Finite Group Databasebeta

← C11×#22554 #14599747

Subgroups — C11×#22554 #14599747

Order 2816.

1224 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×C11×#432C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
4C11×#1924C212yesmaximal, complemented
5C11×#1924C212yesmaximal, complemented
6C11×#1850C212yesmaximal, complemented
7C11×#1817C211yesmaximal, characteristic, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C11×#1779C211yesmaximal, characteristic
10C11×#1752C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C8×C11C2212yes—
14C22×C11×C22⋊C4C411yescharacteristic
15C22×C11×C22⋊C4C411yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#432—24no—
19C2×C11×C4⋊C8C2212yescomplemented
20C2×C11×C4⋊C8C2212yescomplemented
21C2×C11×C22⋊C8—24no—
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×#97C2212yescomplemented
30C2×C11×#97C2212yescomplemented
31C4×C11×C22⋊C4C411yescharacteristic
32C4×C11×C22⋊C4C411yescharacteristic
33C4×C11×C22⋊C4C411yescharacteristic
34C4×C11×C22⋊C4C411yescharacteristic
35C4×C11×C22⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4C2211yescharacteristic
37C4×C11×C22⋊C4C2211yescharacteristic
38C4×C11×C22⋊C4C2211yescharacteristic
39C2×C11×#95C411yescharacteristic
40C2×C11×#95C411yescharacteristic
41C11×#336C2212yescomplemented
42C11×#336C2212yescomplemented
43C11×#336C2212yescomplemented
44C11×#336C2212yescomplemented
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
60C22×C8×C11—24no—
61C22×C8×C11—24no—
62C22×C8×C11—42no—
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C22×C8×C11C2312yes—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—42no—
80C2×C42×C11C2×C411yescharacteristic
81C2×C42×C11C2×C411yescharacteristic
82C2×C42×C11C2×C411yescharacteristic
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C11×C4⋊C8—24no—
89C11×C4⋊C8—42no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—22no—
92C11×C22⋊C8—24no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8—24no—
95C11×C22⋊C8—42no—
96C11×C22⋊C8D414yes—
97C11×#97—24no—
98C11×#97—42no—
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C11×#95C2×C411yescharacteristic
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107#22554C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—41no—
113C24×C11—41no—
114C24×C11M1614yes—
115C24×C11C22×C411yescharacteristic
116C24×C11C22×C411yescharacteristic
117C24×C11C22×C411yescharacteristic
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
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—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—48no—
149C22×C4×C11—48no—
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
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—48no—
177C2×C8×C11C2×D414yes—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4M1614yes—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—41no—
195C42×C11—41no—
196C2×#432C2×C1111yescharacteristic, complemented
197C22×C22⋊C8C2×C1111yescharacteristic
198C2×C4×C22⋊C4C2×C1111yescharacteristic
199#1924C2×C1112yescomplemented
200#1924C2×C1112yescomplemented
201#1850C2×C1112yescomplemented
202#1817C2×C1111yescharacteristic, complemented
203#1797C2×C1111yescharacteristic, complemented
204#1779C2×C1111yescharacteristic
205#1752C2×C1112yescomplemented
206#1749C2×C1111yescharacteristic, complemented
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×C11C2×M1612yes—
231C23×C11C2×M1612yes—
232C23×C11C2×M1612yes—
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—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—44no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11—44no—
273C2×C4×C11—44no—
274C2×C4×C11—44no—
275C2×C4×C11—44no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11#11712yes—
279C2×C4×C11C4×D412yes—
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—
