Finite Group Databasebeta

← C2×C11×#2467 #14611858

Subgroups — C2×C11×#2467 #14611858

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#126C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic, complemented
3C11×#2467C2116yesmaximal, direct product factor
4C2×C11×#399C211yesmaximal, characteristic, complemented
5C2×C11×#394C211yesmaximal, characteristic, complemented
6C2×C11×#394C211yesmaximal, characteristic, complemented
7C2×C11×#392C211yesmaximal, characteristic
8C2×C11×#390C211yesmaximal, characteristic, complemented
9C2×C11×#388C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#387C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic, complemented
14C2×C11×#386C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C2×C11×#126—28no—
23C2×C11×#126C2218yescomplemented
24C2×C4×D4×C11—28no—
25C2×C4×D4×C11C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C11×C22⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C11×C22⋊C4C2211yescharacteristic
43C22×C11×C22⋊C4C2211yescharacteristic
44C22×C11×C22⋊C4C2211yescharacteristic
45C22×C42×C11C2211yescharacteristic
46C22×C42×C11C2211yescharacteristic
47C22×C42×C11C2211yescharacteristic
48C11×#399C2218yescomplemented
49C11×#394C2218yescomplemented
50C11×#394C2218yescomplemented
51C11×#392C2218yes—
52C11×#390C2218yescomplemented
53C11×#388C2218yescomplemented
54C11×#388C2218yescomplemented
55C11×#387C2218yescomplemented
56C11×#387C2218yescomplemented
57C11×#386C2218yescomplemented
58C11×#386C2218yescomplemented
59C11×#380C2218yescomplemented
60C4×C11×C22⋊C4C2218yescomplemented
61C2×C11×#95C2211yescharacteristic
62C2×C11×#95C2211yescharacteristic
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11—42no—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C23×C4×C11—24no—
85C23×C4×C11—24no—
86C23×C4×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—42no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2314yes—
98C23×C4×C11C2314yes—
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C11×#126—232no—
105C4×D4×C11—232no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4—24no—
108C2×C11×C4⋊C4—24no—
109C2×C11×C4⋊C4—42no—
110C2×C11×C4⋊C4—42no—
111C2×C11×C4⋊C4D418yescomplemented
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4—42no—
129C2×C11×C22⋊C4—42no—
130C2×C11×C22⋊C4—42no—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C42×C11—24no—
145C2×C42×C11—24no—
146C2×C42×C11—42no—
147C2×C42×C11C2314yes—
148C2×C42×C11C2314yes—
149C2×C42×C11C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C2×#2467C1111yesmaximal, characteristic, direct product factor, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11#4114yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—232no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11—28no—
190C2×D4×C11—28no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—416no—
195C2×D4×C11—416no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—28no—
228C22×C4×C11—28no—
229C22×C4×C11—28no—
230C22×C4×C11—28no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—416no—
234C22×C4×C11—416no—
235C22×C4×C11C2×D414yes—
236C22×C4×C11C2×D414yes—
237C22×C4×C11C2×D414yes—
238C22×C4×C11#4114yes—
239C22×C4×C11#4114yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—28no—
254C11×C4⋊C4—28no—
255C11×C4⋊C4—44no—
256C11×C4⋊C4—44no—
257C11×C4⋊C4C2×D4116yescomplemented
258C11×C22⋊C4—28no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—28no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—28no—
265C11×C22⋊C4—28no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—44no—
