Finite Group Databasebeta

← C2×C11×#3282 #14638235

Subgroups — C2×C11×#3282 #14638235

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C23×C11×SD16C211yesmaximal, characteristic, complemented
3C2×C11×#548C211yesmaximal, characteristic, complemented
4C2×C11×#546C211yesmaximal, characteristic, complemented
5C11×#3282C2116yesmaximal, direct product factor
6C2×C11×#495C211yesmaximal, characteristic, complemented
7C2×C11×#465C211yesmaximal, characteristic, complemented
8C2×C11×#465C211yesmaximal, characteristic, complemented
9C2×C11×#464C211yesmaximal, characteristic, complemented
10C2×C11×#463C211yesmaximal, characteristic, complemented
11C2×C11×#452C211yesmaximal, characteristic, complemented
12C2×C11×#449C211yesmaximal, characteristic, complemented
13C2×C11×#451C211yesmaximal, characteristic, complemented
14C2×C11×#447C211yesmaximal, characteristic, complemented
15C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
16C2×C8×D4×C11C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic, complemented
19C23×Q8×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C2×C11×#135—28no—
22C2×C11×#135C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic, complemented
24C22×C11×Q16C2211yescharacteristic, complemented
25C22×C11×SD16—28no—
26C22×C11×SD16C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic
28C22×C11×SD16C2211yescharacteristic
29C22×C11×SD16C2211yescharacteristic
30C22×C11×SD16C2218yescomplemented
31C22×C11×SD16C2211yescharacteristic, complemented
32C22×C11×D8C2211yescharacteristic
33C22×C11×D8C2211yescharacteristic
34C23×C8×C11C2211yescharacteristic
35C23×C8×C11C2211yescharacteristic, complemented
36C11×#548—24no—
37C11×#548C2218yescomplemented
38C11×#546—24no—
39C11×#546C2218yescomplemented
40C2×C11×#124—21no—
41C2×C11×#124C2211yescharacteristic
42C2×C11×#124C2211yescharacteristic, complemented
43C2×C11×#123—21no—
44C2×C11×C22⋊Q8—21no—
45C2×C11×C22⋊Q8C2211yescharacteristic
46C2×C11×C22⋊Q8C2211yescharacteristic, complemented
47C2×C11×#121—21no—
48C2×C11×#121—21no—
49C2×C11×#121C2211yescharacteristic
50C2×C11×#121C2211yescharacteristic
51C2×C11×#120—21no—
52C2×C4×Q8×C11C2211yescharacteristic, complemented
53C2×C4×D4×C11—21no—
54C2×C4×D4×C11C2211yescharacteristic
55C2×C4×D4×C11C2211yescharacteristic
56C22×C11×C22⋊C4—21no—
57C11×#495C2218yescomplemented
58C11×#465C2218yescomplemented
59C11×#465C2218yescomplemented
60C11×#464C2218yescomplemented
61C11×#463C2218yescomplemented
62C11×#452C2218yescomplemented
63C11×#451C2218yescomplemented
64C11×#449C2218yescomplemented
65C11×#447C2218yescomplemented
66C4×C11×SD16C2218yescomplemented
67C8×D4×C11C2218yescomplemented
68C2×C11×#106C2211yescharacteristic, complemented
69C2×C11×C4⋊C8C2211yescharacteristic, complemented
70C2×C11×#103C2211yescharacteristic, complemented
71C2×C11×#103C2211yescharacteristic, complemented
72C2×C11×#103C2211yescharacteristic, complemented
73C2×C11×#102C2211yescharacteristic
74C2×C11×#102C2211yescharacteristic
