Finite Group Databasebeta

← #14676009

Subgroups — #14676009

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622590C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066882C212yesmaximal, complemented
8#13066855C212yesmaximal
9#13066853C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C2×C4×C22⋊D11C418yescomplemented
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C11×#380—24no—
32C2×C11×#95C2212yes—
33#10622825—24no—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622600—24no—
41#10622600—24no—
42#10622590—24no—
43C4⋊C4×Dic11—24no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11C2×C414yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C22×C22⋊D11C2×C414yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11C2×C414yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D414yescomplemented
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—42no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—42no—
90C2×C22⋊Dic11C2×C414yes—
91C4×C22⋊D11—232no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11D414yescomplemented
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4C2×C414yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—42no—
112C2×C4×Dic11—42no—
113C2×C4×Dic11C2×C414yes—
114C2×C4×Dic11D414yes—
115C2×C4×Dic11D414yes—
116C11×#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123#13905—111nomaximal, Sylow
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11C22×C412yes—
137C24×C11#4112yes—
138C24×C11#4112yes—
139C24×C11C2411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11C22×C412yes—
153C23×D11#4112yes—
154C23×D11#4112yes—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—28no—
168C22×C4×C11—28no—
169C22×C4×C11—28no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—44no—
178C22×C4×C11—44no—
179C22×C4×C11—44no—
180C22×C4×C11—44no—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11#4112yes—
189C22×C4×C11#4112yes—
190C2×C22⋊D11—28no—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—28no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—28no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—22no—
224C22×Dic11C22×C412yes—
225C22×Dic11C22×C412yes—
226C22×Dic11C22×C412yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D412yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D412yes—
232C2×C4×D11—28no—
233C2×C4×D11—28no—
234C2×C4×D11—28no—
235C2×C4×D11—44no—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C11×C4⋊C4—28no—
240C11×C4⋊C4—44no—
241C11×C22⋊C4—48no—
242C22⋊Dic11—28no—
243C22⋊Dic11—48no—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—48no—
246(C2×D11)⋊C4—48no—
247C4⋊Dic11—28no—
248C4⋊Dic11—44no—
249Dic11⋊C4—28no—
250C4×Dic11—48no—
251C4×Dic11C22⋊C4116yescomplemented
252C22×C4×D4—111no—
253C2×#382—111no—
254C2×#380—111no—
255C2×#380—111no—
256C2×#380—111no—
257C2×#380D1111yescharacteristic, complemented
258C2×C4×C4⋊C4—111no—
259#1445—112no—
260#1438—112no—
261#1437—112no—
262#1437—112no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
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—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
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#11714yes—
298C23×C11C23×C411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D411yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C112−1+411yescharacteristic
312C23×C112−1+411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11#11714yes—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—24no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—42no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—416no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11C2×C22⋊C414yes—
371C2×C4×C11C4×D414yes—
372C2×C4×C11C4×D414yes—
373C2×C4×C11#12114yes—
374C2×C4×C11#12114yes—
375C2×C4×C11#12414yes—
376C2×C4×C11#12714yes—
377C22⋊D11—232no—
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—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—24no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—42no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—42no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—42no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11C2×C22⋊C414yes—
412C2×Dic11C2×C22⋊C414yes—
413C4×D11—416no—
414C23×D4—111no—
415C24×C4—111no—
416C24×C4C2×D1111yescharacteristic
417C2×C4×D4—118no—
418C2×C4×D4—224no—
