Finite Group Databasebeta

← #14757384

Subgroups — #14757384

Order 2816.

1718 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
1C2×#10623078C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic, complemented
3C2×#10622340C211yesmaximal, characteristic, complemented
4C2×#10622340C211yesmaximal, characteristic, complemented
5C2×#10622339C211yesmaximal, characteristic, complemented
6C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
7C2×#10622321C211yesmaximal, characteristic, complemented
8#13069414C211yesmaximal, characteristic, complemented
9#13069412C211yesmaximal, characteristic, complemented
10#13069412C211yesmaximal, characteristic, complemented
11#13069411C211yesmaximal, characteristic, complemented
12#13069409C211yesmaximal, characteristic, complemented
13#13069408C211yesmaximal, characteristic, complemented
14#13069408C211yesmaximal, characteristic, complemented
15C11×#1955C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66992C411yescharacteristic
20C2×#66990C411yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623078—24no—
28#10623078—24no—
29C2×#66949C411yescharacteristic
30C2×#66947C411yescharacteristic
31C2×#66937C411yescharacteristic
32C2×#66936C411yescharacteristic
33C2×#66935C411yescharacteristic
34C2×#66931C411yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic, complemented
41C2×C11×C22⋊C8C2211yescharacteristic, complemented
42C2×C11×#97C2211yescharacteristic, complemented
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×(C2×D11)⋊C8C2211yescharacteristic
51C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
55C2×#66879C2211yescharacteristic, complemented
56C2×Dic11⋊C8C2211yescharacteristic, complemented
57C2×Dic11⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
60C2×C4×C11⋊C8C2211yescharacteristic, complemented
61#10622452—24no—
62#10622340—24no—
63#10622340—24no—
64#10622339—24no—
65D11×C22⋊C8—24no—
66#10622321—24no—
67C24×D11C2×C411yescharacteristic
68C22×D4×C11C2×C411yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11C2×C411yescharacteristic
72C22×C22⋊D11C2×C411yescharacteristic
73C22×C22⋊D11C2×C411yescharacteristic
74C22×C22⋊D11C2×C411yescharacteristic
75C23×Dic11C2×C411yescharacteristic
76C2×#4339—22no—
77C2×#4339—22no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—22no—
82C22×D44C2×C411yescharacteristic
83C22×D44C2×C411yescharacteristic
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11C2×C411yescharacteristic
91C22×C4×D11C2×C411yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×Dic22C2×C411yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2×C411yescharacteristic
107C2×C22⋊Dic11C2×C411yescharacteristic
108#66992—24no—
109#66990—24no—
110C4×C22⋊D11—22no—
111C4×C22⋊D11—22no—
112C4×C22⋊D11—22no—
113C4×C22⋊D11—22no—
114C2×(C2×D11)⋊C4C2×C411yescharacteristic
115C2×(C2×D11)⋊C4C2×C411yescharacteristic
116C2×(C2×D11)⋊C4C2×C411yescharacteristic
117C2×(C2×D11)⋊C4C2×C411yescharacteristic
118C2×(C2×D11)⋊C4C2×C411yescharacteristic
119C2×(C2×D11)⋊C4C2×C411yescharacteristic
120C2×C4⋊Dic11C2×C411yescharacteristic
121C2×Dic11⋊C4C2×C411yescharacteristic
122C2×Dic11⋊C4C2×C411yescharacteristic
123C2×Dic11⋊C4C2×C411yescharacteristic
124C2×Dic11⋊C4C2×C411yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C2×#4313—22no—
131C2×#4313—22no—
132C2×#4313—22no—
133C2×#4313—22no—
134C2×#4313—22no—
135C2×#4313D414yescomplemented
136C2×C8×D11—22no—
137C2×C8×D11—22no—
138C2×C8×D11—22no—
139C2×C8×D11—22no—
140C2×C8×D11—22no—
141C2×C8×D11D414yescomplemented
142#66949—24no—
143#66947—24no—
144#66937—24no—
145#66936—24no—
146#66935—24no—
147#66931—24no—