75C2×C11×#102C2211yescharacteristic, complemented
76C2×C11×C22⋊C8C2211yescharacteristic
77C2×C11×C22⋊C8C2211yescharacteristic, complemented
78C2×C4×C8×C11C2211yescharacteristic, complemented
79C25×C11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—22no—
82C2×C11×#41—24no—
83C2×C11×#41—24no—
84C2×C11×#41—42no—
85C2×C11×#41—42no—
86C2×C11×#41C2314yes—
87C2×C11×#41C2314yescomplemented
88C22×Q8×C11—21no—
89C22×Q8×C11—22no—
90C22×Q8×C11—24no—
91C22×Q8×C11—42no—
92C22×Q8×C11C2311yescharacteristic
93C22×Q8×C11C2311yescharacteristic
94C22×Q8×C11C2314yes—
95C22×Q8×C11C2311yescharacteristic
96C22×D4×C11—24no—
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11—21no—
101C22×D4×C11—21no—
102C22×D4×C11—22no—
103C22×D4×C11—42no—
104C22×D4×C11D411yescharacteristic
105C22×D4×C11C2311yescharacteristic
106C22×D4×C11C2311yescharacteristic
107C22×D4×C11C2314yes—
108C22×D4×C11C2311yescharacteristic
109C23×C4×C11—21no—
110C23×C4×C11—21no—
111C23×C4×C11—21no—
112C23×C4×C11—21no—
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2311yescharacteristic
115C11×#135—232no—
116C2×C11×Q16—24no—
117C2×C11×Q16—42no—
118C2×C11×Q16C2314yescomplemented
119C2×C11×Q16C2314yescomplemented
120C2×C11×SD16—24no—
121C2×C11×SD16—24no—
122C2×C11×SD16—232no—
123C2×C11×SD16—24no—
124C2×C11×SD16—24no—
125C2×C11×SD16D418yescomplemented
126C2×C11×SD16C2314yes—
127C2×C11×SD16C2314yes—
128C2×C11×SD16C2314yes—
129C2×C11×SD16C2314yes—
130C2×C11×SD16C2314yescomplemented
131C2×C11×D8—24no—
132C2×C11×D8—42no—
133C2×C11×D8C2314yes—
134C2×C11×D8C2314yes—
135C22×C8×C11—24no—
136C22×C8×C11—24no—
137C22×C8×C11C2311yescharacteristic
138C22×C8×C11C2311yescharacteristic
139C22×C8×C11C2311yescharacteristic
140C22×C8×C11C2314yes—
141C22×C8×C11C2311yescharacteristic
142C22×C8×C11C2314yescomplemented
143C11×#124—28no—
144C11×#124—22no—
145C11×#124—22no—
146C11×#124C2314yes—
147C11×#124C2314yescomplemented
148C11×#123—28no—
149C11×C22⋊Q8—22no—
150C11×C22⋊Q8—22no—
151C11×C22⋊Q8—28no—
152C11×C22⋊Q8C2314yes—
153C11×C22⋊Q8C2314yescomplemented
154C11×#121—28no—
155C11×#121—22no—
156C11×#121—22no—
157C11×#121—28no—
158C11×#121C2314yes—
159C11×#121C2314yes—
160C11×#120—28no—
161C4×Q8×C11—22no—
162C4×Q8×C11C2314yescomplemented
163C4×D4×C11—28no—
164C4×D4×C11—22no—
165C4×D4×C11D414yes—
166C4×D4×C11C2314yes—
167C4×D4×C11C2314yes—
168C2×C11×C4⋊C4—21no—
169C2×C11×C4⋊C4—21no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4D411yescharacteristic
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4—21no—
175C2×C11×C22⋊C4—21no—
176C2×C11×C22⋊C4—21no—
177C2×C11×C22⋊C4—21no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4—21no—
182C2×C11×C22⋊C4—21no—
183C2×C11×C22⋊C4—28no—
184C2×C11×C22⋊C4D411yescharacteristic
185C2×C11×C22⋊C4D411yescharacteristic
186C2×C42×C11—21no—
187C2×C42×C11C2311yescharacteristic
188C11×#106C2314yescomplemented
189C11×C4⋊C8C2314yescomplemented
190C11×#103C2314yescomplemented
191C11×#103C2314yescomplemented
192C11×#103C2314yescomplemented
193C11×#102C2314yes—
194C11×#102C2314yes—
