Finite Group Databasebeta

← #14676015

Subgroups — #14676015

Order 2816.

2574 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×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C212yesmaximal
3C2×#10622589C211yesmaximal, characteristic, complemented
4C2×#10622825C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×#10622600C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal, complemented
9#13066859C212yesmaximal, complemented
10Dic11⋊#95C212yesmaximal, 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⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C11×#380—24no—
34C2×C11×#95C2212yes—
35#10622825—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622600—24no—
41#10622600—24no—
42#10622589—24no—
43C4⋊C4×Dic11—24no—
44#10622570—28no—
45C25×C11C2311yescharacteristic
46C24×D11C2311yescharacteristic
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—22no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11C2×C414yes—
63C22×C22⋊D11D414yes—
64C22×C22⋊D11Q814yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11C2×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—24no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—42no—
91C2×C22⋊Dic11C2×C414yes—
92C4×C22⋊D11—232no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11D414yescomplemented
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—42no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4C2×C414yes—
117C2×C4×Dic11—24no—
118C2×C4×Dic11—24no—
119C2×C4×Dic11—24no—
120C2×C4×Dic11C2×C414yes—
121C2×C4×Dic11D414yes—
122C2×C4×Dic11D414yes—
123C11×#95—24no—
124C11⋊#95—24no—
125C11⋊#95—24no—
126C11⋊#95—24no—
127C11⋊#95—24no—
128#13906—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×C11C2×Q812yes—
144C24×C11C2411yescharacteristic
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11C22×C412yes—
158C23×D11C2×D412yes—
159C23×D11C2×Q812yes—
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—28no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11—28no—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—28no—
200C2×C22⋊D11—28no—
201C2×C22⋊D11C4⋊C4116yescomplemented
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—22no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—22no—
225C22×Dic11C22×C412yes—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C22×Dic11C2×D414yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×D412yes—
233C22×Dic11C2×D412yes—
234C22×Dic11C2×Q812yes—
235C22×Dic11#4112yes—
236C22×Dic11#4112yes—
237C2×C4×D11—28no—
238C2×C4×D11—28no—
239C2×C4×D11—28no—
240C2×C4×D11—44no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11—44no—
244C11×C4⋊C4—28no—
245C11×C4⋊C4—44no—
246C11×C22⋊C4—48no—
247C22⋊Dic11—28no—
248C22⋊Dic11—48no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—48no—
251(C2×D11)⋊C4—48no—
252C4⋊Dic11—28no—
253C4⋊Dic11—44no—
254Dic11⋊C4—28no—
255Dic11⋊C4—48no—
256Dic11⋊C4—48no—
257C4×Dic11—48no—
258C4×Dic11C22⋊C4116yescomplemented
259C22×C4×D4—111no—
260C2×#390—112no—
261C2×#384—111no—
262C2×#380—111no—
263C2×#380—111no—
264C2×#380—111no—
265C2×#380D1111yescharacteristic, complemented
266C2×C4×C4⋊C4—111no—
267#1439—112no—
268#1439—112no—
269C4⋊#95—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×C11C2×C4⋊C414yes—
305C23×C11C23×C411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×D411yescharacteristic
310C23×C11C22×D411yescharacteristic
311C23×C11C22×Q811yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C112−1+411yescharacteristic
319C23×C112−1+411yescharacteristic
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—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
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—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11C2×C4⋊C414yes—
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—42no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
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—232no—
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—22no—
394C2×Dic11—24no—
395C2×Dic11—24no—
396C2×Dic11—24no—
397C2×Dic11—42no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
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×Dic11—42no—
412C2×Dic11C2×C22⋊C414yes—
413C2×Dic11C2×C22⋊C414yes—
414C2×Dic11C2×C4⋊C414yes—
415C2×Dic11#11714yes—
416C2×Dic11#12114yes—
417C2×Dic11#12114yes—
418C2×Dic11C22⋊Q814yes—
419C2×Dic11C22⋊Q814yes—
420C4×D11—416no—
421C23×D4—111no—
