Finite Group Databasebeta

← C2×C11×#3297 #14638308

Subgroups — C2×C11×#3297 #14638308

Order 2816.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic, complemented
2C2×C11×#546C211yesmaximal, characteristic, complemented
3C11×#3297C2116yesmaximal, direct product factor
4C2×C11×#488C211yesmaximal, characteristic, complemented
5C2×C11×#484C211yesmaximal, characteristic, complemented
6C2×C11×#482C211yesmaximal, characteristic, complemented
7C2×C11×#478C211yesmaximal, characteristic, complemented
8C2×C11×#466C211yesmaximal, characteristic, complemented
9C2×C11×#465C211yesmaximal, characteristic, complemented
10C2×C11×#463C211yesmaximal, characteristic, complemented
11C2×C11×#449C211yesmaximal, characteristic, complemented
12C2×C11×#447C211yesmaximal, characteristic, complemented
13C2×C4×C11×D8C211yesmaximal, 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×SD16C2211yescharacteristic, complemented
20C22×C11×D8C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C23×C8×C11C2211yescharacteristic, complemented
24C11×#553—24no—
25C11×#553C2218yescomplemented
26C11×#546—24no—
27C11×#546C2218yescomplemented
28C2×C11×#126—21no—
29C2×C11×#125C2211yescharacteristic, complemented
30C2×C11×#124C2211yescharacteristic
31C2×C11×#123—21no—
32C2×C11×#123—21no—
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×#121—21no—
35C2×C11×#121—21no—
36C2×C11×#121C2211yescharacteristic
37C2×C11×#121C2211yescharacteristic
38C2×C11×#121C2211yescharacteristic, complemented
39C2×C11×#120—21no—
40C2×C4×D4×C11—21no—
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2211yescharacteristic
43C2×C4×D4×C11C2211yescharacteristic, complemented
44C2×C11×#117C2211yescharacteristic, complemented
45C22×C11×C4⋊C4C2211yescharacteristic
46C22×C11×C22⋊C4—21no—
47C11×#488C2218yescomplemented
48C11×#484C2218yescomplemented
49C11×#482C2218yescomplemented
50C11×#478C2218yescomplemented
51C11×#466C2218yescomplemented
52C11×#465C2218yescomplemented
53C11×#463C2218yescomplemented
54C11×#449C2218yescomplemented
55C11×#447C2218yescomplemented
56C4×C11×D8C2218yescomplemented
57C8×D4×C11C2218yescomplemented
58C2×C11×#107C2211yescharacteristic, complemented
59C2×C11×#107C2211yescharacteristic, 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×#102C2211yescharacteristic
67C2×C11×#102C2211yescharacteristic
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2211yescharacteristic
70C2×C11×#102C2211yescharacteristic
71C2×C11×#102C2211yescharacteristic
72C2×C11×#102C2218yescomplemented
73C2×C11×#102C2211yescharacteristic, complemented
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×D4×C11—24no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—22no—
90C22×D4×C11—42no—
91C22×D4×C11D411yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2314yes—
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11—21no—
98C23×C4×C11—21no—
99C23×C4×C11—21no—
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yescomplemented
104C2×C11×D8—24no—
105C2×C11×D8—42no—
106C2×C11×D8C2314yes—
107C2×C11×D8C2314yes—
108C22×C8×C11—42no—
109C22×C8×C11—42no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2314yes—
115C22×C8×C11C2314yescomplemented
116C11×#126—28no—
117C11×#125—22no—
118C11×#125C2314yescomplemented
119C11×#124—22no—
120C11×#124C2314yes—
121C11×#123—28no—
122C11×#123—28no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8C2314yes—
