Finite Group Databasebeta

← C2×#13072033 #14922096

Subgroups — C2×#13072033 #14922096

Order 2816.

4174 conjugacy classes of subgroups.

The subgroup lattice has 980 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×#66946C211yesmaximal, characteristic, complemented
4C22×#66925C211yesmaximal, characteristic, complemented
5#13072033C2116yesmaximal, direct product factor
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622570C211yesmaximal, characteristic, complemented
13C2×#10622260C211yesmaximal, characteristic, complemented
14C2×#10622603C211yesmaximal, characteristic, complemented
15C2×#10622280C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66946—28no—
49C2×#66946C2218yescomplemented
50C2×#66937—28no—
51C2×#66937—28no—
52C2×#66937C2218yescomplemented
53C2×#66937C2218yescomplemented
54C2×#66925—28no—
55C2×#66925C2218yescomplemented
56C11×#388C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622603C2218yescomplemented
62#10622574C2218yescomplemented
63#10622573C2218yescomplemented
64#10622570C2218yescomplemented
65#10622570C2218yescomplemented
66#10622552C2218yescomplemented
67#10622285C2218yescomplemented
68#10622284C2218yescomplemented
69#10622280C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—42no—
105C22×D44—42no—
106C22×D44—42no—
107C22×D44C2314yes—
108C22×D44C2314yes—
109C22×D44C2314yes—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—24no—
115C22×C4×D11D418yescomplemented
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C42×C11—24no—
127C2×C42×C11C2314yes—
128C2×C22⋊Dic11—42no—
129C2×C22⋊Dic11C2314yes—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×C4⋊Dic11—42no—
151C2×C4⋊Dic11C2314yes—
152C2×Dic11⋊C4—24no—
153C2×Dic11⋊C4—24no—
154C2×Dic11⋊C4—42no—
155C2×Dic11⋊C4D418yescomplemented
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×C4×Dic11—24no—
161C2×C4×Dic11—24no—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164#66946—232no—
165#66937—232no—
166#66937—232no—
167#66925—232no—
168C11×#95C2314yes—
169C11×#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2414—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11C2×D414yes—
202C23×D11#4114yes—
203C23×D11C2412yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11C2×D414yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11#4114yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—416no—
240C2×C22⋊D11—416no—
241C2×C22⋊D11—416no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11C2×D414yes—
254C22×Dic11C2×D414yes—
255C22×Dic11C2×D414yes—
256C22×Dic11#4114yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C2×D44—232no—
263C2×D44—28no—
264C2×D44—28no—
265C2×D44—28no—
266C2×D44—28no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—44no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—416no—
273C2×D44—416no—
274C2×C4×D11—232no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—416no—
281C2×C4×D11C2×D4116yescomplemented
282C11×C4⋊C4—28no—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—28no—
285C11×C22⋊C4—28no—
286C42×C11—28no—
287C22⋊Dic11—44no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—44no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298C4⋊Dic11—44no—
299Dic11⋊C4—28no—
300Dic11⋊C4—28no—
301Dic11⋊C4—44no—
302Dic11⋊C4C2×D4116yescomplemented
303C4×Dic11—28no—
304C4×Dic11—28no—
305C22×#121—111no—
306C22×#121—111no—
307C22×C4×D4—111no—
308C22×#117—111no—
309#2414—1116no—
310C2×#394—111no—
311C2×#394—111no—
312C2×#392—111no—
313C2×#392—111no—
314C2×#390—111no—
315C2×#390—111no—
316C2×#390—111no—
317C2×#389—111no—
318C2×#388—111no—
319C2×#388D1111yescharacteristic, complemented
320C2×#380—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11C22×D412yes—
336C23×C11C22×D412yes—
337C23×C11C2×#4112yes—
338C23×C11C2×#4112yes—
339C23×C11C2×#4112yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11C2511yescharacteristic
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—44no—
373C22×D11—44no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11C22×D414yes—
384C22×D11C2×#4114yes—
385C2×C4×C11—28no—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C22×D414yes—
408C2×C4×C11C2×#4114yes—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C22⋊D11—416no—
