Finite Group Databasebeta

← C2×C11×#3370 #14638505

Subgroups — C2×C11×#3370 #14638505

Order 2816.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic, complemented
2C2×C11×#554C211yesmaximal, characteristic, complemented
3C11×#3370C2116yesmaximal, direct product factor
4C2×C11×#490C211yesmaximal, characteristic, complemented
5C2×C11×#489C211yesmaximal, characteristic, complemented
6C2×C11×#488C211yesmaximal, characteristic, complemented
7C2×C11×#479C211yesmaximal, characteristic, complemented
8C2×C11×#478C211yesmaximal, characteristic, complemented
9C2×C11×#474C211yesmaximal, characteristic, complemented
10C2×C11×#463C211yesmaximal, characteristic, complemented
11C2×C11×#463C211yesmaximal, characteristic, complemented
12C2×C11×#459C211yesmaximal, characteristic
13C2×C11×#446C211yesmaximal, characteristic, complemented
14C2×C11×#442C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic, complemented
16C2×C4×C11×D8C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C11×#559—24no—
21C11×#559C2218yescomplemented
22C11×#554—24no—
23C11×#554C2218yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C2×C11×#124—21no—
29C2×C11×#124C2211yescharacteristic
30C2×C11×#124C2211yescharacteristic
31C2×C11×#123—21no—
32C2×C11×#123—21no—
33C2×C11×C22⋊Q8—21no—
34C2×C11×C22⋊Q8—21no—
35C2×C11×C22⋊Q8—21no—
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×D4×C11—21no—
39C2×C4×D4×C11C2211yescharacteristic
40C2×C4×D4×C11C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2211yescharacteristic
43C2×C4×D4×C11C2211yescharacteristic
44C22×C11×C4⋊C4—21no—
45C11×#490C2218yescomplemented
46C11×#489C2218yescomplemented
47C11×#488C2218yescomplemented
48C11×#479C2218yescomplemented
49C11×#478C2218yescomplemented
50C11×#474C2218yescomplemented
51C11×#463C2218yescomplemented
52C11×#463C2218yescomplemented
53C11×#459C2218yes—
54C11×#446C2218yescomplemented
55C11×#442C2218yescomplemented
56C11×#440C2218yescomplemented
57C4×C11×D8C2218yescomplemented
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#106C2211yescharacteristic
61C2×C11×C4⋊C8C2211yescharacteristic
62C2×C11×C4⋊C8C2211yescharacteristic
63C2×C11×C4⋊C8C2211yescharacteristic
64C2×C11×#103C2211yescharacteristic
65C2×C11×#103C2211yescharacteristic
66C2×C11×#103C2211yescharacteristic
67C2×C11×#102C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2211yescharacteristic
74C2×C11×#97C2211yescharacteristic
75C2×C11×#97C2211yescharacteristic
76C2×C4×C8×C11C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11D411yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C2×C11×SD16—24no—
91C2×C11×SD16C2314yes—
92C2×C11×D8—24no—
93C2×C11×D8—24no—
94C2×C11×D8C2314yes—
95C2×C11×D8C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8C2314yes—
102C11×#127—22no—
103C11×#127C2314yes—
104C11×#125—22no—
105C11×#125—22no—
106C11×#125C2314yes—
107C11×#125C2314yes—
108C11×#124—28no—
109C11×#124—22no—
110C11×#124—22no—
111C11×#124C2314yes—
112C11×#124C2314yes—
113C11×#123—28no—
114C11×#123—28no—
115C11×C22⋊Q8—28no—
116C11×C22⋊Q8—28no—
117C11×C22⋊Q8—28no—
118C4×Q8×C11—22no—
119C4×Q8×C11D414yes—
120C4×Q8×C11C2314yes—
121C4×Q8×C11C2314yes—
122C4×D4×C11—28no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11C2314yes—
129C4×D4×C11C2314yes—
130C4×D4×C11C2314yes—
131C4×D4×C11C2314yes—
132C4×D4×C11C2314yes—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—28no—
140C2×C11×C4⋊C4D411yescharacteristic
141C2×C11×C4⋊C4D411yescharacteristic
142C2×C11×C4⋊C4D411yescharacteristic
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4—21no—
148C2×C11×C22⋊C4—21no—
149C2×C11×C22⋊C4—21no—
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—21no—
152C2×C11×C22⋊C4—21no—
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C42×C11—21no—
