Finite Group Databasebeta

← C2×C11×#3351 #14638437

Subgroups — C2×C11×#3351 #14638437

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C2×C11×#552C211yesmaximal, characteristic, complemented
3C11×#3351C2116yesmaximal, direct product factor
4C2×C11×#499C211yesmaximal, characteristic, complemented
5C2×C11×#481C211yesmaximal, characteristic, complemented
6C2×C11×#485C211yesmaximal, characteristic, complemented
7C2×C11×#482C211yesmaximal, characteristic, complemented
8C2×C11×#483C211yesmaximal, characteristic, complemented
9C2×C11×#479C211yesmaximal, characteristic, complemented
10C2×C11×#478C211yesmaximal, characteristic, complemented
11C2×C11×#468C211yesmaximal, characteristic, complemented
12C2×C11×#468C211yesmaximal, characteristic, complemented
13C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
14C2×C11×#436C211yesmaximal, characteristic, complemented
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C2×C11×#428C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C11×#553—24no—
21C11×#553C2218yes—
22C11×#552—24no—
23C11×#552C2218yescomplemented
24C2×C11×#126—21no—
25C2×C11×#126—21no—
26C2×C11×#125—21no—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#125C2211yescharacteristic
29C2×C11×#123—21no—
30C2×C11×#123—21no—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×C22⋊Q8C2211yescharacteristic
33C2×C11×#121—21no—
34C2×C11×#121C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic
36C2×C4×Q8×C11C2211yescharacteristic
37C2×C4×D4×C11—21no—
38C2×C4×D4×C11C2211yescharacteristic
39C2×C4×D4×C11C2211yescharacteristic
40C2×C11×#117—21no—
41C2×C11×#117C2211yescharacteristic
42C2×C11×#117C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#499C2218yescomplemented
46C11×#485C2218yescomplemented
47C11×#483C2218yescomplemented
48C11×#482C2218yescomplemented
49C11×#481C2218yescomplemented
50C11×#479C2218yescomplemented
51C11×#478C2218yescomplemented
52C11×#468C2218yescomplemented
53C11×#468C2218yescomplemented
54C4×C11×SD16C2218yescomplemented
55C11×#436C2218yescomplemented
56C11×#428C2218yescomplemented
57C11×#428C2218yescomplemented
58C2×C11×#107C2211yescharacteristic
59C2×C11×#107C2211yescharacteristic
60C2×C11×#107C2211yescharacteristic
61C2×C11×#107C2211yescharacteristic
62C2×C11×#106C2211yescharacteristic
63C2×C11×#106C2211yescharacteristic
64C2×C11×#106C2211yescharacteristic
65C2×C11×#106C2211yescharacteristic
66C2×C11×#106C2211yescharacteristic
67C2×C11×C4⋊C8C2211yescharacteristic
68C2×C11×#103C2211yescharacteristic
69C2×C11×#103C2211yescharacteristic
70C2×C11×#103C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2211yescharacteristic
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic
76C2×C4×C8×C11C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C2×C11×SD16—24no—
88C2×C11×SD16C2314yes—
89C2×C11×M16—24no—
90C2×C11×M16—24no—
91C2×C11×M16C2314yes—
92C2×C11×M16C2314yes—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#126—28no—
98C11×#126—28no—
99C11×#125—28no—
100C11×#125—22no—
101C11×#125—22no—
102C11×#125C2314yes—
103C11×#125C2314yes—
104C11×#123—28no—
105C11×#123—28no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8C2314yes—
109C11×C22⋊Q8C2314yes—
110C11×#121—28no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121C2314yes—
114C11×#121C2314yes—
115C4×Q8×C11—22no—
116C4×Q8×C11C2314yes—
117C4×D4×C11—28no—
118C4×D4×C11—22no—
119C4×D4×C11D414yes—
120C4×D4×C11C2314yes—
121C4×D4×C11C2314yes—
122C11×#117—22no—
123C11×#117—22no—
124C11×#117—28no—
125C11×#117C2314yes—
126C11×#117C2314yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—22no—
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2314yes—
144C2×C11×C4⋊C4C2314yes—
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⋊C4D411yescharacteristic
155C2×C11×C22⋊C4D411yescharacteristic
156C2×C42×C11—21no—
