Finite Group Databasebeta

← C11×#22399 #14599592

Subgroups — C11×#22399 #14599592

Order 2816.

1928 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C2×C11×#435C212yesmaximal, complemented
3C2×C11×#407C211yesmaximal, characteristic, complemented
4C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C11×#1955C212yesmaximal, complemented
6C11×#1870C212yesmaximal, complemented
7C11×#1869C212yesmaximal, complemented
8C11×#1797C211yesmaximal, characteristic, complemented
9C11×#1779C211yesmaximal, characteristic, complemented
10C11×#1779C211yesmaximal, characteristic, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C23×D4×C11C411yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×M16C2212yescomplemented
16C23×C8×C11C2212yescomplemented
17C2×C4×D4×C11—28no—
18C2×C4×D4×C11C411yescharacteristic
19C2×C4×D4×C11C411yescharacteristic
20C2×C4×D4×C11C411yescharacteristic
21C2×C4×D4×C11C411yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4C411yescharacteristic
27C22×C11×C22⋊C4C411yescharacteristic
28C22×C11×C22⋊C4C411yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C11×#435—28no—
31C2×C11×C4⋊C8C2212yescomplemented
32C11×#407—24no—
33C2×C11×C22⋊C8—24no—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2212yescomplemented
39C2×C11×C22⋊C8C2212yescomplemented
40C2×C11×C22⋊C8C2212yescomplemented
41C2×C11×C22⋊C8C2212yescomplemented
42C2×C11×C22⋊C8C2212yescomplemented
43C2×C11×C22⋊C8C2212yescomplemented
44C2×C11×#97C2212yescomplemented
45C11×#336C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11C2×C411yescharacteristic
48C25×C11C2×C411yescharacteristic
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11C2×C411yescharacteristic
53C22×D4×C11C2×C411yescharacteristic
54C22×D4×C11C2×C411yescharacteristic
55C22×D4×C11C2×C411yescharacteristic
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—42no—
63C23×C4×C11—42no—
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2×C411yescharacteristic
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C2×C11×M16—24no—
78C2×C11×M16—24no—
79C2×C11×M16—42no—
80C22×C8×C11—24no—
81C22×C8×C11—24no—
82C22×C8×C11—42no—
83C22×C8×C11C2312yes—
84C22×C8×C11C2312yes—
85C22×C8×C11C2312yes—
86C22×C8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—24no—
89C4×D4×C11—24no—
90C4×D4×C11—24no—
91C4×D4×C11—24no—
92C4×D4×C11—24no—
93C4×D4×C11—24no—
94C4×D4×C11D418yes—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C42×C11—24no—
111C2×C42×C11C2×C411yescharacteristic
112C2×C42×C11C2×C411yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×C4⋊C8—24no—
116C11×C22⋊C8—22no—
117C11×C22⋊C8—22no—
118C11×C22⋊C8—24no—
119C11×C22⋊C8—24no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—24no—
122C11×C22⋊C8—24no—
123C11×C22⋊C8—42no—
124C11×C22⋊C8—42no—
125C11×C22⋊C8D414yescomplemented
126C11×#97—24no—
127#22399C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—41no—
138C24×C11—41no—
139C24×C11—41no—
140C24×C11—41no—
141C24×C11M1614yescomplemented
142C24×C11C22×C411yescharacteristic
143C24×C11C22×C411yescharacteristic
144C24×C11C22×C411yescharacteristic
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C2×D4×C11—232no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11C22⋊C414yes—
159C2×D4×C11M1614yescomplemented
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—41no—
194C22×C4×C11—41no—
195C22×C4×C11—41no—
196C22×C4×C11—41no—
197C22×C4×C11—41no—
198C22×C4×C11—41no—
199C22×C4×C11—41no—
200C22×C4×C11—48no—
201C22×C4×C11—48no—
202C22×C4×C11—48no—
203C22×C4×C11—48no—
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11#4112yes—
217C22×C4×C11C2411yescharacteristic
