Finite Group Databasebeta

← C2×C11×#2417 #14611876

Subgroups — C2×C11×#2417 #14611876

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C4×D4×C11C211yesmaximal, characteristic
4C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2417C2116yesmaximal, direct product factor
6C2×C11×#398C212yesmaximal, complemented
7C2×C11×#396C212yesmaximal, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C2×C11×#389C211yesmaximal, characteristic, complemented
10C2×C11×#386C212yesmaximal
11C2×C11×#380C212yesmaximal, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×C4×C11C2212yes—
17C24×C4×C11C2211yescharacteristic
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8—28no—
20C2×C11×C22⋊Q8C2218yescomplemented
21C2×C11×C22⋊Q8C2218yescomplemented
22C2×C4×D4×C11—28no—
23C2×C4×D4×C11C2218yes—
24C22×C11×C4⋊C4—28no—
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2212yes—
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C4⋊C4C2218yescomplemented
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2212yes—
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2212yes—
38C22×C11×C22⋊C4C2212yes—
39C22×C42×C11C2211yescharacteristic
40C11×#398C22116yescomplemented
41C11×#396C22116yescomplemented
42C11×#391C2218yescomplemented
43C11×#389C2218yescomplemented
44C11×#386C22116yes—
45C11×#380C2218yescomplemented
46C11×#380C22116yescomplemented
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49C2×C11×#95C2212yes—
50C2×C11×#95C2212yes—
51C25×C11C2311yescharacteristic
52C25×C11C2311yescharacteristic
53C22×Q8×C11—24no—
54C22×Q8×C11—24no—
55C22×Q8×C11—24no—
56C22×Q8×C11C2314yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11Q818yescomplemented
60C22×D4×C11C2314yes—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11—28no—
64C23×C4×C11—28no—
65C23×C4×C11—24no—
66C23×C4×C11—24no—
67C23×C4×C11—24no—
68C23×C4×C11—44no—
69C23×C4×C11D418yes—
70C23×C4×C11C2314yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2318yes—
77C23×C4×C11C2314yes—
78C23×C4×C11C2312yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C11×C22⋊Q8—232no—
83C11×C22⋊Q8—232no—
84C4×D4×C11—232no—
85C2×C11×C4⋊C4—28no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—28no—
90C2×C11×C4⋊C4—28no—
91C2×C11×C4⋊C4—232no—
92C2×C11×C4⋊C4—44no—
93C2×C11×C4⋊C4D418yescomplemented
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2318yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2318yes—
99C2×C11×C4⋊C4C2318yes—
100C2×C11×C4⋊C4C2318yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—28no—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—28no—
106C2×C11×C22⋊C4—44no—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2318yes—
110C2×C11×C22⋊C4C2318yes—
111C2×C11×C22⋊C4C2318yes—
112C2×C42×C11—24no—
113C2×C42×C11C2314yes—
114C11×#95C2318yes—
115C11×#95C2318yes—
116C11×#95C2318yes—
117C11×#95C2318yes—
118C2×#2417C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C2×D414yes—
130C24×C11C2×Q814yes—
131C24×C11C2×Q814yes—
132C24×C11#4114yes—
133C24×C11C2412yes—
134C24×C11C2412yes—
135C24×C11C2411yescharacteristic
136C2×Q8×C11—28no—
137C2×Q8×C11—28no—
138C2×Q8×C11—28no—
139C2×Q8×C11—416no—
140C2×D4×C11—232no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11C2×Q8116yescomplemented
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—232no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—216no—
161C22×C4×C11—22no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—216no—
170C22×C4×C11—28no—
171C22×C4×C11—28no—
172C22×C4×C11—28no—
173C22×C4×C11—48no—
174C22×C4×C11—432no—
175C22×C4×C11—416no—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D418yes—
178C22×C4×C11C2×D4116yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×Q814yes—