195C11×#102C2314yescomplemented
196C11×C22⋊C8C2314yes—
197C11×C22⋊C8C2314yescomplemented
198C4×C8×C11C2314yescomplemented
199C2×#3282C1111yesmaximal, characteristic, direct product factor, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—24no—
204C24×C11—44no—
205C24×C11—44no—
206C24×C11—82no—
207C24×C11C2×D411yescharacteristic
208C24×C11C2×D411yescharacteristic
209C11×#41—28no—
210C11×#41—28no—
211C11×#41—44no—
212C11×#41—44no—
213C11×#41—48no—
214C11×#41—48no—
215C2×Q8×C11—21no—
216C2×Q8×C11—24no—
217C2×Q8×C11—21no—
218C2×Q8×C11—21no—
219C2×Q8×C11—22no—
220C2×Q8×C11—28no—
221C2×Q8×C11—22no—
222C2×Q8×C11—22no—
223C2×Q8×C11—22no—
224C2×Q8×C11—22no—
225C2×Q8×C11—44no—
226C2×Q8×C11—44no—
227C2×Q8×C11—48no—
228C2×Q8×C11C2×D414yes—
229C2×Q8×C11C2412yes—
230C2×Q8×C11C2412yes—
231C2×Q8×C11C2412yes—
232C2×D4×C11—24no—
233C2×D4×C11—28no—
234C2×D4×C11—24no—
235C2×D4×C11—24no—
236C2×D4×C11—24no—
237C2×D4×C11—24no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—24no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—22no—
245C2×D4×C11—22no—
246C2×D4×C11—22no—
247C2×D4×C11—44no—
248C2×D4×C11—48no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—44no—
252C2×D4×C11—44no—
253C2×D4×C11—82no—
254C2×D4×C11C2×D414yes—
255C2×D4×C11C2×D414yes—
256C2×D4×C11C2412yes—
257C2×D4×C11C2412yes—
258C2×D4×C11C2412yes—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—24no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—24no—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11—44no—
275C22×C4×C11—82no—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C11×Q16—28no—
286C11×Q16—44no—
287C11×SD16—28no—
288C11×SD16—28no—
289C11×SD16—28no—
290C11×SD16—28no—
291C11×SD16C2×D4116yescomplemented
292C11×D8—28no—
293C11×D8—44no—
294C2×C8×C11—28no—
295C2×C8×C11—28no—
296C2×C8×C11—22no—
297C2×C8×C11—22no—
298C2×C8×C11—22no—
299C2×C8×C11C2×D414yes—
300C2×C8×C11C2412yes—
301C2×C8×C11C2412yes—
302C2×C8×C11C2412yes—
303C2×C8×C11C2412yes—
304C11×C4⋊C4—24no—
305C11×C4⋊C4—24no—
306C11×C4⋊C4—24no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2×D414yes—
310C11×C4⋊C4C2412yes—
311C11×C4⋊C4C2412yes—
312C11×C22⋊C4—24no—
313C11×C22⋊C4—24no—
314C11×C22⋊C4—24no—
315C11×C22⋊C4—24no—
316C11×C22⋊C4—24no—
317C11×C22⋊C4—24no—
318C11×C22⋊C4—24no—
319C11×C22⋊C4—24no—
320C11×C22⋊C4—24no—
321C11×C22⋊C4C2×D414yes—
322C11×C22⋊C4C2×D414yes—
323C42×C11—24no—
324C42×C11C2×D412yes—
325C42×C11C2412yes—
326C22×#135C2×C1111yescharacteristic, complemented
327C23×SD16C2×C1111yescharacteristic, complemented
328C2×#548C2×C1111yescharacteristic, complemented
329C2×#546C2×C1111yescharacteristic, complemented
330#3282C2×C11116yesdirect product factor
331C2×#495C2×C1111yescharacteristic, complemented
332C2×#465C2×C1111yescharacteristic, complemented
333C2×#465C2×C1111yescharacteristic, complemented
334C2×#464C2×C1111yescharacteristic, complemented
335C2×#463C2×C1111yescharacteristic, complemented
336C2×#452C2×C1111yescharacteristic, complemented
