Finite Group Databasebeta

← #14759279

Subgroups — #14759279

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D11C211yesmaximal, characteristic, complemented
2C2×#10622319C211yesmaximal, characteristic, complemented
3C2×#10622740C211yesmaximal, characteristic, complemented
4C2×C8×D44C211yesmaximal, characteristic, complemented
5C4×#66935C211yesmaximal, characteristic
6#13068912C211yesmaximal, characteristic, complemented
7#13068911C211yesmaximal, characteristic, complemented
8#13068907C211yesmaximal, characteristic, complemented
9#13068801C211yesmaximal, characteristic, complemented
10#13068800C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068525C211yesmaximal, characteristic, complemented
13#13068399C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×M16×D11—24no—
21C2×M16×D11—24no—
22C2×M16×D11—24no—
23C22×#4313C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic, complemented
28C2×#66935C411yescharacteristic
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic, complemented
33C2×C4×C8×C11C2211yescharacteristic, complemented
34C4×C11×C22⋊C4C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622740—24no—
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
42C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
44C2×#66879C2211yescharacteristic, complemented
45C2×Dic11⋊C8C2211yescharacteristic, complemented
46#10622571C411yescharacteristic
47#10622568C411yescharacteristic
48#10622563C411yescharacteristic
49C4×(C2×D11)⋊C4C2211yescharacteristic
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622319—24no—
54C8×D44—24no—
55#10622281C411yescharacteristic
56#10622281C411yescharacteristic
57#10622278C411yescharacteristic
58#10622278C411yescharacteristic
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, complemented
65C24×D11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C22×D44C2×C411yescharacteristic
70C22×D44C2×C411yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16D414yescomplemented
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94C4×C22⋊D11—22no—
95C4×C22⋊D11—22no—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×C4⋊Dic11C2×C411yescharacteristic
106C2×C4⋊Dic11C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×#4318—22no—
110C2×#4318—22no—
111C2×#4318—22no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116M16×D11—232no—
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—22no—
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313D414yescomplemented
123C2×C8×D11—22no—
124C2×C8×D11—22no—
125C2×C8×D11—22no—
126C2×C8×D11—22no—
127C2×C8×D11—22no—
128C2×C8×D11—22no—
129C2×C8×D11—22no—
130C2×C8×D11—22no—
131C2×C8×D11D414yescomplemented
132#66935—24no—
133C4×D44—22no—
134C4×D44—22no—
135C4×D44—22no—
136C4×D44—22no—
137C11×C22⋊C8—22no—
138C11×#97—22no—
139C4×C8×C11—22no—
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11⋊#95C2×C411yescharacteristic
143C11⋊#95C2×C411yescharacteristic
144C11⋊#95C2×C411yescharacteristic
145C11⋊#95C2×C411yescharacteristic
146C22⋊(C11⋊C8)—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151(C2×D11)⋊C8—22no—
152(C2×D11)⋊C8—22no—
153(C2×D11)⋊C8—22no—
154#66879—22no—
155Dic11⋊C8—22no—
156C4⋊(C11⋊C8)—22no—
157C4⋊(C11⋊C8)—22no—
158#21439—111nomaximal, Sylow
159C24×C11C22×C411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—41no—
166C23×D11—41no—
167C23×D11C22×C411yescharacteristic
168C23×D11C22×C411yescharacteristic
169C23×D11C22×C411yescharacteristic
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11#4112yes—
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—22no—
183C2×C22⋊D11—22no—
184C2×C22⋊D11—41no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C22×Dic11C22×C411yescharacteristic
193C2×D44—22no—
