Finite Group Databasebeta

← C2×C11×#2449 #14611844

Subgroups — C2×C11×#2449 #14611844

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 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×#2449C2116yesmaximal, direct product factor
6C2×C11×#399C211yesmaximal, characteristic, complemented
7C2×C11×#398C211yesmaximal, characteristic, complemented
8C2×C11×#396C211yesmaximal, characteristic, complemented
9C2×C11×#395C211yesmaximal, characteristic, complemented
10C2×C11×#389C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C2×C11×#386C211yesmaximal, characteristic
13C2×C11×#386C211yesmaximal, characteristic
14C2×C11×#385C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C24×C4×C11C2211yescharacteristic
23C2×C11×C22⋊Q8—28no—
24C2×C11×C22⋊Q8—28no—
25C2×C11×C22⋊Q8C2218yescomplemented
26C2×C11×C22⋊Q8C2218yescomplemented
27C2×C4×D4×C11—28no—
28C2×C4×D4×C11C2218yes—
29C22×C11×C4⋊C4—28no—
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×C4⋊C4C2211yescharacteristic
37C22×C11×C4⋊C4C2211yescharacteristic
38C22×C11×C4⋊C4C2211yescharacteristic
39C22×C11×C4⋊C4C2211yescharacteristic
40C22×C11×C4⋊C4C2211yescharacteristic
41C22×C11×C4⋊C4C2211yescharacteristic
42C22×C11×C4⋊C4C2218yescomplemented
43C22×C11×C22⋊C4C2211yescharacteristic
44C22×C11×C22⋊C4C2211yescharacteristic
45C22×C11×C22⋊C4C2211yescharacteristic
46C22×C11×C22⋊C4C2211yescharacteristic
47C22×C11×C22⋊C4C2211yescharacteristic
48C22×C11×C22⋊C4C2211yescharacteristic
49C22×C11×C22⋊C4C2211yescharacteristic
50C22×C11×C22⋊C4C2211yescharacteristic
51C22×C42×C11C2211yescharacteristic
52C11×#399C2218yescomplemented
53C11×#398C2218yescomplemented
54C11×#396C2218yescomplemented
55C11×#395C2218yescomplemented
56C11×#389C2218yescomplemented
57C11×#387C2218yescomplemented
58C11×#386C2218yes—
59C11×#386C2218yes—
60C11×#385C2218yescomplemented
61C11×#385C2218yescomplemented
62C11×#385C2218yescomplemented
63C2×C11×#95C2211yescharacteristic
64C2×C11×#95C2211yescharacteristic
65C2×C11×#95C2211yescharacteristic
66C2×C11×#95C2211yescharacteristic
67C2×C11×#95C2211yescharacteristic
68C2×C11×#95C2211yescharacteristic
69C2×C11×#95C2211yescharacteristic
70C2×C11×#95C2211yescharacteristic
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C22×Q8×C11—24no—
74C22×Q8×C11—24no—
75C22×Q8×C11—42no—
76C22×Q8×C11C2314yes—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11Q818yescomplemented
80C22×D4×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11—24no—
85C23×C4×C11—24no—
86C23×C4×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11—42no—
91C23×C4×C11—42no—
92C23×C4×C11—42no—
93C23×C4×C11C2314yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2314yes—
101C23×C4×C11C2314yes—
102C23×C4×C11C2314yes—
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C11×C22⋊Q8—232no—
111C11×C22⋊Q8—232no—
112C4×D4×C11—232no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—24no—
117C2×C11×C4⋊C4—24no—
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4—24no—
122C2×C11×C4⋊C4—24no—
123C2×C11×C4⋊C4—232no—
124C2×C11×C4⋊C4—42no—
125C2×C11×C4⋊C4D418yescomplemented
126C2×C11×C4⋊C4C2314yes—
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C4⋊C4C2314yes—
129C2×C11×C4⋊C4C2314yes—
130C2×C11×C4⋊C4C2314yes—
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C4⋊C4C2314yes—
