Finite Group Databasebeta

← #14679187

Subgroups — #14679187

Order 2816.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622572C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066865C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066854C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066843C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C4×C11×C22⋊C4—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622826—24no—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622572C418yescomplemented
54#10622569—24no—
55C4×(C2×D11)⋊C4—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11C2×C414yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4C2×C414yescomplemented
97C2×C11×C22⋊C4D414yes—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—41no—
103C2×C42×C11—41no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11C2×C414yescomplemented
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4C2×C414yescomplemented
126C2×(C2×D11)⋊C4C2×C414yescomplemented
127C2×(C2×D11)⋊C4D414yes—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4C2×C414yescomplemented
131C2×C4×Dic11—22no—
132C2×C4×Dic11—22no—
133C2×C4×Dic11—41no—
134C11×#95—22no—
135C11×#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yescomplemented
152#14181—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11C22×C412yes—
166C24×C11C2×D412yes—
167C24×C11#4112yes—
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11C22×C412yes—
182C23×D11C2×D412yes—
183C23×D11#4112yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—28no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11—44no—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11#4112yes—
229C22×C4×C11#4112yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11#4112yes—
289C2×C4×D11—28no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C11×C22⋊C4—28no—
297C11×C22⋊C4—28no—
298C42×C11—44no—
299C42×C11—44no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302C22⋊Dic11—44no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308Dic11⋊C4—44no—
309C4×Dic11—44no—
310C2×#394—111no—
311C2×#386—111no—
312C2×#386—111no—
313C2×C4×C22⋊C4—111no—
314C2×C4×C22⋊C4D1111yescharacteristic, complemented
315#1445—111no—
316#1440—111no—
317#1440—111no—
318#1437—111no—
319#1437—111no—
320#1436—111no—
321#1434—111no—
322#1434—111no—
323C22⋊#95—111no—
324C22⋊#95—111no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11C4×D414yes—
360C23×C11C23×C411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C22×D411yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11C2×#4111yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11C2×#4111yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
373C23×C11H(5,𝔽2)11yescharacteristic
374C23×C11H(5,𝔽2)11yescharacteristic
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11C4×D414yes—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—416no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11#12314yes—
452C2×C4×C11#12314yes—
453C22⋊D11—416no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C4×D11—416no—
504C23×D4—111no—
505C24×C4—111no—
506C24×C4C2×D1111yescharacteristic
507C22×C4⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4C2×D1111yescharacteristic
518C22×C42—111no—
519C22×C42C2×D1111yescharacteristic
520C22×C42C2×D1111yescharacteristic
521#394—118no—
522#386—224no—
523#386—224no—
524C4×C22⋊C4—24no—
525C4×C22⋊C4—224no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95C2×D1111yescharacteristic
543C2×#95C2×D1111yescharacteristic
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11C2×C4×D411yescharacteristic
560C22×C11C2×C4×D411yescharacteristic
561C22×C11C4×#4111yescharacteristic
562C22×C11C4×#4111yescharacteristic
563C22×C11C4×#4111yescharacteristic
564C22×C11#51811yescharacteristic
565C22×C11#51811yescharacteristic
566C22×C11C2×#12311yescharacteristic
567C22×C11C2×#12311yescharacteristic
