Finite Group Databasebeta

← C2×#13071956 #14922083

Subgroups — C2×#13071956 #14922083

Order 2816.

5998 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13071956C2116yesmaximal, direct product factor
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, 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
23C24×Dic11C2211yescharacteristic
24C22×#4341—28no—
25C22×#4341—28no—
26C22×#4341—28no—
27C22×#4341C2218yescomplemented
28C23×D44C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×Dic22C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66949—28no—
51C2×#66949C2218yescomplemented
52C2×#66937—28no—
53C2×#66937C2218yescomplemented
54C2×(C22⋊D11)⋊C4—28no—
55C2×(C22⋊D11)⋊C4C2218yescomplemented
56C11×#394C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622836C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622602C2218yescomplemented
65#10622573C2218yescomplemented
66#10622572C2218yescomplemented
67#10622571C2218yescomplemented
68#10622570C2218yescomplemented
69#10622559C2218yescomplemented
70#10622555C2218yescomplemented
71#10622278C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
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×Dic11—24no—
106C23×Dic11—24no—
107C23×Dic11D418yescomplemented
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2314yes—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2314yes—
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C2×#4341—2128no—
117C2×#4341—232no—
118C2×#4341—232no—
119C2×#4341—232no—
120C22×D44—24no—
121C22×D44—24no—
122C22×D44—42no—
123C22×D44C2314yes—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—24no—
128C22×C4×D11—24no—
129C22×C4×D11—24no—
130C22×C4×D11C2314yes—
131C22×C4×D11C2314yes—
132C22×Dic22—24no—
133C22×Dic22—24no—
134C22×Dic22D418yescomplemented
135C22×Dic22C2314yes—
136C2×C11×C4⋊C4—24no—
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4—42no—
141C2×C11×C22⋊C4—42no—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11—42no—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—42no—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×Dic11⋊C4—24no—
163C2×Dic11⋊C4—24no—
164C2×Dic11⋊C4—24no—
165C2×Dic11⋊C4—24no—
166C2×Dic11⋊C4C2314yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170C2×C4×Dic11—24no—
171C2×C4×Dic11C2314yes—
172#66949—232no—
173#66937—232no—
174(C22⋊D11)⋊C4—232no—
175C11×#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C2×#2407—111nomaximal, Sylow
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×C11C2×D414yes—
196C24×C11C2412yes—
197C24×C11C2412yes—
198C24×C11C2411yescharacteristic
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×D11—22no—
210C23×D11—22no—
211C23×D11C2×D414yes—
212C23×D11#4114yescomplemented
213C23×D11C2412yes—
214C23×D11C2412yes—
215C2×D4×C11—232no—
216C2×D4×C11—28no—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
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×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11C2×D414yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C2×C22⋊D11—232no—
240C2×C22⋊D11—232no—
241C2×C22⋊D11—232no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—416no—
254C2×C22⋊D11C2×D4116yescomplemented
255C22×Dic11—232no—
256C22×Dic11—232no—
257C22×Dic11—28no—
258C22×Dic11—28no—
259C22×Dic11—28no—
260C22×Dic11—28no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—28no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11C2×D414yes—
275C22×Dic11C2×D414yes—
276C22×Dic11C2×D414yes—
277C22×Dic11C2×D414yes—
278C22×Dic11C2×D414yes—
279C22×Dic11C2×D4116yescomplemented
280C22×Dic11#4114yescomplemented
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287#4341—2256no—
288C2×D44—28no—
289C2×D44—28no—
290C2×D44—44no—
291C2×D44—416no—
292C2×C4×D11—232no—