133C2×C11×C4⋊C4C2314yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—24no—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4—42no—
145C2×C11×C22⋊C4D418yes—
146C2×C11×C22⋊C4C2314yes—
147C2×C11×C22⋊C4C2314yes—
148C2×C11×C22⋊C4C2314yes—
149C2×C11×C22⋊C4C2314yes—
150C2×C11×C22⋊C4C2314yes—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yes—
154C2×C42×C11—24no—
155C2×C42×C11C2314yes—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11×#95C2314yes—
163C11×#95C2314yes—
164C2×#2449C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11C2×D414yes—
176C24×C11C2×Q814yes—
177C24×C11C2×Q814yes—
178C24×C11#4114yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C2×Q8×C11—28no—
183C2×Q8×C11—28no—
184C2×Q8×C11—44no—
185C2×Q8×C11—416no—
186C2×D4×C11—232no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11C2×Q8116yescomplemented
190C22×C4×C11—232no—
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—28no—
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—28no—
207C22×C4×C11—28no—
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—28no—
217C22×C4×C11—28no—
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—22no—
228C22×C4×C11—28no—
229C22×C4×C11—28no—
230C22×C4×C11—28no—
231C22×C4×C11—28no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—416no—
236C22×C4×C11—416no—
237C22×C4×C11—416no—
238C22×C4×C11C2×D414yes—
239C22×C4×C11C2×D414yes—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2×Q814yes—
244C22×C4×C11#4114yes—
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—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C11×C4⋊C4—28no—
259C11×C4⋊C4—28no—
260C11×C4⋊C4—28no—
261C11×C4⋊C4—28no—
262C11×C4⋊C4—28no—
263C11×C4⋊C4—28no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—28no—
268C11×C4⋊C4—44no—
269C11×C4⋊C4C2×D4116yescomplemented
270C11×C22⋊C4—28no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—28no—
273C11×C22⋊C4—28no—
274C11×C22⋊C4—28no—
275C11×C22⋊C4—28no—
276C11×C22⋊C4—44no—
277C11×C22⋊C4C2×D4116yes—
278C42×C11—28no—
279C22×C22⋊Q8C2×C1111yescharacteristic, complemented
280C22×C22⋊Q8C2×C1111yescharacteristic, complemented
281C22×C4×D4C2×C1111yescharacteristic
282C23×C4⋊C4C2×C1111yescharacteristic, complemented
283#2449C2×C11116yesdirect product factor
284C2×#399C2×C1111yescharacteristic, complemented
285C2×#398C2×C1111yescharacteristic, complemented
286C2×#396C2×C1111yescharacteristic, complemented
287C2×#395C2×C1111yescharacteristic, complemented
288C2×#389C2×C1111yescharacteristic, complemented
289C2×#387C2×C1111yescharacteristic, complemented
290C2×#386C2×C1111yescharacteristic
291C2×#386C2×C1111yescharacteristic
292C2×#385C2×C1111yescharacteristic, complemented
293C2×#385C2×C1111yescharacteristic, complemented
294C2×#385C2×C1111yescharacteristic, complemented
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—28no—
299C23×C11—28no—
300C23×C11—28no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11C22⋊Q8116yescomplemented
319C23×C11C22×D414yes—
320C23×C11C22×D412yes—
321C23×C11C22×D412yes—
322C23×C11C22×Q814yes—
323C23×C11C22×Q814yes—
324C23×C11C22×Q812yes—
325C23×C11C2×#4114yes—
326C23×C11C2×#4112yes—
327C23×C11C2×#4112yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C112−1+412yes—
330C23×C11C2511yescharacteristic
331Q8×C11—416no—
332D4×C11—232no—
333C2×C4×C11—232no—
334C2×C4×C11—28no—
335C2×C4×C11—28no—