194C2×D44—22no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—41no—
198C2×D44M1614yescomplemented
199C2×C4×D11—28no—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—28no—
203C2×C4×D11—22no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—21no—
214C2×C4×D11—21no—
215C2×C4×D11—21no—
216C2×C4×D11—21no—
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2×D412yes—
225C2×C4×D11#4112yes—
226C2×C4×D11#4112yes—
227C11×M16—28no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11C2×D412yes—
237C2×C8×C11C2×D412yes—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—41no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11—21no—
246C22⋊Dic11—22no—
247(C2×D11)⋊C4—22no—
248(C2×D11)⋊C4—22no—
249(C2×D11)⋊C4—22no—
250(C2×D11)⋊C4—22no—
251(C2×D11)⋊C4—22no—
252(C2×D11)⋊C4—22no—
253(C2×D11)⋊C4—22no—
254(C2×D11)⋊C4—22no—
255(C2×D11)⋊C4—41no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258Dic11⋊C4—22no—
259C4×Dic11—21no—
260C4×Dic11—21no—
261#4318—28no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8C2×D412yes—
273C2×C11⋊C8C2×D412yes—
274#4313—28no—
275#4313—28no—
276C8×D11—28no—
277C8×D11—28no—
278C8×D11—44no—
279C23×M16—111no—
280C2×#435—111no—
281C2×#435—111no—
282C2×C8×D4—111no—
283C4×#120—111no—
284#1870—111no—
285#1870—111no—
286#1869—111no—
287#1851—111no—
288#1851—111no—
289#1850—111no—
290#1779—111no—
291#1753—111no—
292#1753D1111yescharacteristic, complemented
293#1752—111no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11C4×D412yes—
301C23×C11C23×C411yescharacteristic
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—28no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—44no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11C4×D412yes—
326C22×D11C4×D412yes—
327C22×D11C2×M1612yes—
328C22×D11C2×M1612yescomplemented
329C22×D11#13112yes—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11C4×D412yes—
348C2×C4×C11C2×M1612yescomplemented
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C22⋊D11—44no—
356C2×Dic11—28no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11C4×D412yes—
371C2×Dic11C4×D412yes—
372D44—28no—
373D44—44no—
374C4×D11—28no—
375C4×D11—28no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—41no—
385C4×D11—41no—
386C4×D11—41no—
387C4×D11—41no—
388C8×C11—22no—
389C8×C11—41no—
390C8×C11—41no—
391C8×C11#12014yescomplemented
392C11⋊C8—22no—
393C11⋊C8—22no—
394C11⋊C8—41no—
395C11⋊C8—41no—
396C24×C4—111no—
397C22×M16—111no—
398C22×M16—111no—
399C22×M16—111no—
400C22×M16—224no—
401C22×M16—224no—
402C22×M16—224no—
403C22×M16C2×D1111yescharacteristic
404C23×C8—111no—
405C23×C8—111no—
406C23×C8—111no—
407C2×#120—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411#435—224no—
412#435—224no—
413C8×D4—224no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×C4⋊C8—111no—
417C2×C22⋊C8—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421C2×C22⋊C8—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×C22⋊C8C2×D1111yescharacteristic
426C2×#97—111no—
427C2×#97C2×D1111yescharacteristic, complemented
428C2×C4×C8C2×D1111yescharacteristic, complemented
429#386—111no—
430#386—111no—
431#386—111no—
432#385—111no—
433#385—111no—
434#385—111no—
435#379—111no—
436C4×C22⋊C4—111no—
437C4×C22⋊C4—111no—
438C4×C22⋊C4C2×D1111yescharacteristic
439#336—111no—
440#336—111no—
441#336—111no—
442#336—111no—
443#336C2×D1111yescharacteristic, complemented
444#336C2×D1111yescharacteristic, complemented
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11C2×C4×D411yescharacteristic
453C22×C11C2×C4×D411yescharacteristic
454C22×C11C2×C4×D411yescharacteristic
455C22×C11C22×M1611yescharacteristic
456C22×C11C2×#13111yescharacteristic
457C22×C11#56811yescharacteristic
458C22×C11#56811yescharacteristic