125C11×#121—28no—
126C11×#121—22no—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—28no—
130C11×#121C2314yes—
131C11×#121C2314yes—
132C11×#121C2314yescomplemented
133C11×#120—28no—
134C4×D4×C11—28no—
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11D414yes—
138C4×D4×C11C2314yes—
139C4×D4×C11C2314yes—
140C4×D4×C11C2314yescomplemented
141C11×#117—22no—
142C11×#117C2314yescomplemented
143C2×C11×C4⋊C4—21no—
144C2×C11×C4⋊C4—22no—
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—21no—
163C2×C11×C22⋊C4—28no—
164C2×C11×C22⋊C4D411yescharacteristic
165C2×C11×C22⋊C4D411yescharacteristic
166C2×C42×C11—21no—
167C2×C42×C11C2311yescharacteristic
168C11×#107C2314yescomplemented
169C11×#107C2314yescomplemented
170C11×#106C2314yescomplemented
171C11×C4⋊C8C2314yescomplemented
172C11×#103C2314yescomplemented
173C11×#103C2314yescomplemented
174C11×#103C2314yescomplemented
175C11×#102C2314yes—
176C11×#102C2314yes—
177C11×#102C2314yes—
178C11×#102C2314yes—
179C11×#102C2314yes—
180C11×#102C2314yes—
181C11×#102C2314yescomplemented
182C11×C22⋊C8C2314yes—
183C11×C22⋊C8C2314yescomplemented
184C4×C8×C11C2314yescomplemented
185C2×#3297C1111yesmaximal, characteristic, direct product factor, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—24no—
190C24×C11—44no—
191C24×C11—44no—
192C24×C11—82no—
193C24×C11C2×D411yescharacteristic
194C24×C11C2×D411yescharacteristic
195C11×#41—28no—
196C11×#41—44no—
197C11×#41—48no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—24no—
203C2×D4×C11—28no—
204C2×D4×C11—24no—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—21no—
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—22no—
216C2×D4×C11—22no—
217C2×D4×C11—44no—
218C2×D4×C11—48no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—82no—
223C2×D4×C11—82no—
224C2×D4×C11C2×D414yes—
225C2×D4×C11#4114yes—
226C2×D4×C11C2412yes—
227C2×D4×C11C2412yes—
228C2×D4×C11C2412yes—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—24no—
239C22×C4×C11—24no—
240C22×C4×C11—24no—
241C22×C4×C11—24no—
242C22×C4×C11—44no—
243C22×C4×C11—82no—
244C22×C4×C11—82no—
245C22×C4×C11—82no—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C11×SD16—44no—
256C11×D8—28no—
257C11×D8—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11—22no—
262C2×C8×C11—44no—
263C2×C8×C11—44no—
264C2×C8×C11C2412yes—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4C2×D414yes—
277C11×C4⋊C4C2412yes—
278C11×C4⋊C4C2412yes—
279C11×C4⋊C4C2412yes—
280C11×C4⋊C4C2412yes—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4C2×D414yes—
291C11×C22⋊C4C2×D414yes—
292C42×C11—24no—
293C42×C11C2×D412yes—
294C42×C11C2412yes—
295C2×#553C2×C1111yescharacteristic, complemented
296C2×#546C2×C1111yescharacteristic, complemented
297#3297C2×C11116yesdirect product factor
298C2×#488C2×C1111yescharacteristic, complemented
299C2×#484C2×C1111yescharacteristic, complemented
300C2×#482C2×C1111yescharacteristic, complemented
301C2×#478C2×C1111yescharacteristic, complemented
302C2×#466C2×C1111yescharacteristic, complemented
303C2×#465C2×C1111yescharacteristic, complemented
304C2×#463C2×C1111yescharacteristic, complemented
305C2×#449C2×C1111yescharacteristic, complemented
306C2×#447C2×C1111yescharacteristic, complemented
307C2×C4×D8C2×C1111yescharacteristic, complemented
308C2×C8×D4C2×C1111yescharacteristic, complemented