568C22×C11#52511yescharacteristic
569C22×C11#52511yescharacteristic
570C22×C11#52911yescharacteristic
571C22×C11#52911yescharacteristic
572C22×C11#52911yescharacteristic
573C22×C11#52911yescharacteristic
574C22×C11#53811yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#54011yescharacteristic
577C22×C11#54011yescharacteristic
578C22×C11D4211yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54611yescharacteristic
582C22×C11#54611yescharacteristic
583C22×C11#54611yescharacteristic
584C22×C11#54611yescharacteristic
585C22×C11#55111yescharacteristic
586C22×C11#55111yescharacteristic
587C22×C11#55111yescharacteristic
588C22×C11#55311yescharacteristic
589C22×C11#55311yescharacteristic
590C22×C11#55311yescharacteristic
591C22×C11#55311yescharacteristic
592C22×C11#55511yescharacteristic
593C22×C11#55511yescharacteristic
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C4×C11—24no—
610C4×C11—24no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—42no—
615Dic11—42no—
616Dic11—42no—
617Dic11—42no—
618Dic11—42no—
619Dic11—42no—
620Dic11—81no—
621Dic11—81no—
622C25—111no—
623C25C22×D1111yescharacteristic
624C22×D4—114no—
625C22×D4—222no—
626C22×D4—222no—
627C22×D4—222no—
628C22×D4—222no—
629C22×D4—441no—
630C22×D4—441no—
631C23×C4—22no—
632C23×C4—22no—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—41no—
637C23×C4—41no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—222no—
646C23×C4—222no—
647C23×C4—222no—
648C23×C4—222no—
649C23×C4—222no—
650C23×C4—441no—
651C23×C4—441no—
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658C2×C4⋊C4—114no—
659C2×C4⋊C4—441no—
660C2×C4⋊C4—441no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—114no—
667C2×C22⋊C4—114no—
668C2×C22⋊C4—114no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4C4×D1114yescomplemented
690C2×C22⋊C4C22⋊D1114yes—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—22no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—222no—
698C2×C42—222no—
699C2×C42—441no—
700#95—22no—
701#95—22no—
702#95—114no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—222no—
711#95—222no—
712#95—222no—
713#95—441no—
714#95—441no—
715#95—441no—
716#95—441no—
717#95—441no—
718C2×C11—44no—
719C2×C11C4×#12311yescharacteristic
720C2×C11C4×#12311yescharacteristic
721C2×C11#233311yescharacteristic
722C2×C11#235811yescharacteristic
723C2×C11#236411yescharacteristic
724C2×C11#236411yescharacteristic
725C2×C11#237211yescharacteristic
726C2×C11#241811yescharacteristic
727C2×C11#241811yescharacteristic
728C2×C11#242011yescharacteristic
729C2×C11#242011yescharacteristic
730C2×C11#247611yescharacteristic
731C2×C11#247611yescharacteristic
732C2×C11#257811yescharacteristic
733C2×C11#257811yescharacteristic
734D11—44no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—112no—
748C24—112no—
749C24—112no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24C2×C4×D1112yes—
763C24#433912yes—
764C24C2×C22⋊D1112yes—
765C24C23×D1111yescharacteristic
766C2×D4—228no—
767C2×D4—228no—
768C2×D4—444no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—28no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—112no—
817C22×C4—228no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—444no—
863C22×C4—444no—
864C22×C4—444no—
865C22×C4—444no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4C2×C4×D1112yes—
869C22×C4C2×C4×D1112yes—
870C22×C4#433912yes—
871C22×C4#433912yes—
872C22×C4#433912yes—
873C22×C4#433912yes—
874C22×C4D4×D1112yes—
875C22×C4#434112yes—
876C22×C4C2×C22⋊D1112yes—
877C22×C4C2×C22⋊D1112yes—
878C4⋊C4—444no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—228no—
882C22⋊C4—228no—
883C22⋊C4—444no—
884C22⋊C4—444no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C22⋊C4—444no—
888C22⋊C4—444no—
889C42—44no—
890C42—44no—
891C42—444no—
892C11#1418111yescharacteristic, complemented, Sylow
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—114no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23C4×C22⋊D1114yes—
