Finite Group Databasebeta

← C2×#13072049 #14921577

Subgroups — C2×#13072049 #14921577

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×#66991C211yesmaximal, characteristic, complemented
5C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
7#13072049C2116yesmaximal, direct product factor
8C2×#10622561C211yesmaximal, characteristic, complemented
9C2×#10622607C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yescomplemented
37C2×#66991—28no—
38C2×#66991C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×C4⋊C4×D11—28no—
53C2×C4⋊C4×D11C2218yescomplemented
54C2×#66937—28no—
55C2×#66937—28no—
56C2×#66937C2218yescomplemented
57C2×#66937C2218yescomplemented
58C2×(C22⋊D11)⋊C4—28no—
59C2×(C22⋊D11)⋊C4C2218yescomplemented
60C11×#394C2218yescomplemented
61C2×C11×#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622607C2218yescomplemented
66#10622574C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622561C2218yescomplemented
70#10622555C2218yescomplemented
71#10622278C2218yescomplemented
72#10622260C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11D418yescomplemented
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11—24no—
103C23×Dic11—24no—
104C23×Dic11—24no—
105C23×Dic11C2314yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—24no—
115C22×D44C2314yes—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—24no—
121C22×C4×D11—24no—
122C22×C4×D11—42no—
123C22×C4×D11—42no—
124C22×C4×D11D418yescomplemented
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yes—
127C22×C4×D11C2314yes—
128C2×C11×C4⋊C4—24no—
129C2×C11×C4⋊C4C2314yes—
130C2×C11×C22⋊C4—24no—
131C2×C11×C22⋊C4—24no—
132C2×C11×C22⋊C4—24no—
133C2×C11×C22⋊C4—42no—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C22⋊Dic11—24no—
139C2×C22⋊Dic11—24no—
140C2×C22⋊Dic11—24no—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144#66992—232no—
145#66991—232no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—42no—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×C4⋊Dic11—24no—
157C2×C4⋊Dic11—24no—
158C2×C4⋊Dic11C2314yes—
159C2×C4⋊Dic11C2314yes—
160C2×Dic11⋊C4—24no—
161C2×Dic11⋊C4—24no—
162C2×Dic11⋊C4—24no—
163C2×Dic11⋊C4—24no—
164C2×Dic11⋊C4D418yescomplemented
165C2×Dic11⋊C4C2314yes—
166C2×Dic11⋊C4C2314yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170C2×C4×Dic11—24no—
171C2×C4×Dic11C2314yes—
172C4⋊C4×D11—232no—
173#66937—232no—
174#66937—232no—
175(C22⋊D11)⋊C4—232no—
176C11×#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C2×#2416—111nomaximal, Sylow
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11C2×D414yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11C2×D414yes—
210C23×D11C2×D414yes—
211C23×D11#4114yes—
212C23×D11C2412yes—
213C23×D11C2412yes—
214C2×D4×C11—28no—
215C2×D4×C11—28no—
216C2×D4×C11—44no—
217C2×D4×C11—416no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11C2×D414yes—
232C22×C4×C11C2×D414yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—416no—
251C2×C22⋊D11—416no—
252C2×C22⋊D11—416no—
253C2×C22⋊D11C2×D4116yescomplemented
254C22×Dic11—28no—
255C22×Dic11—28no—
256C22×Dic11—28no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—416no—
271C22×Dic11C2×D414yes—
272C22×Dic11C2×D414yes—
273C22×Dic11C2×D414yes—
274C22×Dic11C2×D414yes—
275C22×Dic11#4114yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—28no—
285C2×D44—416no—
286C2×C4×D11—232no—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—28no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—416no—
296C2×C4×D11—416no—
297C2×C4×D11C2×D4116yescomplemented
298C11×C4⋊C4—28no—
299C11×C22⋊C4—28no—
300C11×C22⋊C4—28no—
301C11×C22⋊C4—28no—