337C2×#449C2×C1111yescharacteristic, complemented
338C2×#451C2×C1111yescharacteristic, complemented
339C2×#447C2×C1111yescharacteristic, complemented
340C2×C4×SD16C2×C1111yescharacteristic, complemented
341C2×C8×D4C2×C1111yescharacteristic, complemented
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—24no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—48no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—48no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—84no—
362C23×C11—816no—
363C23×C11#13514yescomplemented
364C23×C11C22×D412yes—
365C23×C11C22×D412yes—
366C23×C11C22×D411yescharacteristic
367Q8×C11—24no—
368Q8×C11—22no—
369Q8×C11—22no—
370Q8×C11—22no—
371Q8×C11—22no—
372Q8×C11—22no—
373Q8×C11—48no—
374Q8×C11—42no—
375Q8×C11—42no—
376Q8×C11C22×D414yes—
377D4×C11—28no—
378D4×C11—24no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—22no—
382D4×C11—22no—
383D4×C11—22no—
384D4×C11—48no—
385D4×C11—48no—
386D4×C11—48no—
387D4×C11—48no—
388D4×C11—42no—
389D4×C11—42no—
390D4×C11—84no—
391D4×C11C22×D414yes—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—24no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—24no—
399C2×C4×C11—24no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—48no—
409C2×C4×C11—48no—
410C2×C4×C11—48no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—42no—
415C2×C4×C11—84no—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D412yes—
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D412yes—
422C2×C4×C11H(5,𝔽2)12yes—
423C2×C4×C11C2511yescharacteristic
424C8×C11—22no—
425C8×C11—22no—
426C8×C11—22no—
427C8×C11C22×D414yes—
428C22×#41C22×C1111yescharacteristic
429C22×#41C22×C1111yescharacteristic, complemented
430C23×Q8C22×C1111yescharacteristic
431C23×D4C22×C1111yescharacteristic
432C2×#135—28no—
433C2×#135C22×C1118yescomplemented
434C22×Q16C22×C1111yescharacteristic, complemented
435C22×Q16C22×C1111yescharacteristic, complemented
436C22×SD16—28no—
437C22×SD16C22×C1111yescharacteristic
438C22×SD16C22×C1111yescharacteristic
439C22×SD16C22×C1111yescharacteristic
440C22×SD16C22×C1111yescharacteristic
441C22×SD16C22×C1118yescomplemented
442C22×SD16C22×C1111yescharacteristic, complemented
443C22×D8C22×C1111yescharacteristic
444C22×D8C22×C1111yescharacteristic
445C23×C8C22×C1111yescharacteristic
446C23×C8C22×C1111yescharacteristic, complemented
447#548—24no—
448#548C22×C1118yescomplemented
449#546—24no—
450#546C22×C1118yescomplemented
451C2×#124—21no—
452C2×#124C22×C1111yescharacteristic
453C2×#124C22×C1111yescharacteristic, complemented
454C2×#123—21no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C1111yescharacteristic
457C2×C22⋊Q8C22×C1111yescharacteristic, complemented
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C22×C1111yescharacteristic
461C2×#121C22×C1111yescharacteristic
462C2×#120—21no—
463C2×C4×Q8C22×C1111yescharacteristic, complemented
464C2×C4×D4—21no—
465C2×C4×D4C22×C1111yescharacteristic
466C2×C4×D4C22×C1111yescharacteristic
467C22×C22⋊C4—21no—