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#106C2314yes—
163C11×C4⋊C8C2314yes—
164C11×C4⋊C8C2314yes—
165C11×C4⋊C8C2314yes—
166C11×#103C2314yes—
167C11×#103C2314yes—
168C11×#103C2314yes—
169C11×#102C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×#97C2314yes—
177C11×#97C2314yes—
178C4×C8×C11C2314yes—
179C2×#3370C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C2×Q8×C11—82no—
189C2×Q8×C11C2×D414yes—
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—44no—
202C2×D4×C11—82no—
203C2×D4×C11#4114yes—
204C2×D4×C11C2412yes—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
217C22×C4×C11—44no—
218C22×C4×C11—82no—
219C22×C4×C11—82no—
220C22×C4×C11—82no—
221C22×C4×C11—82no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2411yescharacteristic
229C11×SD16—28no—
230C11×D8—28no—
231C11×D8—28no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11—22no—
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C2×C8×C11C2412yes—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2×D414yes—
251C11×C4⋊C4C2×D414yes—
252C11×C4⋊C4C2×D414yes—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C42×C11—24no—
267C42×C11C2×D412yes—
268C42×C11C2×D412yes—
269C42×C11C2×D412yes—
270C42×C11C2412yes—
271C42×C11C2412yes—
272C42×C11C2412yes—
273C2×#559C2×C1111yescharacteristic, complemented
274C2×#554C2×C1111yescharacteristic, complemented
275#3370C2×C11116yesdirect product factor
276C2×#490C2×C1111yescharacteristic, complemented
277C2×#489C2×C1111yescharacteristic, complemented
278C2×#488C2×C1111yescharacteristic, complemented
279C2×#479C2×C1111yescharacteristic, complemented
280C2×#478C2×C1111yescharacteristic, complemented
281C2×#474C2×C1111yescharacteristic, complemented
282C2×#463C2×C1111yescharacteristic, complemented
283C2×#463C2×C1111yescharacteristic, complemented
284C2×#459C2×C1111yescharacteristic
285C2×#446C2×C1111yescharacteristic, complemented
286C2×#442C2×C1111yescharacteristic, complemented
287C2×#440C2×C1111yescharacteristic, complemented
288C2×C4×D8C2×C1111yescharacteristic, complemented
289C23×C11—24no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—44no—
305Q8×C11—42no—
306Q8×C11—84no—
307D4×C11—24no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—48no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—84no—
317D4×C11C2×#4114yes—
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—22no—
329C2×C4×C11—48no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—84no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11—84no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C112−1+412yes—
348C2×C4×C11C2511yescharacteristic
349C8×C11—22no—
350C8×C11—22no—
351C8×C11—22no—
352C8×C11—22no—
353C22×SD16C22×C1111yescharacteristic
354C22×D8C22×C1111yescharacteristic
355C22×D8C22×C1111yescharacteristic
356#559—24no—
357#559C22×C1118yescomplemented
358#554—24no—
359#554C22×C1118yescomplemented
360C2×C4⋊Q8C22×C1111yescharacteristic
361C2×#127C22×C1111yescharacteristic
362C2×#125C22×C1111yescharacteristic
363C2×#125C22×C1111yescharacteristic
364C2×#124—21no—
365C2×#124C22×C1111yescharacteristic
366C2×#124C22×C1111yescharacteristic
367C2×#123—21no—
368C2×#123—21no—
369C2×C22⋊Q8—21no—
370C2×C22⋊Q8—21no—
371C2×C22⋊Q8—21no—
372C2×C4×Q8C22×C1111yescharacteristic
373C2×C4×Q8C22×C1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C22×C1111yescharacteristic
376C2×C4×D4C22×C1111yescharacteristic
377C2×C4×D4C22×C1111yescharacteristic
378C2×C4×D4C22×C1111yescharacteristic
379C2×C4×D4C22×C1111yescharacteristic
380C22×C4⋊C4—21no—
381#490C22×C1118yescomplemented
382#489C22×C1118yescomplemented
383#488C22×C1118yescomplemented
384#479C22×C1118yescomplemented
385#478C22×C1118yescomplemented
386#474C22×C1118yescomplemented
387#463C22×C1118yescomplemented
388#463C22×C1118yescomplemented
