Finite Group Databasebeta

← C2×#13072027 #14922091

Subgroups — C2×#13072027 #14922091

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×#66992C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4C22×#66930C211yesmaximal, characteristic, complemented
5#13072027C2116yesmaximal, direct product factor
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622564C211yesmaximal, characteristic, complemented
14C2×#10622283C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, 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
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992—28no—
37C2×#66992C2218yescomplemented
38C2×#66992C2218yescomplemented
39C2×D4×Dic11—28no—
40C2×D4×Dic11C2218yescomplemented
41C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×#66930—28no—
55C2×#66930C2218yescomplemented
56C11×#392C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622836C2218yescomplemented
59#10622835C2218yescomplemented
60#10622834C2218yescomplemented
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622574C2218yescomplemented
65#10622570C2218yescomplemented
66#10622570C2218yescomplemented
67#10622564C2218yescomplemented
68#10622555C2218yescomplemented
69#10622283C2218yescomplemented
70#10622260C2218yescomplemented
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—42no—
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—24no—
108C23×Dic11D418yescomplemented
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2314yes—
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2314yes—
117C23×Dic11C2311yescharacteristic
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—42no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138#66992—232no—
139#66992—232no—
140D4×Dic11—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×C4⋊Dic11—24no—
150C2×C4⋊Dic11—42no—
151C2×C4⋊Dic11C2314yes—
152C2×C4⋊Dic11C2314yes—
153C2×Dic11⋊C4—24no—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—42no—
156C2×Dic11⋊C4D418yescomplemented
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—24no—
163C2×C4×Dic11—24no—
164C2×C4×Dic11C2314yes—
165C2×C4×Dic11C2314yes—
166C2×C4×Dic11C2314yes—
167#66930—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×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—22no—
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—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—232no—
247C22×Dic11—28no—
248C22×Dic11—28no—
249C22×Dic11—28no—
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
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—22no—
268C22×Dic11—416no—
269C22×Dic11C2×D414yes—
270C22×Dic11C2×D414yes—
271C22×Dic11C2×D414yes—
272C22×Dic11C2×D414yes—
273C22×Dic11C2×D4116yescomplemented
274C22×Dic11#4114yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C11×C22⋊C4—28no—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—44no—
285C22⋊Dic11—28no—
286C22⋊Dic11—28no—
287C22⋊Dic11—28no—
288C22⋊Dic11—28no—
289C22⋊Dic11—28no—
290C22⋊Dic11—44no—
291C22⋊Dic11—44no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—44no—
296C4⋊Dic11—28no—
297C4⋊Dic11—44no—
298Dic11⋊C4—28no—
299Dic11⋊C4—28no—
300Dic11⋊C4—44no—
301Dic11⋊C4C2×D4116yescomplemented
302C4×Dic11—28no—
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×#392D1111yescharacteristic, complemented
314C2×#390—111no—
315C2×#390—111no—
316C2×#390—111no—
317C2×#389—111no—
318C2×#388—111no—
319C2×#388—111no—
320C2×#380—111no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—22no—
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—44no—
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×C11C22×D414yes—
362C23×C11C22×D412yes—
363C23×C11C22×D412yes—
364C23×C11C2×#4114yes—
365C23×C11C2×#4112yes—
366C23×C11C2×#4112yes—
367C23×C11C2×#4112yes—
368C23×C11H(5,𝔽2)12yes—
369C23×C11H(5,𝔽2)12yes—
370C23×C11C2511yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385D4×C11—232no—
386D4×C11—416no—
387D4×C11—416no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
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—44no—
401C2×C4×C11—44no—
402C2×C4×C11C22×D414yes—
403C2×C4×C11C2×#4114yes—
404C22⋊D11—416no—
405C22⋊D11—416no—
406C22⋊D11—416no—
407C2×Dic11—28no—
408C2×Dic11—28no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—232no—
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—44no—
427C2×Dic11—44no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430C2×Dic11—416no—
431C2×Dic11#121116yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D414yes—
436C2×Dic11C2×#4114yes—
437C23×D4—111no—
438C23×D4—111no—
439C23×D4—111no—
440C23×D4C2×D1111yescharacteristic
441C23×D4C2×D1111yescharacteristic
442C23×D4C2×D1111yescharacteristic
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⋊C4—111no—
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×C42—111no—
476#394—118no—
477#394—118no—
478#392—118no—
479#392C2×D1118yescomplemented
480#390—118no—
481#390—118no—
482#390—118no—
483#389—118no—
484#388—118no—
485#388—118no—
486#380—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95C2×D1111yescharacteristic
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—42no—
498C22×C11—416no—
499C22×C11—416no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—88no—
515C22×C11C2×#12114yes—
516C22×C11#52514yes—
517C22×C11#53514yes—
518C22×C11#54614yes—
519C22×C11#55014yes—
520C22×C11#55314yes—
521C22×C11#55514yes—
522C22×C11C23×D411yescharacteristic
523C22×C11C23×D411yescharacteristic
524C22×C11C22×#4111yescharacteristic
525C22×C11C22×#4111yescharacteristic
526C22×C11C22×#4111yescharacteristic
527C22×C11C2×H(5,𝔽2)11yescharacteristic
528C22×C11C2×H(5,𝔽2)11yescharacteristic
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—42no—
540C4×C11—42no—
541Dic11—24no—
542Dic11—24no—
543Dic11—42no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11C2×#12118yes—
548C25—111no—
549C25C22×D1111yescharacteristic
550C25C22×D1111yescharacteristic
551C25C22×D1111yescharacteristic
552C22×D4—24no—
553C22×D4—24no—
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—42no—
