Finite Group Databasebeta

← C2×#13071958 #14922080

Subgroups — C2×#13071958 #14922080

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×#4339C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13071958C2116yesmaximal, direct product factor
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622280C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C22×#4339—28no—
25C22×#4339—28no—
26C22×#4339—28no—
27C22×#4339C2218yescomplemented
28C23×D44C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×Dic22C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C2×#66992—28no—
39C2×#66992C2218yescomplemented
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C2×#66931—28no—
55C2×#66931C2218yescomplemented
56C11×#386C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59#10622836C2218yescomplemented
60#10622823C2218yescomplemented
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622574C2218yescomplemented
66#10622573C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622285C2218yescomplemented
70#10622281C2218yescomplemented
71#10622280C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
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—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yescomplemented
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C23×Dic11—24no—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11C2314yes—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C2×#4339—2128no—
117C2×#4339—232no—
118C2×#4339—232no—
119C2×#4339—232no—
120C22×D44—24no—
121C22×D44—24no—
122C22×D44—24no—
123C22×D44C2314yes—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—24no—
128C22×C4×D11—24no—
129C22×C4×D11D418yescomplemented
130C22×C4×D11C2314yes—
131C22×C4×D11C2314yes—
132C22×Dic22—24no—
133C22×Dic22—24no—
134C22×Dic22D418yescomplemented
135C22×Dic22C2314yes—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—42no—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C22⋊Dic11—24no—
143C2×C22⋊Dic11—24no—
144C2×C22⋊Dic11—24no—
145C2×C22⋊Dic11C2314yes—
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2314yes—
148#66992—232no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—42no—
153C2×(C2×D11)⋊C4—42no—
154C2×(C2×D11)⋊C4—42no—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×C4⋊Dic11—24no—
162C2×C4⋊Dic11C2314yes—
163C2×Dic11⋊C4—24no—
164C2×Dic11⋊C4—24no—
165C2×Dic11⋊C4—24no—
166C2×Dic11⋊C4—24no—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2314yes—
171C2×C4×Dic11—24no—
172C2×C4×Dic11C2314yes—
173(C22⋊D11)⋊C4—232no—
174#66931—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×C11#4114yescomplemented
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×D11C2×D414yes—
213C23×D11C2412yes—
214C23×D11C2412yes—
215C2×D4×C11—28no—
216C2×D4×C11—28no—
217C2×D4×C11—44no—
218C2×D4×C11—416no—
219C22×C4×C11—232no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—28no—
225C22×C4×C11—28no—
226C22×C4×C11—28no—
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×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11C2×D414yes—
237C22×C4×C11C2×D414yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—232no—
245C2×C22⋊D11—232no—
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—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—416no—
258C2×C22⋊D11C2×D4116yescomplemented
259C22×Dic11—28no—
260C22×Dic11—28no—
261C22×Dic11—28no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11—416no—
276C22×Dic11C2×D414yes—
277C22×Dic11C2×D414yes—
278C22×Dic11C2×D414yes—
279C22×Dic11C2×D414yes—
280C22×Dic11#4114yescomplemented
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287#4339—2256no—
288C2×D44—232no—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—28no—
292C2×C4×D11—232no—
293C2×C4×D11—232no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11C2×D4116yescomplemented
300C2×Dic22—232no—
301C2×Dic22—28no—
302C2×Dic22—28no—
303C2×Dic22C2×D4116yescomplemented
304C11×C22⋊C4—28no—
305C11×C22⋊C4—28no—
306C11×C22⋊C4—44no—
307C22⋊Dic11—28no—
308C22⋊Dic11—28no—
309C22⋊Dic11—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316C4⋊Dic11—28no—
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×#394—111no—
329C2×#392—111no—
330C2×#392—111no—
331C2×#391—111no—
332C2×#390—111no—
333C2×#386—111no—
334C2×#386D1111yescharacteristic, complemented
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×D412yes—
366C23×C11C22×D412yes—
367C23×C11C22×D412yes—
368C23×C11C2×#4112yes—
369C23×C11C2×#4112yes—
370C23×C11C2×#4114yescomplemented
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×D11C22×D414yes—
402D4×C11—416no—
403C2×C4×C11—232no—
404C2×C4×C11—28no—
405C2×C4×C11—28no—
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—22no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11C22×D414yes—
423C2×C4×C11C22×D414yes—
424C22⋊D11—232no—
425C22⋊D11—232no—
426C22⋊D11—232no—
427C22⋊D11—416no—
428C2×Dic11—28no—
429C2×Dic11—28no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11—416no—
447C2×Dic11#120116yes—
448C2×Dic11C22×D414yes—
449C2×Dic11C22×D414yes—
450C2×Dic11C22×D414yes—
451C2×Dic11C22×D414yes—
452C2×Dic11C2×#4114yescomplemented
453D44—232no—
454C4×D11—232no—
455C4×D11—232no—
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×C4C2×D1111yescharacteristic
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⋊C4—111no—
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⋊C4—111no—
492C22×C22⋊C4C2×D1111yescharacteristic
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C42—111no—
496#394—118no—
497#394—118no—
498#392—118no—
499#392—118no—
500#391—118no—
501#390—118no—
502#386—118no—
503#386C2×D1118yescomplemented
504#385—118no—
505#385—118no—
506#380—118no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95C2×D1111yescharacteristic
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—24no—
561C4×C11—42no—
562C4×C11—42no—
