Finite Group Databasebeta

← C2×#13071996 #14922392

Subgroups — C2×#13071996 #14922392

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic
3C22×#66945C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13071996C2116yesmaximal, direct product factor
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622282C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C4⋊C4C2211yescharacteristic, complemented
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C22×C4⋊Dic11C2211yescharacteristic, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C22×C4×Dic11C2211yescharacteristic, complemented
47C22×C4×Dic11C2211yescharacteristic, complemented
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×#66945—28no—
51C2×#66945C2218yescomplemented
52C2×#66935—28no—
53C2×#66935C2218yes—
54C2×C22⋊C4×D11—28no—
55C2×C22⋊C4×D11C2218yescomplemented
56C11×#396C2218yescomplemented
57C2×C11×#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61#10622607C2218yescomplemented
62#10622604C2218yescomplemented
63#10622602C2218yescomplemented
64#10622601C2218yescomplemented
65#10622574C2218yescomplemented
66#10622570C2218yescomplemented
67#10622568C2218yescomplemented
68#10622557C2218yescomplemented
69#10622282C2218yescomplemented
70#10622278C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C24×D11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44—42no—
104C22×D44C2314yes—
105C22×D44C2314yes—
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—42no—
110C22×C4×D11—42no—
111C22×C4×D11D418yescomplemented
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4—42no—
117C2×C11×C4⋊C4C2314yescomplemented
118C2×C11×C4⋊C4C2314yescomplemented
119C2×C11×C4⋊C4C2314yescomplemented
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—42no—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4D418yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
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)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×(C2×D11)⋊C4C2314yescomplemented
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yescomplemented
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—42no—
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×C4×Dic11—24no—
161C2×C4×Dic11—24no—
162C2×C4×Dic11C2314yescomplemented
163C2×C4×Dic11C2314yescomplemented
164#66947—232no—
165#66945—232no—
166#66935—232no—
167C22⋊C4×D11—232no—
168C11×#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2411—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—232no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—28no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—28no—
195C23×D11—28no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—416no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11C2×D414yes—
214C23×D11C2×D414yes—
215C23×D11#4114yes—
216C23×D11#4114yes—
217C23×D11C2412yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
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×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—
243C22×C4×C11C2412yes—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—416no—
248C22×Dic11—22no—
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×Dic11C2×D414yes—
262C22×Dic11C2×D414yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—28no—
272C2×D44—28no—
273C2×D44—44no—
274C2×D44—416no—
275C2×D44—416no—
276C2×C4×D11—232no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—416no—
283C2×C4×D11C2×D4116yescomplemented
284C11×C4⋊C4—28no—
285C11×C4⋊C4—28no—
286C11×C4⋊C4—44no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—44no—
290C22⋊Dic11—28no—
291C22⋊Dic11—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—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302(C2×D11)⋊C4—44no—
303(C2×D11)⋊C4C2×D4116yes—
304C4⋊Dic11—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—44no—
307C4×Dic11—28no—
308C4×Dic11—28no—
309C22×#123—111no—
310C22×#120—111no—
311C22×#117—111no—
312C23×C22⋊C4—111no—
313#2411—1116no—
314C2×#396—111no—
315C2×#396D1111yescharacteristic, complemented
316C2×#394—111no—
317C2×#394—111no—
318C2×#390—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#385—111no—
324C2×#379—111no—
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—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11C22×D412yes—
339C23×C11C22×D412yes—
340C23×C11C2×#4114yes—
341C23×C11C2×#4112yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11C2511yescharacteristic
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—232no—
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
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—22no—
374C22×D11—416no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—416no—
