Finite Group Databasebeta

← #14770692

Subgroups — #14770692

Order 2816.

1280 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622538C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13069224C212yesmaximal, complemented
4#13069224C212yesmaximal, complemented
5#13068796C212yesmaximal, complemented
6#13068684C211yesmaximal, characteristic, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068526C211yesmaximal, characteristic
9C22⋊C4×C11⋊C8C212yesmaximal, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C411yescharacteristic
14C22×C11×C22⋊C4C411yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C23×C11⋊C8C2212yes—
18C4×C11×C22⋊C4C411yescharacteristic
19C4×C11×C22⋊C4C411yescharacteristic
20C4×C11×C22⋊C4C411yescharacteristic
21C4×C11×C22⋊C4C411yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26C2×C11×#95C411yescharacteristic
27C2×C11×#95C411yescharacteristic
28C2×C22⋊(C11⋊C8)—24no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622538—24no—
37C2×C4⋊(C11⋊C8)C2212yescomplemented
38C2×C4⋊(C11⋊C8)C2212yescomplemented
39C2×C4×C11⋊C8C2212yescomplemented
40C2×C4×C11⋊C8C2212yescomplemented
41#10622162C2212yescomplemented
42#10622162C2212yescomplemented
43#10622162C2212yescomplemented
44#10622162C2212yescomplemented
45C25×C11C2×C411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—42no—
50C23×C4×C11C2×C411yescharacteristic
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11C2×C411yescharacteristic
54C23×C4×C11C2×C411yescharacteristic
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4C818yescomplemented
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11—42no—
73C2×C42×C11C2×C411yescharacteristic
74C2×C42×C11C2×C411yescharacteristic
75C2×C42×C11C2×C411yescharacteristic
76C2×C42×C11C2×C411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C22×C11⋊C8—24no—
82C22×C11⋊C8—24no—
83C22×C11⋊C8—42no—
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2312yes—
88C11×#95C2×C411yescharacteristic
89C11×#95C2×C411yescharacteristic
90C11×#95C2×C411yescharacteristic
91C11×#95C2×C411yescharacteristic
92C11×#95C2×C411yescharacteristic
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)—24no—
101C22⋊(C11⋊C8)—42no—
102C22⋊(C11⋊C8)D414yes—
103C4⋊(C11⋊C8)—24no—
104C4⋊(C11⋊C8)—42no—
105C4×C11⋊C8—24no—
106C4×C11⋊C8—42no—
107#22552—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—41no—
113C24×C11—41no—
114C24×C11C2×C814yes—
115C24×C11C22×C411yescharacteristic
116C24×C11C22×C411yescharacteristic
117C24×C11C22×C411yescharacteristic
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—48no—
147C22×C4×C11—48no—
148C22×C4×C11C2×C814yescomplemented
149C22×C4×C11C2×C814yescomplemented
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4114yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4C2×C814yes—
169C11×C22⋊C4C2×C814yes—
170C11×C22⋊C4C2×C814yescomplemented
171C11×C22⋊C4C2×C814yescomplemented
172C11×C22⋊C4M1614yes—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—41no—
182C42×C11—41no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—48no—
195C2×C11⋊C8C2×D414yes—
196C2×#431—111no—
197C22×C22⋊C8—111no—
198C2×C4×C22⋊C4D1111yescharacteristic
199#1923—112no—
200#1923—112no—
201#1850—112no—
202#1817—111no—
203#1797—111no—
204#1779—111no—
205C8×C22⋊C4—112no—
206C4×C22⋊C8—111no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—28no—
222C23×C11—28no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11#11712yes—
229C23×C11C4×D412yes—
230C23×C11C22×C812yes—
231C23×C11C22×C812yes—
232C23×C11C22×C812yes—
233C23×C11C2×M1612yes—
234C23×C11#13112yes—
235C23×C11C23×C411yescharacteristic
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—28no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—44no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11#11712yes—
275C2×C4×C11C4×D412yes—
276C2×C4×C11C22×C812yes—
