Finite Group Databasebeta

← #14759280

Subgroups — #14759280

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×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622343C211yesmaximal, characteristic, complemented
4C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
5C4×#66990C211yesmaximal, characteristic
6#13068910C211yesmaximal, characteristic, complemented
7#13068905C211yesmaximal, characteristic, complemented
8#13068800C211yesmaximal, characteristic, complemented
9#13068799C211yesmaximal, characteristic, complemented
10#13068795C211yesmaximal, characteristic, complemented
11#13068525C211yesmaximal, characteristic, complemented
12#13068402C211yesmaximal, characteristic, complemented
13#13068398C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66990C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic, complemented
24C2×M16×D11—24no—
25C2×M16×D11—24no—
26C2×M16×D11—24no—
27C22×#4313C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic, complemented
33C2×C11×C22⋊C8C2211yescharacteristic, complemented
34#10622833C411yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66879C2211yescharacteristic, complemented
43C2×Dic11⋊C8C2211yescharacteristic, complemented
44C2×Dic11⋊C8C2211yescharacteristic, complemented
45C2×C8×Dic11C2211yescharacteristic, complemented
46#10622624—24no—
47#10622602C411yescharacteristic
48#10622602C411yescharacteristic
49#10622569C411yescharacteristic
50#10622569C411yescharacteristic
51#10622568C411yescharacteristic
52#10622559C411yescharacteristic
53C4×(C2×D11)⋊C4C2211yescharacteristic
54C4×(C2×D11)⋊C4C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57#10622343—24no—
58(C22⋊D11)⋊C8—24no—
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65C24×D11C2×C411yescharacteristic
66C22×D4×C11C2×C411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11C2×C411yescharacteristic
70C22×C22⋊D11C2×C411yescharacteristic
71C23×Dic11C2×C411yescharacteristic
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16—22no—
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C22⋊C4C2×C411yescharacteristic
93C2×C11×C22⋊C4C2×C411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11C2×C411yescharacteristic
96C2×C22⋊Dic11C2×C411yescharacteristic
97C2×C22⋊Dic11C2×C411yescharacteristic
98C2×C22⋊Dic11C2×C411yescharacteristic
99#66990—24no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C4×C22⋊D11—22no—
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×(C2×D11)⋊C4C2×C411yescharacteristic
106C2×(C2×D11)⋊C4C2×C411yescharacteristic
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×(C2×D11)⋊C4C2×C411yescharacteristic
110C2×Dic11⋊C4C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×#4318—22no—
115C2×#4318—22no—
116C2×#4318D414yescomplemented
117C22×C11⋊C8—22no—
118C22×C11⋊C8—22no—
119C22×C11⋊C8—22no—
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124M16×D11—232no—
125C2×#4313—22no—
126C2×#4313—22no—
127C2×#4313—22no—
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313D414yescomplemented
131C2×C8×D11—22no—
132C2×C8×D11—22no—
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11—22no—
136C2×C8×D11D414yescomplemented
137C11×C22⋊C8—22no—
138C11×C22⋊C8—22no—
139C11×C22⋊C8—22no—
140C11⋊#95C2×C411yescharacteristic
141C11⋊#95C2×C411yescharacteristic
142C11⋊#95C2×C411yescharacteristic
143C11⋊#95C2×C411yescharacteristic
144C11⋊#95C2×C411yescharacteristic
145C11⋊#95C2×C411yescharacteristic
146C22⋊(C11⋊C8)—22no—
147C22⋊(C11⋊C8)—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151(C2×D11)⋊C8—22no—
152#66879—22no—
153Dic11⋊C8—22no—
154Dic11⋊C8—22no—
155C8×Dic11—22no—
156C4⋊(C11⋊C8)—22no—
157#66867—22no—
158#21439—111nomaximal, Sylow
159C24×C11C22×C411yescharacteristic
160C24×C11C22×C411yescharacteristic
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—41no—
167C23×D11—41no—
168C23×D11C22×C411yescharacteristic
169C23×D11C22×C411yescharacteristic
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—41no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11#4112yes—
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11M1614yescomplemented
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203C22×Dic11C22×C411yescharacteristic
204C22×Dic11C22×C411yescharacteristic
205C2×C4×D11—28no—
206C2×C4×D11—28no—
207C2×C4×D11—28no—
208C2×C4×D11—28no—
209C2×C4×D11—22no—
210C2×C4×D11—22no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—22no—
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×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C11×C4⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C42×C11—21no—
244C42×C11—21no—
