Finite Group Databasebeta

← C2×C11×#3296 #14638307

Subgroups — C2×C11×#3296 #14638307

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#546C211yesmaximal, characteristic
3C11×#3296C2116yesmaximal, direct product factor
4C2×C11×#488C211yesmaximal, characteristic, complemented
5C2×C11×#482C211yesmaximal, characteristic, complemented
6C2×C11×#483C211yesmaximal, characteristic, complemented
7C2×C11×#478C211yesmaximal, characteristic, complemented
8C2×C11×#467C211yesmaximal, characteristic, complemented
9C2×C11×#465C211yesmaximal, characteristic, complemented
10C2×C11×#464C211yesmaximal, characteristic, complemented
11C2×C11×#452C211yesmaximal, characteristic, complemented
12C2×C11×#450C211yesmaximal, characteristic, complemented
13C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
14C2×C8×D4×C11C211yesmaximal, characteristic, complemented
15C2×C11×#416C211yesmaximal, characteristic, complemented
16C22×C11×#102C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C23×C8×C11C2211yescharacteristic, complemented
24C11×#552—24no—
25C11×#552C2218yescomplemented
26C11×#546—24no—
27C11×#546C2218yes—
28C2×C11×#126—21no—
29C2×C11×#125—21no—
30C2×C11×#125C2211yescharacteristic, complemented
31C2×C11×#124C2211yescharacteristic
32C2×C11×#123—21no—
33C2×C11×#123—21no—
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C11×C22⋊Q8C2211yescharacteristic
36C2×C11×C22⋊Q8C2211yescharacteristic, complemented
37C2×C11×#121—21no—
38C2×C11×#121C2211yescharacteristic
39C2×C11×#120—21no—
40C2×C4×Q8×C11C2211yescharacteristic, complemented
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2211yescharacteristic
43C2×C11×#117—21no—
44C2×C11×#117C2211yescharacteristic, complemented
45C22×C11×C4⋊C4C2211yescharacteristic
46C22×C11×C22⋊C4—21no—
47C11×#488C2218yescomplemented
48C11×#483C2218yescomplemented
49C11×#482C2218yescomplemented
50C11×#478C2218yescomplemented
51C11×#467C2218yescomplemented
52C11×#465C2218yescomplemented
53C11×#464C2218yescomplemented
54C11×#452C2218yescomplemented
55C11×#450C2218yescomplemented
56C4×C11×SD16C2218yescomplemented
57C8×D4×C11C2218yescomplemented
58C2×C11×#107C2211yescharacteristic, complemented
59C2×C11×#106C2211yescharacteristic, complemented
60C2×C11×#106C2211yescharacteristic, complemented
61C2×C11×C4⋊C8C2211yescharacteristic, complemented
62C11×#416C2218yescomplemented
63C2×C11×#103C2211yescharacteristic, complemented
64C2×C11×#103C2211yescharacteristic, complemented
65C2×C11×#103C2211yescharacteristic, complemented
66C2×C11×#103C2211yescharacteristic, complemented
67C2×C11×#102C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2211yescharacteristic
73C2×C11×#102C2218yescomplemented
74C2×C11×C22⋊C8C2211yescharacteristic
75C2×C11×C22⋊C8C2211yescharacteristic, complemented
76C2×C4×C8×C11C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—24no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—22no—
89C22×D4×C11—42no—
90C22×D4×C11D411yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2314yes—
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11—21no—
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yescomplemented
101C2×C11×SD16—24no—
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yes—
104C2×C11×SD16C2314yes—
105C22×C8×C11—42no—
106C22×C8×C11—42no—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2314yes—
