Finite Group Databasebeta

← C2×#13072740 #14921350

Subgroups — C2×#13072740 #14921350

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66950C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13072740C2116yesmaximal, direct product factor
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic, complemented
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×C4⋊Dic11C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46C2×#66950—28no—
47C2×#66950C2218yescomplemented
48C2×#66938—28no—
49C2×#66938C2218yescomplemented
50C2×#66935—28no—
51C2×#66935C2218yes—
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54C11×#388C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61#10622604C2218yescomplemented
62#10622574C2218yescomplemented
63#10622568C2218yescomplemented
64#10622566C2218yescomplemented
65#10622552C2218yescomplemented
66C4×(C2×D11)⋊C4C2218yescomplemented
67#10622286C2218yescomplemented
68#10622283C2218yescomplemented
69#10622278C2218yescomplemented
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—24no—
110C22×C4×D11—42no—
111C22×C4×D11—42no—
112C22×C4×D11C2314yes—
113C22×C4×D11C2314yes—
114C22×Dic22—24no—
115C22×Dic22—24no—
116C22×Dic22—42no—
117C22×Dic22C2314yescomplemented
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4C2314yescomplemented
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—42no—
122C2×C11×C22⋊C4D418yescomplemented
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C42×C11—42no—
127C2×C42×C11C2314yescomplemented
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
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—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4D418yes—
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×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×(C2×D11)⋊C4C2314yescomplemented
154C2×(C2×D11)⋊C4C2314yescomplemented
155C2×(C2×D11)⋊C4C2314yescomplemented
156C2×C4⋊Dic11—24no—
157C2×C4⋊Dic11—24no—
158C2×C4⋊Dic11C2314yescomplemented
159C2×C4⋊Dic11C2314yescomplemented
160C2×C4×Dic11—24no—
161C2×C4×Dic11C2314yescomplemented
162#66950—232no—
163#66938—232no—
164#66935—232no—
165C22⋊C4×D11—232no—
166C11×#95C2314yescomplemented
167C11×#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2472—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11C2×D414yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—232no—
187C23×D11—28no—
188C23×D11—22no—
189C23×D11—22no—
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×D11#4114yes—
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×C11C2×D414yes—
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×Dic11—22no—
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—28no—
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×D11—416no—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22—44no—
287C2×Dic22—416no—
288C11×C4⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C11×C22⋊C4C2×D4116yescomplemented
292C42×C11—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—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—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4C2×D4116yes—
307C4⋊Dic11—28no—
308C4⋊Dic11—28no—
309C4×Dic11—28no—
310C22×#124—111no—
311C22×C22⋊Q8—111no—
312C22×#120—111no—
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394—111no—
318C2×#393—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388D1111yescharacteristic, complemented
322C2×#386—111no—
323C2×#386—111no—
324C2×#379—111no—
325C2×C4×C22⋊C4—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11C22×D414yes—
340C23×C11C22×D412yes—
341C23×C11C22×D412yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11C2×#4112yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11H(5,𝔽2)12yes—
347C23×C11C2511yescharacteristic
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—232no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
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—22no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—416no—
378C22×D11—416no—
379C22×D11—416no—
380C22×D11—4128no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—416no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11#124116yescomplemented
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398C2×C4×C11—28no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
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—22no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C22×D414yes—
421C2×C4×C11C22×D414yes—
422C22⋊D11—416no—
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—22no—
438C2×Dic11—44no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11C22×D414yes—
443D44—416no—
444D44—416no—
445C4×D11—416no—
446C4×D11—416no—
447Dic22—416no—
448C26—111no—
449C23×Q8—111no—
450C23×D4—111no—
451C23×D4—111no—
452C23×D4—111no—
453C24×C4—111no—
454C24×C4—111no—
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic, complemented
485#397—118no—
486#394—118no—
487#394—118no—
488#393—118no—
489#390—118no—
490#388—118no—
491#388C2×D1118yescomplemented
492#386—118no—
493#386—118no—
494#379—118no—
495C4×C22⋊C4—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95C2×D1111yescharacteristic, complemented
501C2×#95C2×D1111yescharacteristic, complemented
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—416no—
510C22×C11#52514yes—
511C22×C11C2×#12414yes—
512C22×C11#53814yes—
513C22×C11D4214yes—
514C22×C11#54614yes—
515C22×C11#54614yes—
516C22×C11#55114yes—
517C22×C11C23×D411yescharacteristic
518C22×C11C23×D411yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C22×#4111yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C22×C11C2×H(5,𝔽2)11yescharacteristic
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—232no—
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—464no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—416no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—88no—
548C2×D11C2×#12418yescomplemented
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—24no—
552C4×C11—42no—
553C4×C11—42no—
554C4×C11—42no—
555Dic11—24no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—111no—
563C25—114no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—224no—
569C25—442no—
570C25—442no—
571C25C22×D1111yescharacteristic
572C22×Q8—114no—
573C22×Q8—224no—
574C22×Q8—224no—
575C22×Q8—442no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—442no—
587C22×D4—442no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—114no—
594C23×C4—114no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—2232no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—42no—
618C2×C22⋊C4—118no—