182C22×C4×C11#4114yes—
183C22×C4×C11C2414yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2414yes—
186C22×C4×C11C2414yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2414yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C11×C4⋊C4—216no—
193C11×C4⋊C4—28no—
194C11×C4⋊C4—28no—
195C11×C4⋊C4—28no—
196C11×C4⋊C4—216no—
197C11×C4⋊C4—216no—
198C11×C4⋊C4—48no—
199C11×C4⋊C4C2×D4116yescomplemented
200C11×C22⋊C4—28no—
201C11×C22⋊C4—216no—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—216no—
204C11×C22⋊C4—48no—
205C42×C11—28no—
206C22×C22⋊Q8C2×C1111yescharacteristic, complemented
207C22×C22⋊Q8C2×C1111yescharacteristic, complemented
208C22×C4×D4C2×C1111yescharacteristic
209C23×C4⋊C4C2×C1111yescharacteristic, complemented
210#2417C2×C11116yesdirect product factor
211C2×#398C2×C1112yescomplemented
212C2×#396C2×C1112yescomplemented
213C2×#391C2×C1111yescharacteristic, complemented
214C2×#389C2×C1111yescharacteristic, complemented
215C2×#386C2×C1112yes—
216C2×#380C2×C1112yescomplemented
217C2×#380C2×C1111yescharacteristic, complemented
218C23×C11—28no—
219C23×C11—28no—
220C23×C11—28no—
221C23×C11—28no—
222C23×C11—28no—
223C23×C11—28no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—28no—
229C23×C11—28no—
230C23×C11—28no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—44no—
238C23×C11—44no—
239C23×C11—44no—
240C23×C11—44no—
241C23×C11C22⋊Q8116yescomplemented
242C23×C11C22×D414yes—
243C23×C11C22×D412yes—
244C23×C11C22×D412yes—
245C23×C11C22×Q814yes—
246C23×C11C22×Q814yes—
247C23×C11C22×Q812yes—
248C23×C11C2×#4114yes—
249C23×C11C2×#4112yes—
250C23×C11C2×#4112yes—
251C23×C11H(5,𝔽2)12yes—
252C23×C112−1+412yes—
253C23×C11C2511yescharacteristic
254Q8×C11—416no—
255D4×C11—232no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—216no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—232no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—24no—
281C2×C4×C11—432no—
282C2×C4×C11—44no—
283C2×C4×C11—48no—
284C2×C4×C11—44no—
285C2×C4×C11—48no—
286C2×C4×C11—48no—
287C2×C4×C11—416no—
288C2×C4×C11#121116yes—
289C2×C4×C11C22×D414yes—
290C2×C4×C11C22×D418yes—
291C2×C4×C11C22×D414yes—
292C2×C4×C11C22×D414yes—
293C2×C4×C11C22×Q814yes—
294C2×C4×C11C2×#4114yes—
295C23×Q8C22×C1111yescharacteristic
296C23×D4C22×C1111yescharacteristic
297C24×C4C22×C1111yescharacteristic
298C24×C4C22×C1112yes—
299C24×C4C22×C1111yescharacteristic
300C2×C22⋊Q8—28no—
301C2×C22⋊Q8—28no—
302C2×C22⋊Q8C22×C1118yescomplemented
303C2×C22⋊Q8C22×C1118yescomplemented
304C2×C4×D4—28no—
305C2×C4×D4C22×C1118yes—
306C22×C4⋊C4—28no—
307C22×C4⋊C4C22×C1112yes—
308C22×C4⋊C4C22×C1112yes—
309C22×C4⋊C4C22×C1111yescharacteristic
310C22×C4⋊C4C22×C1112yes—
311C22×C4⋊C4C22×C1111yescharacteristic
312C22×C4⋊C4C22×C1111yescharacteristic
313C22×C4⋊C4C22×C1112yes—
314C22×C4⋊C4C22×C1111yescharacteristic
315C22×C4⋊C4C22×C1118yescomplemented
316C22×C22⋊C4C22×C1111yescharacteristic
317C22×C22⋊C4C22×C1112yes—
318C22×C22⋊C4C22×C1111yescharacteristic
319C22×C22⋊C4C22×C1112yes—
320C22×C22⋊C4C22×C1112yes—
321C22×C42C22×C1111yescharacteristic
322#398C22×C11116yescomplemented
323#396C22×C11116yescomplemented
324#391C22×C1118yescomplemented
325#389C22×C1118yescomplemented
326#386C22×C11116yes—
327#380C22×C1118yescomplemented
328#380C22×C11116yescomplemented
329C2×#95C22×C1112yes—
330C2×#95C22×C1112yes—
331C2×#95C22×C1112yes—
332C2×#95C22×C1112yes—
333C22×C11—24no—
334C22×C11—232no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—416no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11C2×#12114yes—
349C22×C11C2×C22⋊Q814yes—
350C22×C11C2×C22⋊Q818yescomplemented
351C22×C11#53714yes—
352C22×C11#54614yes—
353C22×C11D4×Q814yes—
