Finite Group Databasebeta

← C2×C11×#2556 #14612017

Subgroups — C2×C11×#2556 #14612017

Order 2816.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊Q8C211yesmaximal, characteristic
3C11×#2556C2116yesmaximal, direct product factor
4C2×C11×#399C211yesmaximal, characteristic
5C2×C11×#398C211yesmaximal, characteristic, complemented
6C2×C11×#396C211yesmaximal, characteristic
7C2×C11×#395C211yesmaximal, characteristic, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#389C211yesmaximal, characteristic, complemented
10C2×C11×#389C211yesmaximal, characteristic, complemented
11C2×C11×#388C211yesmaximal, characteristic
12C2×C11×#388C211yesmaximal, characteristic
13C2×C11×#387C211yesmaximal, characteristic, complemented
14C2×C11×#385C211yesmaximal, characteristic
15C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C2×C11×#125—28no—
20C2×C11×#125C2218yescomplemented
21C2×C11×C22⋊Q8—28no—
22C2×C11×C22⋊Q8C2218yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊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×C42×C11C2211yescharacteristic
43C22×C42×C11C2211yescharacteristic
44C22×C42×C11C2211yescharacteristic
45C22×C42×C11C2211yescharacteristic
46C11×#399C2218yes—
47C11×#398C2218yescomplemented
48C11×#396C2218yes—
49C11×#395C2218yescomplemented
50C11×#391C2218yescomplemented
51C11×#389C2218yescomplemented
52C11×#389C2218yescomplemented
53C11×#388C2218yes—
54C11×#388C2218yes—
55C11×#387C2218yescomplemented
56C11×#385C2218yes—
57C4×C11×C4⋊C4C2218yescomplemented
58C4×C11×C22⋊C4C2218yes—
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
70C22×Q8×C11—24no—
71C22×Q8×C11—24no—
72C22×Q8×C11—42no—
73C22×Q8×C11C2314yes—
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C11×#125—232no—
93C11×C22⋊Q8—232no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—42no—
106C2×C11×C4⋊C4D418yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
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×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—42no—
125C2×C11×C22⋊C4Q818yescomplemented
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C42×C11—24no—
133C2×C42×C11—24no—
134C2×C42×C11—42no—
135C2×C42×C11—42no—
136C2×C42×C11C2314yes—
137C2×C42×C11C2314yes—
138C2×C42×C11C2314yes—
139C2×C42×C11C2314yes—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C2×#2556C1111yesmaximal, characteristic, direct product factor, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11C2×Q814yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C2×Q8×C11—28no—
161C2×Q8×C11—28no—
162C2×Q8×C11—44no—
163C2×Q8×C11—416no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
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—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—28no—
199C22×C4×C11—28no—
200C22×C4×C11—44no—
201C22×C4×C11—416no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11C2×D414yes—
205C22×C4×C11C2×Q814yes—
206C22×C4×C11C2×Q814yes—
207C22×C4×C11#4114yes—
208C22×C4×C11#4114yes—
209C22×C4×C11#4114yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C11×C4⋊C4—28no—
225C11×C4⋊C4—28no—
226C11×C4⋊C4—28no—
227C11×C4⋊C4—28no—
228C11×C4⋊C4—28no—
229C11×C4⋊C4—28no—
230C11×C4⋊C4—28no—
231C11×C4⋊C4—28no—
232C11×C4⋊C4—28no—
233C11×C4⋊C4—28no—
234C11×C4⋊C4—28no—
235C11×C4⋊C4—44no—
236C11×C4⋊C4C2×D4116yes—
237C11×C22⋊C4—28no—
238C11×C22⋊C4—28no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—28no—