148C4×D44—22no—
149C4×D44—22no—
150#66925D414yes—
151#66925D414yes—
152C11×C4⋊C8—22no—
153C11×C22⋊C8—22no—
154C11×C22⋊C8—22no—
155C11×C22⋊C8—22no—
156C11×C22⋊C8—22no—
157C11×#97—22no—
158C22⋊(C11⋊C8)—22no—
159C22⋊(C11⋊C8)—22no—
160C22⋊(C11⋊C8)—22no—
161C22⋊(C11⋊C8)—22no—
162(C2×D11)⋊C8—22no—
163(C2×D11)⋊C8—22no—
164(C2×D11)⋊C8—22no—
165(C2×D11)⋊C8—22no—
166(C2×D11)⋊C8—22no—
167(C2×D11)⋊C8—22no—
168(C2×D11)⋊C8—22no—
169(C2×D11)⋊C8—22no—
170#66879—22no—
171Dic11⋊C8—22no—
172Dic11⋊C8—22no—
173C8×Dic11—22no—
174C4⋊(C11⋊C8)—22no—
175C4×C11⋊C8—22no—
176#21191—111nomaximal, Sylow
177C24×C11C22×C411yescharacteristic
178C24×C11C22×C411yescharacteristic
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—41no—
185C23×D11—41no—
186C23×D11C22×C411yescharacteristic
187C23×D11C22×C411yescharacteristic
188C23×D11C22×C411yescharacteristic
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—41no—
192C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—22no—
210C2×C22⋊D11—22no—
211C2×C22⋊D11—22no—
212C2×C22⋊D11—22no—
213C2×C22⋊D11—22no—
214C2×C22⋊D11—22no—
215C2×C22⋊D11—22no—
216C2×C22⋊D11—22no—
217C2×C22⋊D11—22no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—41no—
220C2×C22⋊D11—41no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11C22×C411yescharacteristic
225C22×Dic11C22×C411yescharacteristic
226C22×Dic11C22×C411yescharacteristic
227C22×Dic11C22×C411yescharacteristic
228C22×Dic11C22×C411yescharacteristic
229#4339—44no—
230#4339—44no—
231#4339—44no—
232#4339—44no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—22no—
238C2×D44—41no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—21no—
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—21no—
256C2×C4×D11—21no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2×D412yes—
264C2×C4×D11C2×D412yes—
265C2×C4×D11#4112yes—
266C2×C4×D11#4112yes—
267C2×Dic22—22no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11C2×D412yes—
281C2×C8×C11C2×D412yes—
282C11×C4⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C42×C11C2×D412yes—
286C42×C11C2×D412yes—
287C22⋊Dic11—22no—
288C22⋊Dic11—22no—
289(C2×D11)⋊C4—22no—
290(C2×D11)⋊C4—22no—
291(C2×D11)⋊C4—22no—
292(C2×D11)⋊C4—22no—
293(C2×D11)⋊C4C22⋊C414yes—
294(C2×D11)⋊C4C22⋊C414yes—
295C4⋊Dic11—22no—
296Dic11⋊C4—22no—
297Dic11⋊C4—22no—
298Dic11⋊C4C22⋊C414yes—
299Dic11⋊C4C22⋊C414yes—
300C4×Dic11C2×D412yes—
301C4×Dic11C2×D412yes—
302C2×C11⋊C8—21no—
303C2×C11⋊C8—21no—
304C2×C11⋊C8—21no—
305C2×C11⋊C8—21no—
306C2×C11⋊C8—21no—
307C2×C11⋊C8—21no—
308C2×C11⋊C8—21no—
309C2×C11⋊C8—21no—
310C2×C11⋊C8—21no—
311C2×C11⋊C8—21no—
312C2×C11⋊C8C2×D412yes—
313C2×C11⋊C8C2×D412yes—
314#4313—28no—
315#4313—44no—
316C8×D11—28no—
317C8×D11—44no—
318C2×#525—111no—
319C2×#424—111no—
320C2×#408—111no—
321C2×#408—111no—
322C2×#407—111no—
323C22×C22⋊C8—111no—
324C2×#405—111no—
325#1955—111no—
326#1955—111no—
327#1955—111no—
328#1955D1111yescharacteristic, complemented
329#1954—111no—
330#1954—111no—
331#1954—111no—
332#1954—111no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11#13112yes—
347C23×C11C23×C411yescharacteristic
348C22×D11—21no—
349C22×D11—21no—
350C22×D11—21no—
351C22×D11—21no—
352C22×D11—28no—
353C22×D11—21no—
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—21no—
358C22×D11—21no—
359C22×D11—21no—
360C22×D11—21no—
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—21no—
364C22×D11—21no—
365C22×D11—21no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11C2×C22⋊C412yes—
373C22×D11C4×D412yes—
374C22×D11C4×D412yes—
375C22×D11#13112yes—
376D4×C11—44no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11C2×C22⋊C412yes—