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—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—224no—
634C2×C22⋊C4—224no—
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—2232no—
644C2×C22⋊C4—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4D4418yescomplemented
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—42no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42C22×D1114yescomplemented
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95C22×D1114yescomplemented
660#95C22×D1114yescomplemented
661C2×C11—44no—
662C2×C11#247218yescomplemented
663C2×C11C2×#52511yescharacteristic
664C2×C11C22×#12411yescharacteristic
665C2×C11C2×#53811yescharacteristic
666C2×C11C2×D4211yescharacteristic
667C2×C11C2×#54611yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#55111yescharacteristic
670D11—28no—
671D11—44no—
672D11—82no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—114no—
680C24—114no—
681C24—114no—
682C24—112no—
683C24—114no—
684C24—112no—
685C24—112no—
686C24—228no—
687C24—228no—
688C24—228no—
689C24—228no—
690C24—2232no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—228no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—444no—
710C24—444no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24—4416no—
716C24—4416no—
717C24C2×D4414yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—444no—
723C2×Q8—4416no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—444no—
732C2×D4—4416no—
733C2×D4—4416no—
734C2×D4—444no—
735C2×D4—4416no—
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—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—114no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—228no—
758C22×C4—228no—
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—222no—
772C22×C4—222no—
773C22×C4—228no—
774C22×C4—228no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—4416no—
778C22×C4—4416no—
779C22×C4C2×D4414yes—
780C22×C4C2×D4414yes—
781C22×C4D4×D1114yes—
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—28no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—1116no—
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—228no—
803C22⋊C4—228no—
804C22⋊C4—444no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4C2×D44116yescomplemented
808C42—44no—
809C42—228no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—114no—
826C23—114no—
827C23—1116no—
828C23—114no—
829C23—2232no—
830C23—228no—
831C23—228no—
832C23—228no—
833C23—228no—
834C23—228no—
835C23—222no—
836C23—228no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—228no—
841C23—228no—
842C23—228no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—4416no—
860C23—4416no—
861C23—4416no—
862C23—44128no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23C22×D4414yes—
875C23C22×D4412yes—
876C23C2×D4×D1112yes—
877C23#6703712yes—
878C23#41×D1112yes—
879C23#41×D1112yes—
880C23#41×D1112yes—
881C23#6704212yes—
882C23C24×D1111yescharacteristic
883Q8—4416no—
884D4—4416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
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—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—114no—
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—222no—
924C2×C4—4416no—
925C2×C4—4416no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4C22×D4414yes—
931C2×C4C22×D4414yes—
932C2×C4C2×D4×D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—416no—
940C22—42no—
941C22—118no—
942C22—224no—
943C22—224no—
944C22—224no—
945C22—2232no—
946C22—224no—
947C22—224no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—4464no—
953C22—442no—
954C22—442no—
955C22—4416no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—888no—
966C22#1062305514yes—
967C22D4×D4414yes—
968C22#1062308514yes—
969C22#1062314114yes—
970C22#1062318814yes—
971C22D11×#12414yes—
972C22#1062323614yes—
973C22C23×D4411yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C2×#6703711yescharacteristic
976C22C2×#41×D1111yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#6704211yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—44no—
992C2—228no—
993C2—444no—
994C2—882no—
995C2#1307274018yesdirect product factor
996C2C2×#1062305511yescharacteristic
997C2C2×D11×#12411yescharacteristic
998C2C2×#1062318811yescharacteristic
999C2C2×D4×D4411yescharacteristic
1000C2C2×#1062314111yescharacteristic
1001C2C2×#1062308511yescharacteristic
1002C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#388D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66950C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13072740C2direct (N × H)
6. C2×#10622566C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622568C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
23. C23×Dic22C22semidirect
24. C22×C11×C4⋊C4C22semidirect
28. C22×C42×C11C22semidirect
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×C4⋊Dic11C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66950C22semidirect
49. C2×#66938C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C11×#388C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11×#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622604C22semidirect
62. #10622574C22semidirect
63. #10622568C22semidirect
64. #10622566C22semidirect
65. #10622552C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. #10622286C22semidirect
68. #10622283C22semidirect
69. #10622278C22semidirect
70. #10622278C22semidirect
117. C22×Dic22C23semidirect
119. C2×C11×C4⋊C4C23semidirect
122. C2×C11×C22⋊C4D4semidirect
127. C2×C42×C11C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
153. C2×(C2×D11)⋊C4C23semidirect
154. C2×(C2×D11)⋊C4C23semidirect
155. C2×(C2×D11)⋊C4C23semidirect
158. C2×C4⋊Dic11C23semidirect
159. C2×C4⋊Dic11C23semidirect
161. C2×C4×Dic11C23semidirect
166. C11×#95C23semidirect
167. C11×#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
291. C11×C22⋊C4C2×D4semidirect
321. C2×#388D11semidirect
393. C22×D11#124semidirect
463. C22×C4⋊C4C2×D11semidirect
484. C22×C42C2×D11semidirect
491. #388C2×D11semidirect
500. C2×#95C2×D11semidirect
501. C2×#95C2×D11semidirect
548. C2×D11C2×#124semidirect
615. C2×C4⋊C4C22×D11semidirect
647. C2×C22⋊C4D44semidirect
654. C2×C42C22×D11semidirect
659. #95C22×D11semidirect
660. #95C22×D11semidirect
662. C2×C11#2472semidirect
807. C22⋊C4C2×D44semidirect
810. C11C2×#2472semidirect
995. C2#13072740direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669502
C22×#669352
C22×C22⋊C4×D112
#130727402
C2×#106225662
C2×#106226042
C2×#106225742
C2×#106222862
C2×#106225522
C2×#106222832
C2×#106222782
C2×#106225682
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#247211