Finite Group Databasebeta

← #14759273

Subgroups — #14759273

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×#10622724C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
4C4×#66990C211yesmaximal, characteristic
5#13068914C211yesmaximal, characteristic, complemented
6#13068910C211yesmaximal, characteristic, complemented
7#13068905C211yesmaximal, characteristic, complemented
8#13068798C211yesmaximal, characteristic, complemented
9#13068797C211yesmaximal, characteristic, complemented
10#13068792C211yesmaximal, characteristic, complemented
11#13068525C211yesmaximal, characteristic, complemented
12#13068401C211yesmaximal, characteristic, complemented
13#13068397C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66990C411yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×M16×D11—24no—
25C2×M16×D11—24no—
26C2×M16×D11—24no—
27C22×#4313C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31C11×#435—24no—
32C2×C11×C4⋊C8C2211yescharacteristic, complemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic, complemented
35C2×C11×#97C2211yescharacteristic, complemented
36#10622833C411yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
41#10622724—24no—
42C8×C22⋊D11—24no—
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×Dic11⋊C8C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51#10622602C411yescharacteristic
52#10622602C411yescharacteristic
53#10622569C411yescharacteristic
54#10622569C411yescharacteristic
55#10622568C411yescharacteristic
56#10622559C411yescharacteristic
57C4×(C2×D11)⋊C4C2211yescharacteristic
58C4×(C2×D11)⋊C4C2211yescharacteristic
59#10622188C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64#10622162C2211yescharacteristic, 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×M16D414yescomplemented
85C22×C8×C11—22no—
86C22×C8×C11—22no—
87C22×C8×C11—22no—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11C2×C411yescharacteristic
99C2×C22⋊Dic11C2×C411yescharacteristic
100C2×C22⋊Dic11C2×C411yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102#66990—24no—
103C4×C22⋊D11—22no—
104C4×C22⋊D11—22no—
105C4×C22⋊D11—22no—
106C4×C22⋊D11—22no—
107C2×(C2×D11)⋊C4C2×C411yescharacteristic
108C2×(C2×D11)⋊C4C2×C411yescharacteristic
109C2×(C2×D11)⋊C4C2×C411yescharacteristic
110C2×(C2×D11)⋊C4C2×C411yescharacteristic
111C2×(C2×D11)⋊C4C2×C411yescharacteristic
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318—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×C4⋊C8—22no—
138C11×C22⋊C8—22no—
139C11×C22⋊C8—22no—
140C11×#97—22no—
141C11⋊#95C2×C411yescharacteristic
142C11⋊#95C2×C411yescharacteristic
143C11⋊#95C2×C411yescharacteristic
144C11⋊#95C2×C411yescharacteristic
145C11⋊#95C2×C411yescharacteristic
146C11⋊#95C2×C411yescharacteristic
147C22⋊(C11⋊C8)—22no—
148C22⋊(C11⋊C8)—22no—
149C22⋊(C11⋊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—
156Dic11⋊C8—22no—
157C8×Dic11—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—44no—
237C2×C8×C11C2×D412yes—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C2×C8×C11C2×D412yes—
241C11×C4⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C42×C11—21no—
245C42×C11—21no—
246C22⋊Dic11—22no—
247C22⋊Dic11—22no—
248C22⋊Dic11—22no—
249C22⋊Dic11—41no—
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—
256Dic11⋊C4—22no—
257Dic11⋊C4—22no—
258C4×Dic11—21no—
259C4×Dic11—21no—
260C4×Dic11—21no—
261C4×Dic11—21no—
262#4318—28no—
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⋊C8—21no—
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×#435D1111yescharacteristic, complemented
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#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—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×C8C2×D1111yescharacteristic, complemented
407C2×#120—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4C2×D1111yescharacteristic
411#435—24no—
412#435—224no—
413C8×D4—224no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×C4⋊C8C2×D1111yescharacteristic, complemented
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⋊C8C2×D1111yescharacteristic