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11C2311yescharacteristic
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#107C2314yes—
164C11×#106C2314yes—
165C11×#106C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×#106C2314yes—
169C11×C4⋊C8C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173C11×#102C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177C11×C22⋊C8C2314yes—
178C4×C8×C11C2314yes—
179C2×#3351C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—42no—
193C2×D4×C11—44no—
194C2×D4×C11—82no—
195C2×D4×C11C2×D414yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—44no—
212C22×C4×C11—82no—
213C22×C4×C11—82no—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C11×SD16—28no—
224C11×M16—28no—
225C11×M16—28no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11#4114yes—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
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—24no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C2×D414yes—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C11×C22⋊C4—24no—
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⋊C4C2×D414yes—
264C11×C22⋊C4C2×D414yes—
265C42×C11—24no—
266C42×C11—24no—
267C42×C11—24no—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270C2×#553C2×C1111yescharacteristic
271C2×#552C2×C1111yescharacteristic, complemented
272#3351C2×C11116yesdirect product factor
273C2×#499C2×C1111yescharacteristic, complemented
274C2×#481C2×C1111yescharacteristic, complemented
275C2×#485C2×C1111yescharacteristic, complemented
276C2×#482C2×C1111yescharacteristic, complemented
277C2×#483C2×C1111yescharacteristic, complemented
278C2×#479C2×C1111yescharacteristic, complemented
279C2×#478C2×C1111yescharacteristic, complemented
280C2×#468C2×C1111yescharacteristic, complemented
281C2×#468C2×C1111yescharacteristic, complemented
282C2×C4×SD16C2×C1111yescharacteristic, complemented
283C2×#436C2×C1111yescharacteristic, complemented
284C2×#428C2×C1111yescharacteristic, complemented
285C2×#428C2×C1111yescharacteristic, complemented
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11C22×D412yes—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—42no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—44no—
305D4×C11—48no—
306D4×C11—42no—
307D4×C11—84no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—24no—
313C2×C4×C11—24no—
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—48no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—84no—
334C2×C4×C11—84no—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4112yes—
341C2×C4×C112−1+412yes—
342C2×C4×C11C2511yescharacteristic
343C8×C11—22no—
344C8×C11—22no—
345C8×C11—22no—
346C8×C11C2×#4114yes—
347C22×SD16C22×C1111yescharacteristic
348C22×M16C22×C1111yescharacteristic
349C22×M16C22×C1111yescharacteristic
350#553—24no—
351#553C22×C1118yes—
352#552—24no—
353#552C22×C1118yescomplemented
354C2×#126—21no—
355C2×#126—21no—
356C2×#125—21no—
357C2×#125C22×C1111yescharacteristic
358C2×#125C22×C1111yescharacteristic
359C2×#123—21no—
360C2×#123—21no—
361C2×C22⋊Q8C22×C1111yescharacteristic
362C2×C22⋊Q8C22×C1111yescharacteristic
363C2×#121—21no—
364C2×#121C22×C1111yescharacteristic
365C2×#121C22×C1111yescharacteristic
366C2×C4×Q8C22×C1111yescharacteristic
367C2×C4×D4—21no—
368C2×C4×D4C22×C1111yescharacteristic
369C2×C4×D4C22×C1111yescharacteristic
370C2×#117—21no—
371C2×#117C22×C1111yescharacteristic
372C2×#117C22×C1111yescharacteristic
373C22×C4⋊C4C22×C1111yescharacteristic
374C22×C4⋊C4C22×C1111yescharacteristic
375#499C22×C1118yescomplemented
376#485C22×C1118yescomplemented
377#483C22×C1118yescomplemented
378#482C22×C1118yescomplemented
379#481C22×C1118yescomplemented
380#479C22×C1118yescomplemented
381#478C22×C1118yescomplemented
382#468C22×C1118yescomplemented