286C8×C11—24no—
287C8×C11—42no—
288C8×C11—42no—
289C8×C11—42no—
290C24×C4C22×C1111yescharacteristic
291C23×C8C22×C1112yes—
292C22×C22⋊C4C4×C1111yescharacteristic
293C22×C22⋊C4C4×C1111yescharacteristic
294C22×C42C22×C1111yescharacteristic
295C22×C42C22×C1111yescharacteristic
296#432—24no—
297C2×C4⋊C8C22×C1112yescomplemented
298C2×C4⋊C8C22×C1112yescomplemented
299C2×C22⋊C8—24no—
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×C22⋊C8C22×C1111yescharacteristic
302C2×C22⋊C8C22×C1111yescharacteristic
303C2×C22⋊C8C22×C1112yes—
304C2×C22⋊C8C22×C1112yes—
305C2×C22⋊C8C22×C1112yes—
306C2×C22⋊C8C22×C1111yescharacteristic
307C2×#97C22×C1112yescomplemented
308C2×#97C22×C1112yescomplemented
309C4×C22⋊C4C4×C1111yescharacteristic
310C4×C22⋊C4C4×C1111yescharacteristic
311C4×C22⋊C4C4×C1111yescharacteristic
312C4×C22⋊C4C4×C1111yescharacteristic
313C4×C22⋊C4C22×C1111yescharacteristic
314C4×C22⋊C4C22×C1111yescharacteristic
315C4×C22⋊C4C22×C1111yescharacteristic
316C4×C22⋊C4C22×C1111yescharacteristic
317C2×#95C4×C1111yescharacteristic
318C2×#95C4×C1111yescharacteristic
319#336C22×C1112yescomplemented
320#336C22×C1112yescomplemented
321#336C22×C1112yescomplemented
322#336C22×C1112yescomplemented
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#43214yescomplemented
344C22×C11#43514yes—
345C22×C11C2×#11711yescharacteristic
346C22×C11C2×C4×D411yescharacteristic
347C22×C11#51811yescharacteristic
348C22×C11C22×M1611yescharacteristic
349C22×C11C22×M1611yescharacteristic
350C22×C11C2×#13111yescharacteristic
351C22×C11#56811yescharacteristic
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#54612yes—
364C4×C11#55112yes—
365C25C2×C4×C1111yescharacteristic
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4C2×C4×C1111yescharacteristic
371C23×C4C2×C4×C1111yescharacteristic
372C23×C4C2×C4×C1111yescharacteristic
373C23×C4C2×C4×C1111yescharacteristic
374C23×C4C2×C4×C1111yescharacteristic
375C23×C4C2×C4×C1111yescharacteristic
376C23×C4C2×C4×C1111yescharacteristic
377C23×C4C23×C1111yescharacteristic
378C23×C4C23×C1111yescharacteristic
379C23×C4C23×C1111yescharacteristic
380C22×C8—24no—
381C22×C8—24no—
382C22×C8—42no—
383C22×C8C23×C1112yes—
384C22×C8C23×C1112yes—
385C22×C8C23×C1112yes—
386C22×C8C23×C1112yes—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C1111yescharacteristic
390C2×C22⋊C4C2×C4×C1111yescharacteristic
391C2×C22⋊C4C2×C4×C1111yescharacteristic
392C2×C22⋊C4C2×C4×C1111yescharacteristic
393C2×C22⋊C4C2×C4×C1111yescharacteristic
394C2×C22⋊C4C2×C4×C1111yescharacteristic
395C2×C22⋊C4C2×C4×C1111yescharacteristic
396C2×C22⋊C4C2×C4×C1111yescharacteristic
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—42no—
400C2×C42C2×C4×C1111yescharacteristic
401C2×C42C2×C4×C1111yescharacteristic
402C2×C42C2×C4×C1111yescharacteristic
403C2×C42C2×C4×C1111yescharacteristic
404C2×C42C23×C1111yescharacteristic
405C2×C42C23×C1111yescharacteristic
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408C4⋊C8—24no—
409C4⋊C8—42no—
410C22⋊C8—22no—
411C22⋊C8—22no—
412C22⋊C8—24no—
413C22⋊C8—22no—
414C22⋊C8—24no—
415C22⋊C8—42no—
416C22⋊C8D4×C1114yes—
417#97—24no—
418#97—42no—
419#95C2×C4×C1111yescharacteristic
420#95C2×C4×C1111yescharacteristic
421#95C2×C4×C1111yescharacteristic
422#95C2×C4×C1111yescharacteristic
423#95C2×C4×C1111yescharacteristic
424#95C2×C4×C1111yescharacteristic
425#95C2×C4×C1111yescharacteristic
426#95C2×C4×C1111yescharacteristic
427C2×C11—24no—
428C2×C11—24no—
429C2×C11—42no—
430C2×C11#234211yescharacteristic
431C2×C11C2×#43211yescharacteristic
432C2×C11#292411yescharacteristic
433C2×C11C2×#43511yescharacteristic
434C2×C11D4×M1611yescharacteristic
435C2×C11#297311yescharacteristic
436C2×C11#297411yescharacteristic
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—41no—
442C24—41no—
443C24C11×M1614yes—