309C2×#416C2×C1111yescharacteristic, complemented
310C22×#102C2×C1111yescharacteristic, complemented
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—24no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—48no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—48no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—84no—
331C23×C11—816no—
332C23×C11#13514yes—
333C23×C11C22×D412yes—
334C23×C11C22×D412yes—
335C23×C11C22×D411yescharacteristic
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339D4×C11—28no—
340D4×C11—24no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—48no—
347D4×C11—48no—
348D4×C11—48no—
349D4×C11—42no—
350D4×C11—42no—
351D4×C11—84no—
352D4×C11—84no—
353D4×C11C2×#4114yes—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—24no—
359C2×C4×C11—24no—
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—48no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—84no—
376C2×C4×C11—84no—
377C2×C4×C11—84no—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C2×#4112yes—
384C2×C4×C11H(5,𝔽2)12yes—
385C2×C4×C11C2511yescharacteristic
386C8×C11—22no—
387C8×C11—22no—
388C8×C11—22no—
389C8×C11—22no—
390C22×#41C22×C1111yescharacteristic
391C23×D4C22×C1111yescharacteristic
392C22×SD16C22×C1111yescharacteristic, complemented
393C22×D8C22×C1111yescharacteristic
394C22×D8C22×C1111yescharacteristic
395C23×C8C22×C1111yescharacteristic
396C23×C8C22×C1111yescharacteristic, complemented
397#553—24no—
398#553C22×C1118yescomplemented
399#546—24no—
400#546C22×C1118yescomplemented
401C2×#126—21no—
402C2×#125C22×C1111yescharacteristic, complemented
403C2×#124C22×C1111yescharacteristic
404C2×#123—21no—
405C2×#123—21no—
406C2×C22⋊Q8C22×C1111yescharacteristic
407C2×#121—21no—
408C2×#121—21no—
409C2×#121C22×C1111yescharacteristic
410C2×#121C22×C1111yescharacteristic
411C2×#121C22×C1111yescharacteristic, complemented
412C2×#120—21no—
413C2×C4×D4—21no—
414C2×C4×D4C22×C1111yescharacteristic
415C2×C4×D4C22×C1111yescharacteristic
416C2×C4×D4C22×C1111yescharacteristic, complemented
417C2×#117C22×C1111yescharacteristic, complemented
418C22×C4⋊C4C22×C1111yescharacteristic
419C22×C22⋊C4—21no—
420#488C22×C1118yescomplemented
421#484C22×C1118yescomplemented
422#482C22×C1118yescomplemented
423#478C22×C1118yescomplemented
424#466C22×C1118yescomplemented
425#465C22×C1118yescomplemented
426#463C22×C1118yescomplemented
427#449C22×C1118yescomplemented
428#447C22×C1118yescomplemented
429C4×D8C22×C1118yescomplemented
430C8×D4C22×C1118yescomplemented
431C2×#107C22×C1111yescharacteristic, complemented
432C2×#107C22×C1111yescharacteristic, complemented
433C2×#106C22×C1111yescharacteristic, complemented
434C2×C4⋊C8C22×C1111yescharacteristic, complemented
435#416C22×C1118yescomplemented
436C2×#103C22×C1111yescharacteristic, complemented
437C2×#103C22×C1111yescharacteristic, complemented
438C2×#103C22×C1111yescharacteristic, complemented
439C2×#102C22×C1111yescharacteristic
440C2×#102C22×C1111yescharacteristic
441C2×#102C22×C1111yescharacteristic
442C2×#102C22×C1111yescharacteristic
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445C2×#102C22×C1118yescomplemented
446C2×#102C22×C1111yescharacteristic, complemented
447C2×C22⋊C8C22×C1111yescharacteristic
448C2×C22⋊C8C22×C1111yescharacteristic, complemented
449C2×C4×C8C22×C1111yescharacteristic, complemented
450C22×C11—22no—