268C11×C22⋊C4—44no—
269C11×C22⋊C4—44no—
270C11×C22⋊C4—44no—
271C42×C11—28no—
272C42×C11—28no—
273C42×C11—44no—
274C22×#126C2×C1111yescharacteristic, complemented
275C22×C4×D4C2×C1111yescharacteristic, complemented
276#2467C2×C11116yesdirect product factor
277C2×#399C2×C1111yescharacteristic, complemented
278C2×#394C2×C1111yescharacteristic, complemented
279C2×#394C2×C1111yescharacteristic, complemented
280C2×#392C2×C1111yescharacteristic
281C2×#390C2×C1111yescharacteristic, complemented
282C2×#388C2×C1111yescharacteristic, complemented
283C2×#388C2×C1111yescharacteristic, complemented
284C2×#387C2×C1111yescharacteristic, complemented
285C2×#387C2×C1111yescharacteristic, complemented
286C2×#386C2×C1111yescharacteristic, complemented
287C2×#386C2×C1111yescharacteristic, complemented
288C2×#380C2×C1111yescharacteristic, complemented
289C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11C22×D412yes—
331C23×C11C2×#4114yes—
332C23×C11C2×#4114yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C11H(5,𝔽2)12yes—
339C23×C11C2511yescharacteristic
340D4×C11—232no—
341D4×C11—416no—
342D4×C11—416no—
343C2×C4×C11—28no—
344C2×C4×C11—28no—
345C2×C4×C11—28no—
346C2×C4×C11—28no—
347C2×C4×C11—28no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—416no—
380C2×C4×C11—416no—
381C2×C4×C11—44no—
382C2×C4×C11—44no—
383C2×C4×C11—44no—
384C2×C4×C11—44no—
385C2×C4×C11—44no—
386C2×C4×C11—44no—
387C2×C4×C11—44no—
388C2×C4×C11C22×D414yes—
389C2×C4×C11C22×D414yes—
390C2×C4×C11C22×D414yes—
391C2×C4×C11C2×#4114yes—
392C2×C4×C11C2×#4114yes—
393C23×D4C22×C1111yescharacteristic
394C23×D4C22×C1111yescharacteristic
395C23×D4C22×C1111yescharacteristic
396C24×C4C22×C1111yescharacteristic
397C24×C4C22×C1111yescharacteristic
398C2×#126—28no—
399C2×#126C22×C1118yescomplemented
400C2×C4×D4—28no—
401C2×C4×D4C22×C1118yescomplemented
402C22×C4⋊C4C22×C1111yescharacteristic
403C22×C4⋊C4C22×C1111yescharacteristic
404C22×C4⋊C4C22×C1111yescharacteristic
405C22×C4⋊C4C22×C1111yescharacteristic
406C22×C4⋊C4C22×C1111yescharacteristic
407C22×C4⋊C4C22×C1111yescharacteristic
408C22×C22⋊C4C22×C1111yescharacteristic
409C22×C22⋊C4C22×C1111yescharacteristic
410C22×C22⋊C4C22×C1111yescharacteristic
411C22×C22⋊C4C22×C1111yescharacteristic
412C22×C22⋊C4C22×C1111yescharacteristic
413C22×C22⋊C4C22×C1111yescharacteristic
414C22×C22⋊C4C22×C1111yescharacteristic
415C22×C22⋊C4C22×C1111yescharacteristic
416C22×C22⋊C4C22×C1111yescharacteristic
417C22×C22⋊C4C22×C1111yescharacteristic
418C22×C22⋊C4C22×C1111yescharacteristic
419C22×C22⋊C4C22×C1111yescharacteristic
420C22×C22⋊C4C22×C1111yescharacteristic
421C22×C42C22×C1111yescharacteristic
422C22×C42C22×C1111yescharacteristic
423C22×C42C22×C1111yescharacteristic
424#399C22×C1118yescomplemented
425#394C22×C1118yescomplemented
426#394C22×C1118yescomplemented
427#392C22×C1118yes—
428#390C22×C1118yescomplemented
429#388C22×C1118yescomplemented
430#388C22×C1118yescomplemented
431#387C22×C1118yescomplemented
432#387C22×C1118yescomplemented
433#386C22×C1118yescomplemented
434#386C22×C1118yescomplemented
435#380C22×C1118yescomplemented
436C4×C22⋊C4C22×C1118yescomplemented
437C2×#95C22×C1111yescharacteristic
438C2×#95C22×C1111yescharacteristic
439C2×#95C22×C1111yescharacteristic
440C2×#95C22×C1111yescharacteristic
441C2×#95C22×C1111yescharacteristic
442C2×#95C22×C1111yescharacteristic
443C2×#95C22×C1111yescharacteristic
444C2×#95C22×C1111yescharacteristic
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—416no—
