Finite Group Databasebeta

← C2×C11×#2557 #14612018

Subgroups — C2×C11×#2557 #14612018

Order 2816.

3330 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#124C211yesmaximal, characteristic, complemented
2C22×C11×#123C211yesmaximal, characteristic, complemented
3C11×#2557C2116yesmaximal, direct product factor
4C2×C11×#397C211yesmaximal, characteristic, complemented
5C2×C11×#397C211yesmaximal, characteristic, complemented
6C2×C11×#393C211yesmaximal, characteristic, complemented
7C2×C11×#392C211yesmaximal, characteristic
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C2×C11×#388C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#386C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic, complemented
14C2×C11×#386C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic
23C2×C11×#124—28no—
24C2×C11×#124C2218yescomplemented
25C2×C11×#123—28no—
26C2×C11×#123C2218yescomplemented
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊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×C42×C11C2211yescharacteristic
44C22×C42×C11C2211yescharacteristic
45C22×C42×C11C2211yescharacteristic
46C11×#397C2218yescomplemented
47C11×#397C2218yescomplemented
48C11×#393C2218yescomplemented
49C11×#392C2218yes—
50C11×#391C2218yescomplemented
51C11×#390C2218yescomplemented
52C11×#388C2218yescomplemented
53C11×#387C2218yescomplemented
54C11×#386C2218yescomplemented
55C11×#386C2218yescomplemented
56C11×#386C2218yescomplemented
57C4×C11×C22⋊C4C2218yescomplemented
58C4×C11×C22⋊C4C2218yescomplemented
59C2×C11×#95C2211yescharacteristic
60C2×C11×#95C2211yescharacteristic
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×Q8×C11—24no—
73C22×Q8×C11—24no—
74C22×Q8×C11—42no—
75C22×Q8×C11C2314yes—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—42no—
83C22×D4×C11—42no—
84C22×D4×C11—42no—
85C22×D4×C11C2314yes—
86C22×D4×C11C2314yes—
87C22×D4×C11C2314yes—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11—24no—
91C23×C4×C11—42no—
92C23×C4×C11—42no—
93C23×C4×C11—42no—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2314yes—
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2314yes—
108C11×#124—232no—
109C11×#123—232no—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—24no—
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—42no—
126C2×C11×C22⋊C4—42no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4D418yescomplemented
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
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×C42×C11—24no—
143C2×C42×C11—42no—
144C2×C42×C11—42no—
145C2×C42×C11C2314yes—
146C2×C42×C11C2314yes—
147C2×C42×C11C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C2×#2557C1111yesmaximal, 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×C11C2×D414yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C2×Q8×C11—28no—
185C2×Q8×C11—28no—
186C2×Q8×C11—44no—
187C2×Q8×C11—416no—
188C2×D4×C11—28no—
189C2×D4×C11—28no—
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—416no—
198C2×D4×C11—416no—
199C2×D4×C11—416no—
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—28no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—28no—
233C22×C4×C11—28no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—416no—
238C22×C4×C11—416no—
239C22×C4×C11C2×D414yes—
240C22×C4×C11C2×D414yes—
241C22×C4×C11#4114yes—
242C22×C4×C11#4114yes—
243C22×C4×C11#4114yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C11×C4⋊C4—28no—
257C11×C4⋊C4—28no—
258C11×C4⋊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—28no—
268C11×C22⋊C4—44no—
269C11×C22⋊C4—44no—
270C11×C22⋊C4—44no—
271C11×C22⋊C4C2×D4116yescomplemented
272C42×C11—28no—
273C42×C11—44no—
274C42×C11—44no—
275C22×#124C2×C1111yescharacteristic, complemented
276C22×#123C2×C1111yescharacteristic, complemented
277#2557C2×C11116yesdirect product factor
278C2×#397C2×C1111yescharacteristic, complemented
279C2×#397C2×C1111yescharacteristic, complemented
280C2×#393C2×C1111yescharacteristic, complemented
281C2×#392C2×C1111yescharacteristic
282C2×#391C2×C1111yescharacteristic, complemented
283C2×#390C2×C1111yescharacteristic, complemented
284C2×#388C2×C1111yescharacteristic, complemented
285C2×#387C2×C1111yescharacteristic, complemented
286C2×#386C2×C1111yescharacteristic, complemented
287C2×#386C2×C1111yescharacteristic, complemented
288C2×#386C2×C1111yescharacteristic, complemented
289C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