451C22×C11—28no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—24no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—44no—
458C22×C11—48no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—816no—
468C22×C11—84no—
469C22×C11—84no—
470C22×C11#54612yes—
471C22×C11C2×#13514yes—
472C22×C11C2×#13512yes—
473C22×C11#57612yes—
474C22×C11C23×D411yescharacteristic
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11#54612yes—
485C4×C11C22×#4111yescharacteristic
486C4×C11C2×H(5,𝔽2)11yescharacteristic
487C25—21no—
488C2×#41—22no—
489C2×#41—24no—
490C2×#41—42no—
491C2×#41C23×C1114yes—
492C22×Q8C23×C1111yescharacteristic
493C22×D4—24no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—42no—
501C22×D4D4×C1111yescharacteristic
502C22×D4C23×C1111yescharacteristic
503C22×D4C23×C1111yescharacteristic
504C22×D4C23×C1114yes—
505C22×D4C23×C1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C23×C1111yescharacteristic
511C23×C4C23×C1111yescharacteristic
512C2×SD16—42no—
513C2×SD16C23×C1114yescomplemented
514C2×D8—24no—
515C2×D8—42no—
516C2×D8C23×C1114yes—
517C2×D8C23×C1114yes—
518C22×C8—42no—
519C22×C8—42no—
520C22×C8C23×C1111yescharacteristic
521C22×C8C23×C1111yescharacteristic
522C22×C8C23×C1111yescharacteristic
523C22×C8C23×C1111yescharacteristic
524C22×C8C23×C1114yes—
525C22×C8C23×C1114yescomplemented
526#126—28no—
527#125—22no—
528#125C23×C1114yescomplemented
529#124—22no—
530#124C23×C1114yes—
531#123—28no—
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8C23×C1114yes—
535#121—28no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—28no—
540#121C23×C1114yes—
541#121C23×C1114yes—
542#121C23×C1114yescomplemented
543#120—28no—
544C4×D4—28no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4D4×C1114yes—
548C4×D4C23×C1114yes—
549C4×D4C23×C1114yes—
550C4×D4C23×C1114yescomplemented
551#117—22no—
552#117C23×C1114yescomplemented
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4D4×C1111yescharacteristic
559C2×C4⋊C4C23×C1111yescharacteristic
560C2×C4⋊C4C23×C1111yescharacteristic
561C2×C4⋊C4C23×C1114yes—
562C2×C4⋊C4C23×C1111yescharacteristic
563C2×C4⋊C4C23×C1111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—28no—
574C2×C22⋊C4D4×C1111yescharacteristic
575C2×C22⋊C4D4×C1111yescharacteristic
576C2×C42—21no—
577C2×C42C23×C1111yescharacteristic
578#107C23×C1114yescomplemented
579#107C23×C1114yescomplemented
580#106C23×C1114yescomplemented
581C4⋊C8C23×C1114yescomplemented
582#103C23×C1114yescomplemented
583#103C23×C1114yescomplemented
584#103C23×C1114yescomplemented
585#102C23×C1114yes—
586#102C23×C1114yes—
587#102C23×C1114yes—
588#102C23×C1114yes—
589#102C23×C1114yes—
590#102C23×C1114yes—
591#102C23×C1114yescomplemented
592C22⋊C8C23×C1114yes—
593C22⋊C8C23×C1114yescomplemented
594C4×C8C23×C1114yescomplemented
595C2×C11—24no—
596C2×C11—42no—
597C2×C11—44no—
598C2×C11—82no—
599C2×C11—82no—
600C2×C11#329714yesdirect product factor
601C2×C11C2×#54611yescharacteristic
602C2×C11C22×#13511yescharacteristic
603C2×C11C2×#57611yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—44no—
609C24—44no—
610C24—82no—
611C24C2×D4×C1111yescharacteristic
612C24C2×D4×C1111yescharacteristic
613#41—28no—
614#41—44no—
615#41—48no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8C24×C1112yes—
620C2×D4—24no—
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—44no—
636C2×D4—48no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—82no—
