Finite Group Databasebeta

← C2×#13072031 #14922092

Subgroups — C2×#13072031 #14922092

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×#66992C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4C22×#66925C211yesmaximal, characteristic, complemented
5#13072031C2116yesmaximal, direct product factor
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622585C211yesmaximal, characteristic, complemented
13C2×#10622558C211yesmaximal, characteristic, complemented
14C2×#10622553C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66992—28no—
35C2×#66992C2218yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66937—28no—
51C2×#66937C2218yescomplemented
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C2×#66925—28no—
55C2×#66925C2218yescomplemented
56C11×#390C2218yescomplemented
57#10622836C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622604C2218yescomplemented
63#10622585C2218yescomplemented
64#10622573C2218yescomplemented
65#10622572C2218yescomplemented
66#10622570C2218yescomplemented
67#10622570C2218yescomplemented
68#10622558C2218yescomplemented
69#10622555C2218yescomplemented
70#10622553C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
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—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—24no—
103C23×Dic11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—42no—
112C22×D44—42no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11D418yescomplemented
117C22×C4×D11C2314yes—
118C2×C11×C4⋊C4—42no—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C42×C11—24no—
129C2×C42×C11C2314yes—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—42no—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66992—232no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
151C2×Dic11⋊C4—24no—
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×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66937—232no—
166(C22⋊D11)⋊C4—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×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
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×D11—22no—
202C23×D11—22no—
203C23×D11C2×D414yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
209C2×D4×C11—416no—
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×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
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—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—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—416no—
263C22×Dic11C2×D414yes—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—28no—
275C2×D44—44no—
276C2×D44—44no—
277C2×D44—416no—
278C2×C4×D11—232no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11C2×D4116yescomplemented
282C11×C4⋊C4—44no—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—28no—
285C11×C22⋊C4—44no—
286C11×C22⋊C4—44no—
287C42×C11—28no—
288C22⋊Dic11—28no—
289C22⋊Dic11—28no—
290C22⋊Dic11—44no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298Dic11⋊C4—28no—
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×#390D1111yescharacteristic, complemented
317C2×#389—111no—
318C2×#388—111no—
319C2×#388—111no—
320C2×#380—111no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
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—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11C22×D412yes—
349C23×C11C22×D412yes—
350C23×C11C2×#4114yes—
351C23×C11C2×#4112yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11H(5,𝔽2)12yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11C2511yescharacteristic
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—28no—
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—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
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×D11—44no—
384C22×D11C22×D414yes—
385D4×C11—416no—
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—44no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11C22×D414yes—
405C2×C4×C11C22×D414yes—
406C22⋊D11—232no—
407C22⋊D11—416no—
408C22⋊D11—416no—
409C22⋊D11—416no—
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—44no—
426C2×Dic11—44no—
427C2×Dic11—44no—
428C2×Dic11—416no—
429C2×Dic11#121116yes—
430C2×Dic11C22×D414yes—
431C2×Dic11C22×D414yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C2×#4114yes—
434C2×Dic11C2×#4114yes—
435D44—416no—
436C4×D11—232no—
437C23×D4—111no—
438C23×D4—111no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
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⋊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⋊C4C2×D1111yescharacteristic
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#390C2×D1118yescomplemented
483#389—118no—
484#388—118no—
485#388—118no—
486#380—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—42no—
495C22×C11—416no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—88no—
507C22×C11C2×#12114yes—
508C22×C11#52514yes—
509C22×C11#53514yes—
510C22×C11#54614yes—
511C22×C11#55014yes—
512C22×C11#55314yes—
513C22×C11#55514yes—
514C22×C11C23×D411yescharacteristic
515C22×C11C23×D411yescharacteristic
516C22×C11C22×#4111yescharacteristic
517C22×C11C22×#4111yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C2×H(5,𝔽2)11yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—416no—
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—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11C2×#12118yes—
548C25—111no—
549C25—111no—
550C25C22×D1111yescharacteristic
551C25C22×D1111yescharacteristic
552C22×D4—24no—
553C22×D4—24no—
554C22×D4—42no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