277C2×C4×C11C22×C812yes—
278C2×C4×C11C22×C812yes—
279C2×C4×C11C22×C812yes—
280C2×C4×C11C2×M1612yes—
281C2×C4×C11C2×M1612yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4112yes—
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)12yes—
286C11⋊C8—24no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289C11⋊C8—42no—
290C24×C4C2×D1111yescharacteristic
291C23×C8—112no—
292C22×C22⋊C4Dic1111yescharacteristic
293C22×C22⋊C4Dic1111yescharacteristic
294C22×C42C2×D1111yescharacteristic
295C22×C42C2×D1111yescharacteristic
296#431—224no—
297C2×C4⋊C8—112no—
298C2×C4⋊C8—112no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×C22⋊C8—111no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8—112no—
304C2×C22⋊C8—112no—
305C2×C22⋊C8—112no—
306C2×C22⋊C8—224no—
307C2×C4×C8—112no—
308C2×C4×C8—112no—
309C4×C22⋊C4Dic1111yescharacteristic
310C4×C22⋊C4Dic1111yescharacteristic
311C4×C22⋊C4Dic1111yescharacteristic
312C4×C22⋊C4Dic1111yescharacteristic
313C4×C22⋊C4C2×D1111yescharacteristic
314C4×C22⋊C4C2×D1111yescharacteristic
315C4×C22⋊C4C2×D1111yescharacteristic
316C4×C22⋊C4C2×D1111yescharacteristic
317C2×#95Dic1111yescharacteristic
318C2×#95Dic1111yescharacteristic
319#336—112no—
320#336—112no—
321#336—112no—
322#336—112no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—416no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11#43114yescomplemented
344C22×C11C8×D414yes—
345C22×C11C2×#11711yescharacteristic
346C22×C11C2×C4×D411yescharacteristic
347C22×C11#51811yescharacteristic
348C22×C11C23×C811yescharacteristic
349C22×C11C22×M1611yescharacteristic
350C22×C11C2×#13111yescharacteristic
351C22×C11#56811yescharacteristic
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#54612yes—
364C4×C11#55112yes—
365C25C2×Dic1111yescharacteristic
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4C2×Dic1111yescharacteristic
371C23×C4C2×Dic1111yescharacteristic
372C23×C4C2×Dic1111yescharacteristic
373C23×C4C2×Dic1111yescharacteristic
374C23×C4C2×Dic1111yescharacteristic
375C23×C4C2×Dic1111yescharacteristic
376C23×C4C2×Dic1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C22×C8—112no—
381C22×C8—112no—
382C22×C8—112no—
383C22×C8—112no—
384C22×C8—224no—
385C22×C8—224no—
386C22×C8—442no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4C11⋊C818yescomplemented
389C2×C22⋊C4C2×Dic1111yescharacteristic
390C2×C22⋊C4C2×Dic1111yescharacteristic
391C2×C22⋊C4C2×Dic1111yescharacteristic
392C2×C22⋊C4C2×Dic1111yescharacteristic
393C2×C22⋊C4C2×Dic1111yescharacteristic
394C2×C22⋊C4C2×Dic1111yescharacteristic
395C2×C22⋊C4C2×Dic1111yescharacteristic
396C2×C22⋊C4C2×Dic1111yescharacteristic
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—42no—
400C2×C42C2×Dic1111yescharacteristic
401C2×C42C2×Dic1111yescharacteristic
402C2×C42C2×Dic1111yescharacteristic
403C2×C42C2×Dic1111yescharacteristic
404C2×C42C22×D1111yescharacteristic
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C4⋊C8—224no—
409C4⋊C8—442no—
410C22⋊C8—114no—
411C22⋊C8—224no—
412C22⋊C8—224no—
413C22⋊C8—222no—
414C22⋊C8—222no—
415C22⋊C8—222no—
416C22⋊C8—442no—
417C4×C8—224no—
418C4×C8—442no—
419#95C2×Dic1111yescharacteristic
420#95C2×Dic1111yescharacteristic
421#95C2×Dic1111yescharacteristic
422#95C2×Dic1111yescharacteristic
423#95C2×Dic1111yescharacteristic
424#95C2×Dic1111yescharacteristic
425#95C2×Dic1111yescharacteristic
426#95C2×Dic1111yescharacteristic
427C2×C11—24no—
428C2×C11—24no—
429C2×C11—42no—
430C2×C11#234211yescharacteristic
431C2×C11C2×#43111yescharacteristic
432C2×C11#292411yescharacteristic
433C2×C11C2×C8×D411yescharacteristic
434C2×C11D4×M1611yescharacteristic
435C2×C11#297211yescharacteristic
436C2×C11#297411yescharacteristic
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—41no—
442C24—41no—
443C24C2×C11⋊C814yes—
444C24C22×Dic1111yescharacteristic