241C11×C22⋊C4—44no—
242C11×C22⋊C4C2×Q8116yescomplemented
243C42×C11—28no—
244C42×C11—28no—
245C42×C11—44no—
246C42×C11—44no—
247C22×#125C2×C1111yescharacteristic, complemented
248C22×C22⋊Q8C2×C1111yescharacteristic
249#2556C2×C11116yesdirect product factor
250C2×#399C2×C1111yescharacteristic
251C2×#398C2×C1111yescharacteristic, complemented
252C2×#396C2×C1111yescharacteristic
253C2×#395C2×C1111yescharacteristic, complemented
254C2×#391C2×C1111yescharacteristic, complemented
255C2×#389C2×C1111yescharacteristic, complemented
256C2×#389C2×C1111yescharacteristic, complemented
257C2×#388C2×C1111yescharacteristic
258C2×#388C2×C1111yescharacteristic
259C2×#387C2×C1111yescharacteristic, complemented
260C2×#385C2×C1111yescharacteristic
261C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
262C2×C4×C22⋊C4C2×C1111yescharacteristic
263C23×C11—28no—
264C23×C11—28no—
265C23×C11—28no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—44no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11C22×D412yes—
277C23×C11C22×Q814yes—
278C23×C11C22×Q812yes—
279C23×C11C2×#4112yes—
280C23×C11C2×#4112yes—
281C23×C11C2×#4112yes—
282C23×C11H(5,𝔽2)12yes—
283C23×C112−1+412yes—
284C23×C11C2511yescharacteristic
285Q8×C11—416no—
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—28no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—416no—
329C2×C4×C11—44no—
330C2×C4×C11—44no—
331C2×C4×C11—44no—
332C2×C4×C11—44no—
333C2×C4×C11—44no—
334C2×C4×C11—44no—
335C2×C4×C11C22×D414yes—
336C2×C4×C11C22×D414yes—
337C2×C4×C11C22×D414yes—
338C2×C4×C11C22×Q814yes—
339C2×C4×C11C22×Q814yes—
340C2×C4×C11C2×#4114yes—
341C2×C4×C11C2×#4114yes—
342C2×C4×C11C2×#4114yes—
343C23×Q8C22×C1111yescharacteristic
344C24×C4C22×C1111yescharacteristic
345C2×#125—28no—
346C2×#125C22×C1118yescomplemented
347C2×C22⋊Q8—28no—
348C2×C22⋊Q8C22×C1118yes—
349C22×C4⋊C4C22×C1111yescharacteristic
350C22×C4⋊C4C22×C1111yescharacteristic
351C22×C4⋊C4C22×C1111yescharacteristic
352C22×C4⋊C4C22×C1111yescharacteristic
353C22×C4⋊C4C22×C1111yescharacteristic
354C22×C4⋊C4C22×C1111yescharacteristic
355C22×C4⋊C4C22×C1111yescharacteristic
356C22×C4⋊C4C22×C1111yescharacteristic
357C22×C4⋊C4C22×C1111yescharacteristic
358C22×C4⋊C4C22×C1111yescharacteristic
359C22×C4⋊C4C22×C1111yescharacteristic
360C22×C4⋊C4C22×C1111yescharacteristic
361C22×C4⋊C4C22×C1111yescharacteristic
362C22×C22⋊C4C22×C1111yescharacteristic
363C22×C22⋊C4C22×C1111yescharacteristic
364C22×C22⋊C4C22×C1111yescharacteristic
365C22×C22⋊C4C22×C1111yescharacteristic
366C22×C22⋊C4C22×C1111yescharacteristic
367C22×C22⋊C4C22×C1111yescharacteristic
368C22×C42C22×C1111yescharacteristic
369C22×C42C22×C1111yescharacteristic
370C22×C42C22×C1111yescharacteristic
371C22×C42C22×C1111yescharacteristic
372#399C22×C1118yes—
373#398C22×C1118yescomplemented
374#396C22×C1118yes—
375#395C22×C1118yescomplemented
376#391C22×C1118yescomplemented
377#389C22×C1118yescomplemented
378#389C22×C1118yescomplemented
379#388C22×C1118yes—
380#388C22×C1118yes—
381#387C22×C1118yescomplemented
382#385C22×C1118yes—
383C4×C4⋊C4C22×C1118yescomplemented
384C4×C22⋊C4C22×C1118yes—
385C2×#95C22×C1111yescharacteristic
386C2×#95C22×C1111yescharacteristic
387C2×#95C22×C1111yescharacteristic
388C2×#95C22×C1111yescharacteristic
389C2×#95C22×C1111yescharacteristic
390C2×#95C22×C1111yescharacteristic