412C2×Dic11—28no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—44no—
425C2×Dic11—44no—
426C2×Dic11—44no—
427C2×Dic11#121116yes—
428C2×Dic11C22×D414yes—
429C2×Dic11C22×D414yes—
430C2×Dic11C22×D414yes—
431C2×Dic11C2×#4114yes—
432D44—232no—
433D44—416no—
434D44—416no—
435C4×D11—232no—
436C4×D11—416no—
437C23×D4—111no—
438C23×D4—111no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C24×C4—111no—
444C24×C4—111no—
445C2×#121—118no—
446C2×#121—118no—
447C2×#121—228no—
448C2×#121—228no—
449C2×C4×D4—118no—
450C2×C4×D4—228no—
451C2×#117—118no—
452C2×#117—228no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4C2×D1111yescharacteristic
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42C2×D1111yescharacteristic
476#394—118no—
477#394—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#390—118no—
482#390—118no—
483#389—118no—
484#388—118no—
485#388C2×D1118yescomplemented
486#380—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—88no—
499C22×C11C2×#12114yes—
500C22×C11#52514yes—
501C22×C11#53514yes—
502C22×C11#54614yes—
503C22×C11#55014yes—
504C22×C11#55314yes—
505C22×C11#55514yes—
506C22×C11C23×D411yescharacteristic
507C22×C11C23×D411yescharacteristic
508C22×C11C22×#4111yescharacteristic
509C22×C11C22×#4111yescharacteristic
510C22×C11C22×#4111yescharacteristic
511C22×C11C2×H(5,𝔽2)11yescharacteristic
512C22×C11C2×H(5,𝔽2)11yescharacteristic
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—42no—
520C2×D11—416no—
521C2×D11—416no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—88no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—24no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11C2×#12118yes—
548C25—111no—
549C25—111no—
550C25—111no—
551C25C22×D1111yescharacteristic
552C22×D4—114no—
553C22×D4—114no—
554C22×D4—114no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—224no—
559C22×D4—224no—
560C22×D4—224no—
561C22×D4—224no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
565C22×D4—224no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—442no—
571C22×D4—442no—
572C22×D4—442no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4—442no—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—118no—
579C23×C4—114no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—114no—
584C23×C4—224no—
585C23×C4—224no—
586C23×C4—224no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4C22×D1111yescharacteristic
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595#121—2232no—
596#121—2232no—
597C4×D4—2232no—
598#117—2232no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—118no—
601C2×C4⋊C4—114no—
602C2×C4⋊C4—114no—
603C2×C4⋊C4—114no—
604C2×C4⋊C4—114no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—224no—
607C2×C4⋊C4—224no—
608C2×C4⋊C4—442no—
609C2×C4⋊C4—442no—
610C2×C4⋊C4C22×D1114yes—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—224no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—442no—
633C2×C22⋊C4—442no—
634C2×C22⋊C4—442no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—24no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—224no—
643C2×C42—224no—
644C2×C42C22×D1114yes—
645#95—114no—
646#95—114no—
647#95C22×D1114yes—
648#95C22×D1114yes—
649C2×C11—82no—
650C2×C11#241418yescomplemented
651C2×C11C22×#12111yescharacteristic
652C2×C11C2×#52511yescharacteristic
653C2×C11C2×#53511yescharacteristic
654C2×C11C2×#54611yescharacteristic
655C2×C11C2×#55011yescharacteristic
656C2×C11C2×#55311yescharacteristic
657C2×C11C2×#55511yescharacteristic
658D11—44no—
659D11—44no—
660D11—82no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—114no—
669C24—114no—
670C24—112no—
671C24—112no—
672C24—112no—
673C24—222no—
674C24—222no—
675C24—222no—
676C24—222no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24C23×D1112yes—
693C24C23×D1111yescharacteristic
694C2×D4—228no—
695C2×D4—228no—
696C2×D4—2232no—
697C2×D4—228no—
698C2×D4—228no—
699C2×D4—228no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—444no—
708C2×D4—444no—
709C2×D4—444no—
710C2×D4—4416no—
711C2×D4—4416no—
712C2×D4—4416no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—4416no—
717C2×D4—4416no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—112no—
737C22×C4—114no—
738C22×C4—112no—