378C22×D11—4128no—
379C22×D11—416no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—416no—
385C22×D11—44no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11#121116yes—
393C22×D11C22×D414yes—
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C2×C4×C11—28no—
398C2×C4×C11—28no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
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—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C22×D414yes—
421C22⋊D11—416no—
422C2×Dic11—28no—
423C2×Dic11—28no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—44no—
438C2×Dic11—44no—
439C2×Dic11—44no—
440C2×Dic11C22×D414yes—
441C2×Dic11C22×D414yes—
442D44—416no—
443D44—416no—
444C4×D11—232no—
445C4×D11—416no—
446C26—111no—
447C23×D4—111no—
448C23×D4—111no—
449C23×D4—111no—
450C24×C4—111no—
451C24×C4—111no—
452C2×#123—118no—
453C2×#123—228no—
454C2×#120—118no—
455C2×#120—228no—
456C2×#117—118no—
457C2×#117—228no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4C2×D1111yescharacteristic, complemented
462C22×C4⋊C4C2×D1111yescharacteristic, complemented
463C22×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—118no—
479C22×C22⋊C4—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C42—111no—
484C22×C42—111no—
485#396—118no—
486#396C2×D1118yescomplemented
487#394—118no—
488#394—118no—
489#390—118no—
490#390—118no—
491#388—118no—
492#388—118no—
493#386—118no—
494#385—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95C2×D1111yescharacteristic, complemented
500C22×C11—24no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—42no—
504C22×C11—416no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11C2×#12114yes—
509C22×C11#52514yes—
510C22×C11#53514yes—
511C22×C11#54614yes—
512C22×C11#54614yes—
513C22×C11#55114yes—
514C22×C11#55114yes—
515C22×C11C23×D411yescharacteristic
516C22×C11C23×D411yescharacteristic
517C22×C11C22×#4111yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C2×D11—232no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—24no—
531C2×D11—24no—
532C2×D11—464no—
533C2×D11—42no—
534C2×D11—416no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—88no—
546C2×D11C2×#12118yes—
547C4×C11—24no—
548C4×C11—24no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558C25—111no—
559C25—111no—
560C25—111no—
561C25—114no—
562C25—224no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—442no—
568C25—442no—
569C25C22×D1111yescharacteristic
570C22×D4—114no—
571C22×D4—114no—
572C22×D4—114no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—442no—
581C22×D4—442no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—118no—
585C23×C4—114no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#120—2232no—
603#117—2232no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—42no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—442no—
613C2×C4⋊C4C22×D1114yescomplemented
614C2×C4⋊C4C22×D1114yescomplemented
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—118no—
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—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—2232no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—224no—
640C2×C22⋊C4—224no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—224no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95C22×D1114yescomplemented
659C2×C11—44no—
660C2×C11#241118yescomplemented
661C2×C11C22×#12111yescharacteristic
662C2×C11C2×#52511yescharacteristic
663C2×C11C2×#53511yescharacteristic
664C2×C11C2×#54611yescharacteristic
665C2×C11C2×#54611yescharacteristic
666C2×C11C2×#55111yescharacteristic
667C2×C11C2×#55111yescharacteristic
668D11—28no—
669D11—44no—
670D11—82no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—114no—
678C24—114no—
679C24—114no—
680C24—112no—
681C24—114no—
682C24—112no—
683C24—112no—
684C24—228no—
685C24—228no—
686C24—228no—
687C24—228no—
688C24—2232no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—228no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24#434314yes—
716C24C23×D1112yes—
717C24C23×D1111yescharacteristic
718C2×D4—228no—
719C2×D4—228no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—228no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—444no—
726C2×D4—4416no—
727C2×D4—4416no—
728C2×D4—444no—
729C2×D4—4416no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—114no—
747C22×C4—114no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—1116no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—228no—
755C22×C4—2232no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—4416no—
774C22×C4D4×D1114yes—
775C22×C4D4×D1114yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—44no—
785C4⋊C4—228no—
786C4⋊C4—228no—