468#495C22×C1118yescomplemented
469#465C22×C1118yescomplemented
470#465C22×C1118yescomplemented
471#464C22×C1118yescomplemented
472#463C22×C1118yescomplemented
473#452C22×C1118yescomplemented
474#451C22×C1118yescomplemented
475#449C22×C1118yescomplemented
476#447C22×C1118yescomplemented
477C4×SD16C22×C1118yescomplemented
478C8×D4C22×C1118yescomplemented
479C2×#106C22×C1111yescharacteristic, complemented
480C2×C4⋊C8C22×C1111yescharacteristic, complemented
481C2×#103C22×C1111yescharacteristic, complemented
482C2×#103C22×C1111yescharacteristic, complemented
483C2×#103C22×C1111yescharacteristic, complemented
484C2×#102C22×C1111yescharacteristic
485C2×#102C22×C1111yescharacteristic
486C2×#102C22×C1111yescharacteristic, complemented
487C2×C22⋊C8C22×C1111yescharacteristic
488C2×C22⋊C8C22×C1111yescharacteristic, complemented
489C2×C4×C8C22×C1111yescharacteristic, complemented
490C22×C11—22no—
491C22×C11—28no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—24no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—44no—
498C22×C11—48no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—816no—
508C22×C11—84no—
509C22×C11—84no—
510C22×C11D4212yes—
511C22×C11C2×#13512yes—
512C22×C11C2×#13514yescomplemented
513C22×C11#57712yes—
514C22×C11C23×D411yescharacteristic
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—24no—
518C4×C11—22no—
519C4×C11—22no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11D4212yes—
525C4×C11C23×D411yescharacteristic
526C4×C11C2×H(5,𝔽2)11yescharacteristic
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—24no—
531C2×#41—24no—
532C2×#41—42no—
533C2×#41—42no—
534C2×#41C23×C1114yes—
535C2×#41C23×C1114yescomplemented
536C22×Q8—21no—
537C22×Q8—22no—
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8C23×C1111yescharacteristic
541C22×Q8C23×C1111yescharacteristic
542C22×Q8C23×C1114yes—
543C22×Q8C23×C1111yescharacteristic
544C22×D4—24no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—22no—
551C22×D4—42no—
552C22×D4D4×C1111yescharacteristic
553C22×D4C23×C1111yescharacteristic
554C22×D4C23×C1111yescharacteristic
555C22×D4C23×C1114yes—
556C22×D4C23×C1111yescharacteristic
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—21no—
560C23×C4—21no—
561C23×C4C23×C1111yescharacteristic
562C23×C4C23×C1111yescharacteristic
563#135—232no—
564C2×Q16—24no—
565C2×Q16—42no—
566C2×Q16C23×C1114yescomplemented
567C2×Q16C23×C1114yescomplemented
568C2×SD16—24no—
569C2×SD16—24no—
570C2×SD16—232no—
571C2×SD16—24no—
572C2×SD16—24no—
573C2×SD16D4×C1118yescomplemented
574C2×SD16C23×C1114yes—
575C2×SD16C23×C1114yes—
576C2×SD16C23×C1114yes—
577C2×SD16C23×C1114yes—
578C2×SD16C23×C1114yescomplemented
579C2×D8—24no—
580C2×D8—42no—
581C2×D8C23×C1114yes—
582C2×D8C23×C1114yes—
583C22×C8—24no—
584C22×C8—24no—
585C22×C8C23×C1111yescharacteristic
586C22×C8C23×C1114yes—
587C22×C8C23×C1111yescharacteristic
588C22×C8C23×C1111yescharacteristic
589C22×C8C23×C1111yescharacteristic
590C22×C8C23×C1114yescomplemented
591#124—28no—