419C2×C4×D4—224no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4C2×D1111yescharacteristic
424C22×C4⋊C4C2×D1111yescharacteristic
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—112no—
428C22×C22⋊C4—112no—
429C22×C22⋊C4—112no—
430C22×C22⋊C4C2×D1112yes—
431C22×C42—111no—
432C22×C42—112no—
433#382—224no—
434#380—24no—
435#380—224no—
436#380—224no—
437#380—224no—
438C4×C4⋊C4—224no—
439C2×#95—112no—
440C2×#95—112no—
441C2×#95—112no—
442C2×#95—112no—
443C2×#95—112no—
444C2×#95—112no—
445C2×#95C2×D1112yes—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11C22×C22⋊C411yescharacteristic
462C22×C11C2×#11711yescharacteristic
463C22×C11C2×#11711yescharacteristic
464C22×C11C2×C4×D411yescharacteristic
465C22×C11C2×C4×D411yescharacteristic
466C22×C11#52011yescharacteristic
467C22×C11#52011yescharacteristic
468C22×C11C2×#12111yescharacteristic
469C22×C11C2×#12111yescharacteristic
470C22×C11#52511yescharacteristic
471C22×C11#52511yescharacteristic
472C22×C11#52511yescharacteristic
473C22×C11#52511yescharacteristic
474C22×C11C2×#12411yescharacteristic
475C22×C11C2×#12711yescharacteristic
476C22×C11#53511yescharacteristic
477C22×C11#53611yescharacteristic
478C22×C11#53711yescharacteristic
479C22×C11#53711yescharacteristic
480C22×C11#54611yescharacteristic
481C22×C11#54611yescharacteristic
482C22×C11#54611yescharacteristic
483C22×C11#54611yescharacteristic
484C22×C11#54811yescharacteristic
485C22×C11#54811yescharacteristic
486C22×C11#54811yescharacteristic
487C22×C11#54811yescharacteristic
488C22×C11#55211yescharacteristic
489C22×C11#55211yescharacteristic
490C22×C11#55211yescharacteristic
491C22×C11#55211yescharacteristic
492C22×C11#55311yescharacteristic
493C22×C11#55311yescharacteristic
494C22×C11#55311yescharacteristic
495C22×C11#55311yescharacteristic
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—24no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C4×C11—44no—
512C4×C11—42no—
513C4×C11—82no—
514C4×C11#39018yes—
515Dic11—24no—
516Dic11—24no—
517Dic11—44no—
518Dic11—42no—
519Dic11—82no—
520C25—111no—
521C25C22×D1111yescharacteristic
522C22×D4—114no—
523C22×D4—222no—
524C22×D4—222no—
525C22×D4—222no—
526C22×D4—222no—
527C22×D4—222no—
528C22×D4—222no—
529C23×C4—22no—
530C23×C4—22no—
531C23×C4—22no—
532C23×C4—22no—
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—112no—
538C23×C4—111no—
539C23×C4—114no—
540C23×C4—112no—
541C23×C4—222no—
542C23×C4—222no—
543C23×C4—222no—
544C23×C4—222no—
545C23×C4—222no—
546C23×C4—222no—
547C23×C4C4×D1114yes—
548C23×C4C22×D1112yes—
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1112yes—
551C23×C4C22×D1111yescharacteristic
552C4×D4—2232no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4C22⋊D1114yescomplemented
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—224no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4—442no—
586C2×C42—114no—
587C2×C42—114no—
588C2×C42—114no—
589C2×C42—224no—
590C2×C42—442no—
591C2×C42—442no—
592#95—24no—
593#95—224no—
594#95—224no—
595#95—224no—
596#95—224no—
597#95—224no—
598#95—224no—
599C2×C11—44no—
600C2×C11#228011yescharacteristic
601C2×C11C2×#39011yescharacteristic
602C2×C11#231111yescharacteristic
603C2×C11#235211yescharacteristic
604C2×C11#235211yescharacteristic
605C2×C11#235211yescharacteristic
606C2×C11#235211yescharacteristic
607C2×C11#253511yescharacteristic
608C2×C11#253511yescharacteristic
609C2×C11#253611yescharacteristic
610C2×C11#253611yescharacteristic
611C2×C11#254011yescharacteristic
612C2×C11#254011yescharacteristic
613C2×C11#256211yescharacteristic
614C2×C11#256211yescharacteristic
615D11—44no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—112no—
629C24—112no—
630C24—112no—
631C24—221no—
632C24—221no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24C2×C4×D1112yes—
644C24#434112yes—
645C24#434312yes—
646C24C23×D1111yescharacteristic
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—228no—
653C2×D4—228no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—114no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—222no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—221no—
708C22×C4—228no—
709C22×C4—228no—
710C22×C4—228no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—444no—
719C22×C4—444no—
720C22×C4—444no—
721C22×C4—444no—
722C22×C4C2×C4×D1112yes—
723C22×C4C2×C4×D1112yes—
724C22×C4#433912yes—
725C22×C4D4×D1112yes—
726C22×C4D4×D1112yes—