290C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
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—22no—
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×C11—44no—
331C23×C11C22×D414yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4112yes—
338C23×C11H(5,𝔽2)12yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11C2511yescharacteristic
341Q8×C11—416no—
342D4×C11—416no—
343D4×C11—416no—
344D4×C11—416no—
345C2×C4×C11—28no—
346C2×C4×C11—28no—
347C2×C4×C11—28no—
348C2×C4×C11—28no—
349C2×C4×C11—28no—
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—22no—
380C2×C4×C11—22no—
381C2×C4×C11—416no—
382C2×C4×C11—416no—
383C2×C4×C11—44no—
384C2×C4×C11—44no—
385C2×C4×C11—44no—
386C2×C4×C11—44no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11C22×D414yes—
391C2×C4×C11C22×D414yes—
392C2×C4×C11C2×#4114yes—
393C2×C4×C11C2×#4114yes—
394C2×C4×C11C2×#4114yes—
395C23×Q8C22×C1111yescharacteristic
396C23×D4C22×C1111yescharacteristic
397C23×D4C22×C1111yescharacteristic
398C23×D4C22×C1111yescharacteristic
399C24×C4C22×C1111yescharacteristic
400C24×C4C22×C1111yescharacteristic
401C2×#124—28no—
402C2×#124C22×C1118yescomplemented
403C2×#123—28no—
404C2×#123C22×C1118yescomplemented
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#397C22×C1118yescomplemented
425#397C22×C1118yescomplemented
426#393C22×C1118yescomplemented
427#392C22×C1118yes—
428#391C22×C1118yescomplemented
429#390C22×C1118yescomplemented
430#388C22×C1118yescomplemented
431#387C22×C1118yescomplemented
432#386C22×C1118yescomplemented
433#386C22×C1118yescomplemented
434#386C22×C1118yescomplemented
435C4×C22⋊C4C22×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
445C2×#95C22×C1111yescharacteristic
446C2×#95C22×C1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—416no—
462C22×C11—416no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—88no—
471C22×C11#52914yes—
472C22×C11#53214yes—
473C22×C11#53814yes—
474C22×C11#54614yes—
475C22×C11#54614yes—
476C22×C11#55114yes—
477C22×C11#55914yes—
478C22×C11C23×D411yescharacteristic
479C22×C11C22×#4111yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×H(5,𝔽2)11yescharacteristic
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—24no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497C25C23×C1111yescharacteristic
498C25C23×C1111yescharacteristic
499C25C23×C1111yescharacteristic
500C22×Q8—24no—
501C22×Q8—24no—
502C22×Q8—42no—
503C22×Q8C23×C1114yes—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—42no—
511C22×D4—42no—
512C22×D4—42no—
513C22×D4C23×C1114yes—
514C22×D4C23×C1114yes—
515C22×D4C23×C1114yes—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—42no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4C23×C1111yescharacteristic
523C23×C4C23×C1111yescharacteristic
524C23×C4C23×C1111yescharacteristic
525C23×C4C23×C1111yescharacteristic
526C23×C4C23×C1111yescharacteristic
527C23×C4C23×C1111yescharacteristic
528C23×C4C23×C1111yescharacteristic
529C23×C4C23×C1114yes—
530C23×C4C23×C1111yescharacteristic
531C23×C4C23×C1111yescharacteristic
532C23×C4C23×C1111yescharacteristic
533C23×C4C23×C1111yescharacteristic
534C23×C4C23×C1111yescharacteristic
535C23×C4C23×C1114yes—
536#124—232no—
537#123—232no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
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⋊C4D4×C1118yescomplemented
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—42no—
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—
584#95C23×C1114yes—
585#95C23×C1114yes—
586C2×C11—44no—
587C2×C11—44no—
588C2×C11—82no—
589C2×C11#255718yesdirect product factor
590C2×C11C2×#52911yescharacteristic
591C2×C11C2×#53211yescharacteristic
592C2×C11C2×#53811yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#54611yescharacteristic
595C2×C11C2×#55111yescharacteristic
596C2×C11C2×#55911yescharacteristic
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—
614C24—22no—
615C24—22no—
616C24C2×D4×C1114yes—
617C24C11×#4114yes—
618C24C24×C1112yes—
619C24C24×C1112yes—
620C24C24×C1112yes—
621C24C24×C1111yescharacteristic
622C2×Q8—28no—
623C2×Q8—28no—
624C2×Q8—44no—
625C2×Q8—416no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—416no—
636C2×D4—416no—
637C2×D4—416no—
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—28no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—416no—
676C22×C4—416no—
677C22×C4C2×D4×C1114yes—
678C22×C4C2×D4×C1114yes—
679C22×C4C11×#4114yes—
680C22×C4C11×#4114yes—
681C22×C4C11×#4114yes—