592#124—22no—
593#124—22no—
594#124C23×C1114yes—
595#124C23×C1114yescomplemented
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—28no—
600C22⋊Q8C23×C1114yes—
601C22⋊Q8C23×C1114yescomplemented
602#121—28no—
603#121—22no—
604#121—22no—
605#121—28no—
606#121C23×C1114yes—
607#121C23×C1114yes—
608#120—28no—
609C4×Q8—22no—
610C4×Q8C23×C1114yescomplemented
611C4×D4—28no—
612C4×D4—22no—
613C4×D4D4×C1114yes—
614C4×D4C23×C1114yes—
615C4×D4C23×C1114yes—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4D4×C1111yescharacteristic
620C2×C4⋊C4C23×C1111yescharacteristic
621C2×C4⋊C4C23×C1111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—28no—
632C2×C22⋊C4D4×C1111yescharacteristic
633C2×C22⋊C4D4×C1111yescharacteristic
634C2×C42—21no—
635C2×C42C23×C1111yescharacteristic
636#106C23×C1114yescomplemented
637C4⋊C8C23×C1114yescomplemented
638#103C23×C1114yescomplemented
639#103C23×C1114yescomplemented
640#103C23×C1114yescomplemented
641#102C23×C1114yes—
642#102C23×C1114yes—
643#102C23×C1114yescomplemented
644C22⋊C8C23×C1114yes—
645C22⋊C8C23×C1114yescomplemented
646C4×C8C23×C1114yescomplemented
647C2×C11—24no—
648C2×C11—42no—
649C2×C11—44no—
650C2×C11—82no—
651C2×C11—82no—
652C2×C11#328214yesdirect product factor
653C2×C11C2×D4211yescharacteristic
654C2×C11C22×#13511yescharacteristic
655C2×C11C2×#57711yescharacteristic
656C24—21no—
657C24—21no—
658C24—21no—
659C24—24no—
660C24—44no—
661C24—44no—
662C24—82no—
663C24C2×D4×C1111yescharacteristic
664C24C2×D4×C1111yescharacteristic
665#41—28no—
666#41—28no—
667#41—44no—
668#41—44no—
669#41—48no—
670#41—48no—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—22no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—48no—
684C2×Q8C2×D4×C1114yes—
685C2×Q8C24×C1112yes—
686C2×Q8C24×C1112yes—
687C2×Q8C24×C1112yes—
688C2×D4—24no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—24no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—82no—
710C2×D4C2×D4×C1114yes—
711C2×D4C2×D4×C1114yes—
712C2×D4C24×C1112yes—
713C2×D4C24×C1112yes—
714C2×D4C24×C1112yes—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—82no—
732C22×C4C2×D4×C1111yescharacteristic
733C22×C4C2×D4×C1111yescharacteristic
734C22×C4C2×D4×C1111yescharacteristic
735C22×C4C2×D4×C1111yescharacteristic
736C22×C4C2×D4×C1112yes—
737C22×C4C2×D4×C1112yes—
738C22×C4C24×C1112yes—
739C22×C4C24×C1112yes—
740C22×C4C24×C1111yescharacteristic
741Q16—28no—
742Q16—44no—
743SD16—28no—
744SD16—28no—
745SD16—28no—
746SD16—28no—
747SD16C2×D4×C11116yescomplemented
748D8—28no—
749D8—44no—
750C2×C8—22no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—28no—
754C2×C8—28no—
755C2×C8C2×D4×C1114yes—
756C2×C8C24×C1112yes—
757C2×C8C24×C1112yes—
758C2×C8C24×C1112yes—
759C2×C8C24×C1112yes—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C1114yes—
766C4⋊C4C24×C1112yes—
767C4⋊C4C24×C1112yes—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4C2×D4×C1114yes—
778C22⋊C4C2×D4×C1114yes—
779C42—24no—
780C42C2×D4×C1112yes—
781C42C24×C1112yes—