963C23C22×C4×D1111yescharacteristic
964C23C2×#433911yescharacteristic
965C23C2×#433911yescharacteristic
966C23C2×#433911yescharacteristic
967C23C2×#433911yescharacteristic
968C23C2×#433911yescharacteristic
969C23C2×D4×D1111yescharacteristic
970C23C2×#434111yescharacteristic
971C23#6703711yescharacteristic
972C23#6703711yescharacteristic
973C23#41×D1111yescharacteristic
974C23#41×D1111yescharacteristic
975C23#6704211yescharacteristic
976C23#6704211yescharacteristic
977C23C22×C22⋊D1111yescharacteristic
978D4—4416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—416no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—4416no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4#6693614yes—
1071C2×C4#6698214yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—224no—
1088C22—224no—
1089C22—224no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22C4×#433911yescharacteristic
1103C22C4×#433911yescharacteristic
1104C22#1062301011yescharacteristic
1105C22#1062301011yescharacteristic
1106C22C2×#6693611yescharacteristic
1107C22#1062302111yescharacteristic
1108C22#1062302511yescharacteristic
1109C22#1062302611yescharacteristic
1110C22#1062305911yescharacteristic
1111C22#1062306111yescharacteristic
1112C22#1062306311yescharacteristic
1113C22#1062306611yescharacteristic
1114C22C4×#434111yescharacteristic
1115C22#1062307111yescharacteristic
1116C22C4×D4×D1111yescharacteristic
1117C22#1062307611yescharacteristic
1118C22#1062307611yescharacteristic
1119C22#1062307811yescharacteristic
1120C22#1062308111yescharacteristic
1121C22#1062308111yescharacteristic
1122C22#1062308711yescharacteristic
1123C22#1062308711yescharacteristic
1124C22#1062308811yescharacteristic
1125C22#1062308911yescharacteristic
1126C22#1062309111yescharacteristic
1127C22#1062309311yescharacteristic
1128C22#1062309411yescharacteristic
1129C22#1062309611yescharacteristic
1130C22C2×C4×C22⋊D1111yescharacteristic
1131C22C2×#6698211yescharacteristic
1132C22#1062332211yescharacteristic
1133C22D4×C22⋊D1111yescharacteristic
1134C22#1062333711yescharacteristic
1135C22#1062336011yescharacteristic
1136C22#1062336011yescharacteristic
1137C4—24no—
1138C4—24no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—442no—
1144C4—442no—
1145C4—442no—
1146C4—442no—
1147C4—442no—
1148C4—881no—
1149C4—881no—
1150C2—44no—
1151C2—444no—
1152C2C4×#6693611yescharacteristic
1153C2C4×#6698211yescharacteristic
1154C2#1307137611yescharacteristic
1155C2#1307159311yescharacteristic
1156C2#1307166111yescharacteristic
1157C2#1307166711yescharacteristic
1158C2#1307172411yescharacteristic
1159C2#1307207211yescharacteristic
1160C2#1307207811yescharacteristic
1161C2#1307210211yescharacteristic
1162C2#1307210811yescharacteristic
1163C2#1307279611yescharacteristic
1164C2#1307280211yescharacteristic
1165C2#1307394411yescharacteristic
1166C2#1307395011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14181
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×(C2×D11)⋊C4C2semidirect
5. #13066882C2semidirect
6. #13066865C2semidirect
7. #13066864C2semidirect
8. #13066854C2semidirect
9. #13066853C2semidirect
10. #13066849C2semidirect
11. #13066843C2semidirect
12. #13066842C2semidirect
13. #13066839C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
53. #10622572C4semidirect
96. C2×C11×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic11C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
130. C2×Dic11⋊C4C2×C4semidirect
151. C11⋊#95C2×C4semidirect
314. C2×C4×C22⋊C4D11semidirect
689. C2×C22⋊C4C4×D11semidirect
892. C11#14181semidirect

Maximal subgroups

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

subgroupindex
C2×#106225722
C2×#106228262
C2×#106225692
C2×C4×(C2×D11)⋊C42
#130668822
#130668652
#130668642
#130668542
#130668532
#130668492
#130668432
#130668422
#130668392
(C2×D11)⋊#952
C2×C4×C11×C22⋊C42
#1418111