641C2×D4—82no—
642C2×D4C2×D4×C1114yes—
643C2×D4C11×#4114yes—
644C2×D4C24×C1112yes—
645C2×D4C24×C1112yes—
646C2×D4C24×C1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—44no—
661C22×C4—82no—
662C22×C4—82no—
663C22×C4—82no—
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C2×D4×C1111yescharacteristic
666C22×C4C2×D4×C1111yescharacteristic
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C2×D4×C1112yes—
669C22×C4C2×D4×C1112yes—
670C22×C4C24×C1112yes—
671C22×C4C24×C1112yes—
672C22×C4C24×C1111yescharacteristic
673SD16—44no—
674D8—28no—
675D8—44no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—44no—
681C2×C8—44no—
682C2×C8C24×C1112yes—
683C2×C8C24×C1112yes—
684C2×C8C24×C1112yes—
685C2×C8C24×C1112yes—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4C2×D4×C1114yes—
695C4⋊C4C24×C1112yes—
696C4⋊C4C24×C1112yes—
697C4⋊C4C24×C1112yes—
698C4⋊C4C24×C1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4C2×D4×C1114yes—
709C22⋊C4C2×D4×C1114yes—
710C42—24no—
711C42C2×D4×C1112yes—
712C42C24×C1112yes—
713C11C2×#329711yescharacteristic, direct product factor, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—48no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—48no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—84no—
734C23—816no—
735C23C11×#13514yes—
736C23C22×D4×C1112yes—
737C23C22×D4×C1112yes—
738C23C22×D4×C1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—28no—
743D4—24no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—48no—
750D4—48no—
751D4—48no—
752D4—42no—
753D4—42no—
754D4—84no—
755D4—84no—
756D4C2×C11×#4114yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
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—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4C22×D4×C1112yes—
782C2×C4C22×D4×C1112yes—
783C2×C4C22×D4×C1112yes—
784C2×C4C22×D4×C1112yes—
785C2×C4C22×D4×C1111yescharacteristic
786C2×C4C2×C11×#4112yes—
787C2×C4C11×H(5,𝔽2)12yes—
788C2×C4C25×C1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—28no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—22no—
799C22—22no—
800C22—44no—
801C22—48no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—816no—
811C22—84no—
812C22—84no—
813C22C11×#54612yes—
814C22C2×C11×#13514yes—
815C22C2×C11×#13512yes—
816C22C11×#57612yes—
817C22C23×D4×C1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4C11×#54612yes—
828C4C22×C11×#4111yescharacteristic
829C4C2×C11×H(5,𝔽2)11yescharacteristic
830C2—24no—
831C2—42no—
832C2—44no—
833C2—82no—
834C2—82no—
835C2C11×#329714yesdirect product factor
836C2C2×C11×#54611yescharacteristic
837C2C22×C11×#13511yescharacteristic
838C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
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×#553C2semidirect
2. C2×C11×#546C2semidirect
3. C11×#3297C2direct (N × H)
4. C2×C11×#488C2semidirect
5. C2×C11×#484C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#478C2semidirect
8. C2×C11×#466C2semidirect
9. C2×C11×#465C2semidirect
10. C2×C11×#463C2semidirect
11. C2×C11×#449C2semidirect
12. C2×C11×#447C2semidirect
13. C2×C4×C11×D8C2semidirect
14. C2×C8×D4×C11C2semidirect
15. C2×C11×#416C2semidirect
16. C22×C11×#102C2semidirect
19. C22×C11×SD16C22semidirect
23. C23×C8×C11C22semidirect
25. C11×#553C22semidirect
27. C11×#546C22semidirect
29. C2×C11×#125C22semidirect