460C22×C11—416no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—88no—
469C22×C11#52514yes—
470C22×C11#52914yes—
471C22×C11#53814yes—
472C22×C11#54614yes—
473C22×C11#55014yes—
474C22×C11#55114yes—
475C22×C11#55314yes—
476C22×C11C23×D411yescharacteristic
477C22×C11C22×#4111yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C2×H(5,𝔽2)11yescharacteristic
482C22×C11C2×H(5,𝔽2)11yescharacteristic
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11—42no—
495C25C23×C1111yescharacteristic
496C25C23×C1111yescharacteristic
497C25C23×C1111yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—42no—
505C22×D4—42no—
506C22×D4—42no—
507C22×D4C23×C1114yes—
508C22×D4C23×C1114yes—
509C22×D4C23×C1114yes—
510C23×C4—24no—
511C23×C4—24no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—42no—
515C23×C4—42no—
516C23×C4C23×C1111yescharacteristic
517C23×C4C23×C1111yescharacteristic
518C23×C4C23×C1111yescharacteristic
519C23×C4C23×C1111yescharacteristic
520C23×C4C23×C1111yescharacteristic
521C23×C4C23×C1111yescharacteristic
522C23×C4C23×C1111yescharacteristic
523C23×C4C23×C1114yes—
524C23×C4C23×C1114yes—
525C23×C4C23×C1111yescharacteristic
526C23×C4C23×C1111yescharacteristic
527C23×C4C23×C1111yescharacteristic
528C23×C4C23×C1111yescharacteristic
529C23×C4C23×C1111yescharacteristic
530#126—232no—
531C4×D4—232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—42no—
537C2×C4⋊C4D4×C1118yescomplemented
538C2×C4⋊C4C23×C1114yes—
539C2×C4⋊C4C23×C1114yes—
540C2×C4⋊C4C23×C1114yes—
541C2×C4⋊C4C23×C1114yes—
542C2×C4⋊C4C23×C1114yes—
543C2×C4⋊C4C23×C1114yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4C23×C1114yes—
558C2×C22⋊C4C23×C1114yes—
559C2×C22⋊C4C23×C1114yes—
560C2×C22⋊C4C23×C1114yes—
561C2×C22⋊C4C23×C1114yes—
562C2×C22⋊C4C23×C1114yes—
563C2×C22⋊C4C23×C1114yes—
564C2×C22⋊C4C23×C1114yes—
565C2×C22⋊C4C23×C1114yes—
566C2×C22⋊C4C23×C1114yes—
567C2×C22⋊C4C23×C1114yes—
568C2×C22⋊C4C23×C1114yes—
569C2×C22⋊C4C23×C1114yes—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—42no—
573C2×C42C23×C1114yes—
574C2×C42C23×C1114yes—
575C2×C42C23×C1114yes—
576#95C23×C1114yes—
577#95C23×C1114yes—
578#95C23×C1114yes—
579#95C23×C1114yes—
580#95C23×C1114yes—
581#95C23×C1114yes—
582#95C23×C1114yes—
583#95C23×C1114yes—
584C2×C11—44no—
585C2×C11—44no—
586C2×C11—82no—
587C2×C11#246718yesdirect product factor
588C2×C11C2×#52511yescharacteristic
589C2×C11C2×#52911yescharacteristic
590C2×C11C2×#53811yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#55011yescharacteristic
593C2×C11C2×#55111yescharacteristic
594C2×C11C2×#55311yescharacteristic
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24C11×#4114yes—
615C24C11×#4114yes—
616C24C24×C1112yes—
617C24C24×C1112yes—
618C24C24×C1112yes—
619C24C24×C1111yescharacteristic
620C2×D4—232no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—416no—
631C2×D4—416no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—28no—
666C22×C4—28no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—416no—
671C22×C4C2×D4×C1114yes—
672C22×C4C2×D4×C1114yes—
673C22×C4C2×D4×C1114yes—
674C22×C4C11×#4114yes—
675C22×C4C11×#4114yes—
676C22×C4C24×C1112yes—
677C22×C4C24×C1112yes—
678C22×C4C24×C1112yes—
679C22×C4C24×C1112yes—
680C22×C4C24×C1112yes—
681C22×C4C24×C1112yes—
682C22×C4C24×C1112yes—
683C22×C4C24×C1112yes—
684C22×C4C24×C1112yes—
685C22×C4C24×C1112yes—
686C22×C4C24×C1112yes—
687C22×C4C24×C1112yes—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4C2×D4×C11116yescomplemented
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C42—28no—
708C42—28no—