336C2×C4×C11—28no—
337C2×C4×C11—28no—
338C2×C4×C11—28no—
339C2×C4×C11—28no—
340C2×C4×C11—28no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
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—416no—
374C2×C4×C11—416no—
375C2×C4×C11—416no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11—44no—
380C2×C4×C11—44no—
381C2×C4×C11—44no—
382C2×C4×C11C22×D414yes—
383C2×C4×C11C22×D414yes—
384C2×C4×C11C22×D414yes—
385C2×C4×C11C22×D414yes—
386C2×C4×C11C22×D414yes—
387C2×C4×C11C22×Q814yes—
388C2×C4×C11C2×#4114yes—
389C23×Q8C22×C1111yescharacteristic
390C23×D4C22×C1111yescharacteristic
391C24×C4C22×C1111yescharacteristic
392C24×C4C22×C1111yescharacteristic
393C24×C4C22×C1111yescharacteristic
394C24×C4C22×C1111yescharacteristic
395C2×C22⋊Q8—28no—
396C2×C22⋊Q8—28no—
397C2×C22⋊Q8C22×C1118yescomplemented
398C2×C22⋊Q8C22×C1118yescomplemented
399C2×C4×D4—28no—
400C2×C4×D4C22×C1118yes—
401C22×C4⋊C4—28no—
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×C4⋊C4C22×C1111yescharacteristic
409C22×C4⋊C4C22×C1111yescharacteristic
410C22×C4⋊C4C22×C1111yescharacteristic
411C22×C4⋊C4C22×C1111yescharacteristic
412C22×C4⋊C4C22×C1111yescharacteristic
413C22×C4⋊C4C22×C1111yescharacteristic
414C22×C4⋊C4C22×C1118yescomplemented
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×C22⋊C4C22×C1111yescharacteristic
422C22×C22⋊C4C22×C1111yescharacteristic
423C22×C42C22×C1111yescharacteristic
424#399C22×C1118yescomplemented
425#398C22×C1118yescomplemented
426#396C22×C1118yescomplemented
427#395C22×C1118yescomplemented
428#389C22×C1118yescomplemented
429#387C22×C1118yescomplemented
430#386C22×C1118yes—
431#386C22×C1118yes—
432#385C22×C1118yescomplemented
433#385C22×C1118yescomplemented
434#385C22×C1118yescomplemented
435C2×#95C22×C1111yescharacteristic
436C2×#95C22×C1111yescharacteristic
437C2×#95C22×C1111yescharacteristic
438C2×#95C22×C1111yescharacteristic
439C2×#95C22×C1111yescharacteristic
440C2×#95C22×C1111yescharacteristic
441C2×#95C22×C1111yescharacteristic
442C2×#95C22×C1111yescharacteristic
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—232no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—416no—
458C22×C11C2×C22⋊Q814yes—
459C22×C11C2×C22⋊Q818yescomplemented
460C22×C11#52514yes—
461C22×C11#53914yes—
462C22×C11D4214yes—
463C22×C11#54714yes—
464C22×C11D4×Q814yes—
465C22×C11#55414yes—
466C22×C11C23×D411yescharacteristic
467C22×C11C23×D411yescharacteristic
468C22×C11C23×Q811yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×2−1+411yescharacteristic
473C4×C11—24no—
474C4×C11—24no—
475C4×C11—24no—
476C4×C11—24no—
477C4×C11—24no—
478C4×C11—24no—
479C4×C11—24no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C25C23×C1111yescharacteristic
487C25C23×C1111yescharacteristic
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C23×C1114yes—
492C22×D4—24no—
493C22×D4—24no—
494C22×D4Q8×C1118yescomplemented
495C22×D4C23×C1114yes—
496C23×C4—24no—
497C23×C4—24no—
498C23×C4—24no—
499C23×C4—24no—
500C23×C4—24no—
501C23×C4—24no—
502C23×C4—24no—
503C23×C4—24no—
504C23×C4—24no—
505C23×C4—42no—
506C23×C4—42no—
507C23×C4—42no—
508C23×C4C23×C1111yescharacteristic
509C23×C4C23×C1111yescharacteristic
510C23×C4C23×C1111yescharacteristic
511C23×C4C23×C1111yescharacteristic
512C23×C4C23×C1111yescharacteristic
513C23×C4C23×C1111yescharacteristic
514C23×C4C23×C1114yes—