302C11×C22⋊C4—44no—
303C22⋊Dic11—28no—
304C22⋊Dic11—28no—
305C22⋊Dic11—28no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—28no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—44no—
311C4⋊Dic11—28no—
312C4⋊Dic11—28no—
313Dic11⋊C4—28no—
314Dic11⋊C4—28no—
315Dic11⋊C4—28no—
316Dic11⋊C4—28no—
317Dic11⋊C4C2×D4116yescomplemented
318C4×Dic11—28no—
319C22×#121—111no—
320C22×#121—111no—
321C22×#121—111no—
322C22×#121—111no—
323C22×C4×D4—111no—
324C23×C4⋊C4—111no—
325#2416—1116no—
326C2×#396—111no—
327C2×#396—111no—
328C2×#394—111no—
329C2×#394D1111yescharacteristic, complemented
330C2×#390—111no—
331C2×#389—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#380—111no—
335C23×C11—28no—
336C23×C11—28no—
337C23×C11—28no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11C22×D414yes—
363C23×C11C22×D412yes—
364C23×C11C22×D412yes—
365C23×C11C22×D412yes—
366C23×C11C2×#4112yes—
367C23×C11C2×#4112yes—
368C23×C11H(5,𝔽2)12yes—
369C23×C112−1+412yes—
370C23×C11C2511yescharacteristic
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—28no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11#121116yescomplemented
396C22×D11C22×D414yes—
397C22×D11C22×D414yes—
398C22×D11C2×#4114yes—
399D4×C11—416no—
400C2×C4×C11—28no—
401C2×C4×C11—28no—
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—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11C22×D414yes—
419C2×C4×C11C22×D414yes—
420C22⋊D11—232no—
421C22⋊D11—416no—
422C22⋊D11—416no—
423C22⋊D11—416no—
424C2×Dic11—28no—
425C2×Dic11—28no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11—416no—
443C2×Dic11#121116yescomplemented
444C2×Dic11C22×D414yes—
445C2×Dic11C22×D414yes—
446C2×Dic11C22×D414yes—
447C2×Dic11C22×D414yes—
448C2×Dic11C2×#4114yes—
449D44—416no—
450C4×D11—232no—
451C4×D11—416no—
452C4×D11—416no—
453C23×D4—111no—
454C23×D4—111no—
455C23×D4—111no—
456C23×D4—111no—
457C23×D4—111no—
458C23×D4C2×D1111yescharacteristic
459C24×C4—111no—
460C24×C4—111no—
461C24×C4—111no—
462C24×C4—111no—
463C2×#121—118no—
464C2×#121—118no—
465C2×#121—118no—
466C2×#121—118no—
467C2×#121—228no—
468C2×#121—228no—
469C2×#121—228no—
470C2×#121—228no—
471C2×C4×D4—118no—
472C2×C4×D4—228no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—118no—
481C22×C4⋊C4—228no—
482C22×C4⋊C4C2×D1111yescharacteristic
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4C2×D1111yescharacteristic
492C22×C22⋊C4C2×D1111yescharacteristic
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C42—111no—
496#396—118no—
497#396—118no—
498#394—118no—
499#394C2×D1118yescomplemented
500#390—118no—
501#389—118no—
502#386—118no—
503#386—118no—
504#380—118no—
505C2×#95—111no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95C2×D1111yescharacteristic
509C22×C11—24no—
510C22×C11—24no—
511C22×C11—24no—
512C22×C11—42no—
513C22×C11—416no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—88no—
525C22×C11C2×#12114yes—
526C22×C11C2×#12114yes—
527C22×C11#53714yes—
528C22×C11D4214yes—
529C22×C11#54714yes—
530C22×C11#54814yes—
531C22×C11#55314yes—
532C22×C11C23×D411yescharacteristic
533C22×C11C23×D411yescharacteristic
534C22×C11C23×D411yescharacteristic
535C22×C11C22×#4111yescharacteristic
536C22×C11C22×#4111yescharacteristic
537C22×C11C2×H(5,𝔽2)11yescharacteristic
538C22×C11C2×2−1+411yescharacteristic
539C2×D11—24no—
540C2×D11—232no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—88no—
554C2×D11C2×#12118yescomplemented
555C4×C11—24no—
556C4×C11—24no—
557C4×C11—42no—
558C4×C11—42no—
559C4×C11—42no—
560Dic11—24no—
561Dic11—24no—
562Dic11—42no—
563Dic11—42no—
564Dic11—42no—
565Dic11C2×#12118yescomplemented
566C25—111no—
567C25—111no—