293C2×C4×D11—28no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—416no—
300C2×Dic22—232no—
301C2×Dic22—28no—
302C2×Dic22—28no—
303C2×Dic22C2×D4116yescomplemented
304C11×C4⋊C4—28no—
305C11×C22⋊C4—28no—
306C11×C22⋊C4—28no—
307C11×C22⋊C4—44no—
308C11×C22⋊C4—44no—
309C22⋊Dic11—28no—
310C22⋊Dic11—44no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—44no—
317Dic11⋊C4—28no—
318Dic11⋊C4—28no—
319Dic11⋊C4—28no—
320Dic11⋊C4—28no—
321C4×Dic11—28no—
322C23×#41—111no—
323C22×C22⋊Q8—111no—
324C22×#121—111no—
325C22×C4×D4—111no—
326#2407—1116no—
327C2×#394—111no—
328C2×#394D1111yescharacteristic, complemented
329C2×#392—111no—
330C2×#392—111no—
331C2×#391—111no—
332C2×#390—111no—
333C2×#386—111no—
334C2×#386—111no—
335C2×#385—111no—
336C2×#385—111no—
337C2×#380—111no—
338C23×C11—28no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—28no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—44no—
364C23×C11C22×D414yes—
365C23×C11C22×D414yes—
366C23×C11C22×D412yes—
367C23×C11C22×D412yes—
368C23×C11C22×D412yes—
369C23×C11C2×#4112yes—
370C23×C11C2×#4112yes—
371C23×C11H(5,𝔽2)12yes—
372C23×C112−1+412yes—
373C23×C11C2511yescharacteristic
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—28no—
377C22×D11—28no—
378C22×D11—28no—
379C22×D11—28no—
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—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11—44no—
399C22×D11—44no—
400C22×D11C22×D414yes—
401C22×D11C2×#4114yescomplemented
402D4×C11—232no—
403C2×C4×C11—28no—
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—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—44no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11C22×D414yes—
423C22⋊D11—232no—
424C22⋊D11—232no—
425C22⋊D11—232no—
426C22⋊D11—416no—
427C2×Dic11—232no—
428C2×Dic11—28no—
429C2×Dic11—28no—
430C2×Dic11—28no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—232no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11#120116yes—
447C2×Dic11C22×D414yes—
448C2×Dic11C22×D414yes—
449C2×Dic11C22×D414yes—
450C2×Dic11C22×D414yes—
451C2×Dic11C22×D414yes—
452C2×Dic11C2×#4114yescomplemented
453D44—416no—
454C4×D11—232no—
455C4×D11—416no—
456Dic22—232no—
457C22×#41—118no—
458C22×#41—228no—
459C22×#41—228no—
460C22×#41—228no—
461C23×Q8—111no—
462C23×D4—111no—
463C23×D4—111no—
464C23×D4—111no—
465C23×D4—111no—
466C23×D4—111no—
467C23×D4C2×D1111yescharacteristic
468C24×C4—111no—
469C24×C4—111no—
470C24×C4—111no—
471C24×C4—111no—
472C2×C22⋊Q8—118no—
473C2×C22⋊Q8—228no—
474C2×#121—118no—
475C2×#121—228no—
476C2×C4×D4—118no—
477C2×C4×D4—228no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4—111no—
480C22×C4⋊C4—111no—
481C22×C4⋊C4—111no—
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#394—118no—
497#394C2×D1118yescomplemented
498#392—118no—
499#392—118no—
500#391—118no—
501#390—118no—
502#386—118no—
503#386—118no—
504#385—118no—
505#385—118no—
506#380—118no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95C2×D1111yescharacteristic
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—416no—
520C22×C11—416no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11C2×#12014yes—
530C22×C11#52514yes—
531C22×C11#53714yes—
532C22×C11#54614yes—
533C22×C11#54714yes—
534C22×C11#54814yes—
535C22×C11#55014yes—
536C22×C11C23×D411yescharacteristic
537C22×C11C23×D411yescharacteristic
538C22×C11C23×D411yescharacteristic
539C22×C11C22×#4111yescharacteristic
540C22×C11C22×#4111yescharacteristic
541C22×C11C2×H(5,𝔽2)11yescharacteristic
542C22×C11C2×2−1+411yescharacteristic
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—416no—
550C2×D11—416no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C4×C11—24no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—42no—
563C4×C11—42no—
564Dic11—24no—
565Dic11—24no—
566Dic11—24no—