727C22×C4D4×D1112yes—
728C22×C4#434112yes—
729C22×C4C2×C22⋊D1114yes—
730C22×C4C2×C22⋊D1112yes—
731C4⋊C4—28no—
732C4⋊C4—44no—
733C4⋊C4—228no—
734C4⋊C4—228no—
735C4⋊C4—444no—
736C22⋊C4—48no—
737C22⋊C4—228no—
738C22⋊C4—228no—
739C22⋊C4—448no—
740C22⋊C4—448no—
741C22⋊C4—448no—
742C42—1116no—
743C42—448no—
744C11#1390511yescharacteristic, complemented, Sylow
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—114no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23#6694514yes—
815C23C22×C4×D1111yescharacteristic
816C23C2×#433911yescharacteristic
817C23C2×D4×D1111yescharacteristic
818C23C2×D4×D1111yescharacteristic
819C23C2×D4×D1111yescharacteristic
820C23C2×#434111yescharacteristic
821C23C2×#434111yescharacteristic
822C23#6703711yescharacteristic
823C23C2×#434311yescharacteristic
824C23#6704011yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#6704211yescharacteristic
828C23#6704311yescharacteristic
829C23C22×C22⋊D1111yescharacteristic
830D4—2232no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—416no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—114no—
854C2×C4—114no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—224no—
870C2×C4—222no—
871C2×C4—224no—
872C2×C4—224no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—442no—
876C2×C4—442no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—442no—
880C2×C4—442no—
881C2×C4—4416no—
882C2×C4—442no—
883C2×C4—442no—
884C2×C4—442no—
885C2×C4—442no—
886C2×C4—442no—
887C2×C4—442no—
888C2×C4—442no—
889C2×C4C22⋊C4×D1114yes—
890C2×C4(C22⋊D11)⋊C414yes—
891C2×C4#6693714yes—
892C2×C4#6693814yes—
893C2×C4C4×C22⋊D1114yes—
894C2×C4#6699214yes—
895C2×C4#6699314yes—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—224no—
912C22—224no—
913C22—224no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22C2×C22⋊C4×D1111yescharacteristic
927C22C2×(C22⋊D11)⋊C411yescharacteristic
928C22C2×#6693711yescharacteristic
929C22C2×#6693811yescharacteristic
930C22C2×#6694511yescharacteristic
931C22#1062303511yescharacteristic
932C22#1062304411yescharacteristic
933C22#1062304511yescharacteristic
934C22D11×#11711yescharacteristic
935C22#1062305411yescharacteristic
936C22#1062306011yescharacteristic
937C22#1062306111yescharacteristic
938C22#1062312911yescharacteristic
939C22#1062313711yescharacteristic
940C22#1062313711yescharacteristic
941C22#1062313811yescharacteristic
942C22#1062313911yescharacteristic
943C22#1062314311yescharacteristic
944C22#1062314511yescharacteristic
945C22#1062314911yescharacteristic
946C22#1062315811yescharacteristic
947C22#1062315811yescharacteristic
948C22#1062315911yescharacteristic
949C22#1062316011yescharacteristic
950C22#1062316111yescharacteristic
951C22#1062316411yescharacteristic
952C22#1062317011yescharacteristic
953C22#1062317311yescharacteristic
954C22C2×C4×C22⋊D1111yescharacteristic
955C22C2×#6699211yescharacteristic
956C22C2×#6699311yescharacteristic
957C22#1062333711yescharacteristic
958C22#1062334811yescharacteristic
959C22#1062336011yescharacteristic
960C22#1062336211yescharacteristic
961C4—44no—
962C4—42no—
963C4—82no—
964C4—224no—
965C4—224no—
966C4—444no—
967C4—442no—
968C4—882no—
969C4#1062257018yes—
970C2—44no—
971C2—444no—
972C2#1307099811yescharacteristic
973C2C2×#1062257011yescharacteristic
974C2#1307120511yescharacteristic
975C2#1307153811yescharacteristic
976C2#1307154111yescharacteristic
977C2#1307154611yescharacteristic
978C2#1307154711yescharacteristic
979C2#1307351511yescharacteristic
980C2#1307351911yescharacteristic
981C2#1307352311yescharacteristic
982C2#1307352711yescharacteristic
983C2#1307355211yescharacteristic
984C2#1307355411yescharacteristic
985C2#1307377911yescharacteristic
986C2#1307378111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#13905
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622590C2semidirect
3. C2×#10622825C2semidirect
4. C2×#10622600C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. #13066882C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. C2×C11×#380C2semidirect
22. C2×C4×C22⋊D11C4semidirect
81. C2×C11×C4⋊C4D4semidirect
106. C2×C4⋊Dic11D4semidirect
251. C4×Dic11C22⋊C4semidirect
257. C2×#380D11semidirect
567. C2×C4⋊C4C22⋊D11semidirect
744. C11#13905semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225902
C2×#106228252
C2×#106226002
C2×C4⋊C4×Dic112
#130668822
#130668552
#130668532
#130668522
C2×C11×#3802
#1390511