425C2×C22⋊C8C2×D1111yescharacteristic, complemented
426C2×#97—111no—
427C2×#97C2×D1111yescharacteristic, complemented
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#336—111no—
444#336—111no—
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—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×M16C22⋊D1114yescomplemented
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—114no—
531C22×C8—111no—
532C22×C8—111no—
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—22no—
568C4⋊C8—222no—
569C4⋊C8—222no—
570C22⋊C8—22no—
571C22⋊C8—22no—
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—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×C4#433912yes—
665C22×C4C2×C22⋊D1112yes—
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—44no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—228no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—228no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8D4×D1112yes—
695C2×C8D4×D1112yes—
696C2×C8C2×C22⋊D1112yes—
697C2×C8C2×C22⋊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—
753C23M16×D1112yescomplemented
754C23C4×C22⋊D1112yes—
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×C4C4×C22⋊D1112yes—
808C2×C4C2×#433911yescharacteristic
809C2×C4C2×D4×D1111yescharacteristic
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4#41×D1111yescharacteristic
812C2×C4#41×D1111yescharacteristic
813C2×C4C22×C22⋊D1111yescharacteristic
814C8—22no—
815C8—41no—
816C8—41no—
817C8—222no—
818C8—222no—
819C8—441no—
820C8—441no—
821C8#6699014yescomplemented
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—
851C22C4×D4×D1111yescharacteristic
852C22C4×D4×D1111yescharacteristic
853C22C2×M16×D1111yescharacteristic
854C22#1062327611yescharacteristic
855C22D11×#13111yescharacteristic
856C22#1062328111yescharacteristic
857C22C2×C4×C22⋊D1111yescharacteristic
858C4—22no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—222no—
863C4—222no—
864C4—222no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4#1062307811yescharacteristic
869C4#1062307811yescharacteristic
870C4C2×#6699011yescharacteristic
871C4#1062335911yescharacteristic
872C2—42no—
873C2—42no—
874C2—224no—
875C2—442no—
876C2C4×#6699011yescharacteristic
877C2D11×#43511yescharacteristic
878C2#1307731411yescharacteristic
879C2#1307733811yescharacteristic
880C2#1307733911yescharacteristic
881C2#1307734911yescharacteristic
882C2M16×C22⋊D1111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#435C2
prime radicalC2×#66990C4
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#21439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×M16×D11C2semidirect
2. C2×#10622724C2semidirect
3. C2×C8×C22⋊D11C2semidirect
5. #13068914C2semidirect
6. #13068910C2semidirect
7. #13068905C2semidirect
8. #13068798C2semidirect
9. #13068797C2semidirect
10. #13068792C2semidirect
11. #13068525C2semidirect
12. #13068401C2semidirect
13. #13068397C2semidirect
14. #13068393C2semidirect
15. C2×C11×#435C2semidirect
18. C23×C8×C11C22semidirect
32. C2×C11×C4⋊C8C22semidirect
34. C2×C11×C22⋊C8C22semidirect
35. C2×C11×#97C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
47. C2×#66879C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. C2×C8×Dic11C22semidirect
59. #10622188C22semidirect
60. #10622188C22semidirect
61. #10622188C22semidirect
62. #10622188C22semidirect
63. #10622162C22semidirect
64. #10622162C22semidirect
84. C2×C11×M16D4semidirect
130. C2×#4313D4semidirect
136. C2×C8×D11D4semidirect
195. C2×C22⋊D11M16semidirect
281. C2×#435D11semidirect
307. C23×C11C2×M16semidirect
377. C2×Dic11C2×M16semidirect
391. C8×C11#120semidirect
406. C23×C8C2×D11semidirect
416. C2×C4⋊C8C2×D11semidirect
425. C2×C22⋊C8C2×D11semidirect
427. C2×#97C2×D11semidirect
480. C2×D11#435semidirect
524. C2×M16C22⋊D11semidirect
719. C11#21439semidirect
753. C23M16×D11semidirect
821. C8#66990semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D112
C2×#106227242
C2×C8×C22⋊D112
C4×#669902
#130689142
#130689102
#130689052
#130687982
#130687972
#130687922
#130685252
#130684012
#130683972
#130683932
C2×C11×#4352
#2143911