444C24C22×C4×C1111yescharacteristic
445C24C22×C4×C1111yescharacteristic
446C24C22×C4×C1111yescharacteristic
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
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—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4C22×C4×C1111yescharacteristic
480C22×C4C22×C4×C1111yescharacteristic
481C22×C4C22×C4×C1111yescharacteristic
482C22×C4C22×C4×C1111yescharacteristic
483C22×C4C22×C4×C1111yescharacteristic
484C22×C4C22×C4×C1111yescharacteristic
485C22×C4C22×C4×C1111yescharacteristic
486C22×C4C22×C4×C1111yescharacteristic
487C22×C4C22×C4×C1111yescharacteristic
488C22×C4C22×C4×C1111yescharacteristic
489C22×C4C22×C4×C1111yescharacteristic
490C22×C4C2×D4×C1112yes—
491C22×C4C11×#4114yes—
492C22×C4C11×#4112yes—
493C22×C4C24×C1111yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—48no—
506C2×C8C2×D4×C1114yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4C11×M1614yes—
515C42—22no—
516C42—22no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—22no—
522C42—22no—
523C42—41no—
524C42—41no—
525C11#2255411yescharacteristic, direct product factor, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—28no—
541C23—28no—
542C23—44no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23C11×#11712yes—
548C23C4×D4×C1112yes—
549C23C2×C11×M1612yes—
550C23C2×C11×M1612yes—
551C23C2×C11×M1612yes—
552C23C2×C11×M1612yes—
553C23C11×#13112yes—
554C23C23×C4×C1111yescharacteristic
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—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
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—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C11×#11712yes—
598C2×C4C4×D4×C1112yes—
599C2×C4C2×C11×M1612yes—
600C2×C4C2×C11×M1612yes—
601C2×C4C22×D4×C1111yescharacteristic
602C2×C4C2×C11×#4112yes—
603C2×C4C2×C11×#4111yescharacteristic
604C2×C4C11×H(5,𝔽2)12yes—
605C8—24no—
606C8—42no—
607C8—42no—
608C8—42no—
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—
629C22C11×#43214yescomplemented
630C22C11×#43514yes—
631C22C2×C11×#11711yescharacteristic
632C22C2×C4×D4×C1111yescharacteristic
633C22C11×#51811yescharacteristic
634C22C22×C11×M1611yescharacteristic
635C22C22×C11×M1611yescharacteristic
636C22C2×C11×#13111yescharacteristic
637C22C11×#56811yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4C11×#54612yes—
650C4C11×#55112yes—
651C2—24no—
652C2—24no—
653C2—42no—
654C2C11×#234211yescharacteristic
655C2C2×C11×#43211yescharacteristic
656C2C11×#292411yescharacteristic
657C2C2×C11×#43511yescharacteristic
658C2D4×C11×M1611yescharacteristic
659C2C11×#297311yescharacteristic
660C2C11×#297411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#432C2semidirect
4. C11×#1924C2semidirect
5. C11×#1924C2semidirect
6. C11×#1850C2semidirect
7. C11×#1817C2semidirect
8. C11×#1797C2semidirect
10. C11×#1752C2semidirect
11. C11×#1749C2semidirect
19. C2×C11×C4⋊C8C22semidirect
20. C2×C11×C4⋊C8C22semidirect
29. C2×C11×#97C22semidirect
30. C2×C11×#97C22semidirect
41. C11×#336C22semidirect
42. C11×#336C22semidirect
43. C11×#336C22semidirect
44. C11×#336C22semidirect
107. #22554C11direct (N × H)
196. C2×#432C2×C11semidirect
199. #1924C2×C11semidirect
200. #1924C2×C11semidirect
201. #1850C2×C11semidirect
202. #1817C2×C11semidirect
203. #1797C2×C11semidirect
205. #1752C2×C11semidirect
206. #1749C2×C11semidirect
297. C2×C4⋊C8C22×C11semidirect
298. C2×C4⋊C8C22×C11semidirect
307. C2×#97C22×C11semidirect
308. C2×#97C22×C11semidirect
319. #336C22×C11semidirect
320. #336C22×C11semidirect
321. #336C22×C11semidirect
322. #336C22×C11semidirect
343. C22×C11#432semidirect
525. C11#22554direct (N × H)
629. C22C11×#432semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C22×C11×C22⋊C82
C2×C4×C11×C22⋊C42
C11×#19242
C11×#18502
C11×#18172
C11×#17972
C11×#17792
C11×#17522
C11×#17492
#2255411