396C2×C4×C11C2×C22⋊C412yes—
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C2×#4111yescharacteristic
402C2×C4×C11C2×#4111yescharacteristic
403C22⋊D11—44no—
404C22⋊D11—44no—
405C22⋊D11—44no—
406C22⋊D11—44no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—21no—
414C2×Dic11—21no—
415C2×Dic11—21no—
416C2×Dic11—21no—
417C2×Dic11—44no—
418C2×Dic11C2×C22⋊C412yes—
419C2×Dic11C2×C22⋊C412yes—
420C2×Dic11C2×C22⋊C412yes—
421C2×Dic11C4×D412yes—
422C2×Dic11C4×D412yes—
423D44—44no—
424D44—44no—
425C4×D11—44no—
426C4×D11—41no—
427C4×D11—41no—
428C4×D11—41no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—41no—
433C4×D11—41no—
434C4×D11—44no—
435C4×D11#12114yes—
436C4×D11#12114yes—
437C4×D11#12414yes—
438C4×D11#12714yes—
439Dic22—44no—
440C8×C11—22no—
441C8×C11—22no—
442C8×C11—41no—
443C8×C11—41no—
444C11⋊C8—22no—
445C11⋊C8—22no—
446C11⋊C8—41no—
447C11⋊C8—41no—
448C22×#41—111no—
449C24×C4—111no—
450C22×M16—111no—
451C22×M16—111no—
452C23×C8—111no—
453C23×C8—111no—
454#525—224no—
455#525—224no—
456C2×#123—111no—
457C2×#123—111no—
458C2×C22⋊Q8—111no—
459C2×C22⋊Q8—111no—
460C2×#121—111no—
461C2×#121—111no—
462C2×#120—111no—
463C2×#120—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—111no—
467C2×C4×D4C2×D1111yescharacteristic
468C2×#117—111no—
469#424—224no—
470C2×C4⋊C8—111no—
471C2×C4⋊C8—111no—
472C2×C4⋊C8—111no—
473C2×C4⋊C8C2×D1111yescharacteristic, complemented
474#408—224no—
475#408—224no—
476#407—224no—
477C2×C22⋊C8—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C22⋊C8—111no—
481C2×C22⋊C8—111no—
482C2×C22⋊C8—111no—
483C2×C22⋊C8—111no—
484C2×C22⋊C8—111no—
485C2×C22⋊C8—111no—
486C2×C22⋊C8—111no—
487C2×C22⋊C8—111no—
488C2×C22⋊C8—111no—
489C2×C22⋊C8—224no—
490C2×C22⋊C8C2×D1111yescharacteristic
491C2×C22⋊C8C2×D1111yescharacteristic
492C2×C22⋊C8C2×D1111yescharacteristic, complemented
493C2×C22⋊C8C2×D1111yescharacteristic, complemented
494#405—224no—
495C2×#97—111no—
496C2×#97C2×D1111yescharacteristic, complemented
497C2×C4×C8—111no—
498C2×C4×C8—111no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11C22×C22⋊C411yescharacteristic
514C22×C11C2×C4×D411yescharacteristic
515C22×C11C2×C4×D411yescharacteristic
516C22×C11C2×#13111yescharacteristic
517C22×C11C2×#13111yescharacteristic
518C22×C11#56811yescharacteristic
519C22×C11#56811yescharacteristic
520C2×D11—22no—
521C2×D11—22no—
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—22no—
525C2×D11—22no—
526C2×D11—22no—
527C2×D11—22no—
528C2×D11—22no—
529C2×D11—416no—
530C2×D11—41no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—41no—
534C2×D11—41no—
535C2×D11—41no—
536C2×D11—41no—
537C2×D11—41no—
538C2×D11—41no—
539C2×D11—41no—
540C2×D11—41no—
541C2×D11#39014yes—
542C4×C11—22no—
543C4×C11—22no—
544C4×C11—41no—
545C4×C11—41no—
546C4×C11C2×#12111yescharacteristic
547C4×C11C2×#12111yescharacteristic
548C4×C11C2×#12411yescharacteristic
549C4×C11C2×#12711yescharacteristic
550Dic11—22no—
551Dic11—22no—
552Dic11—41no—
553Dic11—41no—
554Dic11#39014yes—
555C25—111no—
556C2×#41—222no—
557C2×#41—222no—
558C2×#41—222no—
559C2×#41—222no—
560C2×#41—222no—
561C2×#41—222no—
562C22×Q8—111no—
563C22×D4—111no—
564C22×D4—111no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—111no—
568C22×D4—111no—
569C22×D4C4×D1111yescharacteristic
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—222no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—222no—
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C2×M16—114no—
585C2×M16—222no—
586C2×M16—222no—
587C2×M16—222no—
588C2×M16—222no—
589C2×M16—222no—
590C22×C8—111no—
591C22×C8—111no—
592C22×C8—114no—