245C22⋊Dic11—22no—
246C22⋊Dic11—22no—
247C22⋊Dic11—22no—
248C22⋊Dic11—41no—
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—41no—
255Dic11⋊C4—22no—
256Dic11⋊C4—22no—
257C4×Dic11—21no—
258C4×Dic11—21no—
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—44no—
271C2×C11⋊C8C2×D412yes—
272C2×C11⋊C8C2×D412yes—
273C2×C11⋊C8C2×D412yes—
274C2×C11⋊C8C2×D412yes—
275#4313—28no—
276#4313—28no—
277C8×D11—28no—
278C8×D11—28no—
279C23×M16—111no—
280C2×#435—111no—
281C2×#435—111no—
282C2×C8×D4—111no—
283C4×#120—111no—
284#1870—111no—
285#1870D1111yescharacteristic, complemented
286#1869—111no—
287#1851—111no—
288#1851—111no—
289#1850—111no—
290#1779—111no—
291#1753—111no—
292#1753—111no—
293#1752—111no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11C4×D412yes—
307C23×C11C2×M1612yescomplemented
308C23×C11C23×C411yescharacteristic
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—28no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—44no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11C4×D412yes—
327C22×D11C4×D412yes—
328C22×D11C2×M1612yes—
329C22×D11#13112yes—
330D4×C11—44no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—21no—
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—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11C4×D412yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C22⋊D11—28no—
358C22⋊D11—44no—
359C2×Dic11—28no—
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×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11C4×D412yes—
376C2×Dic11C4×D412yes—
377C2×Dic11C2×M1612yescomplemented
378C4×D11—28no—
379C4×D11—28no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C8×C11—22no—
389C8×C11—22no—
390C8×C11—41no—
391C8×C11—41no—
392C11⋊C8—22no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C11⋊C8#12014yescomplemented
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×D4C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
424C2×C22⋊C8C2×D1111yescharacteristic, complemented
425C2×C22⋊C8C2×D1111yescharacteristic, complemented
426C2×#97—111no—
427C2×#97—111no—
428C2×C4×C8—111no—
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⋊C4—111no—
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—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11C2×C4×D411yescharacteristic
460C22×C11C2×C4×D411yescharacteristic
461C22×C11C2×C4×D411yescharacteristic
462C22×C11C22×M1611yescharacteristic
463C22×C11C2×#13111yescharacteristic
464C22×C11#56811yescharacteristic
465C22×C11#56811yescharacteristic
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—416no—
476C2×D11—41no—
477C2×D11—41no—
478C2×D11—41no—
479C2×D11—41no—
480C2×D11#43514yescomplemented
481C4×C11—22no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11C2×#12011yescharacteristic
486C4×C11#52511yescharacteristic
487C4×C11#52511yescharacteristic
488C4×C11#52511yescharacteristic
489Dic11—22no—
490Dic11—22no—
491Dic11—22no—
492Dic11—41no—
493Dic11—41no—
494Dic11—41no—
495C25—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4C4×D1111yescharacteristic
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—222no—
505C23×C4—222no—
506C23×C4—222no—
507C23×C4—222no—
508C23×C4—222no—
509C23×C4—222no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—114no—
516C2×M16—114no—
517C2×M16—222no—
518C2×M16—222no—
519C2×M16—222no—
520C2×M16—222no—
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—2232no—
524C2×M16—222no—
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—22no—
544C4×D4—22no—
545C4×D4—222no—
546C4×D4—222no—
547C4×D4—222no—
548C4×D4—222no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4C4×D1111yescharacteristic
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×C42—111no—
566C2×C42C22×D1111yescharacteristic
567C4⋊C8—222no—
568C4⋊C8—222no—
569C4⋊C8—222no—
570C22⋊C8—22no—
571C22⋊C8—22no—
572C22⋊C8—22no—
573C22⋊C8—222no—
574C22⋊C8—222no—
575C22⋊C8—222no—
576C22⋊C8—222no—
577C22⋊C8—222no—
578C22⋊C8—222no—
579#97—222no—
580#97—222no—
581C4×C8—222no—
582#95—111no—
583#95—111no—
584#95—111no—
585#95—111no—
586#95—111no—
587#95—111no—
588C2×C11—42no—
589C2×C11—42no—
590C2×C11C4×#12011yescharacteristic
591C2×C11C2×#43511yescharacteristic
592C2×C11#293011yescharacteristic
593C2×C11#293311yescharacteristic
594C2×C11#293311yescharacteristic
595C2×C11D4×M1611yescharacteristic
596C2×C11D4×M1611yescharacteristic
597D11—24no—
598D11—42no—
599C24—111no—
600C24—111no—
601C24—222no—
602C24—222no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—441no—
607C24—441no—
608C24C2×C4×D1111yescharacteristic
609C24C2×C4×D1111yescharacteristic