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×D4C22×D1114yes—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—118no—
580C23×C4—114no—
581C23×C4—114no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—224no—
586C23×C4—224no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—224no—
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—42no—
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—224no—
609C2×C4⋊C4—442no—
610C2×C4⋊C4C22×D1114yes—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—42no—
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⋊C4C22×D1114yes—
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#95—114no—
648#95—114no—
649C2×C11—44no—
650C2×C11—82no—
651C2×C11#241418yescomplemented
652C2×C11C22×#12111yescharacteristic
653C2×C11C2×#52511yescharacteristic
654C2×C11C2×#53511yescharacteristic
655C2×C11C2×#54611yescharacteristic
656C2×C11C2×#55011yescharacteristic
657C2×C11C2×#55311yescharacteristic
658C2×C11C2×#55511yescharacteristic
659D11—44no—
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—114no—
675C24—112no—
676C24—112no—
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#433914yes—
691C24C23×D1112yes—
692C24C23×D1112yes—
693C24C23×D1111yescharacteristic
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—416no—
698C2×D4—228no—
699C2×D4—228no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—2232no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—444no—
710C2×D4—444no—
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—114no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—112no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—112no—
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—222no—
761C22×C4—222no—
762C22×C4—4416no—
763C22×C4D4×D1114yes—
764C22×C4D4×D1114yes—
765C22×C4C23×D1112yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1112yes—
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C4⋊C4—44no—
771C4⋊C4—1116no—
772C4⋊C4—228no—
773C4⋊C4—228no—
774C4⋊C4—228no—
775C4⋊C4—444no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—228no—
781C22⋊C4—228no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—444no—
789C22⋊C4—444no—
790C42—28no—
791C42—228no—
792C42—228no—
793C11C2×#241411yescharacteristic, complemented, Sylow
794C23—28no—
795C23—28no—
796C23—28no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—114no—
822C23—228no—
823C23—228no—
824C23—228no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23C2×#433914yes—
850C23C2×#433912yes—
851C23C2×D4×D1112yes—
852C23C2×D4×D1112yes—
853C23#6703712yes—
854C23#6703712yes—
855C23#41×D1112yes—
856C23#41×D1112yes—
857C23C24×D1111yescharacteristic
858D4—416no—
859D4—2232no—
860D4—4416no—
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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—1116no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—2232no—
889C2×C4—228no—
890C2×C4—228no—
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—4416no—
905C2×C4—444no—
906C2×C4—444no—
907C2×C4—444no—
908C2×C4C2×D4×D1114yes—
909C2×C4C2×D4×D1114yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—416no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—88no—
926C22—224no—
927C22—224no—
928C22—224no—
929C22—442no—
930C22—442no—
931C22—4416no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—888no—
942C22#1062302114yes—
943C22#1062307114yes—
944C22#1062307814yes—
945C22#1062313014yes—
946C22D11×#12114yes—
947C22#1062320114yes—
948C22#1062324614yes—
949C22C22×#433911yescharacteristic
950C22C22×D4×D1111yescharacteristic
951C22C22×D4×D1111yescharacteristic
952C22C2×#6703711yescharacteristic
953C22C2×#6703711yescharacteristic
954C22C2×#41×D1111yescharacteristic
955C22C2×#41×D1111yescharacteristic
956C4—24no—
957C4—24no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—118no—
962C4—224no—
963C4—224no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—44no—
968C2—82no—
969C2—444no—
970C2—882no—
971C2#1307203118yesdirect product factor
972C2C2×D11×#12111yescharacteristic
973C2C2×#1062307811yescharacteristic
974C2C2×#1062324611yescharacteristic
975C2C2×#1062302111yescharacteristic
976C2C2×#1062313011yescharacteristic
977C2C2×#1062307111yescharacteristic
978C2C2×#1062320111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
hypercenterC2×#390D11
hypocenterC11C2×#2414
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66992C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. C22×#66925C2semidirect
5. #13072031C2direct (N × H)
6. C2×#10622604C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622585C2semidirect
13. C2×#10622558C2semidirect
14. C2×#10622553C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#390C2semidirect
35. C2×#66992C22semidirect
51. C2×#66937C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×#66925C22semidirect
56. C11×#390C22semidirect
57. #10622836C22semidirect
62. #10622604C22semidirect
63. #10622585C22semidirect
64. #10622573C22semidirect
65. #10622572C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
68. #10622558C22semidirect
69. #10622555C22semidirect
70. #10622553C22semidirect
116. C22×C4×D11D4semidirect
155. C2×Dic11⋊C4D4semidirect
281. C2×C4×D11C2×D4semidirect
302. Dic11⋊C4C2×D4semidirect
316. C2×#390D11semidirect
482. #390C2×D11semidirect
651. C2×C11#2414semidirect
793. C11C2×#2414semidirect
971. C2#13072031direct (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×(C22⋊D11)⋊C42
C22×#669252
#130720312
C2×#106226042
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106225852
C2×#106225582
C2×#106225532
C2×#106225552
C2×C11×#3902
C2×#241411