38. C2×C11×#121C22semidirect
43. C2×C4×D4×C11C22semidirect
44. C2×C11×#117C22semidirect
47. C11×#488C22semidirect
48. C11×#484C22semidirect
49. C11×#482C22semidirect
50. C11×#478C22semidirect
51. C11×#466C22semidirect
52. C11×#465C22semidirect
53. C11×#463C22semidirect
54. C11×#449C22semidirect
55. C11×#447C22semidirect
56. C4×C11×D8C22semidirect
57. C8×D4×C11C22semidirect
58. C2×C11×#107C22semidirect
59. C2×C11×#107C22semidirect
60. C2×C11×#106C22semidirect
61. C2×C11×C4⋊C8C22semidirect
62. C11×#416C22semidirect
63. C2×C11×#103C22semidirect
64. C2×C11×#103C22semidirect
65. C2×C11×#103C22semidirect
72. C2×C11×#102C22semidirect
73. C2×C11×#102C22semidirect
75. C2×C11×C22⋊C8C22semidirect
76. C2×C4×C8×C11C22semidirect
103. C2×C11×SD16C23semidirect
115. C22×C8×C11C23semidirect
118. C11×#125C23semidirect
132. C11×#121C23semidirect
140. C4×D4×C11C23semidirect
142. C11×#117C23semidirect
168. C11×#107C23semidirect
169. C11×#107C23semidirect
170. C11×#106C23semidirect
171. C11×C4⋊C8C23semidirect
172. C11×#103C23semidirect
173. C11×#103C23semidirect
174. C11×#103C23semidirect
181. C11×#102C23semidirect
183. C11×C22⋊C8C23semidirect
184. C4×C8×C11C23semidirect
185. C2×#3297C11direct (N × H)
295. C2×#553C2×C11semidirect
296. C2×#546C2×C11semidirect
297. #3297C2×C11direct (N × H)
298. C2×#488C2×C11semidirect
299. C2×#484C2×C11semidirect
300. C2×#482C2×C11semidirect
301. C2×#478C2×C11semidirect
302. C2×#466C2×C11semidirect
303. C2×#465C2×C11semidirect
304. C2×#463C2×C11semidirect
305. C2×#449C2×C11semidirect
306. C2×#447C2×C11semidirect
307. C2×C4×D8C2×C11semidirect
308. C2×C8×D4C2×C11semidirect
309. C2×#416C2×C11semidirect
310. C22×#102C2×C11semidirect
392. C22×SD16C22×C11semidirect
396. C23×C8C22×C11semidirect
398. #553C22×C11semidirect
400. #546C22×C11semidirect
402. C2×#125C22×C11semidirect
411. C2×#121C22×C11semidirect
416. C2×C4×D4C22×C11semidirect
417. C2×#117C22×C11semidirect
420. #488C22×C11semidirect
421. #484C22×C11semidirect
422. #482C22×C11semidirect
423. #478C22×C11semidirect
424. #466C22×C11semidirect
425. #465C22×C11semidirect
426. #463C22×C11semidirect
427. #449C22×C11semidirect
428. #447C22×C11semidirect
429. C4×D8C22×C11semidirect
430. C8×D4C22×C11semidirect
431. C2×#107C22×C11semidirect
432. C2×#107C22×C11semidirect
433. C2×#106C22×C11semidirect
434. C2×C4⋊C8C22×C11semidirect
435. #416C22×C11semidirect
436. C2×#103C22×C11semidirect
437. C2×#103C22×C11semidirect
438. C2×#103C22×C11semidirect
445. C2×#102C22×C11semidirect
446. C2×#102C22×C11semidirect
448. C2×C22⋊C8C22×C11semidirect
449. C2×C4×C8C22×C11semidirect
513. C2×SD16C23×C11semidirect
525. C22×C8C23×C11semidirect
528. #125C23×C11semidirect
542. #121C23×C11semidirect
550. C4×D4C23×C11semidirect
552. #117C23×C11semidirect
578. #107C23×C11semidirect
579. #107C23×C11semidirect
580. #106C23×C11semidirect
581. C4⋊C8C23×C11semidirect
582. #103C23×C11semidirect
583. #103C23×C11semidirect
584. #103C23×C11semidirect
591. #102C23×C11semidirect
593. C22⋊C8C23×C11semidirect
594. C4×C8C23×C11semidirect
600. C2×C11#3297direct (N × H)
713. C11C2×#3297direct (N × H)
835. C2C11×#3297direct (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×#5462
C11×#32972
C2×C11×#4882
C2×C11×#4842
C2×C11×#4822
C2×C11×#4782
C2×C11×#4662
C2×C11×#4652
C2×C11×#4632
C2×C11×#4492
C2×C11×#4472
C2×C4×C11×D82
C2×C8×D4×C112
C2×C11×#4162
C22×C11×#1022
C2×#329711