Finite Group Databasebeta

← C2×#13072509 #14921278

Subgroups — C2×#13072509 #14921278

Order 2816.

4282 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072509C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622268C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×#10622281C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66991—28no—
37C2×#66991C2218yescomplemented
38C2×#66988—28no—
39C2×#66988C2218yescomplemented
40C2×D4×Dic11—28no—
41C2×D4×Dic11C2218yescomplemented
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C11×#392C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56#10622836C2218yescomplemented
57#10622836C2218yescomplemented
58#10622833C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622571C2218yescomplemented
65#10622570C2218yescomplemented
66#10622564C2218yescomplemented
67#10622561C2218yescomplemented
68#10622558C2218yescomplemented
69#10622281C2218yescomplemented
70#10622268C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11—42no—
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C22×D4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—42no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C23×Dic11—24no—
104C23×Dic11—24no—
105C23×Dic11—24no—
106C23×Dic11—24no—
107C23×Dic11—42no—
108C23×Dic11—42no—
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2314yes—
113C23×Dic11C2314yes—
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—42no—
121C22×C4×D11C2314yes—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—42no—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—42no—
134C2×C22⋊Dic11D418yescomplemented
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142#66991—232no—
143#66988—232no—
144D4×Dic11—232no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—42no—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×C4⋊Dic11—24no—
152C2×C4⋊Dic11—24no—
153C2×C4⋊Dic11C2314yes—
154C2×C4⋊Dic11C2314yes—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—42no—
157C2×Dic11⋊C4D418yescomplemented
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165(C22⋊D11)⋊C4—232no—
166C11×#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2456—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
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×C11C2×D414yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
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#4114yes—
205C23×D11C2412yes—
206C2×D4×C11—232no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C2×D4×C11—28no—
211C2×D4×C11—28no—
212C2×D4×C11—28no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—416no—
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×C11C2×D414yes—
229C22×C4×C11#4114yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—232no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—28no—
247C22×Dic11—28no—
248C22×Dic11—28no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—28no—
256C22×Dic11—22no—
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—44no—
268C22×Dic11—44no—
269C22×Dic11—416no—
270C22×Dic11—416no—
271C22×Dic11C2×D414yes—
272C22×Dic11C2×D414yes—
273C22×Dic11C2×D414yes—
274C22×Dic11C2×D414yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—416no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—44no—
289C22⋊Dic11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295C22⋊Dic11C2×D4116yescomplemented
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—44no—
299C4⋊Dic11—28no—
300C4⋊Dic11—28no—
301Dic11⋊C4—28no—
302Dic11⋊C4—44no—
303Dic11⋊C4C2×D4116yescomplemented
304C4×Dic11—28no—
305C4×Dic11—28no—
306C22×#123—111no—
307C22×#121—111no—
308C22×C4×D4—111no—
309C22×C4×D4—111no—
310#2456—1116no—
311C2×#396—111no—
312C2×#392—111no—
313C2×#392—111no—
314C2×#392D1111yescharacteristic, complemented
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#387—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
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—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
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×C11C2×#4114yes—
366C23×C11C2×#4112yes—
367C23×C11C2×#4112yes—
368C23×C11C2×#4112yes—
369C23×C11H(5,𝔽2)12yes—
370C23×C11H(5,𝔽2)12yes—
371C23×C11C2511yescharacteristic
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11C2×#4114yes—
386D4×C11—232no—
387D4×C11—416no—
388D4×C11—416no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
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—44no—
402C2×C4×C11—44no—
403C2×C4×C11C22×D414yes—
404C2×C4×C11C2×#4114yes—
405C22⋊D11—232no—
406C22⋊D11—416no—
407C22⋊D11—416no—
408C2×Dic11—28no—
409C2×Dic11—28no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—22no—
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—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—416no—
430C2×Dic11—416no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11—44no—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D414yes—
436C2×Dic11C22×D414yes—
437C2×Dic11C22×D414yes—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4C2×D1111yescharacteristic
443C23×D4C2×D1111yescharacteristic
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4—111no—
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—228no—
452C2×C4×D4—118no—
453C2×C4×D4—118no—
454C2×C4×D4—228no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊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⋊C4—111no—
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42—111no—
476#396—118no—
477#392—118no—
478#392—118no—
479#392C2×D1118yescomplemented
480#390—118no—
481#388—118no—
482#388—118no—
483#387—118no—
484#386—118no—
485#386—118no—
486#385—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
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—416no—
508C22×C11—416no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—88no—
517C22×C11#52514yes—
518C22×C11#52514yes—
519C22×C11#53814yes—