422C24×C4—111no—
423C24×C4C2×D1111yescharacteristic
424C2×C4×D4—118no—
425C2×C4×D4—224no—
426C2×C4×D4—224no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—112no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4—112no—
432C22×C4⋊C4C2×D1111yescharacteristic
433C22×C4⋊C4C2×D1111yescharacteristic
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4—112no—
438C22×C22⋊C4—112no—
439C22×C22⋊C4C2×D1112yes—
440C22×C42—111no—
441C22×C42—112no—
442#390—228no—
443#384—224no—
444#380—24no—
445#380—224no—
446#380—224no—
447#380—224no—
448C4×C4⋊C4—224no—
449C2×#95—112no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95—112no—
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×C11C22×C4⋊C411yescharacteristic
471C22×C11C2×#11711yescharacteristic
472C22×C11C2×C4×D411yescharacteristic
473C22×C11C2×C4×D411yescharacteristic
474C22×C11#52011yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11C2×#12111yescharacteristic
477C22×C11C2×#12111yescharacteristic
478C22×C11C2×#12111yescharacteristic
479C22×C11C2×#12111yescharacteristic
480C22×C11C2×C22⋊Q811yescharacteristic
481C22×C11C2×C22⋊Q811yescharacteristic
482C22×C11C2×#12411yescharacteristic
483C22×C11C2×#12711yescharacteristic
484C22×C11#53511yescharacteristic
485C22×C11#53611yescharacteristic
486C22×C11#53711yescharacteristic
487C22×C11#53711yescharacteristic
488C22×C11D4211yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11#54711yescharacteristic
491C22×C11#54711yescharacteristic
492C22×C11#54711yescharacteristic
493C22×C11#54711yescharacteristic
494C22×C11D4×Q811yescharacteristic
495C22×C11D4×Q811yescharacteristic
496C22×C11#55011yescharacteristic
497C22×C11#55011yescharacteristic
498C22×C11#55411yescharacteristic
499C22×C11#55411yescharacteristic
500C22×C11#55511yescharacteristic
501C22×C11#55511yescharacteristic
502C22×C11#55611yescharacteristic
503C22×C11#55611yescharacteristic
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C4×C11—44no—
520C4×C11—42no—
521C4×C11—82no—
522C4×C11#39018yescomplemented
523Dic11—24no—
524Dic11—44no—
525Dic11—42no—
526Dic11—82no—
527Dic11#38018yescomplemented
528C25—111no—
529C25C22×D1111yescharacteristic
530C22×D4—114no—
531C22×D4—114no—
532C22×D4—114no—
533C22×D4—222no—
534C22×D4—222no—
535C22×D4—222no—
536C22×D4—222no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—22no—
540C23×C4—22no—
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—111no—
547C23×C4—114no—
548C23×C4—112no—
549C23×C4—222no—
550C23×C4—222no—
551C23×C4—222no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4C4×D1114yes—
556C23×C4C22×D1112yes—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560C4×D4—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—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—224no—
573C2×C4⋊C4—224no—
574C2×C4⋊C4—224no—
575C2×C4⋊C4—224no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—442no—
580C2×C4⋊C4—442no—
581C2×C4⋊C4C22⋊D1114yescomplemented
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—442no—
598C2×C22⋊C4—442no—
599C2×C22⋊C4—442no—
600C2×C42—114no—
601C2×C42—114no—
602C2×C42—114no—
603C2×C42—224no—
604C2×C42—224no—
605C2×C42—224no—
606#95—24no—
607#95—224no—
608#95—224no—
609#95—224no—
610#95—224no—
611C2×C11—44no—
612C2×C11C2×#38011yescharacteristic
613C2×C11C2×#39011yescharacteristic
614C2×C11#231111yescharacteristic
615C2×C11D4×C4⋊C411yescharacteristic
616C2×C11D4×C4⋊C411yescharacteristic
617C2×C11#235411yescharacteristic
618C2×C11#235411yescharacteristic
619C2×C11#253711yescharacteristic
620C2×C11#253711yescharacteristic
621C2×C11#253811yescharacteristic
622C2×C11#253811yescharacteristic
623C2×C11#254111yescharacteristic
624C2×C11#254211yescharacteristic
625C2×C11#254711yescharacteristic
626C2×C11#256311yescharacteristic
627D11—44no—
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—112no—
641C24—112no—
642C24—112no—
643C24—221no—
644C24—221no—
645C24—221no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24C2×C4×D1112yes—
656C24D4×D1112yes—
657C24Q8×D1112yes—
658C24C23×D1111yescharacteristic
659C2×D4—1116no—
660C2×D4—228no—
661C2×D4—228no—
662C2×D4—228no—
663C2×D4—228no—
664C2×D4—228no—
665C2×D4—228no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—114no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—222no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—228no—
721C22×C4—228no—
722C22×C4—228no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—444no—