354C22×C11#55214yes—
355C22×C11#55414yes—
356C22×C11C23×D411yescharacteristic
357C22×C11C23×D411yescharacteristic
358C22×C11C23×Q811yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C22×#4111yescharacteristic
361C22×C11C2×H(5,𝔽2)11yescharacteristic
362C22×C11C2×2−1+411yescharacteristic
363C4×C11—24no—
364C4×C11—24no—
365C4×C11—28no—
366C4×C11—42no—
367C4×C11—44no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11—44no—
371C4×C11C2×#12118yes—
372C25C23×C1111yescharacteristic
373C25C23×C1111yescharacteristic
374C22×Q8—24no—
375C22×Q8—24no—
376C22×Q8—24no—
377C22×Q8C23×C1114yes—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4Q8×C1118yescomplemented
381C22×D4C23×C1114yes—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—28no—
385C23×C4—28no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—44no—
390C23×C4D4×C1118yes—
391C23×C4C23×C1112yes—
392C23×C4C23×C1112yes—
393C23×C4C23×C1111yescharacteristic
394C23×C4C23×C1111yescharacteristic
395C23×C4C23×C1112yes—
396C23×C4C23×C1114yes—
397C23×C4C23×C1118yes—
398C23×C4C23×C1111yescharacteristic
399C23×C4C23×C1112yes—
400C23×C4C23×C1114yes—
401C23×C4C23×C1111yescharacteristic
402C23×C4C23×C1111yescharacteristic
403C22⋊Q8—232no—
404C22⋊Q8—232no—
405C4×D4—232no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—28no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—232no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4D4×C1118yescomplemented
415C2×C4⋊C4C23×C1114yes—
416C2×C4⋊C4C23×C1118yes—
417C2×C4⋊C4C23×C1114yes—
418C2×C4⋊C4C23×C1114yes—
419C2×C4⋊C4C23×C1118yes—
420C2×C4⋊C4C23×C1118yes—
421C2×C4⋊C4C23×C1118yes—
422C2×C4⋊C4C23×C1114yes—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4C23×C1114yes—
429C2×C22⋊C4C23×C1114yes—
430C2×C22⋊C4C23×C1118yes—
431C2×C22⋊C4C23×C1118yes—
432C2×C22⋊C4C23×C1118yes—
433C2×C42—24no—
434C2×C42C23×C1114yes—
435#95C23×C1118yes—
436#95C23×C1118yes—
437#95C23×C1118yes—
438#95C23×C1118yes—
439C2×C11—28no—
440C2×C11—44no—
441C2×C11#241718yesdirect product factor
442C2×C11C22×#12111yescharacteristic
443C2×C11C22×C22⋊Q811yescharacteristic
444C2×C11C2×#53711yescharacteristic
445C2×C11C2×#54611yescharacteristic
446C2×C11C2×D4×Q811yescharacteristic
447C2×C11C2×#55211yescharacteristic
448C2×C11C2×#55411yescharacteristic
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C2×D4×C1114yes—
460C24C2×Q8×C1114yes—
461C24C2×Q8×C1114yes—
462C24C11×#4114yes—
463C24C24×C1112yes—
464C24C24×C1112yes—
465C24C24×C1111yescharacteristic
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—416no—
470C2×D4—232no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4C2×Q8×C11116yescomplemented
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—232no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—216no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—216no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—48no—
504C22×C4—432no—
505C22×C4—416no—
506C22×C4C2×D4×C1114yes—
507C22×C4C2×D4×C1118yes—
508C22×C4C2×D4×C11116yes—
509C22×C4C2×D4×C1114yes—
510C22×C4C2×D4×C1114yes—
511C22×C4C2×Q8×C1114yes—
512C22×C4C11×#4114yes—
513C22×C4C24×C1114yes—
514C22×C4C24×C1112yes—
515C22×C4C24×C1114yes—
516C22×C4C24×C1114yes—
517C22×C4C24×C1112yes—
518C22×C4C24×C1114yes—
519C22×C4C24×C1112yes—
520C22×C4C24×C1112yes—
521C22×C4C24×C1112yes—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—216no—
527C4⋊C4—216no—
528C4⋊C4—48no—
529C4⋊C4C2×D4×C11116yescomplemented
530C22⋊C4—28no—
531C22⋊C4—216no—
532C22⋊C4—28no—
533C22⋊C4—216no—
534C22⋊C4—48no—
535C42—28no—
536C11C2×#241711yescharacteristic, direct product factor, Sylow
537C23—28no—
538C23—28no—
539C23—28no—
540C23—28no—
541C23—28no—