739C22×C4—1116no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—228no—
744C22×C4—2232no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—4416no—
761C22×C4#433914yes—
762C22×C4D4×D1114yes—
763C22×C4D4×D1114yes—
764C22×C4C23×D1112yes—
765C22×C4C23×D1112yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1112yes—
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C4⋊C4—28no—
771C4⋊C4—1116no—
772C4⋊C4—228no—
773C4⋊C4—228no—
774C4⋊C4—444no—
775C4⋊C4—444no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—228no—
780C22⋊C4—228no—
781C22⋊C4—228no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—444no—
787C22⋊C4—444no—
788C22⋊C4—444no—
789C22⋊C4—444no—
790C42—28no—
791C42—228no—
792C42—228no—
793C11C2×#241411yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—114no—
809C23—114no—
810C23—228no—
811C23—228no—
812C23—228no—
813C23—228no—
814C23—228no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—228no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—444no—
836C23—444no—
837C23—444no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23C2×#433912yes—
851C23C2×D4×D1112yes—
852C23C2×D4×D1112yes—
853C23#41×D1112yes—
854C23#41×D1112yes—
855C23#6704212yes—
856C23#6704212yes—
857C23C24×D1111yescharacteristic
858D4—2232no—
859D4—4416no—
860D4—4416no—
861D4—4416no—
862D4—4416no—
863D4—4416no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—1116no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—114no—
890C2×C4—2232no—
891C2×C4—228no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—4416no—
904C2×C4—444no—
905C2×C4—444no—
906C2×C4—444no—
907C2×C4C2×#433914yes—
908C2×C4C2×D4×D1114yes—
909C2×C4C2×D4×D1114yes—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—88no—
918C22—224no—
919C22—224no—
920C22—224no—
921C22—224no—
922C22—224no—
923C22—224no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—4416no—
929C22—4416no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—888no—
942C22#1062306314yes—
943C22#1062307814yes—
944C22#1062308414yes—
945C22D11×#12114yes—
946C22#1062318514yes—
947C22#1062320514yes—
948C22#1062324014yes—
949C22C22×#433911yescharacteristic
950C22C22×D4×D1111yescharacteristic
951C22C22×D4×D1111yescharacteristic
952C22C2×#41×D1111yescharacteristic
953C22C2×#41×D1111yescharacteristic
954C22C2×#6704211yescharacteristic
955C22C2×#6704211yescharacteristic
956C4—24no—
957C4—24no—
958C4—24no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—118no—
963C4—224no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—82no—
968C2—444no—
969C2—444no—
970C2—882no—
971C2#1307203318yesdirect product factor
972C2C2×D11×#12111yescharacteristic
973C2C2×#1062307811yescharacteristic
974C2C2×#1062320511yescharacteristic
975C2C2×#1062318511yescharacteristic
976C2C2×#1062308411yescharacteristic
977C2C2×#1062324011yescharacteristic
978C2C2×#1062306311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
hypercenterC2×#388D11
hypocenterC11C2×#2414
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66937C2semidirect
3. C22×#66946C2semidirect
4. C22×#66925C2semidirect
5. #13072033C2direct (N × H)
6. C2×#10622285C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622570C2semidirect
13. C2×#10622260C2semidirect
14. C2×#10622603C2semidirect
15. C2×#10622280C2semidirect
16. C2×C11×#388C2semidirect
49. C2×#66946C22semidirect
52. C2×#66937C22semidirect
53. C2×#66937C22semidirect
55. C2×#66925C22semidirect
56. C11×#388C22semidirect
61. #10622603C22semidirect
62. #10622574C22semidirect
63. #10622573C22semidirect
64. #10622570C22semidirect
65. #10622570C22semidirect
66. #10622552C22semidirect
67. #10622285C22semidirect
68. #10622284C22semidirect
69. #10622280C22semidirect
70. #10622260C22semidirect
115. C22×C4×D11D4semidirect
155. C2×Dic11⋊C4D4semidirect
281. C2×C4×D11C2×D4semidirect
302. Dic11⋊C4C2×D4semidirect
319. C2×#388D11semidirect
485. #388C2×D11semidirect
650. C2×C11#2414semidirect
793. C11C2×#2414semidirect
971. C2#13072033direct (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×#669462
C22×#669252
#130720332
C2×#106222852
C2×#106225742
C2×#106222842
C2×#106225732
C2×#106225522
C2×#106225702
C2×#106222602
C2×#106226032
C2×#106222802
C2×C11×#3882
C2×#241411