391C2×#95C22×C1111yescharacteristic
392C2×#95C22×C1111yescharacteristic
393C2×#95C22×C1111yescharacteristic
394C2×#95C22×C1111yescharacteristic
395C22×C11—24no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—416no—
403C22×C11#53214yes—
404C22×C11#53314yes—
405C22×C11#53914yes—
406C22×C11#54614yes—
407C22×C11D4×Q814yes—
408C22×C11#55214yes—
409C22×C11#55414yes—
410C22×C11C23×D411yescharacteristic
411C22×C11C23×Q811yescharacteristic
412C22×C11C22×#4111yescharacteristic
413C22×C11C22×#4111yescharacteristic
414C22×C11C22×#4111yescharacteristic
415C22×C11C2×H(5,𝔽2)11yescharacteristic
416C22×C11C2×2−1+411yescharacteristic
417C4×C11—24no—
418C4×C11—24no—
419C4×C11—24no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—24no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C25C23×C1111yescharacteristic
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—42no—
435C22×Q8C23×C1114yes—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4C23×C1111yescharacteristic
440C23×C4C23×C1111yescharacteristic
441C23×C4C23×C1111yescharacteristic
442C23×C4C23×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444C23×C4C23×C1111yescharacteristic
445C23×C4C23×C1114yes—
446C23×C4C23×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448C23×C4C23×C1111yescharacteristic
449C23×C4C23×C1111yescharacteristic
450C23×C4C23×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C23×C4C23×C1111yescharacteristic
453C23×C4C23×C1111yescharacteristic
454#125—232no—
455C22⋊Q8—232no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4D4×C1118yes—
469C2×C4⋊C4C23×C1114yes—
470C2×C4⋊C4C23×C1114yes—
471C2×C4⋊C4C23×C1114yes—
472C2×C4⋊C4C23×C1114yes—
473C2×C4⋊C4C23×C1114yes—
474C2×C4⋊C4C23×C1114yes—
475C2×C4⋊C4C23×C1114yes—
476C2×C4⋊C4C23×C1114yes—
477C2×C4⋊C4C23×C1114yes—
478C2×C4⋊C4C23×C1114yes—
479C2×C4⋊C4C23×C1114yes—
480C2×C4⋊C4C23×C1114yes—
481C2×C4⋊C4C23×C1114yes—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4Q8×C1118yescomplemented
488C2×C22⋊C4C23×C1114yes—
489C2×C22⋊C4C23×C1114yes—
490C2×C22⋊C4C23×C1114yes—
491C2×C22⋊C4C23×C1114yes—
492C2×C22⋊C4C23×C1114yes—
493C2×C22⋊C4C23×C1114yes—
494C2×C42—24no—
495C2×C42—24no—
496C2×C42—42no—
497C2×C42—42no—
498C2×C42C23×C1114yes—
499C2×C42C23×C1114yes—
500C2×C42C23×C1114yes—
501C2×C42C23×C1114yes—
502#95C23×C1114yes—
503#95C23×C1114yes—
504#95C23×C1114yes—
505#95C23×C1114yes—
506#95C23×C1114yes—
507#95C23×C1114yes—
508#95C23×C1114yes—
509#95C23×C1114yes—
510#95C23×C1114yes—
511#95C23×C1114yes—
512C2×C11—44no—
513C2×C11#255618yesdirect product factor
514C2×C11C2×#53211yescharacteristic
515C2×C11C2×#53311yescharacteristic
516C2×C11C2×#53911yescharacteristic
517C2×C11C2×#54611yescharacteristic
518C2×C11C2×D4×Q811yescharacteristic
519C2×C11C2×#55211yescharacteristic
520C2×C11C2×#55411yescharacteristic
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24C2×Q8×C1114yes—
528C24C24×C1112yes—
529C24C24×C1111yescharacteristic
530C2×Q8—28no—
531C2×Q8—28no—
532C2×Q8—44no—
533C2×Q8—416no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—44no—
571C22×C4—416no—
572C22×C4C2×D4×C1114yes—
573C22×C4C2×D4×C1114yes—
574C22×C4C2×D4×C1114yes—
575C22×C4C2×Q8×C1114yes—
576C22×C4C2×Q8×C1114yes—
577C22×C4C11×#4114yes—
578C22×C4C11×#4114yes—
579C22×C4C11×#4114yes—
580C22×C4C24×C1112yes—
581C22×C4C24×C1112yes—
582C22×C4C24×C1112yes—
583C22×C4C24×C1112yes—