731C22×C4—444no—
732C22×C4—444no—
733C22×C4—444no—
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—228no—
746C4⋊C4—228no—
747C4⋊C4—448no—
748C4⋊C4—448no—
749C4⋊C4—444no—
750C22⋊C4—48no—
751C22⋊C4—228no—
752C22⋊C4—228no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C22⋊C4—448no—
756C42—1116no—
757C42—448no—
758C11#1390611yescharacteristic, 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—114no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23C4⋊C4×D1114yes—
829C23C22×C4×D1111yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23C2×D4×D1111yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×#434111yescharacteristic
836C23#6703711yescharacteristic
837C23C2×Q8×D1111yescharacteristic
838C23#6704011yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#6704211yescharacteristic
842C23#6704311yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—2232no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—416no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—114no—
868C2×C4—114no—
869C2×C4—114no—
870C2×C4—114no—
871C2×C4—114no—
872C2×C4—114no—
873C2×C4—114no—
874C2×C4—114no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—224no—
884C2×C4—222no—
885C2×C4—224no—
886C2×C4—224no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—442no—
890C2×C4—442no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—442no—
894C2×C4—442no—
895C2×C4—4416no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4—442no—
899C2×C4—442no—
900C2×C4—442no—
901C2×C4—442no—
902C2×C4—442no—
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—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22C2×C22⋊C4×D1111yescharacteristic
941C22C2×(C22⋊D11)⋊C411yescharacteristic
942C22C2×#6693711yescharacteristic
943C22C2×#6693811yescharacteristic
944C22C2×C4⋊C4×D1111yescharacteristic
945C22#1062303511yescharacteristic
946C22#1062303811yescharacteristic
947C22#1062304211yescharacteristic
948C22D11×#11711yescharacteristic
949C22#1062305411yescharacteristic
950C22#1062306311yescharacteristic
951C22#1062306411yescharacteristic
952C22#1062313011yescharacteristic
953C22D11×#12111yescharacteristic
954C22D11×#12111yescharacteristic
955C22#1062313811yescharacteristic
956C22#1062313911yescharacteristic
957C22#1062314011yescharacteristic
958C22#1062314211yescharacteristic
959C22#1062314711yescharacteristic
960C22D11×C22⋊Q811yescharacteristic
961C22D11×C22⋊Q811yescharacteristic
962C22#1062315911yescharacteristic
963C22#1062316011yescharacteristic
964C22#1062316211yescharacteristic
965C22#1062316311yescharacteristic
966C22#1062316611yescharacteristic
967C22#1062317211yescharacteristic
968C22C2×C4×C22⋊D1111yescharacteristic
969C22D4×C22⋊D1111yescharacteristic
970C22C2×#6699211yescharacteristic
971C22C2×#6699311yescharacteristic
972C22Q8×C22⋊D1111yescharacteristic
973C22#1062335511yescharacteristic
974C22#1062336511yescharacteristic
975C4—44no—
976C4—42no—
977C4—82no—
978C4—118no—
979C4—224no—
980C4—444no—
981C4—442no—
982C4—882no—
983C4#1062257018yescomplemented
984C2—44no—
985C2—444no—
986C2D11×#38011yescharacteristic
987C2C2×#1062257011yescharacteristic
988C2#1307120511yescharacteristic
989C2#1307151211yescharacteristic
990C2C4⋊C4×C22⋊D1111yescharacteristic
991C2#1307156011yescharacteristic
992C2#1307156611yescharacteristic
993C2#1307353011yescharacteristic
994C2#1307353111yescharacteristic
995C2#1307353511yescharacteristic
996C2#1307354011yescharacteristic
997C2#1307355911yescharacteristic
998C2#1307356611yescharacteristic
999C2#1307361011yescharacteristic
1000C2#1307378611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#13906
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#10622589C2semidirect
4. C2×#10622825C2semidirect
5. C2×#10622600C2semidirect
6. C2×#10622600C2semidirect
7. C2×C4⋊C4×Dic11C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. Dic11⋊#95C2semidirect
11. C2×C11×#380C2semidirect
22. C2×C4×C22⋊D11C4semidirect
82. C2×C11×C4⋊C4D4semidirect
107. C2×C4⋊Dic11D4semidirect
201. C2×C22⋊D11C4⋊C4semidirect
258. C4×Dic11C22⋊C4semidirect
265. C2×#380D11semidirect
522. C4×C11#390semidirect
527. Dic11#380semidirect
581. C2×C4⋊C4C22⋊D11semidirect
758. C11#13906semidirect
983. C4#10622570semidirect

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×#106225702
C2×#106225892
C2×#106228252
C2×#106226002
C2×C4⋊C4×Dic112
#130668602
#130668592
Dic11⋊#952
C2×C11×#3802
#1390611