520C22×C11D4214yes—
521C22×C11#54614yes—
522C22×C11#55014yes—
523C22×C11#55314yes—
524C22×C11C23×D411yescharacteristic
525C22×C11C23×D411yescharacteristic
526C22×C11C22×#4111yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C2×H(5,𝔽2)11yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25C22×D1111yescharacteristic
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4C22×D1114yes—
576C22×D4C22×D1114yes—
577C22×D4C22×D1114yes—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—114no—
586C23×C4—114no—
587C23×C4—114no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4—442no—
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603C4×D4—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—118no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—442no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—118no—
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—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4C22×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11—44no—
653C2×C11—82no—
654C2×C11#245618yescomplemented
655C2×C11C2×#52511yescharacteristic
656C2×C11C2×#52511yescharacteristic
657C2×C11C2×#53811yescharacteristic
658C2×C11C2×D4211yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#55011yescharacteristic
661C2×C11C2×#55311yescharacteristic
662D11—44no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—114no—
683C24—112no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24D4×D1114yes—
691C24#434114yes—
692C24C23×D1112yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—232no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—416no—
707C2×D4—416no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—2232no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—4416no—
719C2×D4—4416no—
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—114no—
731C22×C4—114no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—228no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
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—228no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—228no—
764C22×C4—444no—
765C22×C4—4416no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4—4416no—
770C22×C4D4×D1114yes—
771C22×C4#434114yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—1116no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—444no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—1116no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—444no—
793C22⋊C4—444no—
794C42—228no—
795C42—228no—
796C11C2×#245611yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—28no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—114no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23C2×D4×D1114yes—
852C23C2×D4×D1112yes—
853C23C2×D4×D1112yes—
854C23C2×#434114yes—
855C23C2×#434112yes—
856C23C2×#434112yes—
857C23#6703712yes—
858C23#6703712yes—
859C23#41×D1112yes—
860C23C24×D1111yescharacteristic
861D4—232no—
862D4—416no—
863D4—416no—
864D4—2232no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
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—44no—
880C2×C4—44no—
881C2×C4—114no—
882C2×C4—114no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—228no—
886C2×C4—228no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
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—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—4416no—
907C2×C4—4416no—
908C2×C4—4416no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4—444no—
912C2×C4C2×D4×D1114yes—
913C2×C4C2×#434114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—416no—
925C22—416no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—88no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—442no—
942C22—4416no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22#1062311714yes—
947C22#1062312114yes—
948C22#1062312414yes—
949C22#1062313714yes—
950C22#1062314114yes—
951C22#1062314514yes—
952C22#1062324914yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×#434111yescharacteristic
956C22C22×#434111yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#6703711yescharacteristic
959C22C2×#41×D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—224no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—44no—
973C2—82no—
974C2—444no—
975C2#1307250918yesdirect product factor
976C2C2×#1062311711yescharacteristic
977C2C2×#1062313711yescharacteristic
978C2C2×#1062312411yescharacteristic
979C2C2×#1062312111yescharacteristic
980C2C2×#1062314111yescharacteristic
981C2C2×#1062324911yescharacteristic
982C2C2×#1062314511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2456
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×#66991C2semidirect
3. C22×D4×Dic11C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072509C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622268C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622571C2semidirect
15. C2×#10622281C2semidirect
16. C2×C11×#392C2semidirect
37. C2×#66991C22semidirect
39. C2×#66988C22semidirect
41. C2×D4×Dic11C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C11×#392C22semidirect
56. #10622836C22semidirect
57. #10622836C22semidirect
58. #10622833C22semidirect
64. #10622571C22semidirect
65. #10622570C22semidirect
66. #10622564C22semidirect
67. #10622561C22semidirect
68. #10622558C22semidirect
69. #10622281C22semidirect
70. #10622268C22semidirect
134. C2×C22⋊Dic11D4semidirect
157. C2×Dic11⋊C4D4semidirect
295. C22⋊Dic11C2×D4semidirect
303. Dic11⋊C4C2×D4semidirect
314. C2×#392D11semidirect
479. #392C2×D11semidirect
654. C2×C11#2456semidirect
796. C11C2×#2456semidirect
975. C2#13072509direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×#669912
C22×D4×Dic112
C22×(C22⋊D11)⋊C42
#130725092
C2×#106225612
C2×#106228362
C2×#106225702
C2×#106225582
C2×#106225642
C2×#106222682
C2×#106228332
C2×#106225712
C2×#106222812
C2×C11×#3922
C2×#245611