515C23×C4C23×C1114yes—
516C23×C4C23×C1114yes—
517C23×C4C23×C1114yes—
518C23×C4C23×C1111yescharacteristic
519C23×C4C23×C1111yescharacteristic
520C23×C4C23×C1111yescharacteristic
521C23×C4C23×C1111yescharacteristic
522C23×C4C23×C1111yescharacteristic
523C23×C4C23×C1111yescharacteristic
524C23×C4C23×C1111yescharacteristic
525C22⋊Q8—232no—
526C22⋊Q8—232no—
527C4×D4—232no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—232no—
539C2×C4⋊C4—42no—
540C2×C4⋊C4D4×C1118yescomplemented
541C2×C4⋊C4C23×C1114yes—
542C2×C4⋊C4C23×C1114yes—
543C2×C4⋊C4C23×C1114yes—
544C2×C4⋊C4C23×C1114yes—
545C2×C4⋊C4C23×C1114yes—
546C2×C4⋊C4C23×C1114yes—
547C2×C4⋊C4C23×C1114yes—
548C2×C4⋊C4C23×C1114yes—
549C2×C4⋊C4C23×C1114yes—
550C2×C4⋊C4C23×C1114yes—
551C2×C4⋊C4C23×C1114yes—
552C2×C4⋊C4C23×C1114yes—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4D4×C1118yes—
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×C42—24no—
570C2×C42C23×C1114yes—
571#95C23×C1114yes—
572#95C23×C1114yes—
573#95C23×C1114yes—
574#95C23×C1114yes—
575#95C23×C1114yes—
576#95C23×C1114yes—
577#95C23×C1114yes—
578#95C23×C1114yes—
579C2×C11—28no—
580C2×C11—44no—
581C2×C11#244918yesdirect product factor
582C2×C11C22×C22⋊Q811yescharacteristic
583C2×C11C2×#52511yescharacteristic
584C2×C11C2×#53911yescharacteristic
585C2×C11C2×D4211yescharacteristic
586C2×C11C2×#54711yescharacteristic
587C2×C11C2×D4×Q811yescharacteristic
588C2×C11C2×#55411yescharacteristic
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24C2×D4×C1114yes—
600C24C2×Q8×C1114yes—
601C24C2×Q8×C1114yes—
602C24C11×#4114yes—
603C24C24×C1112yes—
604C24C24×C1112yes—
605C24C24×C1111yescharacteristic
606C2×Q8—28no—
607C2×Q8—28no—
608C2×Q8—44no—
609C2×Q8—416no—
610C2×D4—232no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4C2×Q8×C11116yescomplemented
614C22×C4—232no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—28no—
631C22×C4—28no—
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—28no—
641C22×C4—28no—
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—28no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—416no—
660C22×C4—416no—
661C22×C4—416no—
662C22×C4C2×D4×C1114yes—
663C22×C4C2×D4×C1114yes—
664C22×C4C2×D4×C1114yes—
665C22×C4C2×D4×C1114yes—
666C22×C4C2×D4×C1114yes—
667C22×C4C2×Q8×C1114yes—
668C22×C4C11×#4114yes—
669C22×C4C24×C1112yes—
670C22×C4C24×C1112yes—
671C22×C4C24×C1112yes—
672C22×C4C24×C1112yes—
673C22×C4C24×C1112yes—
674C22×C4C24×C1112yes—
675C22×C4C24×C1112yes—
676C22×C4C24×C1112yes—
677C22×C4C24×C1112yes—
678C22×C4C24×C1112yes—
679C22×C4C24×C1112yes—
680C22×C4C24×C1112yes—
681C22×C4C24×C1112yes—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—28no—
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—44no—
701C22⋊C4C2×D4×C11116yes—
702C42—28no—
703C11C2×#244911yescharacteristic, direct product factor, Sylow
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23C11×C22⋊Q8116yescomplemented
728C23C22×D4×C1114yes—
729C23C22×D4×C1112yes—
730C23C22×D4×C1112yes—
731C23C22×Q8×C1114yes—
732C23C22×Q8×C1114yes—
733C23C22×Q8×C1112yes—
734C23C2×C11×#4114yes—
735C23C2×C11×#4112yes—
736C23C2×C11×#4112yes—
737C23C11×H(5,𝔽2)12yes—
738C23C11×2−1+412yes—
739C23C25×C1111yescharacteristic
740Q8—416no—
741D4—232no—
742C2×C4—232no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