682C22×C4C24×C1112yes—
683C22×C4C24×C1112yes—
684C22×C4C24×C1112yes—
685C22×C4C24×C1112yes—
686C22×C4C24×C1112yes—
687C22×C4C24×C1112yes—
688C22×C4C24×C1112yes—
689C22×C4C24×C1112yes—
690C22×C4C24×C1112yes—
691C22×C4C24×C1112yes—
692C22×C4C24×C1112yes—
693C22×C4C24×C1112yes—
694C4⋊C4—28no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4C2×D4×C11116yescomplemented
710C42—28no—
711C42—44no—
712C42—44no—
713C11C2×#255711yescharacteristic, direct product factor, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
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—22no—
737C23—22no—
738C23—22no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23C22×D4×C1114yes—
755C23C22×D4×C1112yes—
756C23C2×C11×#4114yes—
757C23C2×C11×#4112yes—
758C23C2×C11×#4112yes—
759C23C2×C11×#4112yes—
760C23C2×C11×#4112yes—
761C23C11×H(5,𝔽2)12yes—
762C23C11×H(5,𝔽2)12yes—
763C23C25×C1111yescharacteristic
764Q8—416no—
765D4—416no—
766D4—416no—
767D4—416no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
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—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—416no—
805C2×C4—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4C22×D4×C1114yes—
814C2×C4C22×D4×C1114yes—
815C2×C4C2×C11×#4114yes—
816C2×C4C2×C11×#4114yes—
817C2×C4C2×C11×#4114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—416no—
833C22—416no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—88no—
842C22C11×#52914yes—
843C22C11×#53214yes—
844C22C11×#53814yes—
845C22C11×#54614yes—
846C22C11×#54614yes—
847C22C11×#55114yes—
848C22C11×#55914yes—
849C22C23×D4×C1111yescharacteristic
850C22C22×C11×#4111yescharacteristic
851C22C22×C11×#4111yescharacteristic
852C22C22×C11×#4111yescharacteristic
853C22C22×C11×#4111yescharacteristic
854C22C2×C11×H(5,𝔽2)11yescharacteristic
855C22C2×C11×H(5,𝔽2)11yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—24no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—42no—
868C2—44no—
869C2—44no—
870C2—82no—
871C2C11×#255718yesdirect product factor
872C2C2×C11×#52911yescharacteristic
873C2C2×C11×#53211yescharacteristic
874C2C2×C11×#53811yescharacteristic
875C2C2×C11×#54611yescharacteristic
876C2C2×C11×#54611yescharacteristic
877C2C2×C11×#55111yescharacteristic
878C2C2×C11×#55911yescharacteristic
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×#124C2semidirect
2. C22×C11×#123C2semidirect
3. C11×#2557C2direct (N × H)
4. C2×C11×#397C2semidirect
5. C2×C11×#397C2semidirect
6. C2×C11×#393C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#390C2semidirect
10. C2×C11×#388C2semidirect
11. C2×C11×#387C2semidirect
12. C2×C11×#386C2semidirect
13. C2×C11×#386C2semidirect
14. C2×C11×#386C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
24. C2×C11×#124C22semidirect
26. C2×C11×#123C22semidirect
46. C11×#397C22semidirect
47. C11×#397C22semidirect
48. C11×#393C22semidirect
50. C11×#391C22semidirect
51. C11×#390C22semidirect
52. C11×#388C22semidirect
53. C11×#387C22semidirect
54. C11×#386C22semidirect
55. C11×#386C22semidirect
56. C11×#386C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. C4×C11×C22⋊C4C22semidirect
128. C2×C11×C22⋊C4D4semidirect
158. C2×#2557C11direct (N × H)
271. C11×C22⋊C4C2×D4semidirect
275. C22×#124C2×C11semidirect
276. C22×#123C2×C11semidirect
277. #2557C2×C11direct (N × H)
278. C2×#397C2×C11semidirect
279. C2×#397C2×C11semidirect
280. C2×#393C2×C11semidirect
282. C2×#391C2×C11semidirect
283. C2×#390C2×C11semidirect
284. C2×#388C2×C11semidirect
285. C2×#387C2×C11semidirect
286. C2×#386C2×C11semidirect
287. C2×#386C2×C11semidirect
288. C2×#386C2×C11semidirect
289. C2×C4×C22⋊C4C2×C11semidirect
290. C2×C4×C22⋊C4C2×C11semidirect
402. C2×#124C22×C11semidirect
404. C2×#123C22×C11semidirect
424. #397C22×C11semidirect
425. #397C22×C11semidirect
426. #393C22×C11semidirect
428. #391C22×C11semidirect
429. #390C22×C11semidirect
430. #388C22×C11semidirect
431. #387C22×C11semidirect
432. #386C22×C11semidirect
433. #386C22×C11semidirect
434. #386C22×C11semidirect
435. C4×C22⋊C4C22×C11semidirect
436. C4×C22⋊C4C22×C11semidirect
556. C2×C22⋊C4D4×C11semidirect
589. C2×C11#2557direct (N × H)
709. C22⋊C4C2×D4×C11semidirect
713. C11C2×#2557direct (N × H)
871. C2C11×#2557direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C11×#1232
C11×#25572
C2×C11×#3972
C2×C11×#3932
C2×C11×#3922
C2×C11×#3912
C2×C11×#3902
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C4×C11×C22⋊C42
C2×#255711