787C4⋊C4—444no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—44no—
791C22⋊C4—1116no—
792C22⋊C4—228no—
793C22⋊C4—228no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C42—228no—
806C42—228no—
807C11C2×#241111yescharacteristic, complemented, Sylow
808C23—28no—
809C23—28no—
810C23—28no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—1116no—
822C23—114no—
823C23—114no—
824C23—114no—
825C23—114no—
826C23—2232no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—228no—
832C23—228no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—228no—
838C23—228no—
839C23—228no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—4416no—
854C23—4416no—
855C23—4416no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—44128no—
860C23—444no—
861C23—444no—
862C23—444no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23C2×D4×D1112yes—
872C23C2×D4×D1112yes—
873C23#6703712yes—
874C23C2×#434314yes—
875C23C2×#434312yes—
876C23#41×D1112yes—
877C23#41×D1112yes—
878C23#6704212yes—
879C23C24×D1111yescharacteristic
880D4—4416no—
881D4—4416no—
882D4—4416no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—2232no—
908C2×C4—228no—
909C2×C4—228no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—4416no—
924C2×C4—444no—
925C2×C4—444no—
926C2×C4—444no—
927C2×C4C2×D4×D1114yes—
928C2×C4C2×D4×D1114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—416no—
935C22—42no—
936C22—42no—
937C22—118no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—224no—
942C22—2232no—
943C22—224no—
944C22—224no—
945C22—224no—
946C22—224no—
947C22—224no—
948C22—4464no—
949C22—442no—
950C22—442no—
951C22—4416no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—888no—
962C22D11×#12114yes—
963C22#1062313814yes—
964C22#1062314114yes—
965C22#1062315814yes—
966C22#1062316114yes—
967C22#1062316814yes—
968C22#1062323614yes—
969C22C22×D4×D1111yescharacteristic
970C22C22×D4×D1111yescharacteristic
971C22C2×#6703711yescharacteristic
972C22C22×#434311yescharacteristic
973C22C2×#41×D1111yescharacteristic
974C22C2×#41×D1111yescharacteristic
975C22C2×#6704211yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—224no—
983C4—224no—
984C4—442no—
985C4—442no—
986C4—442no—
987C2—44no—
988C2—228no—
989C2—444no—
990C2—882no—
991C2#1307199618yesdirect product factor
992C2C2×D11×#12111yescharacteristic
993C2C2×#1062315811yescharacteristic
994C2C2×#1062313811yescharacteristic
995C2C2×#1062314111yescharacteristic
996C2C2×#1062316111yescharacteristic
997C2C2×#1062323611yescharacteristic
998C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#396D11
hypocenterC11C2×#2411
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
3. C22×#66945C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13071996C2direct (N × H)
6. C2×#10622607C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622282C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#396C2semidirect
23. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C4⋊C4C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×(C2×D11)⋊C4C22semidirect
43. C22×C4⋊Dic11C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
46. C22×C4×Dic11C22semidirect
47. C22×C4×Dic11C22semidirect
49. C2×#66947C22semidirect
51. C2×#66945C22semidirect
55. C2×C22⋊C4×D11C22semidirect
56. C11×#396C22semidirect
57. C2×C11×#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622607C22semidirect
62. #10622604C22semidirect
63. #10622602C22semidirect
64. #10622601C22semidirect
65. #10622574C22semidirect
66. #10622570C22semidirect
67. #10622568C22semidirect
68. #10622557C22semidirect
69. #10622282C22semidirect
70. #10622278C22semidirect
111. C22×C4×D11D4semidirect
117. C2×C11×C4⋊C4C23semidirect
118. C2×C11×C4⋊C4C23semidirect
119. C2×C11×C4⋊C4C23semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
153. C2×(C2×D11)⋊C4C23semidirect
155. C2×C4⋊Dic11C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
162. C2×C4×Dic11C23semidirect
163. C2×C4×Dic11C23semidirect
168. C11×#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
283. C2×C4×D11C2×D4semidirect
315. C2×#396D11semidirect
461. C22×C4⋊C4C2×D11semidirect
462. C22×C4⋊C4C2×D11semidirect
463. C22×C4⋊C4C2×D11semidirect
486. #396C2×D11semidirect
499. C2×#95C2×D11semidirect
613. C2×C4⋊C4C22×D11semidirect
614. C2×C4⋊C4C22×D11semidirect
615. C2×C4⋊C4C22×D11semidirect
658. #95C22×D11semidirect
660. C2×C11#2411semidirect
807. C11C2×#2411semidirect
991. C2#13071996direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669352
C22×#669452
C22×C22⋊C4×D112
#130719962
C2×#106226072
C2×#106226042
C2×#106225742
C2×#106226012
C2×#106225702
C2×#106222822
C2×#106225572
C2×#106222782
C2×#106226022
C2×#106225682
C2×C11×#3962
C2×#241111