389#459C22×C1118yes—
390#446C22×C1118yescomplemented
391#442C22×C1118yescomplemented
392#440C22×C1118yescomplemented
393C4×D8C22×C1118yescomplemented
394C2×#107C22×C1111yescharacteristic
395C2×#107C22×C1111yescharacteristic
396C2×#106C22×C1111yescharacteristic
397C2×C4⋊C8C22×C1111yescharacteristic
398C2×C4⋊C8C22×C1111yescharacteristic
399C2×C4⋊C8C22×C1111yescharacteristic
400C2×#103C22×C1111yescharacteristic
401C2×#103C22×C1111yescharacteristic
402C2×#103C22×C1111yescharacteristic
403C2×#102C22×C1111yescharacteristic
404C2×#102C22×C1111yescharacteristic
405C2×#102C22×C1111yescharacteristic
406C2×#102C22×C1111yescharacteristic
407C2×#102C22×C1111yescharacteristic
408C2×#102C22×C1111yescharacteristic
409C2×#102C22×C1111yescharacteristic
410C2×#97C22×C1111yescharacteristic
411C2×#97C22×C1111yescharacteristic
412C2×C4×C8C22×C1111yescharacteristic
413C22×C11—24no—
414C22×C11—48no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11—84no—
425C22×C11#54812yes—
426C22×C11#57512yes—
427C22×C11#57612yes—
428C22×C11C23×D411yescharacteristic
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11#54812yes—
441C4×C11C22×#4111yescharacteristic
442C4×C11C2×2−1+411yescharacteristic
443C22×Q8—21no—
444C22×Q8D4×C1111yescharacteristic
445C22×Q8C23×C1111yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C23×C1111yescharacteristic
449C22×D4C23×C1111yescharacteristic
450C22×D4C23×C1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C2×SD16—24no—
457C2×SD16C23×C1114yes—
458C2×D8—24no—
459C2×D8—24no—
460C2×D8C23×C1114yes—
461C2×D8C23×C1114yes—
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1111yescharacteristic
464C22×C8C23×C1111yescharacteristic
465C22×C8C23×C1111yescharacteristic
466C4⋊Q8—22no—
467C4⋊Q8C23×C1114yes—
468#127—22no—
469#127C23×C1114yes—
470#125—22no—
471#125—22no—
472#125C23×C1114yes—
473#125C23×C1114yes—
474#124—28no—
475#124—22no—
476#124—22no—
477#124C23×C1114yes—
478#124C23×C1114yes—
479#123—28no—
480#123—28no—
481C22⋊Q8—28no—
482C22⋊Q8—28no—
483C22⋊Q8—28no—
484C4×Q8—22no—
485C4×Q8D4×C1114yes—
486C4×Q8C23×C1114yes—
487C4×Q8C23×C1114yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4C23×C1114yes—
495C4×D4C23×C1114yes—
496C4×D4C23×C1114yes—
497C4×D4C23×C1114yes—
498C4×D4C23×C1114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4D4×C1111yescharacteristic
507C2×C4⋊C4D4×C1111yescharacteristic
508C2×C4⋊C4D4×C1111yescharacteristic
509C2×C4⋊C4C23×C1111yescharacteristic
510C2×C4⋊C4C23×C1111yescharacteristic
511C2×C4⋊C4C23×C1111yescharacteristic
512C2×C4⋊C4C23×C1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C42—21no—
523C2×C42C23×C1111yescharacteristic
524C2×C42C23×C1111yescharacteristic
525C2×C42C23×C1111yescharacteristic
526#107C23×C1114yes—
527#107C23×C1114yes—
528#106C23×C1114yes—
529C4⋊C8C23×C1114yes—
530C4⋊C8C23×C1114yes—
531C4⋊C8C23×C1114yes—
532#103C23×C1114yes—
533#103C23×C1114yes—
534#103C23×C1114yes—
535#102C23×C1114yes—
536#102C23×C1114yes—
537#102C23×C1114yes—
538#102C23×C1114yes—
539#102C23×C1114yes—
540#102C23×C1114yes—
541#102C23×C1114yes—
542#97C23×C1114yes—
543#97C23×C1114yes—
544C4×C8C23×C1114yes—
545C2×C11—44no—
546C2×C11—82no—
547C2×C11—82no—
548C2×C11#337014yesdirect product factor
549C2×C11C2×#54811yescharacteristic
550C2×C11C2×#57511yescharacteristic
551C2×C11C2×#57611yescharacteristic
552C24—21no—
553C24—21no—
554C24—21no—
555C2×Q8—21no—
556C2×Q8—24no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—82no—
561C2×Q8C2×D4×C1114yes—
562C2×Q8C24×C1112yes—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4C11×#4114yes—
576C2×D4C24×C1112yes—
577C2×D4C24×C1112yes—
578C2×D4C24×C1112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—44no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4C2×D4×C1111yescharacteristic
