C22#1062314011yescharacteristic
959C22#1062315011yescharacteristic
960C22#1062315511yescharacteristic
961C22#1062315811yescharacteristic
962C22#1062316011yescharacteristic
963C22#1062316111yescharacteristic
964C22#1062316111yescharacteristic
965C22#1062316411yescharacteristic
966C22#1062316411yescharacteristic
967C22#1062317411yescharacteristic
968C22C2×C4×C22⋊D1111yescharacteristic
969C22D4×C22⋊D1111yescharacteristic
970C22C2×#6699211yescharacteristic
971C22C2×#6699311yescharacteristic
972C22#1062334811yescharacteristic
973C22#1062336011yescharacteristic
974C22#1062336511yescharacteristic
975C4—44no—
976C4—42no—
977C4—82no—
978C4—228no—
979C4—224no—
980C4—442no—
981C4—442no—
982C4—442no—
983C4#1062257018yescomplemented
984C2—44no—
985C2—884no—
986C2C2×#1062257011yescharacteristic
987C2#1307112211yescharacteristic
988C2#1307130511yescharacteristic
989C2#1307143611yescharacteristic
990C2#1307145311yescharacteristic
991C2#1307163211yescharacteristic
992C2#1307165411yescharacteristic
993C2#1307203611yescharacteristic
994C2#1307205811yescharacteristic
995C2#1307218411yescharacteristic
996C2#1307220611yescharacteristic
997C2#1307296411yescharacteristic
998C2#1307297511yescharacteristic
999C2#1307355411yescharacteristic
1000C2#1307355911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×#380D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622601C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622586C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. C2×C4×C22⋊Dic11C2semidirect
8. #13066860C2semidirect
9. #13066855C2semidirect
10. #13066852C2semidirect
11. C2×C11×#380C2semidirect
22. C2×#66983C4semidirect
82. C2×C11×C4⋊C4D4semidirect
91. C2×C22⋊Dic11D4semidirect
122. C2×C4×Dic11D4semidirect
254. C4⋊Dic11C22⋊C4semidirect
264. C2×#380D11semidirect
419. C2×Dic11#121semidirect
522. C4×C11#390semidirect
572. C2×C4⋊C4C22⋊D11semidirect
758. C11#13998semidirect
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×#106226012
C2×#106225702
C2×#106225862
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668602
#130668552
#130668522
C2×C11×#3802
#1399811