218C11×M16—48no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11—48no—
231C2×C8×C11C2×D414yescomplemented
232C11×C4⋊C4—22no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4C22⋊C414yes—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4C22⋊C414yes—
243C11×C22⋊C4C22⋊C414yes—
244C42×C11—22no—
245C42×C11—22no—
246C42×C11—22no—
247C42×C11C2×D414yes—
248C22×C4×D4C2×C1111yescharacteristic
249C2×#435C2×C1112yescomplemented
250C2×#407C2×C1111yescharacteristic, complemented
251C22×C22⋊C8C2×C1111yescharacteristic, complemented
252#1955C2×C1112yescomplemented
253#1870C2×C1112yescomplemented
254#1869C2×C1112yescomplemented
255#1797C2×C1111yescharacteristic, complemented
256#1779C2×C1111yescharacteristic, complemented
257#1779C2×C1111yescharacteristic, complemented
258#1749C2×C1111yescharacteristic, complemented
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—28no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—28no—
287C23×C11—28no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11C2×C22⋊C412yes—
300C23×C11C2×C22⋊C412yes—
301C23×C11C4×D412yes—
302C23×C11C2×M1612yes—
303C23×C11C2×M1612yes—
304C23×C11C2×M1612yes—
305C23×C11C2×M1612yes—
306C23×C11C2×M1612yes—
307C23×C11#13112yes—
308C23×C11C23×C411yescharacteristic
309D4×C11—28no—
310D4×C11—28no—
311D4×C11—28no—
312D4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—44no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—44no—
345C2×C4×C11—44no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C2×C22⋊C412yes—
354C2×C4×C11C2×C22⋊C412yes—
355C2×C4×C11C2×C22⋊C412yes—
356C2×C4×C11C4×D412yes—
357C2×C4×C11C2×M1612yes—
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D412yes—
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)12yes—
362C8×C11—24no—
363C8×C11—42no—
364C8×C11—42no—
365C8×C11—42no—
366C23×D4C4×C1111yescharacteristic
367C24×C4C22×C1111yescharacteristic
368C24×C4C22×C1111yescharacteristic
369C22×M16C22×C1112yescomplemented
370C23×C8C22×C1112yescomplemented
371C2×C4×D4—28no—
372C2×C4×D4C4×C1111yescharacteristic
373C2×C4×D4C4×C1111yescharacteristic
374C2×C4×D4C4×C1111yescharacteristic
375C2×C4×D4C4×C1111yescharacteristic
376C2×C4×D4C22×C1111yescharacteristic
377C2×C4×D4C22×C1111yescharacteristic
378C2×C4×D4C22×C1111yescharacteristic
379C2×C4×D4C22×C1111yescharacteristic
380C22×C4⋊C4C4×C1111yescharacteristic
381C22×C22⋊C4C4×C1111yescharacteristic
382C22×C22⋊C4C4×C1111yescharacteristic
383C22×C42C22×C1111yescharacteristic
384#435—28no—
385C2×C4⋊C8C22×C1112yescomplemented
386#407—24no—
387C2×C22⋊C8—24no—
388C2×C22⋊C8C22×C1111yescharacteristic
389C2×C22⋊C8C22×C1111yescharacteristic
390C2×C22⋊C8C22×C1111yescharacteristic
391C2×C22⋊C8C22×C1111yescharacteristic
392C2×C22⋊C8C22×C1112yescomplemented
393C2×C22⋊C8C22×C1112yescomplemented
394C2×C22⋊C8C22×C1112yescomplemented
395C2×C22⋊C8C22×C1112yescomplemented
396C2×C22⋊C8C22×C1112yescomplemented
397C2×C22⋊C8C22×C1112yescomplemented
398C2×#97C22×C1112yescomplemented
399#336C22×C1112yescomplemented
400#336C22×C1112yescomplemented
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—416no—
423C22×C11—416no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11#40714yescomplemented
437C22×C11#43514yescomplemented
438C22×C11C22×C22⋊C411yescharacteristic
439C22×C11C2×C4×D411yescharacteristic
440C22×C11#51811yescharacteristic
441C22×C11C22×M1611yescharacteristic
442C22×C11C22×M1611yescharacteristic
443C22×C11C2×#13111yescharacteristic
444C22×C11#56811yescharacteristic
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11D4212yes—
455C4×C11#54612yes—
456C25C2×C4×C1111yescharacteristic
457C25C2×C4×C1111yescharacteristic
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—24no—