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—41no—
613C2×D4—114no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—222no—
618C2×D4—441no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—111no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—228no—
644C22×C4—228no—
645C22×C4—228no—
646C22×C4—228no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4C2×C4×D1111yescharacteristic
661C22×C4C2×C4×D1111yescharacteristic
662C22×C4C2×C4×D1111yescharacteristic
663C22×C4C2×C4×D1111yescharacteristic
664C22×C4D4×D1112yes—
665C22×C4#434112yes—
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—21no—
680C2×C8—21no—
681C2×C8—112no—
682C2×C8—112no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—228no—
686C2×C8—228no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—444no—
696C2×C8D4×D1112yes—
697C2×C8D4×D1112yes—
698C4⋊C4—22no—
699C4⋊C4—222no—
700C4⋊C4—222no—
701C22⋊C4—22no—
702C22⋊C4—22no—
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—441no—
712C22⋊C4—441no—
713C42—21no—
714C42—21no—
715C42—221no—
716C42—221no—
717C42—221no—
718C42—221no—
719C11#2143911yescharacteristic, complemented, Sylow
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—112no—
733C23—112no—
734C23—112no—
735C23—112no—
736C23—228no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23(C22⋊D11)⋊C412yes—
754C23M16×D1112yescomplemented
755C23C22×C4×D1111yescharacteristic
756D4—44no—
757D4—228no—
758D4—444no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—112no—
781C2×C4—228no—
782C2×C4—228no—
783C2×C4—228no—
784C2×C4—221no—
785C2×C4—221no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4(C22⋊D11)⋊C412yes—
808C2×C4C2×D4×D1111yescharacteristic
809C2×C4C2×D4×D1111yescharacteristic
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4C2×#434111yescharacteristic
812C2×C4#41×D1111yescharacteristic
813C2×C4#41×D1111yescharacteristic
814C8—22no—
815C8—22no—
816C8—41no—
817C8—41no—
818C8—114no—
819C8—222no—
820C8—441no—
821C8—441no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—114no—
837C22—222no—
838C22—222no—
839C22—222no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—222no—
845C22—222no—
846C22—4416no—
847C22—441no—
848C22—441no—
849C22—441no—
850C22—441no—
851C22C2×(C22⋊D11)⋊C411yescharacteristic
852C22C4×D4×D1111yescharacteristic
853C22C4×D4×D1111yescharacteristic
854C22C2×M16×D1111yescharacteristic
855C22#1062327611yescharacteristic
856C22D11×#13111yescharacteristic
857C22#1062328111yescharacteristic
858C4—22no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—222no—
863C4—222no—
864C4—222no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4D11×#12011yescharacteristic
869C4#1062313711yescharacteristic
870C4#1062313711yescharacteristic
871C4#1062318711yescharacteristic
872C2—42no—
873C2—42no—
874C2—224no—
875C2—442no—
876C2#1307112111yescharacteristic
877C2D11×#43511yescharacteristic
878C2#1307731611yescharacteristic
879C2#1307734511yescharacteristic
880C2#1307734611yescharacteristic
881C2#1307734811yescharacteristic
882C2#1307734911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#21439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C22×M16×D11C2semidirect
2. C2×#10622624C2semidirect
3. C2×#10622343C2semidirect
4. C2×(C22⋊D11)⋊C8C2semidirect
6. #13068910C2semidirect
7. #13068905C2semidirect
8. #13068800C2semidirect
9. #13068799C2semidirect
10. #13068795C2semidirect
11. #13068525C2semidirect
12. #13068402C2semidirect
13. #13068398C2semidirect
14. #13068391C2semidirect
15. C11×#1870C2semidirect
23. C23×C11⋊C8C22semidirect
32. C2×C11×C22⋊C8C22semidirect
33. C2×C11×C22⋊C8C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×#66879C22semidirect
43. C2×Dic11⋊C8C22semidirect
44. C2×Dic11⋊C8C22semidirect
45. C2×C8×Dic11C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×#66867C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
61. #10622188C22semidirect
62. #10622188C22semidirect
63. #10622188C22semidirect
64. #10622188C22semidirect
116. C2×#4318D4semidirect
130. C2×#4313D4semidirect
136. C2×C8×D11D4semidirect
195. C2×C22⋊D11M16semidirect
285. #1870D11semidirect
307. C23×C11C2×M16semidirect
377. C2×Dic11C2×M16semidirect
395. C11⋊C8#120semidirect
424. C2×C22⋊C8C2×D11semidirect
425. C2×C22⋊C8C2×D11semidirect
443. #336C2×D11semidirect
444. #336C2×D11semidirect
480. C2×D11#435semidirect
719. C11#21439semidirect
754. C23M16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D112
C2×#106226242
C2×#106223432
C2×(C22⋊D11)⋊C82
C4×#669902
#130689102
#130689052
#130688002
#130687992
#130687952
#130685252
#130684022
#130683982
#130683912
C11×#18702
#2143911