383#468C22×C1118yescomplemented
384C4×SD16C22×C1118yescomplemented
385#436C22×C1118yescomplemented
386#428C22×C1118yescomplemented
387#428C22×C1118yescomplemented
388C2×#107C22×C1111yescharacteristic
389C2×#107C22×C1111yescharacteristic
390C2×#107C22×C1111yescharacteristic
391C2×#107C22×C1111yescharacteristic
392C2×#106C22×C1111yescharacteristic
393C2×#106C22×C1111yescharacteristic
394C2×#106C22×C1111yescharacteristic
395C2×#106C22×C1111yescharacteristic
396C2×#106C22×C1111yescharacteristic
397C2×C4⋊C8C22×C1111yescharacteristic
398C2×#103C22×C1111yescharacteristic
399C2×#103C22×C1111yescharacteristic
400C2×#103C22×C1111yescharacteristic
401C2×#102C22×C1111yescharacteristic
402C2×#102C22×C1111yescharacteristic
403C2×#102C22×C1111yescharacteristic
404C2×C22⋊C8C22×C1111yescharacteristic
405C2×C22⋊C8C22×C1111yescharacteristic
406C2×C4×C8C22×C1111yescharacteristic
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—84no—
419C22×C11#54712yes—
420C22×C11#57512yes—
421C22×C11#57712yes—
422C22×C11C23×D411yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11#54712yes—
435C4×C11C22×#4111yescharacteristic
436C4×C11C2×2−1+411yescharacteristic
437C22×Q8C23×C1111yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4D4×C1111yescharacteristic
441C22×D4C23×C1111yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—21no—
445C23×C4C23×C1111yescharacteristic
446C23×C4C23×C1111yescharacteristic
447C2×SD16—24no—
448C2×SD16C23×C1114yes—
449C2×M16—24no—
450C2×M16—24no—
451C2×M16C23×C1114yes—
452C2×M16C23×C1114yes—
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457#126—28no—
458#126—28no—
459#125—28no—
460#125—22no—
461#125—22no—
462#125C23×C1114yes—
463#125C23×C1114yes—
464#123—28no—
465#123—28no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8C23×C1114yes—
469C22⋊Q8C23×C1114yes—
470#121—28no—
471#121—22no—
472#121—22no—
473#121C23×C1114yes—
474#121C23×C1114yes—
475C4×Q8—22no—
476C4×Q8C23×C1114yes—
477C4×D4—28no—
478C4×D4—22no—
479C4×D4D4×C1114yes—
480C4×D4C23×C1114yes—
481C4×D4C23×C1114yes—
482#117—22no—
483#117—22no—
484#117—28no—
485#117C23×C1114yes—
486#117C23×C1114yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4D4×C1111yescharacteristic
499C2×C4⋊C4C23×C1111yescharacteristic
500C2×C4⋊C4C23×C1111yescharacteristic
501C2×C4⋊C4C23×C1111yescharacteristic
502C2×C4⋊C4C23×C1111yescharacteristic
503C2×C4⋊C4C23×C1114yes—
504C2×C4⋊C4C23×C1114yes—
505C2×C4⋊C4C23×C1111yescharacteristic
506C2×C4⋊C4C23×C1111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4D4×C1111yescharacteristic
515C2×C22⋊C4D4×C1111yescharacteristic
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C23×C1111yescharacteristic
520#107C23×C1114yes—
521#107C23×C1114yes—
522#107C23×C1114yes—
523#107C23×C1114yes—
524#106C23×C1114yes—
525#106C23×C1114yes—
526#106C23×C1114yes—
527#106C23×C1114yes—
528#106C23×C1114yes—
529C4⋊C8C23×C1114yes—
530#103C23×C1114yes—
531#103C23×C1114yes—
532#103C23×C1114yes—
533#102C23×C1114yes—
534#102C23×C1114yes—
535#102C23×C1114yes—
536C22⋊C8C23×C1114yes—
537C22⋊C8C23×C1114yes—
538C4×C8C23×C1114yes—
539C2×C11—42no—
540C2×C11—42no—
541C2×C11—82no—
542C2×C11#335114yesdirect product factor
543C2×C11C2×#54711yescharacteristic
544C2×C11C2×#57511yescharacteristic
545C2×C11C2×#57711yescharacteristic
546C24—21no—
547C24C2×D4×C1111yescharacteristic
548C24C2×D4×C1111yescharacteristic
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8C24×C1112yes—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—42no—
559C2×D4—44no—
560C2×D4—82no—
561C2×D4C2×D4×C1114yes—
562C2×D4C24×C1112yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—44no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4C2×D4×C1111yescharacteristic
581C22×C4C2×D4×C1111yescharacteristic
582C22×C4C2×D4×C1111yescharacteristic
583C22×C4C2×D4×C1111yescharacteristic