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—416no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—41no—
477C2×D11—41no—
478C2×D11—41no—
479C2×D11—41no—
480C2×D11#43514yescomplemented
481C4×C11—22no—
482C4×C11—22no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11—41no—
486C4×C11C2×#12011yescharacteristic
487C4×C11#52511yescharacteristic
488C4×C11#52511yescharacteristic
489C4×C11#52511yescharacteristic
490Dic11—22no—
491Dic11—22no—
492Dic11—41no—
493Dic11—41no—
494Dic11—41no—
495C25—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—222no—
506C23×C4—222no—
507C23×C4—222no—
508C23×C4—222no—
509C23×C4—222no—
510C23×C4—222no—
511C23×C4C22×D1111yescharacteristic
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—114no—
515C2×M16—222no—
516C2×M16—222no—
517C2×M16—222no—
518C2×M16—222no—
519C2×M16—2232no—
520C2×M16—222no—
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—222no—
524C2×M16D4414yescomplemented
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—114no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—222no—
531C22×C8—222no—
532C22×C8—222no—
533C22×C8—222no—
534C22×C8—222no—
535C22×C8—222no—
536C22×C8—222no—
537C22×C8—222no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C22×C8C22×D1111yescharacteristic
542#120—224no—
543C4×D4—222no—
544C4×D4—222no—
545C4×D4—222no—
546C4×D4—222no—
547C4×D4—222no—
548C4×D4—222no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—111no—
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4C4×D1111yescharacteristic
563C2×C22⋊C4C4×D1111yescharacteristic
564C2×C42—111no—
565C2×C42C22×D1111yescharacteristic
566C2×C42C22×D1111yescharacteristic
567C4⋊C8—222no—
568C4⋊C8—222no—
569C4⋊C8—222no—
570C22⋊C8—22no—
571C22⋊C8—222no—
572C22⋊C8—222no—
573C22⋊C8—222no—
574C22⋊C8—222no—
575C22⋊C8—222no—
576C22⋊C8—222no—
577C22⋊C8—222no—
578C22⋊C8—222no—
579#97—22no—
580#97—222no—
581C4×C8—22no—
582#95—111no—
583#95—111no—
584#95—111no—
585#95—111no—
586#95C4×D1111yescharacteristic
587#95C4×D1111yescharacteristic
588C2×C11—42no—
589C2×C11C4×#12011yescharacteristic
590C2×C11C2×#43511yescharacteristic
591C2×C11#293011yescharacteristic
592C2×C11#293311yescharacteristic
593C2×C11#293311yescharacteristic
594C2×C11D4×M1611yescharacteristic
595C2×C11D4×M1611yescharacteristic
596D11—24no—
597D11—42no—
598D11—42no—
599C24—111no—
600C24—111no—
601C24—111no—
602C24—222no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—441no—
608C24—441no—
609C24C2×C4×D1111yescharacteristic
610C2×D4—114no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—441no—
618C2×D4—441no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—228no—
637C22×C4—228no—
638C22×C4—228no—
639C22×C4—228no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4C2×C4×D1111yescharacteristic
660C22×C4C2×C4×D1111yescharacteristic
661C22×C4C2×C4×D1111yescharacteristic
662C22×C4C2×C4×D1111yescharacteristic
663C22×C4C2×C4×D1111yescharacteristic
664C22×C4C2×D4412yes—
665C22×C4#433912yes—
666C22×C4C23×D1111yescharacteristic
667M16—28no—
668M16—228no—
669M16—228no—
670M16—228no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—228no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—228no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—444no—
694C2×C8C2×D4412yes—
695C2×C8C2×D4412yes—
696C2×C8D4×D1112yes—
697C2×C8D4×D1112yes—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—222no—
704C22⋊C4—222no—
705C22⋊C4—222no—
706C22⋊C4—222no—
707C22⋊C4—222no—
708C22⋊C4—222no—
709C22⋊C4—222no—
710C22⋊C4—222no—
711C22⋊C4—222no—
712C22⋊C4—441no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—221no—
718C42—221no—
719C11#2143911yescharacteristic, complemented, Sylow
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—112no—