461C22×D4C2×C4×C1111yescharacteristic
462C22×D4C2×C4×C1111yescharacteristic
463C22×D4C2×C4×C1111yescharacteristic
464C22×D4C2×C4×C1111yescharacteristic
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—42no—
472C23×C4—42no—
473C23×C4C2×C4×C1111yescharacteristic
474C23×C4C2×C4×C1111yescharacteristic
475C23×C4C2×C4×C1111yescharacteristic
476C23×C4C2×C4×C1111yescharacteristic
477C23×C4C2×C4×C1111yescharacteristic
478C23×C4C2×C4×C1111yescharacteristic
479C23×C4C2×C4×C1111yescharacteristic
480C23×C4C2×C4×C1111yescharacteristic
481C23×C4C23×C1111yescharacteristic
482C23×C4C23×C1111yescharacteristic
483C23×C4C23×C1111yescharacteristic
484C23×C4C23×C1111yescharacteristic
485C23×C4C23×C1111yescharacteristic
486C2×M16—24no—
487C2×M16—24no—
488C2×M16—42no—
489C22×C8—24no—
490C22×C8—24no—
491C22×C8—42no—
492C22×C8C23×C1112yes—
493C22×C8C23×C1112yes—
494C22×C8C23×C1112yes—
495C22×C8C23×C1112yes—
496C4×D4—24no—
497C4×D4—24no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—24no—
501C4×D4—24no—
502C4×D4—24no—
503C4×D4D4×C1118yes—
504C2×C4⋊C4—24no—
505C2×C4⋊C4C2×C4×C1111yescharacteristic
506C2×C4⋊C4C2×C4×C1111yescharacteristic
507C2×C4⋊C4C2×C4×C1111yescharacteristic
508C2×C4⋊C4C2×C4×C1111yescharacteristic
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4C2×C4×C1111yescharacteristic
512C2×C22⋊C4C2×C4×C1111yescharacteristic
513C2×C22⋊C4C2×C4×C1111yescharacteristic
514C2×C22⋊C4C2×C4×C1111yescharacteristic
515C2×C22⋊C4C2×C4×C1111yescharacteristic
516C2×C22⋊C4C2×C4×C1111yescharacteristic
517C2×C22⋊C4C2×C4×C1111yescharacteristic
518C2×C22⋊C4C2×C4×C1111yescharacteristic
519C2×C42—24no—
520C2×C42C2×C4×C1111yescharacteristic
521C2×C42C2×C4×C1111yescharacteristic
522C2×C42C23×C1111yescharacteristic
523C2×C42C23×C1111yescharacteristic
524C4⋊C8—24no—
525C22⋊C8—22no—
526C22⋊C8—22no—
527C22⋊C8—24no—
528C22⋊C8—24no—
529C22⋊C8—22no—
530C22⋊C8—24no—
531C22⋊C8—24no—
532C22⋊C8—42no—
533C22⋊C8—42no—
534C22⋊C8D4×C1114yescomplemented
535#97—24no—
536C2×C11—24no—
537C2×C11—24no—
538C2×C11—42no—
539C2×C11—42no—
540C2×C11—42no—
541C2×C11D4×C22⋊C411yescharacteristic
542C2×C11C2×#40711yescharacteristic
543C2×C11#288011yescharacteristic
544C2×C11C2×#43511yescharacteristic
545C2×C11D4×M1611yescharacteristic
546C2×C11#297311yescharacteristic
547C2×C11#297411yescharacteristic
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—41no—
558C24—41no—
559C24—41no—
560C24—41no—
561C24C11×M1614yescomplemented
562C24C22×C4×C1111yescharacteristic
563C24C22×C4×C1111yescharacteristic
564C24C22×C4×C1111yescharacteristic
565C24C22×C4×C1111yescharacteristic
566C24C22×C4×C1111yescharacteristic
567C2×D4—232no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4C11×C22⋊C414yes—
579C2×D4C11×M1614yescomplemented
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4C22×C4×C1111yescharacteristic
625C22×C4C22×C4×C1111yescharacteristic
626C22×C4C22×C4×C1111yescharacteristic
627C22×C4C22×C4×C1111yescharacteristic
628C22×C4C22×C4×C1111yescharacteristic
629C22×C4C22×C4×C1111yescharacteristic
630C22×C4C22×C4×C1111yescharacteristic
631C22×C4C22×C4×C1111yescharacteristic
632C22×C4C22×C4×C1111yescharacteristic
633C22×C4C2×D4×C1114yes—
634C22×C4C2×D4×C1114yes—
635C22×C4C2×D4×C1112yes—
636C22×C4C11×#4112yes—
637C22×C4C24×C1111yescharacteristic
638M16—48no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—48no—
651C2×C8C2×D4×C1114yescomplemented
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4C11×C22⋊C414yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4C11×C22⋊C414yes—
663C22⋊C4C11×C22⋊C414yes—
664C42—22no—
665C42—22no—
666C42—22no—
667C42C2×D4×C1114yes—