112C22×C8×C11C2314yescomplemented
113C11×#126—28no—
114C11×#125—28no—
115C11×#125—22no—
116C11×#125C2314yescomplemented
117C11×#124—22no—
118C11×#124C2314yes—
119C11×#123—28no—
120C11×#123—28no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8C2314yes—
125C11×C22⋊Q8C2314yes—
126C11×C22⋊Q8C2314yescomplemented
127C11×#121—22no—
128C11×#121—28no—
129C11×#121C2314yes—
130C11×#120—28no—
131C4×Q8×C11—22no—
132C4×Q8×C11C2314yescomplemented
133C4×D4×C11—22no—
134C4×D4×C11D414yes—
135C4×D4×C11C2314yes—
136C4×D4×C11C2314yes—
137C11×#117—22no—
138C11×#117—28no—
139C11×#117C2314yescomplemented
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4—22no—
142C2×C11×C4⋊C4—21no—
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—21no—
145C2×C11×C4⋊C4—21no—
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4—21no—
148C2×C11×C4⋊C4D411yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2314yes—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—21no—
162C2×C11×C22⋊C4—28no—
163C2×C11×C22⋊C4D411yescharacteristic
164C2×C11×C22⋊C4D411yescharacteristic
165C2×C42×C11—21no—
166C2×C42×C11—21no—
167C2×C42×C11C2311yescharacteristic
168C11×#107C2314yescomplemented
169C11×#106C2314yescomplemented
170C11×#106C2314yescomplemented
171C11×C4⋊C8C2314yescomplemented
172C11×#103C2314yescomplemented
173C11×#103C2314yescomplemented
174C11×#103C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177C11×#102C2314yes—
178C11×#102C2314yes—
179C11×#102C2314yes—
180C11×#102C2314yes—
181C11×#102C2314yes—
182C11×C22⋊C8C2314yes—
183C11×C22⋊C8C2314yescomplemented
184C4×C8×C11C2314yescomplemented
185C2×#3296C1111yesmaximal, characteristic, direct product factor, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—24no—
189C24×C11—44no—
190C24×C11—44no—
191C24×C11—82no—
192C24×C11C2×D411yescharacteristic
193C24×C11C2×D411yescharacteristic
194C11×#41—28no—
195C11×#41—44no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×Q8×C11C2412yes—
205C2×D4×C11—24no—
206C2×D4×C11—28no—
207C2×D4×C11—24no—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—24no—
211C2×D4×C11—21no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—44no—
216C2×D4×C11—48no—
217C2×D4×C11—44no—
218C2×D4×C11—44no—
219C2×D4×C11—82no—
220C2×D4×C11C2×D414yes—
221C2×D4×C11#4114yes—
222C2×D4×C11C2412yes—
223C2×D4×C11C2412yes—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—24no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—82no—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C11×Q16—44no—
250C11×SD16—28no—
251C11×SD16—44no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11—22no—
256C2×C8×C11—44no—
257C2×C8×C11—44no—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4C2×D414yes—
274C11×C4⋊C4C2412yes—
275C11×C4⋊C4C2412yes—
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2412yes—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4C2×D414yes—
287C11×C22⋊C4C2×D414yes—
288C42×C11—24no—
289C42×C11—24no—
290C42×C11C2×D412yes—
291C42×C11C2412yes—
292C2×#552C2×C1111yescharacteristic, complemented
293C2×#546C2×C1111yescharacteristic
294#3296C2×C11116yesdirect product factor
295C2×#488C2×C1111yescharacteristic, complemented
296C2×#482C2×C1111yescharacteristic, complemented
297C2×#483C2×C1111yescharacteristic, complemented
298C2×#478C2×C1111yescharacteristic, complemented
299C2×#467C2×C1111yescharacteristic, complemented