567Dic11—42no—
568Dic11—42no—
569Dic11C2×#12018yes—
570C25—111no—
571C25—111no—
572C25C22×D1111yescharacteristic
573C25C22×D1111yescharacteristic
574C2×#41—2232no—
575C2×#41—2232no—
576C2×#41—2232no—
577C2×#41—22128no—
578C22×Q8—118no—
579C22×Q8—114no—
580C22×Q8—224no—
581C22×Q8—224no—
582C22×D4—24no—
583C22×D4—24no—
584C22×D4—24no—
585C22×D4—118no—
586C22×D4—114no—
587C22×D4—114no—
588C22×D4—114no—
589C22×D4—114no—
590C22×D4—114no—
591C22×D4—224no—
592C22×D4—224no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—224no—
603C22×D4—442no—
604C22×D4—442no—
605C22×D4C22×D1114yes—
606C23×C4—111no—
607C23×C4—118no—
608C23×C4—114no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—114no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—114no—
616C23×C4—114no—
617C23×C4—224no—
618C23×C4—224no—
619C23×C4—224no—
620C23×C4—224no—
621C23×C4—224no—
622C23×C4—224no—
623C23×C4—224no—
624C23×C4—224no—
625C23×C4—224no—
626C23×C4—224no—
627C23×C4—224no—
628C23×C4C22×D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C22⋊Q8—2232no—
634#121—2232no—
635C4×D4—2232no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—114no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—224no—
642C2×C4⋊C4—224no—
643C2×C4⋊C4—224no—
644C2×C4⋊C4—224no—
645C2×C4⋊C4C22×D1114yes—
646C2×C22⋊C4—24no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4—42no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—442no—
665C2×C22⋊C4—442no—
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D1114yes—
668C2×C22⋊C4C22×D1114yes—
669C2×C22⋊C4C22×D1114yes—
670C2×C42—114no—
671C2×C42—224no—
672#95—114no—
673#95—114no—
674#95—114no—
675#95—114no—
676#95—114no—
677#95C22×D1114yes—
678C2×C11—44no—
679C2×C11—44no—
680C2×C11#240718yescomplemented
681C2×C11C22×#12011yescharacteristic
682C2×C11C2×#52511yescharacteristic
683C2×C11C2×#53711yescharacteristic
684C2×C11C2×#54611yescharacteristic
685C2×C11C2×#54711yescharacteristic
686C2×C11C2×#54811yescharacteristic
687C2×C11C2×#55011yescharacteristic
688D11—44no—
689D11—44no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—114no—
703C24—114no—
704C24—112no—
705C24—112no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—222no—
718C24D4×D1114yes—
719C24D4×D1114yes—
720C24C23×D1112yes—
721C24C23×D1112yes—
722C24C23×D1111yescharacteristic
723#41—22256no—
724C2×Q8—1116no—
725C2×Q8—2232no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×D4—232no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—1116no—
733C2×D4—228no—
734C2×D4—228no—
735C2×D4—2232no—
736C2×D4—228no—
737C2×D4—228no—
738C2×D4—228no—
739C2×D4—228no—
740C2×D4—228no—
741C2×D4—228no—
742C2×D4—2232no—
743C2×D4—2232no—
744C2×D4—228no—
745C2×D4—228no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—444no—
749C2×D4—4416no—
750C2×D4—444no—
751C2×D4—4416no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—114no—
769C22×C4—112no—
770C22×C4—114no—
771C22×C4—114no—
772C22×C4—1116no—
773C22×C4—114no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—228no—
780C22×C4—228no—
781C22×C4—228no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—2232no—
785C22×C4—2232no—
786C22×C4—228no—
787C22×C4—228no—
788C22×C4—228no—
789C22×C4—228no—
790C22×C4—2232no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—228no—
797C22×C4—222no—
798C22×C4—228no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—4416no—
806C22×C4D4×D1114yes—
807C22×C4C23×D1112yes—
808C22×C4C23×D1112yes—
809C22×C4C23×D1112yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1112yes—
812C4⋊C4—28no—
813C4⋊C4—228no—
814C4⋊C4—228no—
815C4⋊C4—228no—
816C4⋊C4—228no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—228no—
822C22⋊C4—228no—
823C22⋊C4—228no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—444no—
828C22⋊C4—444no—