782C11C2×#328211yescharacteristic, direct product factor, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—48no—
800C23—42no—
801C23—42no—
802C23—84no—
803C23—816no—
804C23C11×#13514yescomplemented
805C23C22×D4×C1112yes—
806C23C22×D4×C1112yes—
807C23C22×D4×C1111yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—48no—
815Q8—42no—
816Q8—42no—
817Q8C22×D4×C1114yes—
818D4—28no—
819D4—24no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—48no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—42no—
830D4—42no—
831D4—84no—
832D4C22×D4×C1114yes—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—48no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—84no—
857C2×C4C22×D4×C1112yes—
858C2×C4C22×D4×C1112yes—
859C2×C4C22×D4×C1112yes—
860C2×C4C22×D4×C1112yes—
861C2×C4C22×D4×C1111yescharacteristic
862C2×C4C22×D4×C1112yes—
863C2×C4C11×H(5,𝔽2)12yes—
864C2×C4C25×C1111yescharacteristic
865C8—22no—
866C8—22no—
867C8—22no—
868C8C22×D4×C1114yes—
869C22—22no—
870C22—28no—
871C22—22no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—44no—
877C22—48no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—816no—
887C22—84no—
888C22—84no—
889C22D42×C1112yes—
890C22C2×C11×#13512yes—
891C22C2×C11×#13514yescomplemented
892C22C11×#57712yes—
893C22C23×D4×C1111yescharacteristic
894C4—22no—
895C4—22no—
896C4—24no—
897C4—22no—
898C4—22no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—42no—
903C4D42×C1112yes—
904C4C23×D4×C1111yescharacteristic
905C4C2×C11×H(5,𝔽2)11yescharacteristic
906C2—24no—
907C2—42no—
908C2—44no—
909C2—82no—
910C2—82no—
911C2C11×#328214yesdirect product factor
912C2C2×D42×C1111yescharacteristic
913C2C22×C11×#13511yescharacteristic
914C2C2×C11×#57711yescharacteristic
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. C22×C11×#135C2semidirect
2. C23×C11×SD16C2semidirect
3. C2×C11×#548C2semidirect
4. C2×C11×#546C2semidirect
5. C11×#3282C2direct (N × H)
6. C2×C11×#495C2semidirect
7. C2×C11×#465C2semidirect
8. C2×C11×#465C2semidirect
9. C2×C11×#464C2semidirect
10. C2×C11×#463C2semidirect
11. C2×C11×#452C2semidirect
12. C2×C11×#449C2semidirect
13. C2×C11×#451C2semidirect
14. C2×C11×#447C2semidirect
15. C2×C4×C11×SD16C2semidirect
16. C2×C8×D4×C11C2semidirect
18. C22×C11×#41C22semidirect
22. C2×C11×#135C22semidirect
23. C22×C11×Q16C22semidirect
24. C22×C11×Q16C22semidirect
30. C22×C11×SD16C22semidirect
31. C22×C11×SD16C22semidirect
35. C23×C8×C11C22semidirect
37. C11×#548C22semidirect
39. C11×#546C22semidirect
42. C2×C11×#124C22semidirect
46. C2×C11×C22⋊Q8C22semidirect
52. C2×C4×Q8×C11C22semidirect
57. C11×#495C22semidirect
58. C11×#465C22semidirect
59. C11×#465C22semidirect
60. C11×#464C22semidirect
61. C11×#463C22semidirect
62. C11×#452C22semidirect
63. C11×#451C22semidirect
64. C11×#449C22semidirect
65. C11×#447C22semidirect
66. C4×C11×SD16C22semidirect
67. C8×D4×C11C22semidirect
68. C2×C11×#106C22semidirect
69. C2×C11×C4⋊C8C22semidirect
70. C2×C11×#103C22semidirect
71. C2×C11×#103C22semidirect