300C2×#465C2×C1111yescharacteristic, complemented
301C2×#464C2×C1111yescharacteristic, complemented
302C2×#452C2×C1111yescharacteristic, complemented
303C2×#450C2×C1111yescharacteristic, complemented
304C2×C4×SD16C2×C1111yescharacteristic, complemented
305C2×C8×D4C2×C1111yescharacteristic, complemented
306C2×#416C2×C1111yescharacteristic, complemented
307C22×#102C2×C1111yescharacteristic, complemented
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—24no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—48no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—48no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—84no—
324C23×C11—816no—
325C23×C11#13514yes—
326C23×C11C22×D412yes—
327C23×C11C22×D412yes—
328C23×C11C22×D411yescharacteristic
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—42no—
335D4×C11—28no—
336D4×C11—24no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11—48no—
342D4×C11—42no—
343D4×C11—84no—
344D4×C11C2×#4114yes—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
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—48no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—48no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—84no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D412yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C2×#4112yes—
376C2×C4×C11H(5,𝔽2)12yes—
377C2×C4×C11C2511yescharacteristic
378C8×C11—22no—
379C8×C11—22no—
380C8×C11—22no—
381C8×C11—22no—
382C22×#41C22×C1111yescharacteristic
383C23×D4C22×C1111yescharacteristic
384C22×Q16C22×C1111yescharacteristic, complemented
385C22×SD16C22×C1111yescharacteristic
386C22×SD16C22×C1111yescharacteristic
387C23×C8C22×C1111yescharacteristic
388C23×C8C22×C1111yescharacteristic, complemented
389#552—24no—
390#552C22×C1118yescomplemented
391#546—24no—
392#546C22×C1118yes—
393C2×#126—21no—
394C2×#125—21no—
395C2×#125C22×C1111yescharacteristic, complemented
396C2×#124C22×C1111yescharacteristic
397C2×#123—21no—
398C2×#123—21no—
399C2×C22⋊Q8C22×C1111yescharacteristic
400C2×C22⋊Q8C22×C1111yescharacteristic
401C2×C22⋊Q8C22×C1111yescharacteristic, complemented
402C2×#121—21no—
403C2×#121C22×C1111yescharacteristic
404C2×#120—21no—
405C2×C4×Q8C22×C1111yescharacteristic, complemented
406C2×C4×D4C22×C1111yescharacteristic
407C2×C4×D4C22×C1111yescharacteristic
408C2×#117—21no—
409C2×#117C22×C1111yescharacteristic, complemented
410C22×C4⋊C4C22×C1111yescharacteristic
411C22×C22⋊C4—21no—
412#488C22×C1118yescomplemented
413#483C22×C1118yescomplemented
414#482C22×C1118yescomplemented
415#478C22×C1118yescomplemented
416#467C22×C1118yescomplemented
417#465C22×C1118yescomplemented
418#464C22×C1118yescomplemented
419#452C22×C1118yescomplemented
420#450C22×C1118yescomplemented
421C4×SD16C22×C1118yescomplemented
422C8×D4C22×C1118yescomplemented
423C2×#107C22×C1111yescharacteristic, complemented
424C2×#106C22×C1111yescharacteristic, complemented
425C2×#106C22×C1111yescharacteristic, complemented
426C2×C4⋊C8C22×C1111yescharacteristic, complemented
427#416C22×C1118yescomplemented
428C2×#103C22×C1111yescharacteristic, complemented
429C2×#103C22×C1111yescharacteristic, complemented
430C2×#103C22×C1111yescharacteristic, complemented
431C2×#103C22×C1111yescharacteristic, complemented
432C2×#102C22×C1111yescharacteristic
433C2×#102C22×C1111yescharacteristic