595C22×C4C2×D4×C1111yescharacteristic
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1111yescharacteristic
600C22×C4C24×C1111yescharacteristic
601SD16—28no—
602D8—28no—
603D8—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8C24×C1112yes—
609C2×C8C24×C1112yes—
610C2×C8C24×C1112yes—
611C2×C8C24×C1112yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4C2×D4×C1114yes—
623C4⋊C4C2×D4×C1114yes—
624C4⋊C4C2×D4×C1114yes—
625C4⋊C4C24×C1112yes—
626C4⋊C4C24×C1112yes—
627C4⋊C4C24×C1112yes—
628C4⋊C4C24×C1112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C42—24no—
639C42C2×D4×C1112yes—
640C42C2×D4×C1112yes—
641C42C2×D4×C1112yes—
642C42C24×C1112yes—
643C42C24×C1112yes—
644C42C24×C1112yes—
645C11C2×#337011yescharacteristic, direct product factor, Sylow
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C22×D4×C1111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—84no—
664D4—24no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—42no—
672D4—42no—
673D4—84no—
674D4C2×C11×#4114yes—
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C22×D4×C1112yes—
697C2×C4C22×D4×C1112yes—
698C2×C4C22×D4×C1112yes—
699C2×C4C22×D4×C1112yes—
700C2×C4C22×D4×C1112yes—
701C2×C4C22×D4×C1112yes—
702C2×C4C22×D4×C1111yescharacteristic
703C2×C4C2×C11×#4112yes—
704C2×C4C11×2−1+412yes—
705C2×C4C25×C1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22—84no—
722C22C11×#54812yes—
723C22C11×#57512yes—
724C22C11×#57612yes—
725C22C23×D4×C1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4C11×#54812yes—
738C4C22×C11×#4111yescharacteristic
739C4C2×C11×2−1+411yescharacteristic
740C2—44no—
741C2—82no—
742C2—82no—
743C2C11×#337014yesdirect product factor
744C2C2×C11×#54811yescharacteristic
745C2C2×C11×#57511yescharacteristic
746C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#559C2semidirect
2. C2×C11×#554C2semidirect
3. C11×#3370C2direct (N × H)
4. C2×C11×#490C2semidirect
5. C2×C11×#489C2semidirect
6. C2×C11×#488C2semidirect
7. C2×C11×#479C2semidirect
8. C2×C11×#478C2semidirect
9. C2×C11×#474C2semidirect
10. C2×C11×#463C2semidirect
11. C2×C11×#463C2semidirect
13. C2×C11×#446C2semidirect
14. C2×C11×#442C2semidirect
15. C2×C11×#440C2semidirect
16. C2×C4×C11×D8C2semidirect
21. C11×#559C22semidirect
23. C11×#554C22semidirect
45. C11×#490C22semidirect
46. C11×#489C22semidirect
47. C11×#488C22semidirect
48. C11×#479C22semidirect
49. C11×#478C22semidirect
50. C11×#474C22semidirect
51. C11×#463C22semidirect
52. C11×#463C22semidirect
54. C11×#446C22semidirect
55. C11×#442C22semidirect
56. C11×#440C22semidirect
57. C4×C11×D8C22semidirect
179. C2×#3370C11direct (N × H)
273. C2×#559C2×C11semidirect
274. C2×#554C2×C11semidirect
275. #3370C2×C11direct (N × H)
276. C2×#490C2×C11semidirect
277. C2×#489C2×C11semidirect
278. C2×#488C2×C11semidirect
279. C2×#479C2×C11semidirect
280. C2×#478C2×C11semidirect
281. C2×#474C2×C11semidirect
282. C2×#463C2×C11semidirect
283. C2×#463C2×C11semidirect
285. C2×#446C2×C11semidirect
286. C2×#442C2×C11semidirect
287. C2×#440C2×C11semidirect
288. C2×C4×D8C2×C11semidirect
357. #559C22×C11semidirect
359. #554C22×C11semidirect
381. #490C22×C11semidirect
382. #489C22×C11semidirect
383. #488C22×C11semidirect
384. #479C22×C11semidirect
385. #478C22×C11semidirect
386. #474C22×C11semidirect
387. #463C22×C11semidirect
388. #463C22×C11semidirect
390. #446C22×C11semidirect
391. #442C22×C11semidirect
392. #440C22×C11semidirect
393. C4×D8C22×C11semidirect
548. C2×C11#3370direct (N × H)
645. C11C2×#3370direct (N × H)
743. C2C11×#3370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C2×C11×#5542
C11×#33702
C2×C11×#4902
C2×C11×#4892
C2×C11×#4882
C2×C11×#4792
C2×C11×#4782
C2×C11×#4742
C2×C11×#4632
C2×C11×#4592
C2×C11×#4462
C2×C11×#4422
C2×C11×#4402
C2×C4×C11×D82
C2×#337011