445C24C22×Dic1111yescharacteristic
446C24C22×Dic1111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4C2×C11⋊C814yescomplemented
478C22×C4C2×C11⋊C814yescomplemented
479C22×C4#433914yes—
480C22×C4D4×D1112yes—
481C22×C4#434112yes—
482C22×C4C22×Dic1111yescharacteristic
483C22×C4C22×Dic1111yescharacteristic
484C22×C4C22×Dic1111yescharacteristic
485C22×C4C22×Dic1111yescharacteristic
486C22×C4C22×Dic1111yescharacteristic
487C22×C4C22×Dic1111yescharacteristic
488C22×C4C22×Dic1111yescharacteristic
489C22×C4C22×Dic1111yescharacteristic
490C22×C4C22×Dic1111yescharacteristic
491C22×C4C22×Dic1111yescharacteristic
492C22×C4C22×Dic1111yescharacteristic
493C22×C4C23×D1111yescharacteristic
494C2×C8—114no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C2×C8—222no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—448no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4C2×C11⋊C814yes—
511C22⋊C4C2×C11⋊C814yes—
512C22⋊C4C2×C11⋊C814yescomplemented
513C22⋊C4C2×C11⋊C814yescomplemented
514C22⋊C4#431814yes—
515C42—22no—
516C42—22no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—22no—
522C42—22no—
523C42—41no—
524C42—41no—
525C11#2255211yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—28no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—28no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23C22×C11⋊C812yes—
548C23C22×C11⋊C812yes—
549C23C22×C11⋊C812yes—
550C23C2×#431812yes—
551C23#6697912yes—
552C23D4×Dic1112yes—
553C23#6700112yes—
554C23C23×Dic1111yescharacteristic
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—28no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4C22×C11⋊C812yes—
594C2×C4C22×C11⋊C812yes—
595C2×C4C22×C11⋊C812yes—
596C2×C4C22×C11⋊C812yes—
597C2×C4C2×#431812yes—
598C2×C4C2×#431812yes—
599C2×C4#6697912yes—
600C2×C4D4×Dic1112yes—
601C2×C4C2×#433912yes—
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4#6703712yes—
605C8—224no—
606C8—442no—
607C8—442no—
608C8—442no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—416no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22#1062253814yescomplemented
630C22D4×C11⋊C814yes—
631C22C23×C11⋊C811yescharacteristic
632C22C22×#431811yescharacteristic
633C22C2×#6697911yescharacteristic
634C22C2×D4×Dic1111yescharacteristic
635C22#1062332911yescharacteristic
636C22C2×#6700111yescharacteristic
637C22#1062335011yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4#1062302112yes—
650C4#1062302612yes—
651C2—24no—
652C2—24no—
653C2—42no—
654C2#1307146511yescharacteristic
655C2C2×#1062253811yescharacteristic
656C2#1307727411yescharacteristic
657C2C2×D4×C11⋊C811yescharacteristic
658C2D4×#431811yescharacteristic
659C2#1307764011yescharacteristic
660C2#1307765111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#22552
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622538C2semidirect
3. #13069224C2semidirect
4. #13069224C2semidirect
5. #13068796C2semidirect
6. #13068684C2semidirect
7. #13068596C2semidirect
9. C22⋊C4×C11⋊C8C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
38. C2×C4⋊(C11⋊C8)C22semidirect
39. C2×C4×C11⋊C8C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. #10622162C22semidirect
42. #10622162C22semidirect
43. #10622162C22semidirect
44. #10622162C22semidirect
61. C2×C11×C22⋊C4C8semidirect
148. C22×C4×C11C2×C8semidirect
149. C22×C4×C11C2×C8semidirect
170. C11×C22⋊C4C2×C8semidirect
171. C11×C22⋊C4C2×C8semidirect
343. C22×C11#431semidirect
388. C2×C22⋊C4C11⋊C8semidirect
477. C22×C4C2×C11⋊C8semidirect
478. C22×C4C2×C11⋊C8semidirect
512. C22⋊C4C2×C11⋊C8semidirect
513. C22⋊C4C2×C11⋊C8semidirect
525. C11#22552semidirect
629. C22#10622538semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
C22×C22⋊(C11⋊C8)2
#130692242
#130687962
#130686842
#130685962
#130685262
C22⋊C4×C11⋊C82
C4×C22⋊(C11⋊C8)2
C2×C4×C11×C22⋊C42
#2255211