568C25C22×D1111yescharacteristic
569C25C22×D1111yescharacteristic
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—42no—
573C22×D4—118no—
574C22×D4—114no—
575C22×D4—114no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—224no—
587C22×D4—224no—
588C22×D4—224no—
589C22×D4—224no—
590C22×D4—224no—
591C22×D4—224no—
592C22×D4—442no—
593C22×D4C22×D1114yes—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—118no—
598C23×C4—114no—
599C23×C4—114no—
600C23×C4—111no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—114no—
604C23×C4—114no—
605C23×C4—224no—
606C23×C4—224no—
607C23×C4—224no—
608C23×C4—224no—
609C23×C4—224no—
610C23×C4—224no—
611C23×C4—224no—
612C23×C4—224no—
613C23×C4—224no—
614C23×C4—442no—
615C23×C4—442no—
616C23×C4C22×D1111yescharacteristic
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621#121—2232no—
622#121—2232no—
623#121—2232no—
624#121—2232no—
625C4×D4—2232no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—118no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—2232no—
636C2×C4⋊C4—224no—
637C2×C4⋊C4—224no—
638C2×C4⋊C4—224no—
639C2×C4⋊C4—224no—
640C2×C4⋊C4—224no—
641C2×C4⋊C4—224no—
642C2×C4⋊C4C22×D1114yes—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—224no—
656C2×C22⋊C4—224no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—442no—
663C2×C22⋊C4C22×D1114yes—
664C2×C22⋊C4C22×D1114yes—
665C2×C22⋊C4C22×D1114yes—
666C2×C22⋊C4C22×D1114yes—
667C2×C42—114no—
668C2×C42—224no—
669#95—114no—
670#95—114no—
671#95—114no—
672#95C22×D1114yes—
673C2×C11—44no—
674C2×C11—82no—
675C2×C11#241618yescomplemented
676C2×C11C22×#12111yescharacteristic
677C2×C11C22×#12111yescharacteristic
678C2×C11C2×#53711yescharacteristic
679C2×C11C2×D4211yescharacteristic
680C2×C11C2×#54711yescharacteristic
681C2×C11C2×#54811yescharacteristic
682C2×C11C2×#55311yescharacteristic
683D11—28no—
684D11—82no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—114no—
699C24—114no—
700C24—114no—
701C24—112no—
702C24—112no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24D4×D1114yes—
715C24C23×D1112yes—
716C24C23×D1112yes—
717C24C23×D1111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—44no—
721C2×D4—416no—
722C2×D4—1116no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—2232no—
732C2×D4—228no—
733C2×D4—228no—
734C2×D4—228no—
735C2×D4—228no—
736C2×D4—228no—
737C2×D4—4416no—
738C2×D4—4416no—
739C2×D4—444no—
740C2×D4—4416no—
741C2×D4—4416no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—114no—
758C22×C4—112no—
759C22×C4—114no—
760C22×C4—114no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—1116no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—228no—
768C22×C4—2232no—
769C22×C4—228no—
770C22×C4—228no—
771C22×C4—228no—
772C22×C4—228no—
773C22×C4—228no—
774C22×C4—228no—
775C22×C4—228no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—228no—
790C22×C4—444no—
791C22×C4—444no—
792C22×C4—4416no—
793C22×C4—4416no—
794C22×C4—4416no—
795C22×C4D4×D1114yes—
796C22×C4D4×D1114yes—
797C22×C4C23×D1112yes—
798C22×C4C23×D1112yes—
799C22×C4C23×D1112yes—
800C22×C4C23×D1112yes—
801C22×C4C23×D1112yes—
802C4⋊C4—28no—
803C4⋊C4—1116no—
804C4⋊C4—228no—
805C4⋊C4—228no—
806C4⋊C4—228no—
807C4⋊C4—228no—
808C4⋊C4—228no—
809C4⋊C4—228no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—44no—
814C22⋊C4—228no—
815C22⋊C4—228no—
816C22⋊C4—228no—
817C22⋊C4—228no—
818C22⋊C4—228no—
819C22⋊C4—228no—
820C22⋊C4—228no—
821C22⋊C4—444no—
822C42—228no—
823C11C2×#241611yescharacteristic, complemented, Sylow
824C23—28no—
825C23—28no—
826C23—28no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—1116no—
852C23—114no—
853C23—114no—