593C22×C8—111no—
594C22×C8—111no—
595C22×C8—222no—
596C22×C8—222no—
597C22×C8—222no—
598C22×C8—222no—
599C22×C8—222no—
600C22×C8C22×D1111yescharacteristic
601C22×C8C22×D1111yescharacteristic
602C22×C8C22×D1111yescharacteristic
603C22×C8C22×D1111yescharacteristic
604#123—224no—
605#123—224no—
606C22⋊Q8—224no—
607C22⋊Q8—224no—
608#121—224no—
609#121—224no—
610#120—224no—
611#120—224no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4—222no—
617C4×D4—222no—
618C4×D4—222no—
619C4×D4—222no—
620#117—114no—
621#117—114no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4C4×D1111yescharacteristic
628C2×C22⋊C4—111no—
629C2×C22⋊C4—111no—
630C2×C22⋊C4—111no—
631C2×C22⋊C4—111no—
632C2×C22⋊C4—111no—
633C2×C22⋊C4—111no—
634C2×C22⋊C4—111no—
635C2×C22⋊C4—111no—
636C2×C22⋊C4C4×D1111yescharacteristic
637C2×C22⋊C4C4×D1111yescharacteristic
638C2×C42—111no—
639C2×C42C22×D1111yescharacteristic
640C4⋊C8—22no—
641C4⋊C8—222no—
642C4⋊C8—222no—
643C4⋊C8—222no—
644C22⋊C8—22no—
645C22⋊C8—22no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—222no—
649C22⋊C8—222no—
650C22⋊C8—222no—
651C22⋊C8—222no—
652C22⋊C8—222no—
653C22⋊C8—222no—
654C22⋊C8—222no—
655C22⋊C8—222no—
656C22⋊C8—222no—
657C22⋊C8—222no—
658C22⋊C8—222no—
659C22⋊C8—222no—
660#97—22no—
661#97—222no—
662C4×C8—222no—
663C4×C8—222no—
664C2×C11—42no—
665C2×C11—81no—
666C2×C11C2×#39011yescharacteristic
667C2×C11#288011yescharacteristic
668C2×C11#288011yescharacteristic
669C2×C11#292911yescharacteristic
670C2×C11#293011yescharacteristic
671C2×C11#293311yescharacteristic
672C2×C11#293311yescharacteristic
673D11—24no—
674D11—42no—
675D11—81no—
676C24—111no—
677C24—111no—
678C24—111no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—441no—
685C24—441no—
686C24C2×C4×D1111yescharacteristic
687C24C2×C4×D1111yescharacteristic
688#41—444no—
689#41—444no—
690#41—444no—
691#41—444no—
692C2×Q8—222no—
693C2×Q8—222no—
694C2×Q8—222no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—41no—
698C2×D4—222no—
699C2×D4—222no—
700C2×D4—222no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—222no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—441no—
714C2×D4—441no—
715C2×D4—441no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—111no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—112no—
734C22×C4—112no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4C2×C4×D1111yescharacteristic
765C22×C4C2×C4×D1111yescharacteristic
766C22×C4C2×C4×D1111yescharacteristic
767C22×C4C2×C4×D1111yescharacteristic
768C22×C4C23×D1111yescharacteristic
769M16—228no—
770M16—444no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—112no—
782C2×C8—112no—
783C2×C8—228no—
784C2×C8—221no—
785C2×C8—221no—
786C2×C8—221no—
787C2×C8—221no—
788C2×C8—221no—
789C2×C8—221no—
790C2×C8—221no—
791C2×C8—221no—
792C2×C8—221no—
793C2×C8—221no—
794C2×C8—444no—
795C2×C8D4×D1112yes—
796C2×C8D4×D1112yes—
797C4⋊C4—22no—
798C4⋊C4—114no—
799C4⋊C4—114no—
800C4⋊C4—222no—
801C4⋊C4—222no—
802C4⋊C4—222no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—114no—
806C22⋊C4—114no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—222no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4—222no—
813C42—112no—
814C42—112no—
815C42D4×D1112yes—
816C42D4×D1112yes—
817C11#2119111yescharacteristic, complemented, Sylow
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—112no—
832C23—112no—
833C23—112no—
834C23—112no—
835C23—228no—
836C23—221no—
837C23—221no—
838C23—221no—
839C23—221no—
840C23—221no—
841C23—221no—
842C23—221no—
843C23—221no—
844C23—221no—
845C23—221no—
846C23—221no—
847C23—221no—
848C23—221no—