727C23—112no—
728C23—112no—
729C23—112no—
730C23—112no—
731C23—228no—
732C23—221no—
733C23—221no—
734C23—221no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23C4×D4412yes—
755C23C22×C4×D1111yescharacteristic
756D4—228no—
757D4—444no—
758D4—444no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—112no—
777C2×C4—112no—
778C2×C4—228no—
779C2×C4—228no—
780C2×C4—228no—
781C2×C4—221no—
782C2×C4—221no—
783C2×C4—221no—
784C2×C4—221no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4C4×D4412yes—
807C2×C4M16×D1112yescomplemented
808C2×C4C22×D4411yescharacteristic
809C2×C4C2×#433911yescharacteristic
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4C2×D4×D1111yescharacteristic
812C2×C4#41×D1111yescharacteristic
813C2×C4#41×D1111yescharacteristic
814C8—22no—
815C8—41no—
816C8—41no—
817C8—222no—
818C8—222no—
819C8—441no—
820C8—441no—
821C8#6693514yescomplemented
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—114no—
830C22—222no—
831C22—222no—
832C22—222no—
833C22—222no—
834C22—222no—
835C22—222no—
836C22—222no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—222no—
841C22—222no—
842C22—4416no—
843C22—441no—
844C22—441no—
845C22—441no—
846C22—441no—
847C22—441no—
848C22—441no—
849C22—441no—
850C22—441no—
851C22C2×C4×D4411yescharacteristic
852C22C4×D4×D1111yescharacteristic
853C22C4×D4×D1111yescharacteristic
854C22C2×M16×D1111yescharacteristic
855C22#1062327611yescharacteristic
856C22D11×#13111yescharacteristic
857C22#1062328111yescharacteristic
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—222no—
864C4—222no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4C2×#6693511yescharacteristic
869C4#1062305511yescharacteristic
870C4#1062307811yescharacteristic
871C4#1062307811yescharacteristic
872C2—42no—
873C2—224no—
874C2—442no—
875C2—442no—
876C2C4×#6693511yescharacteristic
877C2D11×#43511yescharacteristic
878C2#1307731411yescharacteristic
879C2#1307734411yescharacteristic
880C2#1307734511yescharacteristic
881C2#1307735211yescharacteristic
882C2M16×D4411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1753C2
prime radicalC2×#66935C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#21439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C22×M16×D11C2semidirect
2. C2×#10622319C2semidirect
3. C2×#10622740C2semidirect
4. C2×C8×D44C2semidirect
6. #13068912C2semidirect
7. #13068911C2semidirect
8. #13068907C2semidirect
9. #13068801C2semidirect
10. #13068800C2semidirect
11. #13068795C2semidirect
12. #13068525C2semidirect
13. #13068399C2semidirect
14. #13068393C2semidirect
15. C11×#1753C2semidirect
27. C22×C8×D11C22semidirect
32. C2×C11×#97C22semidirect
33. C2×C4×C8×C11C22semidirect
41. C2×(C2×D11)⋊C8C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. C2×(C2×D11)⋊C8C22semidirect
44. C2×#66879C22semidirect
45. C2×Dic11⋊C8C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×C4⋊(C11⋊C8)C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
61. #10622188C22semidirect
62. #10622188C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
84. C2×C11×M16D4semidirect
122. C2×#4313D4semidirect
131. C2×C8×D11D4semidirect
198. C2×D44M16semidirect
292. #1753D11semidirect
328. C22×D11C2×M16semidirect
348. C2×C4×C11C2×M16semidirect
391. C8×C11#120semidirect
427. C2×#97C2×D11semidirect
428. C2×C4×C8C2×D11semidirect
443. #336C2×D11semidirect
444. #336C2×D11semidirect
480. C2×D11#435semidirect
524. C2×M16D44semidirect
719. C11#21439semidirect
807. C2×C4M16×D11semidirect
821. C8#66935semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D112
C2×#106223192
C2×#106227402
C2×C8×D442
C4×#669352
#130689122
#130689112
#130689072
#130688012
#130688002
#130687952
#130685252
#130683992
#130683932
C11×#17532
#2143911