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—416no—
783C2×C4—416no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4C22×D4×C1114yes—
792C2×C4C22×D4×C1114yes—
793C2×C4C22×D4×C1114yes—
794C2×C4C22×D4×C1114yes—
795C2×C4C22×D4×C1114yes—
796C2×C4C22×Q8×C1114yes—
797C2×C4C2×C11×#4114yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—232no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—416no—
813C22C2×C11×C22⋊Q814yes—
814C22C2×C11×C22⋊Q818yescomplemented
815C22C11×#52514yes—
816C22C11×#53914yes—
817C22D42×C1114yes—
818C22C11×#54714yes—
819C22D4×Q8×C1114yes—
820C22C11×#55414yes—
821C22C23×D4×C1111yescharacteristic
822C22C23×D4×C1111yescharacteristic
823C22C23×Q8×C1111yescharacteristic
824C22C22×C11×#4111yescharacteristic
825C22C22×C11×#4111yescharacteristic
826C22C2×C11×H(5,𝔽2)11yescharacteristic
827C22C2×C11×2−1+411yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—24no—
834C4—24no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C2—28no—
842C2—44no—
843C2C11×#244918yesdirect product factor
844C2C22×C11×C22⋊Q811yescharacteristic
845C2C2×C11×#52511yescharacteristic
846C2C2×C11×#53911yescharacteristic
847C2C2×D42×C1111yescharacteristic
848C2C2×C11×#54711yescharacteristic
849C2C2×D4×Q8×C1111yescharacteristic
850C2C2×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×#2449C2direct (N × H)
6. C2×C11×#399C2semidirect
7. C2×C11×#398C2semidirect
8. C2×C11×#396C2semidirect
9. C2×C11×#395C2semidirect
10. C2×C11×#389C2semidirect
11. C2×C11×#387C2semidirect
14. C2×C11×#385C2semidirect
15. C2×C11×#385C2semidirect
16. C2×C11×#385C2semidirect
25. C2×C11×C22⋊Q8C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
42. C22×C11×C4⋊C4C22semidirect
52. C11×#399C22semidirect
53. C11×#398C22semidirect
54. C11×#396C22semidirect
55. C11×#395C22semidirect
56. C11×#389C22semidirect
57. C11×#387C22semidirect
60. C11×#385C22semidirect
61. C11×#385C22semidirect
62. C11×#385C22semidirect
79. C22×D4×C11Q8semidirect
125. C2×C11×C4⋊C4D4semidirect
164. C2×#2449C11direct (N × H)
189. C2×D4×C11C2×Q8semidirect
269. C11×C4⋊C4C2×D4semidirect
279. C22×C22⋊Q8C2×C11semidirect
280. C22×C22⋊Q8C2×C11semidirect
282. C23×C4⋊C4C2×C11semidirect
283. #2449C2×C11direct (N × H)
284. C2×#399C2×C11semidirect
285. C2×#398C2×C11semidirect
286. C2×#396C2×C11semidirect
287. C2×#395C2×C11semidirect
288. C2×#389C2×C11semidirect
289. C2×#387C2×C11semidirect
292. C2×#385C2×C11semidirect
293. C2×#385C2×C11semidirect
294. C2×#385C2×C11semidirect
318. C23×C11C22⋊Q8semidirect
397. C2×C22⋊Q8C22×C11semidirect
398. C2×C22⋊Q8C22×C11semidirect
414. C22×C4⋊C4C22×C11semidirect
424. #399C22×C11semidirect
425. #398C22×C11semidirect
426. #396C22×C11semidirect
427. #395C22×C11semidirect
428. #389C22×C11semidirect
429. #387C22×C11semidirect
432. #385C22×C11semidirect
433. #385C22×C11semidirect
434. #385C22×C11semidirect
459. C22×C11C2×C22⋊Q8semidirect
494. C22×D4Q8×C11semidirect
540. C2×C4⋊C4D4×C11semidirect
581. C2×C11#2449direct (N × H)
613. C2×D4C2×Q8×C11semidirect
693. C4⋊C4C2×D4×C11semidirect
703. C11C2×#2449direct (N × H)
727. C23C11×C22⋊Q8semidirect
814. C22C2×C11×C22⋊Q8semidirect
843. C2C11×#2449direct (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×#24492
C2×C11×#3992
C2×C11×#3982
C2×C11×#3962
C2×C11×#3952
C2×C11×#3892
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×#244911