829C42—228no—
830C11C2×#240711yescharacteristic, complemented, Sylow
831C23—28no—
832C23—28no—
833C23—28no—
834C23—28no—
835C23—28no—
836C23—28no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—114no—
858C23—114no—
859C23—228no—
860C23—228no—
861C23—228no—
862C23—228no—
863C23—228no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—228no—
877C23—444no—
878C23—444no—
879C23—444no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23—444no—
885C23C2×D4×D1114yes—
886C23C2×D4×D1114yes—
887C23C2×D4×D1112yes—
888C23C2×D4×D1112yes—
889C23C2×D4×D1112yes—
890C23#6703712yes—
891C23#41×D1112yes—
892C23#41×D1112yes—
893C23#6704312yes—
894C23C24×D1111yescharacteristic
895Q8—2232no—
896D4—232no—
897D4—2232no—
898D4—2232no—
899D4—2232no—
900D4—4416no—
901D4—4416no—
902C2×C4—28no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—1116no—
922C2×C4—114no—
923C2×C4—114no—
924C2×C4—114no—
925C2×C4—114no—
926C2×C4—114no—
927C2×C4—114no—
928C2×C4—2232no—
929C2×C4—2232no—
930C2×C4—2232no—
931C2×C4—228no—
932C2×C4—228no—
933C2×C4—228no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—4416no—
947C2×C4—444no—
948C2×C4—444no—
949C2×C4C2×D4×D1114yes—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—42no—
957C22—416no—
958C22—416no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—224no—
967C22—224no—
968C22—224no—
969C22—224no—
970C22—224no—
971C22—224no—
972C22—442no—
973C22—442no—
974C22—4416no—
975C22—4416no—
976C22—442no—
977C22—442no—
978C22—442no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22D11×#12014yes—
983C22#1062312814yes—
984C22#1062313014yes—
985C22#1062314114yes—
986C22#1062318614yes—
987C22#1062318714yes—
988C22#1062320814yes—
989C22C22×D4×D1111yescharacteristic
990C22C22×D4×D1111yescharacteristic
991C22C22×D4×D1111yescharacteristic
992C22C2×#6703711yescharacteristic
993C22C2×#41×D1111yescharacteristic
994C22C2×#41×D1111yescharacteristic
995C22C2×#6704311yescharacteristic
996C4—24no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—118no—
1002C4—224no—
1003C4—224no—
1004C4—224no—
1005C4—442no—
1006C4—442no—
1007C2—44no—
1008C2—44no—
1009C2—444no—
1010C2—444no—
1011C2#1307195618yesdirect product factor
1012C2C2×D11×#12011yescharacteristic
1013C2C2×#1062318711yescharacteristic
1014C2C2×#1062312811yescharacteristic
1015C2C2×#1062314111yescharacteristic
1016C2C2×#1062318611yescharacteristic
1017C2C2×#1062320811yescharacteristic
1018C2C2×#1062313011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66949C2semidirect
3. C22×#66937C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13071956C2direct (N × H)
6. C2×#10622572C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#394C2semidirect
27. C22×#4341C22semidirect
51. C2×#66949C22semidirect
53. C2×#66937C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. C11×#394C22semidirect
58. #10622836C22semidirect
64. #10622602C22semidirect
65. #10622573C22semidirect
66. #10622572C22semidirect
67. #10622571C22semidirect
68. #10622570C22semidirect
69. #10622559C22semidirect
70. #10622555C22semidirect
71. #10622278C22semidirect
72. #10622259C22semidirect
97. C22×C22⋊D11D4semidirect
107. C23×Dic11D4semidirect
134. C22×Dic22D4semidirect
212. C23×D11#41semidirect
254. C2×C22⋊D11C2×D4semidirect
279. C22×Dic11C2×D4semidirect
280. C22×Dic11#41semidirect
303. C2×Dic22C2×D4semidirect
328. C2×#394D11semidirect
401. C22×D11C2×#41semidirect
452. C2×Dic11C2×#41semidirect
497. #394C2×D11semidirect
680. C2×C11#2407semidirect
830. C11C2×#2407semidirect
1011. C2#13071956direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669492
C22×#669372
C22×(C22⋊D11)⋊C42
#130719562
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106222782
C2×#106225712
C2×#106225592
C2×#106226022
C2×#106225552
C2×C11×#3942
C2×#240711