559C22×D4—42no—
560C22×D4—42no—
561C22×D4—114no—
562C22×D4—114no—
563C22×D4—114no—
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×D4C22×D1114yes—
574C22×D4C22×D1114yes—
575C22×D4C22×D1114yes—
576C23×C4—111no—
577C23×C4—118no—
578C23×C4—114no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—114no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—224no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
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—118no—
600C2×C4⋊C4—114no—
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—224no—
609C2×C4⋊C4—442no—
610C2×C4⋊C4—442no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—42no—
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—224no—
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—114no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—224no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95C22×D1114yes—
649C2×C11—44no—
650C2×C11—44no—
651C2×C11—82no—
652C2×C11#241418yescomplemented
653C2×C11C22×#12111yescharacteristic
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#53511yescharacteristic
656C2×C11C2×#54611yescharacteristic
657C2×C11C2×#55011yescharacteristic
658C2×C11C2×#55311yescharacteristic
659C2×C11C2×#55511yescharacteristic
660D11—82no—
661C24—22no—
662C24—22no—
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—112no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24D4×D1114yes—
689C24#434114yes—
690C24C23×D1112yes—
691C24C23×D1112yes—
692C24C23×D1112yes—
693C24C23×D1111yescharacteristic
694C2×D4—232no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—416no—
705C2×D4—416no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
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—114no—
729C22×C4—114no—
730C22×C4—114no—
731C22×C4—112no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—1116no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—228no—
742C22×C4—2232no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—228no—
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—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—4416no—
764C22×C4D4×D1114yes—
765C22×C4#434114yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1112yes—
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C4⋊C4—1116no—
771C4⋊C4—228no—
772C4⋊C4—228no—
773C4⋊C4—228no—
774C4⋊C4—444no—
775C4⋊C4—444no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—228no—
780C22⋊C4—228no—
781C22⋊C4—228no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—444no—
788C22⋊C4—444no—
789C22⋊C4—444no—
790C42—228no—
791C42—228no—
792C42—228no—
793C11C2×#241411yescharacteristic, complemented, Sylow
794C23—28no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
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—44no—
820C23—44no—
821C23—44no—
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—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23C2×D4×D1114yes—
849C23C2×D4×D1112yes—
850C23C2×D4×D1112yes—
851C23C2×#434114yes—
852C23C2×#434112yes—
853C23C2×#434112yes—
854C23#6703712yes—
855C23#6703712yes—
856C23#41×D1112yes—
857C23C24×D1111yescharacteristic
858D4—232no—
859D4—416no—
860D4—416no—
861D4—4416no—
862D4—4416no—
863D4—4416no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—22no—
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—44no—
877C2×C4—44no—
878C2×C4—1116no—
879C2×C4—114no—
880C2×C4—114no—
881C2×C4—114no—
882C2×C4—114no—
883C2×C4—114no—
884C2×C4—2232no—
885C2×C4—228no—
886C2×C4—228no—
887C2×C4—222no—
888C2×C4—222no—
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—4416no—
904C2×C4—444no—
905C2×C4—444no—
906C2×C4—444no—
907C2×C4—444no—
908C2×C4C2×D4×D1114yes—
909C2×C4C2×#434114yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—416no—
921C22—416no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—88no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—888no—
942C22#1062311714yes—
943C22#1062312214yes—
944C22#1062312314yes—
945C22#1062313214yes—
946C22D11×#12114yes—
947C22#1062314714yes—
948C22#1062324914yes—
949C22C22×D4×D1111yescharacteristic
950C22C22×D4×D1111yescharacteristic
951C22C22×#434111yescharacteristic
952C22C22×#434111yescharacteristic
953C22C2×#6703711yescharacteristic
954C22C2×#6703711yescharacteristic
955C22C2×#41×D1111yescharacteristic
956C4—24no—
957C4—24no—
958C4—42no—
959C4—42no—
960C4—118no—
961C4—224no—
962C4—224no—
963C4—442no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—44no—
968C2—44no—
969C2—82no—
970C2—882no—
971C2#1307202718yesdirect product factor
972C2C2×D11×#12111yescharacteristic
973C2C2×#1062311711yescharacteristic
974C2C2×#1062312311yescharacteristic
975C2C2×#1062312211yescharacteristic
976C2C2×#1062324911yescharacteristic
977C2C2×#1062313211yescharacteristic
978C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2414
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#66992C2semidirect
3. C22×D4×Dic11C2semidirect
4. C22×#66930C2semidirect
5. #13072027C2direct (N × H)
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622564C2semidirect
14. C2×#10622283C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#392C2semidirect
37. C2×#66992C22semidirect
38. C2×#66992C22semidirect
40. C2×D4×Dic11C22semidirect
55. C2×#66930C22semidirect
56. C11×#392C22semidirect
58. #10622836C22semidirect
59. #10622835C22semidirect
60. #10622834C22semidirect
64. #10622574C22semidirect
65. #10622570C22semidirect
66. #10622570C22semidirect
67. #10622564C22semidirect
68. #10622555C22semidirect
69. #10622283C22semidirect
70. #10622260C22semidirect
108. C23×Dic11D4semidirect
156. C2×Dic11⋊C4D4semidirect
273. C22×Dic11C2×D4semidirect
301. Dic11⋊C4C2×D4semidirect
313. C2×#392D11semidirect
479. #392C2×D11semidirect
652. C2×C11#2414semidirect
793. C11C2×#2414semidirect
971. C2#13072027direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×D4×Dic112
C22×#669302
#130720272
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106225702
C2×#106222602
C2×#106225642
C2×#106222832
C2×#106225552
C2×C11×#3922
C2×#241411