849C23—221no—
850C23—221no—
851C23—221no—
852C23—221no—
853C23—444no—
854C23—444no—
855C23—444no—
856C23—444no—
857C23—444no—
858C23—444no—
859C23#6696012yes—
860C23C22×C4×D1111yescharacteristic
861Q8—444no—
862D4—44no—
863D4—444no—
864D4—444no—
865D4—444no—
866D4—444no—
867D4—444no—
868D4—444no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—112no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—114no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—221no—
900C2×C4—221no—
901C2×C4—221no—
902C2×C4—221no—
903C2×C4—221no—
904C2×C4—221no—
905C2×C4—221no—
906C2×C4—444no—
907C2×C4—444no—
908C2×C4—444no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4C22⋊C4×D1112yes—
918C2×C4C22⋊C4×D1112yes—
919C2×C4C2×D4×D1111yescharacteristic
920C2×C4C2×D4×D1111yescharacteristic
921C2×C4C2×D4×D1111yescharacteristic
922C2×C4C2×D4×D1111yescharacteristic
923C2×C4#41×D1111yescharacteristic
924C2×C4#41×D1111yescharacteristic
925C8—22no—
926C8—22no—
927C8—41no—
928C8—41no—
929C8—222no—
930C8—222no—
931C8—441no—
932C8—441no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—114no—
948C22—222no—
949C22—222no—
950C22—222no—
951C22—222no—
952C22—222no—
953C22—222no—
954C22—222no—
955C22—222no—
956C22—222no—
957C22—4416no—
958C22—441no—
959C22—441no—
960C22—441no—
961C22—441no—
962C22—441no—
963C22—441no—
964C22—441no—
965C22—441no—
966C22—441no—
967C22—441no—
968C22—441no—
969C22C2×C22⋊C4×D1111yescharacteristic
970C22C4×D4×D1111yescharacteristic
971C22C4×D4×D1111yescharacteristic
972C22C2×#6696011yescharacteristic
973C22#1062327611yescharacteristic
974C22D11×#13111yescharacteristic
975C22#1062328111yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—41no—
980C4—114no—
981C4—222no—
982C4—222no—
983C4—441no—
984C4—441no—
985C4D11×#12111yescharacteristic
986C4D11×#12111yescharacteristic
987C4D11×#12411yescharacteristic
988C4D11×#12711yescharacteristic
989C2—42no—
990C2—81no—
991C2—224no—
992C2—442no—
993C2—881no—
994C2D11×#39011yescharacteristic
995C2#1307706411yescharacteristic
996C2#1307706611yescharacteristic
997C2#1307730711yescharacteristic
998C2#1307731411yescharacteristic
999C2#1307733911yescharacteristic
1000C2#1307734211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1955C2
prime radicalC2×#10623078C2
cosocleC22×C4×C11C24
hypercenter#1955D11
hypocenterC11#21191
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#10622452C2semidirect
3. C2×#10622340C2semidirect
4. C2×#10622340C2semidirect
5. C2×#10622339C2semidirect
6. C2×D11×C22⋊C8C2semidirect
7. C2×#10622321C2semidirect
8. #13069414C2semidirect
9. #13069412C2semidirect
10. #13069412C2semidirect
11. #13069411C2semidirect
12. #13069409C2semidirect
13. #13069408C2semidirect
14. #13069408C2semidirect
15. C11×#1955C2semidirect
37. C2×C11×C4⋊C8C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
42. C2×C11×#97C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×(C2×D11)⋊C8C22semidirect
52. C2×(C2×D11)⋊C8C22semidirect
53. C2×(C2×D11)⋊C8C22semidirect
54. C2×(C2×D11)⋊C8C22semidirect
55. C2×#66879C22semidirect
56. C2×Dic11⋊C8C22semidirect
57. C2×Dic11⋊C8C22semidirect
58. C2×C8×Dic11C22semidirect
59. C2×C4⋊(C11⋊C8)C22semidirect
60. C2×C4×C11⋊C8C22semidirect
135. C2×#4313D4semidirect
141. C2×C8×D11D4semidirect
328. #1955D11semidirect
473. C2×C4⋊C8C2×D11semidirect
492. C2×C22⋊C8C2×D11semidirect
493. C2×C22⋊C8C2×D11semidirect
496. C2×#97C2×D11semidirect
817. C11#21191semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106224522
C2×#106223402
C2×#106223392
C2×D11×C22⋊C82
C2×#106223212
#130694142
#130694122
#130694112
#130694092
#130694082
C11×#19552
#2119111