542C23—28no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—28no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23C11×C22⋊Q8116yescomplemented
561C23C22×D4×C1114yes—
562C23C22×D4×C1112yes—
563C23C22×D4×C1112yes—
564C23C22×Q8×C1114yes—
565C23C22×Q8×C1114yes—
566C23C22×Q8×C1112yes—
567C23C2×C11×#4114yes—
568C23C2×C11×#4112yes—
569C23C2×C11×#4112yes—
570C23C11×H(5,𝔽2)12yes—
571C23C11×2−1+412yes—
572C23C25×C1111yescharacteristic
573Q8—416no—
574D4—232no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—216no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—232no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—432no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—48no—
605C2×C4—48no—
606C2×C4—416no—
607C2×C4C11×#121116yes—
608C2×C4C22×D4×C1114yes—
609C2×C4C22×D4×C1118yes—
610C2×C4C22×D4×C1114yes—
611C2×C4C22×D4×C1114yes—
612C2×C4C22×Q8×C1114yes—
613C2×C4C2×C11×#4114yes—
614C22—24no—
615C22—232no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—42no—
625C22—416no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22C2×C11×#12114yes—
630C22C2×C11×C22⋊Q814yes—
631C22C2×C11×C22⋊Q818yescomplemented
632C22C11×#53714yes—
633C22C11×#54614yes—
634C22D4×Q8×C1114yes—
635C22C11×#55214yes—
636C22C11×#55414yes—
637C22C23×D4×C1111yescharacteristic
638C22C23×D4×C1111yescharacteristic
639C22C23×Q8×C1111yescharacteristic
640C22C22×C11×#4111yescharacteristic
641C22C22×C11×#4111yescharacteristic
642C22C2×C11×H(5,𝔽2)11yescharacteristic
643C22C2×C11×2−1+411yescharacteristic
644C4—24no—
645C4—24no—
646C4—28no—
647C4—42no—
648C4—44no—
649C4—42no—
650C4—44no—
651C4—44no—
652C4C2×C11×#12118yes—
653C2—28no—
654C2—44no—
655C2C11×#241718yesdirect product factor
656C2C22×C11×#12111yescharacteristic
657C2C22×C11×C22⋊Q811yescharacteristic
658C2C2×C11×#53711yescharacteristic
659C2C2×C11×#54611yescharacteristic
660C2C2×D4×Q8×C1111yescharacteristic
661C2C2×C11×#55211yescharacteristic
662C2C2×C11×#55411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊Q8C2semidirect
2. C22×C11×C22⋊Q8C2semidirect
4. C23×C11×C4⋊C4C2semidirect
5. C11×#2417C2direct (N × H)
6. C2×C11×#398C2semidirect
7. C2×C11×#396C2semidirect
8. C2×C11×#391C2semidirect
9. C2×C11×#389C2semidirect
11. C2×C11×#380C2semidirect
12. C2×C11×#380C2semidirect
20. C2×C11×C22⋊Q8C22semidirect
21. C2×C11×C22⋊Q8C22semidirect
33. C22×C11×C4⋊C4C22semidirect
40. C11×#398C22semidirect
41. C11×#396C22semidirect
42. C11×#391C22semidirect
43. C11×#389C22semidirect
45. C11×#380C22semidirect
46. C11×#380C22semidirect
59. C22×D4×C11Q8semidirect
93. C2×C11×C4⋊C4D4semidirect
118. C2×#2417C11direct (N × H)
143. C2×D4×C11C2×Q8semidirect
199. C11×C4⋊C4C2×D4semidirect
206. C22×C22⋊Q8C2×C11semidirect
207. C22×C22⋊Q8C2×C11semidirect
209. C23×C4⋊C4C2×C11semidirect
210. #2417C2×C11direct (N × H)
211. C2×#398C2×C11semidirect
212. C2×#396C2×C11semidirect
213. C2×#391C2×C11semidirect
214. C2×#389C2×C11semidirect
216. C2×#380C2×C11semidirect
217. C2×#380C2×C11semidirect
241. C23×C11C22⋊Q8semidirect
302. C2×C22⋊Q8C22×C11semidirect
303. C2×C22⋊Q8C22×C11semidirect
315. C22×C4⋊C4C22×C11semidirect
322. #398C22×C11semidirect
323. #396C22×C11semidirect
324. #391C22×C11semidirect
325. #389C22×C11semidirect
327. #380C22×C11semidirect
328. #380C22×C11semidirect
350. C22×C11C2×C22⋊Q8semidirect
380. C22×D4Q8×C11semidirect
414. C2×C4⋊C4D4×C11semidirect
441. C2×C11#2417direct (N × H)
473. C2×D4C2×Q8×C11semidirect
529. C4⋊C4C2×D4×C11semidirect
536. C11C2×#2417direct (N × H)
560. C23C11×C22⋊Q8semidirect
631. C22C2×C11×C22⋊Q8semidirect
655. C2C11×#2417direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C4×D4×C112
C23×C11×C4⋊C42
C11×#24172
C2×C11×#3982
C2×C11×#3962
C2×C11×#3912
C2×C11×#3892
C2×C11×#3862
C2×C11×#3802
C2×#241711