434C2×#102C22×C1111yescharacteristic
435C2×#102C22×C1111yescharacteristic
436C2×#102C22×C1111yescharacteristic
437C2×#102C22×C1111yescharacteristic
438C2×#102C22×C1118yescomplemented
439C2×C22⋊C8C22×C1111yescharacteristic
440C2×C22⋊C8C22×C1111yescharacteristic, complemented
441C2×C4×C8C22×C1111yescharacteristic, complemented
442C22×C11—22no—
443C22×C11—28no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—24no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—44no—
450C22×C11—48no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—816no—
457C22×C11—84no—
458C22×C11#54612yes—
459C22×C11C2×#13514yes—
460C22×C11C2×#13512yes—
461C22×C11#57712yes—
462C22×C11C23×D411yescharacteristic
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11#54612yes—
474C4×C11C22×#4111yescharacteristic
475C4×C11C2×H(5,𝔽2)11yescharacteristic
476C25—21no—
477C2×#41—22no—
478C2×#41—24no—
479C2×#41—42no—
480C2×#41C23×C1114yes—
481C22×Q8C23×C1111yescharacteristic
482C22×Q8C23×C1111yescharacteristic
483C22×D4—24no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—22no—
488C22×D4—42no—
489C22×D4D4×C1111yescharacteristic
490C22×D4C23×C1111yescharacteristic
491C22×D4C23×C1114yes—
492C22×D4C23×C1111yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C1111yescharacteristic
497C23×C4C23×C1111yescharacteristic
498C2×Q16—42no—
499C2×Q16C23×C1114yescomplemented
500C2×SD16—24no—
501C2×SD16—42no—
502C2×SD16C23×C1114yes—
503C2×SD16C23×C1114yes—
504C22×C8—42no—
505C22×C8—42no—
506C22×C8C23×C1111yescharacteristic
507C22×C8C23×C1111yescharacteristic
508C22×C8C23×C1111yescharacteristic
509C22×C8C23×C1111yescharacteristic
510C22×C8C23×C1114yes—
511C22×C8C23×C1114yescomplemented
512#126—28no—
513#125—28no—
514#125—22no—
515#125C23×C1114yescomplemented
516#124—22no—
517#124C23×C1114yes—
518#123—28no—
519#123—28no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8C23×C1114yes—
524C22⋊Q8C23×C1114yes—
525C22⋊Q8C23×C1114yescomplemented
526#121—22no—
527#121—28no—
528#121C23×C1114yes—
529#120—28no—
530C4×Q8—22no—
531C4×Q8C23×C1114yescomplemented
532C4×D4—22no—
533C4×D4D4×C1114yes—
534C4×D4C23×C1114yes—
535C4×D4C23×C1114yes—
536#117—22no—
537#117—28no—
538#117C23×C1114yescomplemented
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C1111yescharacteristic
548C2×C4⋊C4C23×C1111yescharacteristic
549C2×C4⋊C4C23×C1111yescharacteristic
550C2×C4⋊C4C23×C1114yes—
551C2×C4⋊C4C23×C1111yescharacteristic
552C2×C4⋊C4C23×C1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—28no—
562C2×C22⋊C4D4×C1111yescharacteristic
563C2×C22⋊C4D4×C1111yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C1111yescharacteristic
567#107C23×C1114yescomplemented
568#106C23×C1114yescomplemented
569#106C23×C1114yescomplemented
570C4⋊C8C23×C1114yescomplemented
571#103C23×C1114yescomplemented
572#103C23×C1114yescomplemented
573#103C23×C1114yescomplemented
574#103C23×C1114yescomplemented
575#102C23×C1114yes—
576#102C23×C1114yes—
577#102C23×C1114yes—
578#102C23×C1114yes—
579#102C23×C1114yes—
580#102C23×C1114yes—
581C22⋊C8C23×C1114yes—
582C22⋊C8C23×C1114yescomplemented
583C4×C8C23×C1114yescomplemented
584C2×C11—24no—
585C2×C11—42no—
586C2×C11—44no—
587C2×C11—82no—
588C2×C11#329614yesdirect product factor
589C2×C11C2×#54611yescharacteristic
590C2×C11C22×#13511yescharacteristic
591C2×C11C2×#57711yescharacteristic
592C24—21no—
593C24—21no—