668C11#2239911yescharacteristic, direct product factor, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—28no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—28no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—28no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23C2×C11×C22⋊C412yes—
710C23C2×C11×C22⋊C412yes—
711C23C4×D4×C1112yes—
712C23C2×C11×M1612yes—
713C23C2×C11×M1612yes—
714C23C2×C11×M1612yes—
715C23C2×C11×M1612yes—
716C23C2×C11×M1612yes—
717C23C11×#13112yes—
718C23C23×C4×C1111yescharacteristic
719D4—28no—
720D4—28no—
721D4—28no—
722D4—28no—
723C2×C4—28no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C2×C11×C22⋊C412yes—
763C2×C4C2×C11×C22⋊C412yes—
764C2×C4C2×C11×C22⋊C412yes—
765C2×C4C2×C11×C22⋊C412yes—
766C2×C4C4×D4×C1112yes—
767C2×C4C2×C11×M1612yes—
768C2×C4C22×D4×C1111yescharacteristic
769C2×C4C22×D4×C1112yes—
770C2×C4C2×C11×#4111yescharacteristic
771C2×C4C11×H(5,𝔽2)12yes—
772C8—24no—
773C8—42no—
774C8—42no—
775C8—42no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—416no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22C11×#40714yescomplemented
812C22C11×#43514yescomplemented
813C22C22×C11×C22⋊C411yescharacteristic
814C22C2×C4×D4×C1111yescharacteristic
815C22C11×#51811yescharacteristic
816C22C22×C11×M1611yescharacteristic
817C22C22×C11×M1611yescharacteristic
818C22C2×C11×#13111yescharacteristic
819C22C11×#56811yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4D42×C1112yes—
830C4C11×#54612yes—
831C2—24no—
832C2—24no—
833C2—42no—
834C2—42no—
835C2—42no—
836C2D4×C11×C22⋊C411yescharacteristic
837C2C2×C11×#40711yescharacteristic
838C2C11×#288011yescharacteristic
839C2C2×C11×#43511yescharacteristic
840C2D4×C11×M1611yescharacteristic
841C2C11×#297311yescharacteristic
842C2C11×#297411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC23×D4×C11C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. C2×C11×#407C2semidirect
4. C22×C11×C22⋊C8C2semidirect
5. C11×#1955C2semidirect
6. C11×#1870C2semidirect
7. C11×#1869C2semidirect
8. C11×#1797C2semidirect
9. C11×#1779C2semidirect
10. C11×#1779C2semidirect
11. C11×#1749C2semidirect
15. C22×C11×M16C22semidirect
16. C23×C8×C11C22semidirect
31. C2×C11×C4⋊C8C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. C2×C11×C22⋊C8C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
42. C2×C11×C22⋊C8C22semidirect
43. C2×C11×C22⋊C8C22semidirect
44. C2×C11×#97C22semidirect
45. C11×#336C22semidirect
46. C11×#336C22semidirect
125. C11×C22⋊C8D4semidirect
127. #22399C11direct (N × H)
141. C24×C11M16semidirect
159. C2×D4×C11M16semidirect
231. C2×C8×C11C2×D4semidirect
249. C2×#435C2×C11semidirect
250. C2×#407C2×C11semidirect
251. C22×C22⋊C8C2×C11semidirect
252. #1955C2×C11semidirect
253. #1870C2×C11semidirect
254. #1869C2×C11semidirect
255. #1797C2×C11semidirect
256. #1779C2×C11semidirect
257. #1779C2×C11semidirect
258. #1749C2×C11semidirect
369. C22×M16C22×C11semidirect
370. C23×C8C22×C11semidirect
385. C2×C4⋊C8C22×C11semidirect
392. C2×C22⋊C8C22×C11semidirect
393. C2×C22⋊C8C22×C11semidirect
394. C2×C22⋊C8C22×C11semidirect
395. C2×C22⋊C8C22×C11semidirect
396. C2×C22⋊C8C22×C11semidirect
397. C2×C22⋊C8C22×C11semidirect
398. C2×#97C22×C11semidirect
399. #336C22×C11semidirect
400. #336C22×C11semidirect
436. C22×C11#407semidirect
437. C22×C11#435semidirect
534. C22⋊C8D4×C11semidirect
561. C24C11×M16semidirect
579. C2×D4C11×M16semidirect
651. C2×C8C2×D4×C11semidirect
668. C11#22399direct (N × H)
811. C22C11×#407semidirect
812. C22C11×#435semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C2×C11×#4352
C2×C11×#4072
C22×C11×C22⋊C82
C11×#19552
C11×#18702
C11×#18692
C11×#17972
C11×#17792
C11×#17492
#2239911