584C22×C4C24×C1112yes—
585C22×C4C24×C1112yes—
586C22×C4C24×C1112yes—
587C22×C4C24×C1112yes—
588C22×C4C24×C1112yes—
589C22×C4C24×C1112yes—
590C22×C4C24×C1112yes—
591C22×C4C24×C1112yes—
592C22×C4C24×C1112yes—
593C22×C4C24×C1112yes—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—44no—
606C4⋊C4C2×D4×C11116yes—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4C2×Q8×C11116yescomplemented
613C42—28no—
614C42—28no—
615C42—44no—
616C42—44no—
617C11C2×#255611yescharacteristic, direct product factor, Sylow
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C22×D4×C1112yes—
632C23C22×Q8×C1114yes—
633C23C22×Q8×C1112yes—
634C23C2×C11×#4112yes—
635C23C2×C11×#4112yes—
636C23C2×C11×#4112yes—
637C23C11×H(5,𝔽2)12yes—
638C23C11×2−1+412yes—
639C23C25×C1111yescharacteristic
640Q8—416no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4C22×D4×C1114yes—
691C2×C4C22×D4×C1114yes—
692C2×C4C22×D4×C1114yes—
693C2×C4C22×Q8×C1114yes—
694C2×C4C22×Q8×C1114yes—
695C2×C4C2×C11×#4114yes—
696C2×C4C2×C11×#4114yes—
697C2×C4C2×C11×#4114yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—416no—
706C22C11×#53214yes—
707C22C11×#53314yes—
708C22C11×#53914yes—
709C22C11×#54614yes—
710C22D4×Q8×C1114yes—
711C22C11×#55214yes—
712C22C11×#55414yes—
713C22C23×D4×C1111yescharacteristic
714C22C23×Q8×C1111yescharacteristic
715C22C22×C11×#4111yescharacteristic
716C22C22×C11×#4111yescharacteristic
717C22C22×C11×#4111yescharacteristic
718C22C2×C11×H(5,𝔽2)11yescharacteristic
719C22C2×C11×2−1+411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C2—44no—
735C2C11×#255618yesdirect product factor
736C2C2×C11×#53211yescharacteristic
737C2C2×C11×#53311yescharacteristic
738C2C2×C11×#53911yescharacteristic
739C2C2×C11×#54611yescharacteristic
740C2C2×D4×Q8×C1111yescharacteristic
741C2C2×C11×#55211yescharacteristic
742C2C2×C11×#55411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#125C2semidirect
3. C11×#2556C2direct (N × H)
5. C2×C11×#398C2semidirect
7. C2×C11×#395C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#389C2semidirect
10. C2×C11×#389C2semidirect
13. C2×C11×#387C2semidirect
15. C2×C4×C11×C4⋊C4C2semidirect
20. C2×C11×#125C22semidirect
47. C11×#398C22semidirect
49. C11×#395C22semidirect
50. C11×#391C22semidirect
51. C11×#389C22semidirect
52. C11×#389C22semidirect
55. C11×#387C22semidirect
57. C4×C11×C4⋊C4C22semidirect
125. C2×C11×C22⋊C4Q8semidirect
150. C2×#2556C11direct (N × H)
242. C11×C22⋊C4C2×Q8semidirect
247. C22×#125C2×C11semidirect
249. #2556C2×C11direct (N × H)
251. C2×#398C2×C11semidirect
253. C2×#395C2×C11semidirect
254. C2×#391C2×C11semidirect
255. C2×#389C2×C11semidirect
256. C2×#389C2×C11semidirect
259. C2×#387C2×C11semidirect
261. C2×C4×C4⋊C4C2×C11semidirect
346. C2×#125C22×C11semidirect
373. #398C22×C11semidirect
375. #395C22×C11semidirect
376. #391C22×C11semidirect
377. #389C22×C11semidirect
378. #389C22×C11semidirect
381. #387C22×C11semidirect
383. C4×C4⋊C4C22×C11semidirect
487. C2×C22⋊C4Q8×C11semidirect
513. C2×C11#2556direct (N × H)
612. C22⋊C4C2×Q8×C11semidirect
617. C11C2×#2556direct (N × H)
735. C2C11×#2556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C22×C11×C22⋊Q82
C11×#25562
C2×C11×#3992
C2×C11×#3982
C2×C11×#3962
C2×C11×#3952
C2×C11×#3912
C2×C11×#3892
C2×C11×#3882
C2×C11×#3872
C2×C11×#3852
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C2×#255611