594C24—24no—
595C24—44no—
596C24—44no—
597C24—82no—
598C24C2×D4×C1111yescharacteristic
599C24C2×D4×C1111yescharacteristic
600#41—28no—
601#41—44no—
602#41—48no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8C24×C1112yes—
610C2×Q8C24×C1112yes—
611C2×D4—24no—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—48no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4C2×D4×C1114yes—
627C2×D4C11×#4114yes—
628C2×D4C24×C1112yes—
629C2×D4C24×C1112yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4C2×D4×C1111yescharacteristic
647C22×C4C2×D4×C1111yescharacteristic
648C22×C4C2×D4×C1111yescharacteristic
649C22×C4C2×D4×C1111yescharacteristic
650C22×C4C2×D4×C1112yes—
651C22×C4C2×D4×C1112yes—
652C22×C4C24×C1112yes—
653C22×C4C24×C1112yes—
654C22×C4C24×C1111yescharacteristic
655Q16—44no—
656SD16—28no—
657SD16—44no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—44no—
664C2×C8C24×C1112yes—
665C2×C8C24×C1112yes—
666C2×C8C24×C1112yes—
667C2×C8C24×C1112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4C2×D4×C1114yes—
680C4⋊C4C24×C1112yes—
681C4⋊C4C24×C1112yes—
682C4⋊C4C24×C1112yes—
683C4⋊C4C24×C1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4C2×D4×C1114yes—
693C22⋊C4C2×D4×C1114yes—
694C42—24no—
695C42—24no—
696C42C2×D4×C1112yes—
697C42C24×C1112yes—
698C11C2×#329611yescharacteristic, direct product factor, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—48no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—48no—
712C23—42no—
713C23—42no—
714C23—84no—
715C23—816no—
716C23C11×#13514yes—
717C23C22×D4×C1112yes—
718C23C22×D4×C1112yes—
719C23C22×D4×C1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—28no—
727D4—24no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—48no—
732D4—48no—
733D4—42no—
734D4—84no—
735D4C2×C11×#4114yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—84no—
761C2×C4C22×D4×C1112yes—
762C2×C4C22×D4×C1112yes—
763C2×C4C22×D4×C1112yes—
764C2×C4C22×D4×C1112yes—
765C2×C4C22×D4×C1111yescharacteristic
766C2×C4C2×C11×#4112yes—
767C2×C4C11×H(5,𝔽2)12yes—
768C2×C4C25×C1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—28no—
775C22—22no—
776C22—22no—
777C22—24no—
778C22—22no—
779C22—22no—
780C22—44no—
781C22—48no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—816no—
788C22—84no—
789C22C11×#54612yes—
790C22C2×C11×#13514yes—
791C22C2×C11×#13512yes—
792C22C11×#57712yes—
793C22C23×D4×C1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4C11×#54612yes—
805C4C22×C11×#4111yescharacteristic
806C4C2×C11×H(5,𝔽2)11yescharacteristic
807C2—24no—
808C2—42no—
809C2—44no—
810C2—82no—
811C2C11×#329614yesdirect product factor
812C2C2×C11×#54611yescharacteristic
813C2C22×C11×#13511yescharacteristic
814C2C2×C11×#57711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#546C2
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
1. C2×C11×#552C2semidirect
3. C11×#3296C2direct (N × H)
4. C2×C11×#488C2semidirect
5. C2×C11×#482C2semidirect
6. C2×C11×#483C2semidirect
7. C2×C11×#478C2semidirect
8. C2×C11×#467C2semidirect
9. C2×C11×#465C2semidirect
10. C2×C11×#464C2semidirect
11. C2×C11×#452C2semidirect
12. C2×C11×#450C2semidirect
13. C2×C4×C11×SD16C2semidirect
14. C2×C8×D4×C11C2semidirect
15. C2×C11×#416C2semidirect
16. C22×C11×#102C2semidirect
19. C22×C11×Q16C22semidirect
23. C23×C8×C11C22semidirect
25. C11×#552C22semidirect