563C4×C11—42no—
564Dic11—24no—
565Dic11—24no—
566Dic11—42no—
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—42no—
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—224no—
604C22×D4—442no—
605C22×D4C22×D1114yes—
606C23×C4—24no—
607C23×C4—24no—
608C23×C4—24no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—118no—
613C23×C4—114no—
614C23×C4—114no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—114no—
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×C4C22×D1114yes—
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—114no—
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⋊C4—224no—
646C2×C22⋊C4—24no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4—114no—
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⋊C4—442no—
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#95C22×D1114yes—
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—
718C24#433914yescomplemented
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—28no—
729C2×D4—28no—
730C2×D4—44no—
731C2×D4—416no—
732C2×D4—1116no—
733C2×D4—228no—
734C2×D4—228no—
735C2×D4—2232no—
736C2×D4—2232no—
737C2×D4—228no—
738C2×D4—228no—
739C2×D4—228no—
740C2×D4—228no—
741C2×D4—228no—
742C2×D4—228no—
743C2×D4—2232no—
744C2×D4—2232no—
745C2×D4—228no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—228no—
750C2×D4—444no—
751C2×D4—4416no—
752C22×C4—232no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—114no—
770C22×C4—114no—
771C22×C4—114no—
772C22×C4—112no—
773C22×C4—114no—
774C22×C4—114no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—1116no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—112no—
781C22×C4—2232no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—228no—
786C22×C4—2232no—
787C22×C4—228no—
788C22×C4—228no—
789C22×C4—228no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—228no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—4416no—
805C22×C4D4×D1114yes—
806C22×C4D4×D1114yes—
807C22×C4C23×D1112yes—
808C22×C4C23×D1112yes—
809C22×C4C23×D1112yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1112yes—
812C4⋊C4—228no—
813C4⋊C4—228no—
814C4⋊C4—228no—
815C4⋊C4—228no—
816C4⋊C4—228no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—44no—
820C22⋊C4—228no—
821C22⋊C4—228no—
822C22⋊C4—228no—
823C22⋊C4—228no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—444no—
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—228no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—444no—
878C23—444no—
879C23—444no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23—444no—
885C23C2×#433912yes—
886C23C2×#433914yescomplemented
887C23C2×D4×D1114yes—
888C23C2×D4×D1112yes—
889C23C2×D4×D1112yes—
890C23C2×D4×D1112yes—
891C23#6703712yes—
892C23#41×D1112yes—
893C23#6704312yes—
894C23C24×D1111yescharacteristic
895Q8—2232no—
896D4—416no—
897D4—2232no—
898D4—2232no—
899D4—2232no—
900D4—2232no—
901D4—4416no—
902C2×C4—232no—
903C2×C4—28no—
904C2×C4—28no—
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—22no—
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—2232no—
928C2×C4—2232no—
929C2×C4—228no—
930C2×C4—228no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
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—4416no—
945C2×C4—444no—
946C2×C4—444no—
947C2×C4—444no—
948C2×C4C2×D4×D1114yes—
949C2×C4C2×D4×D1114yes—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—416no—
960C22—416no—
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—
982C22#1062302114yes—
983C22#1062307814yes—
984C22#1062308314yes—
985C22D11×#12014yes—
986C22#1062313014yes—
987C22#1062313914yes—
988C22#1062318614yes—
989C22C22×#433911yescharacteristic
990C22C22×D4×D1111yescharacteristic
991C22C22×D4×D1111yescharacteristic
992C22C22×D4×D1111yescharacteristic
993C22C2×#6703711yescharacteristic
994C22C2×#41×D1111yescharacteristic
995C22C2×#6704311yescharacteristic
996C4—24no—
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—118no—
1002C4—224no—
1003C4—224no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C2—44no—
1008C2—44no—
1009C2—444no—
1010C2—444no—
1011C2#1307195818yesdirect product factor
1012C2C2×D11×#12011yescharacteristic
1013C2C2×#1062307811yescharacteristic
1014C2C2×#1062313911yescharacteristic
1015C2C2×#1062302111yescharacteristic
1016C2C2×#1062318611yescharacteristic
1017C2C2×#1062308311yescharacteristic
1018C2C2×#1062313011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#66931C2semidirect
3. C22×#66992C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13071958C2direct (N × H)
6. C2×#10622285C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622259C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622280C2semidirect
16. C2×C11×#386C2semidirect
27. C22×#4339C22semidirect
39. C2×#66992C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×#66931C22semidirect
56. C11×#386C22semidirect
59. #10622836C22semidirect
60. #10622823C22semidirect
65. #10622574C22semidirect
66. #10622573C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622285C22semidirect
70. #10622281C22semidirect
71. #10622280C22semidirect
72. #10622259C22semidirect
101. C22×C22⋊D11D4semidirect
129. C22×C4×D11D4semidirect
134. C22×Dic22D4semidirect
195. C24×C11#41semidirect
258. C2×C22⋊D11C2×D4semidirect
280. C22×Dic11#41semidirect
299. C2×C4×D11C2×D4semidirect
303. C2×Dic22C2×D4semidirect
334. C2×#386D11semidirect
370. C23×C11C2×#41semidirect
452. C2×Dic11C2×#41semidirect
503. #386C2×D11semidirect
680. C2×C11#2407semidirect
718. C24#4339semidirect
830. C11C2×#2407semidirect
886. C23C2×#4339semidirect
1011. C2#13071958direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669312
C22×#669922
C22×(C22⋊D11)⋊C42
#130719582
C2×#106222852
C2×#106225742
C2×#106225732
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106225692
C2×#106222812
C2×#106228232
C2×#106222802
C2×C11×#3862
C2×#240711