584C22×C4C2×D4×C1112yes—
585C22×C4C2×D4×C1112yes—
586C22×C4C24×C1112yes—
587C22×C4C24×C1112yes—
588C22×C4C24×C1111yescharacteristic
589SD16—28no—
590M16—28no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8C11×#4114yes—
596C2×C8C24×C1112yes—
597C2×C8C24×C1112yes—
598C2×C8C24×C1112yes—
599C2×C8C24×C1112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4C2×D4×C1114yes—
616C4⋊C4C24×C1112yes—
617C4⋊C4C24×C1112yes—
618C4⋊C4C24×C1112yes—
619C4⋊C4C24×C1112yes—
620C4⋊C4C24×C1112yes—
621C4⋊C4C24×C1112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4C2×D4×C1114yes—
630C22⋊C4C2×D4×C1114yes—
631C42—24no—
632C42—24no—
633C42—24no—
634C42C2×D4×C1112yes—
635C42C24×C1112yes—
636C11C2×#335111yescharacteristic, direct product factor, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×D4×C1112yes—
648C23C22×D4×C1112yes—
649C23C22×D4×C1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—44no—
656D4—48no—
657D4—42no—
658D4—84no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
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—48no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4C22×D4×C1112yes—
687C2×C4C22×D4×C1112yes—
688C2×C4C22×D4×C1112yes—
689C2×C4C22×D4×C1112yes—
690C2×C4C22×D4×C1111yescharacteristic
691C2×C4C2×C11×#4112yes—
692C2×C4C11×2−1+412yes—
693C2×C4C25×C1111yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×C11×#4114yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22C11×#54712yes—
711C22C11×#57512yes—
712C22C11×#57712yes—
713C22C23×D4×C1111yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4C11×#54712yes—
726C4C22×C11×#4111yescharacteristic
727C4C2×C11×2−1+411yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2C11×#335114yesdirect product factor
732C2C2×C11×#54711yescharacteristic
733C2C2×C11×#57511yescharacteristic
734C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#552C2semidirect
3. C11×#3351C2direct (N × H)
4. C2×C11×#499C2semidirect
5. C2×C11×#481C2semidirect
6. C2×C11×#485C2semidirect
7. C2×C11×#482C2semidirect
8. C2×C11×#483C2semidirect
9. C2×C11×#479C2semidirect
10. C2×C11×#478C2semidirect
11. C2×C11×#468C2semidirect
12. C2×C11×#468C2semidirect
13. C2×C4×C11×SD16C2semidirect
14. C2×C11×#436C2semidirect
15. C2×C11×#428C2semidirect
16. C2×C11×#428C2semidirect
23. C11×#552C22semidirect
45. C11×#499C22semidirect
46. C11×#485C22semidirect
47. C11×#483C22semidirect
48. C11×#482C22semidirect
49. C11×#481C22semidirect
50. C11×#479C22semidirect
51. C11×#478C22semidirect
52. C11×#468C22semidirect
53. C11×#468C22semidirect
54. C4×C11×SD16C22semidirect
55. C11×#436C22semidirect
56. C11×#428C22semidirect
57. C11×#428C22semidirect
179. C2×#3351C11direct (N × H)
271. C2×#552C2×C11semidirect
272. #3351C2×C11direct (N × H)
273. C2×#499C2×C11semidirect
274. C2×#481C2×C11semidirect
275. C2×#485C2×C11semidirect
276. C2×#482C2×C11semidirect
277. C2×#483C2×C11semidirect
278. C2×#479C2×C11semidirect
279. C2×#478C2×C11semidirect
280. C2×#468C2×C11semidirect
281. C2×#468C2×C11semidirect
282. C2×C4×SD16C2×C11semidirect
283. C2×#436C2×C11semidirect
284. C2×#428C2×C11semidirect
285. C2×#428C2×C11semidirect
353. #552C22×C11semidirect
375. #499C22×C11semidirect
376. #485C22×C11semidirect
377. #483C22×C11semidirect
378. #482C22×C11semidirect
379. #481C22×C11semidirect
380. #479C22×C11semidirect
381. #478C22×C11semidirect
382. #468C22×C11semidirect
383. #468C22×C11semidirect
384. C4×SD16C22×C11semidirect
385. #436C22×C11semidirect
386. #428C22×C11semidirect
387. #428C22×C11semidirect
542. C2×C11#3351direct (N × H)
636. C11C2×#3351direct (N × H)
731. C2C11×#3351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#5522
C11×#33512
C2×C11×#4992
C2×C11×#4812
C2×C11×#4852
C2×C11×#4822
C2×C11×#4832
C2×C11×#4792
C2×C11×#4782
C2×C11×#4682
C2×C4×C11×SD162
C2×C11×#4362
C2×C11×#4282
C2×#335111