709C42—44no—
710C11C2×#246711yescharacteristic, direct product factor, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23C22×D4×C1112yes—
752C23C2×C11×#4114yes—
753C23C2×C11×#4114yes—
754C23C2×C11×#4112yes—
755C23C2×C11×#4112yes—
756C23C2×C11×#4112yes—
757C23C2×C11×#4112yes—
758C23C11×H(5,𝔽2)12yes—
759C23C11×H(5,𝔽2)12yes—
760C23C25×C1111yescharacteristic
761D4—232no—
762D4—416no—
763D4—416no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4C22×D4×C1114yes—
810C2×C4C22×D4×C1114yes—
811C2×C4C22×D4×C1114yes—
812C2×C4C2×C11×#4114yes—
813C2×C4C2×C11×#4114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—416no—
829C22—416no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22C11×#52514yes—
839C22C11×#52914yes—
840C22C11×#53814yes—
841C22C11×#54614yes—
842C22C11×#55014yes—
843C22C11×#55114yes—
844C22C11×#55314yes—
845C22C23×D4×C1111yescharacteristic
846C22C22×C11×#4111yescharacteristic
847C22C22×C11×#4111yescharacteristic
848C22C22×C11×#4111yescharacteristic
849C22C22×C11×#4111yescharacteristic
850C22C2×C11×H(5,𝔽2)11yescharacteristic
851C22C2×C11×H(5,𝔽2)11yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2C11×#246718yesdirect product factor
868C2C2×C11×#52511yescharacteristic
869C2C2×C11×#52911yescharacteristic
870C2C2×C11×#53811yescharacteristic
871C2C2×C11×#54611yescharacteristic
872C2C2×C11×#55011yescharacteristic
873C2C2×C11×#55111yescharacteristic
874C2C2×C11×#55311yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#126C2semidirect
2. C22×C4×D4×C11C2semidirect
3. C11×#2467C2direct (N × H)
4. C2×C11×#399C2semidirect
5. C2×C11×#394C2semidirect
6. C2×C11×#394C2semidirect
8. C2×C11×#390C2semidirect
9. C2×C11×#388C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#387C2semidirect
12. C2×C11×#387C2semidirect
13. C2×C11×#386C2semidirect
14. C2×C11×#386C2semidirect
15. C2×C11×#380C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
23. C2×C11×#126C22semidirect
25. C2×C4×D4×C11C22semidirect
48. C11×#399C22semidirect
49. C11×#394C22semidirect
50. C11×#394C22semidirect
52. C11×#390C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
56. C11×#387C22semidirect
57. C11×#386C22semidirect
58. C11×#386C22semidirect
59. C11×#380C22semidirect
60. C4×C11×C22⋊C4C22semidirect
111. C2×C11×C4⋊C4D4semidirect
158. C2×#2467C11direct (N × H)
257. C11×C4⋊C4C2×D4semidirect
274. C22×#126C2×C11semidirect
275. C22×C4×D4C2×C11semidirect
276. #2467C2×C11direct (N × H)
277. C2×#399C2×C11semidirect
278. C2×#394C2×C11semidirect
279. C2×#394C2×C11semidirect
281. C2×#390C2×C11semidirect
282. C2×#388C2×C11semidirect
283. C2×#388C2×C11semidirect
284. C2×#387C2×C11semidirect
285. C2×#387C2×C11semidirect
286. C2×#386C2×C11semidirect
287. C2×#386C2×C11semidirect
288. C2×#380C2×C11semidirect
289. C2×C4×C22⋊C4C2×C11semidirect
399. C2×#126C22×C11semidirect
401. C2×C4×D4C22×C11semidirect
424. #399C22×C11semidirect
425. #394C22×C11semidirect
426. #394C22×C11semidirect
428. #390C22×C11semidirect
429. #388C22×C11semidirect
430. #388C22×C11semidirect
431. #387C22×C11semidirect
432. #387C22×C11semidirect
433. #386C22×C11semidirect
434. #386C22×C11semidirect
435. #380C22×C11semidirect
436. C4×C22⋊C4C22×C11semidirect
537. C2×C4⋊C4D4×C11semidirect
587. C2×C11#2467direct (N × H)
693. C4⋊C4C2×D4×C11semidirect
710. C11C2×#2467direct (N × H)
867. C2C11×#2467direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C22×C4×D4×C112
C11×#24672
C2×C11×#3992
C2×C11×#3942
C2×C11×#3922
C2×C11×#3902
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3802
C2×C4×C11×C22⋊C42
C2×#246711