72. C2×C11×#103C22semidirect
75. C2×C11×#102C22semidirect
77. C2×C11×C22⋊C8C22semidirect
78. C2×C4×C8×C11C22semidirect
87. C2×C11×#41C23semidirect
118. C2×C11×Q16C23semidirect
119. C2×C11×Q16C23semidirect
125. C2×C11×SD16D4semidirect
130. C2×C11×SD16C23semidirect
142. C22×C8×C11C23semidirect
147. C11×#124C23semidirect
153. C11×C22⋊Q8C23semidirect
162. C4×Q8×C11C23semidirect
188. C11×#106C23semidirect
189. C11×C4⋊C8C23semidirect
190. C11×#103C23semidirect
191. C11×#103C23semidirect
192. C11×#103C23semidirect
195. C11×#102C23semidirect
197. C11×C22⋊C8C23semidirect
198. C4×C8×C11C23semidirect
199. C2×#3282C11direct (N × H)
291. C11×SD16C2×D4semidirect
326. C22×#135C2×C11semidirect
327. C23×SD16C2×C11semidirect
328. C2×#548C2×C11semidirect
329. C2×#546C2×C11semidirect
330. #3282C2×C11direct (N × H)
331. C2×#495C2×C11semidirect
332. C2×#465C2×C11semidirect
333. C2×#465C2×C11semidirect
334. C2×#464C2×C11semidirect
335. C2×#463C2×C11semidirect
336. C2×#452C2×C11semidirect
337. C2×#449C2×C11semidirect
338. C2×#451C2×C11semidirect
339. C2×#447C2×C11semidirect
340. C2×C4×SD16C2×C11semidirect
341. C2×C8×D4C2×C11semidirect
363. C23×C11#135semidirect
429. C22×#41C22×C11semidirect
433. C2×#135C22×C11semidirect
434. C22×Q16C22×C11semidirect
435. C22×Q16C22×C11semidirect
441. C22×SD16C22×C11semidirect
442. C22×SD16C22×C11semidirect
446. C23×C8C22×C11semidirect
448. #548C22×C11semidirect
450. #546C22×C11semidirect
453. C2×#124C22×C11semidirect
457. C2×C22⋊Q8C22×C11semidirect
463. C2×C4×Q8C22×C11semidirect
468. #495C22×C11semidirect
469. #465C22×C11semidirect
470. #465C22×C11semidirect
471. #464C22×C11semidirect
472. #463C22×C11semidirect
473. #452C22×C11semidirect
474. #451C22×C11semidirect
475. #449C22×C11semidirect
476. #447C22×C11semidirect
477. C4×SD16C22×C11semidirect
478. C8×D4C22×C11semidirect
479. C2×#106C22×C11semidirect
480. C2×C4⋊C8C22×C11semidirect
481. C2×#103C22×C11semidirect
482. C2×#103C22×C11semidirect
483. C2×#103C22×C11semidirect
486. C2×#102C22×C11semidirect
488. C2×C22⋊C8C22×C11semidirect
489. C2×C4×C8C22×C11semidirect
512. C22×C11C2×#135semidirect
535. C2×#41C23×C11semidirect
566. C2×Q16C23×C11semidirect
567. C2×Q16C23×C11semidirect
573. C2×SD16D4×C11semidirect
578. C2×SD16C23×C11semidirect
590. C22×C8C23×C11semidirect
595. #124C23×C11semidirect
601. C22⋊Q8C23×C11semidirect
610. C4×Q8C23×C11semidirect
636. #106C23×C11semidirect
637. C4⋊C8C23×C11semidirect
638. #103C23×C11semidirect
639. #103C23×C11semidirect
640. #103C23×C11semidirect
643. #102C23×C11semidirect
645. C22⋊C8C23×C11semidirect
646. C4×C8C23×C11semidirect
652. C2×C11#3282direct (N × H)
747. SD16C2×D4×C11semidirect
782. C11C2×#3282direct (N × H)
804. C23C11×#135semidirect
891. C22C2×C11×#135semidirect
911. C2C11×#3282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C23×C11×SD162
C2×C11×#5482
C2×C11×#5462
C11×#32822
C2×C11×#4952
C2×C11×#4652
C2×C11×#4642
C2×C11×#4632
C2×C11×#4522
C2×C11×#4492
C2×C11×#4512
C2×C11×#4472
C2×C4×C11×SD162
C2×C8×D4×C112
C2×#328211