30. C2×C11×#125C22semidirect
36. C2×C11×C22⋊Q8C22semidirect
40. C2×C4×Q8×C11C22semidirect
44. C2×C11×#117C22semidirect
47. C11×#488C22semidirect
48. C11×#483C22semidirect
49. C11×#482C22semidirect
50. C11×#478C22semidirect
51. C11×#467C22semidirect
52. C11×#465C22semidirect
53. C11×#464C22semidirect
54. C11×#452C22semidirect
55. C11×#450C22semidirect
56. C4×C11×SD16C22semidirect
57. C8×D4×C11C22semidirect
58. C2×C11×#107C22semidirect
59. C2×C11×#106C22semidirect
60. C2×C11×#106C22semidirect
61. C2×C11×C4⋊C8C22semidirect
62. C11×#416C22semidirect
63. C2×C11×#103C22semidirect
64. C2×C11×#103C22semidirect
65. C2×C11×#103C22semidirect
66. C2×C11×#103C22semidirect
73. C2×C11×#102C22semidirect
75. C2×C11×C22⋊C8C22semidirect
76. C2×C4×C8×C11C22semidirect
100. C2×C11×Q16C23semidirect
112. C22×C8×C11C23semidirect
116. C11×#125C23semidirect
126. C11×C22⋊Q8C23semidirect
132. C4×Q8×C11C23semidirect
139. C11×#117C23semidirect
168. C11×#107C23semidirect
169. C11×#106C23semidirect
170. C11×#106C23semidirect
171. C11×C4⋊C8C23semidirect
172. C11×#103C23semidirect
173. C11×#103C23semidirect
174. C11×#103C23semidirect
175. C11×#103C23semidirect
183. C11×C22⋊C8C23semidirect
184. C4×C8×C11C23semidirect
185. C2×#3296C11direct (N × H)
292. C2×#552C2×C11semidirect
294. #3296C2×C11direct (N × H)
295. C2×#488C2×C11semidirect
296. C2×#482C2×C11semidirect
297. C2×#483C2×C11semidirect
298. C2×#478C2×C11semidirect
299. C2×#467C2×C11semidirect
300. C2×#465C2×C11semidirect
301. C2×#464C2×C11semidirect
302. C2×#452C2×C11semidirect
303. C2×#450C2×C11semidirect
304. C2×C4×SD16C2×C11semidirect
305. C2×C8×D4C2×C11semidirect
306. C2×#416C2×C11semidirect
307. C22×#102C2×C11semidirect
384. C22×Q16C22×C11semidirect
388. C23×C8C22×C11semidirect
390. #552C22×C11semidirect
395. C2×#125C22×C11semidirect
401. C2×C22⋊Q8C22×C11semidirect
405. C2×C4×Q8C22×C11semidirect
409. C2×#117C22×C11semidirect
412. #488C22×C11semidirect
413. #483C22×C11semidirect
414. #482C22×C11semidirect
415. #478C22×C11semidirect
416. #467C22×C11semidirect
417. #465C22×C11semidirect
418. #464C22×C11semidirect
419. #452C22×C11semidirect
420. #450C22×C11semidirect
421. C4×SD16C22×C11semidirect
422. C8×D4C22×C11semidirect
423. C2×#107C22×C11semidirect
424. C2×#106C22×C11semidirect
425. C2×#106C22×C11semidirect
426. C2×C4⋊C8C22×C11semidirect
427. #416C22×C11semidirect
428. C2×#103C22×C11semidirect
429. C2×#103C22×C11semidirect
430. C2×#103C22×C11semidirect
431. C2×#103C22×C11semidirect
438. C2×#102C22×C11semidirect
440. C2×C22⋊C8C22×C11semidirect
441. C2×C4×C8C22×C11semidirect
499. C2×Q16C23×C11semidirect
511. C22×C8C23×C11semidirect
515. #125C23×C11semidirect
525. C22⋊Q8C23×C11semidirect
531. C4×Q8C23×C11semidirect
538. #117C23×C11semidirect
567. #107C23×C11semidirect
568. #106C23×C11semidirect
569. #106C23×C11semidirect
570. C4⋊C8C23×C11semidirect
571. #103C23×C11semidirect
572. #103C23×C11semidirect
573. #103C23×C11semidirect
574. #103C23×C11semidirect
582. C22⋊C8C23×C11semidirect
583. C4×C8C23×C11semidirect
588. C2×C11#3296direct (N × H)
698. C11C2×#3296direct (N × H)
811. C2C11×#3296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#5462
C11×#32962
C2×C11×#4882
C2×C11×#4822
C2×C11×#4832
C2×C11×#4782
C2×C11×#4672
C2×C11×#4652
C2×C11×#4642
C2×C11×#4522
C2×C11×#4502
C2×C4×C11×SD162
C2×C8×D4×C112
C2×C11×#4162
C22×C11×#1022
C2×#329611