854C23—114no—
855C23—228no—
856C23—228no—
857C23—228no—
858C23—228no—
859C23—222no—
860C23—222no—
861C23—228no—
862C23—222no—
863C23—222no—
864C23—228no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—444no—
873C23—444no—
874C23—444no—
875C23—444no—
876C23—444no—
877C23—444no—
878C23—444no—
879C23C2×D4×D1114yes—
880C23C2×D4×D1112yes—
881C23C2×D4×D1112yes—
882C23C2×D4×D1112yes—
883C23#6703712yes—
884C23#41×D1112yes—
885C23#41×D1112yes—
886C23#6704312yes—
887C23C24×D1111yescharacteristic
888D4—416no—
889D4—2232no—
890D4—4416no—
891D4—4416no—
892D4—4416no—
893D4—4416no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—1116no—
913C2×C4—114no—
914C2×C4—114no—
915C2×C4—114no—
916C2×C4—114no—
917C2×C4—114no—
918C2×C4—2232no—
919C2×C4—228no—
920C2×C4—228no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—4416no—
935C2×C4—4416no—
936C2×C4—4416no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4C2×D4×D1114yes—
941C2×C4C2×D4×D1114yes—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—42no—
946C22—42no—
947C22—416no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—88no—
958C22—118no—
959C22—224no—
960C22—224no—
961C22—2232no—
962C22—224no—
963C22—224no—
964C22—224no—
965C22—224no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—888no—
974C22#1062312114yes—
975C22D11×#12114yes—
976C22D11×#12114yes—
977C22#1062313914yes—
978C22#1062318614yes—
979C22#1062319214yes—
980C22#1062320814yes—
981C22C22×D4×D1111yescharacteristic
982C22C22×D4×D1111yescharacteristic
983C22C22×D4×D1111yescharacteristic
984C22C2×#6703711yescharacteristic
985C22C2×#41×D1111yescharacteristic
986C22C2×#41×D1111yescharacteristic
987C22C2×#6704311yescharacteristic
988C4—24no—
989C4—24no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—118no—
994C4—224no—
995C4—224no—
996C4—442no—
997C4—442no—
998C4—442no—
999C2—44no—
1000C2—82no—
1001C2—228no—
1002C2—882no—
1003C2#1307204918yesdirect product factor
1004C2C2×D11×#12111yescharacteristic
1005C2C2×D11×#12111yescharacteristic
1006C2C2×#1062313911yescharacteristic
1007C2C2×#1062312111yescharacteristic
1008C2C2×#1062318611yescharacteristic
1009C2C2×#1062320811yescharacteristic
1010C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2416
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66937C2semidirect
3. C22×#66992C2semidirect
4. C22×#66991C2semidirect
5. C22×(C22⋊D11)⋊C4C2semidirect
6. C22×C4⋊C4×D11C2semidirect
7. #13072049C2direct (N × H)
8. C2×#10622561C2semidirect
9. C2×#10622607C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#394C2semidirect
36. C2×#66992C22semidirect
38. C2×#66991C22semidirect
53. C2×C4⋊C4×D11C22semidirect
56. C2×#66937C22semidirect
57. C2×#66937C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
60. C11×#394C22semidirect
65. #10622607C22semidirect
66. #10622574C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622561C22semidirect
70. #10622555C22semidirect
71. #10622278C22semidirect
72. #10622260C22semidirect
97. C22×C22⋊D11D4semidirect
124. C22×C4×D11D4semidirect
164. C2×Dic11⋊C4D4semidirect
253. C2×C22⋊D11C2×D4semidirect
297. C2×C4×D11C2×D4semidirect
317. Dic11⋊C4C2×D4semidirect
329. C2×#394D11semidirect
395. C22×D11#121semidirect
443. C2×Dic11#121semidirect
499. #394C2×D11semidirect
554. C2×D11C2×#121semidirect
565. Dic11C2×#121semidirect
675. C2×C11#2416semidirect
823. C11C2×#2416semidirect
1003. C2#13072049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669922
C22×#669912
C22×(C22⋊D11)⋊C42
C22×C4⋊C4×D112
#130720492
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225702
C2×#106222602
C2×#106222782
C2×#106225692
C2×#106225552
C2×C11×#3942
C2×#241611