Finite Group Databasebeta

← C2×#13072747 #14921353

Subgroups — C2×#13072747 #14921353

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×#66977C211yesmaximal, characteristic, complemented
3C22×#66990C211yesmaximal, characteristic
4C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072747C2116yesmaximal, direct product factor
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic, complemented
26C22×C11×C22⋊C4C2211yescharacteristic, complemented
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic, complemented
30C22×C22⋊Dic11C2211yescharacteristic, complemented
31C2×#66990—28no—
32C2×#66990C2218yes—
33C22×(C2×D11)⋊C4—28no—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2218yescomplemented
45C22×C4⋊Dic11C2211yescharacteristic, complemented
46C2×#66977—28no—
47C2×#66977C2218yescomplemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic11C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57#10622833C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622574C2218yescomplemented
63#10622572C2218yescomplemented
64#10622570C2218yescomplemented
65#10622568C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67#10622288C2218yescomplemented
68#10622286C2218yescomplemented
69#10622283C2218yescomplemented
70#10622282C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—42no—
79C24×D11—42no—
80C24×D11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C24×D11C2314yes—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—24no—
86C22×D4×C11C2314yes—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11—24no—
105C23×Dic11—24no—
106C23×Dic11—42no—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2314yes—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×Dic22—24no—
115C22×Dic22—24no—
116C22×Dic22—42no—
117C22×Dic22C2314yescomplemented
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yescomplemented
123C2×C11×C22⋊C4C2314yescomplemented
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11D418yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yescomplemented
131C2×C22⋊Dic11C2314yescomplemented
132#66990—232no—
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—232no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4D418yescomplemented
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)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yescomplemented
156#66977—232no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×C4×Dic11—24no—
162C2×C4×Dic11—42no—
163C2×C4×Dic11C2314yescomplemented
164C2×C4×Dic11C2314yescomplemented
165#66938—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×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11C2×D414yes—
185C24×C11#4114yes—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—232no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—28no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—28no—
207C23×D11—28no—
208C23×D11—44no—
209C23×D11—44no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11—416no—
215C23×D11—416no—
216C23×D11C2×D414yes—
217C23×D11#4114yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11—416no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—28no—
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×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—28no—
240C22×C4×C11—44no—
241C22×C4×C11—416no—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—416no—
255C2×C22⋊D11—416no—
256C22×Dic11—28no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—28no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—44no—
274C22×Dic11—416no—
275C22×Dic11C2×D414yes—
276C22×Dic11C2×D414yes—
277C22×Dic11C2×D414yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22—44no—
287C2×Dic22—416no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—44no—
294C22⋊Dic11C2×D4116yes—
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—44no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4C2×D4116yescomplemented
305C4⋊Dic11—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308C4×Dic11—28no—
309C4×Dic11—44no—
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×#388—111no—
322C2×#386—111no—
323C2×#386D1111yescharacteristic, complemented
324C2×#379—111no—
325C2×C4×C22⋊C4—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—28no—
331C23×C11—28no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11#124116yescomplemented
351C23×C11C22×D414yes—
352C23×C11C22×D412yes—
353C23×C11C22×D412yes—
354C23×C11C2×#4114yes—
355C23×C11C2×#4112yes—
356C23×C11C2×#4114yes—
357C23×C11C2×#4112yes—
358C23×C11C2×#4112yes—
359C23×C11H(5,𝔽2)12yes—
360C23×C11H(5,𝔽2)12yes—
361C23×C11C2511yescharacteristic
362C22×D11—232no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—28no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—416no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—416no—
385C22×D11—416no—
386C22×D11—4128no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—416no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11C22×D414yes—
397C22×D11C2×#4114yes—
398D4×C11—416no—
399C2×C4×C11—28no—
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—416no—
415C2×C4×C11—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C22⋊D11—416no—
421C22⋊D11—416no—
422C2×Dic11—28no—
423C2×Dic11—28no—
424C2×Dic11—28no—
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—22no—
439C2×Dic11—22no—
440C2×Dic11—416no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11C22×D414yes—
445C2×Dic11C22×D414yes—
446C2×Dic11C22×D414yes—
447Dic22—416no—
448C26—111no—
449C23×Q8—111no—
450C23×D4—111no—
451C23×D4—111no—
452C23×D4C2×D1111yescharacteristic
453C24×C4—111no—
454C24×C4C2×D1111yescharacteristic
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⋊C4—111no—
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—118no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic, complemented
482C22×C22⋊C4C2×D1111yescharacteristic, complemented
483C22×C42—111no—
484C22×C42—111no—
485#397—118no—
486#394—118no—
487#394—118no—
488#393—118no—
489#390—118no—
490#388—118no—
491#388—118no—
492#386—118no—
493#386C2×D1118yescomplemented
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—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—232no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—88no—
517C22×C11#52514yes—
518C22×C11C2×#12414yes—
519C22×C11C2×#12418yescomplemented
520C22×C11#53814yes—
521C22×C11D4214yes—
522C22×C11#54614yes—
523C22×C11#54614yes—
524C22×C11#55114yes—
525C22×C11C23×D411yescharacteristic
526C22×C11C23×D411yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C22×#4111yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C22×C11C2×H(5,𝔽2)11yescharacteristic
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—464no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—416no—
548C2×D11—416no—
549C4×C11—24no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—24no—
556Dic11—24no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—114no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—442no—
569C25—442no—
570C25C22×D1111yescharacteristic
571C25C22×D1111yescharacteristic
572C22×Q8—114no—
573C22×Q8—224no—
574C22×Q8—224no—
575C22×Q8—442no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—114no—
580C22×D4—114no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—442no—
586C22×D4—442no—
587C22×D4C22×D1114yes—
588C23×C4—24no—
589C23×C4—24no—
590C23×C4—42no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—114no—
598C23×C4—224no—
599C23×C4—224no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1114yes—
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—2232no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4—224no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—118no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—118no—
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—114no—
635C2×C22⋊C4—2232no—
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×D1114yescomplemented
650C2×C22⋊C4C22×D1114yescomplemented
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—442no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95C22×D1114yescomplemented
660#95C22×D1114yescomplemented
661C2×C11—28no—
662C2×C11—82no—
663C2×C11#247218yescomplemented
664C2×C11C2×#52511yescharacteristic
665C2×C11C22×#12411yescharacteristic
666C2×C11C2×#53811yescharacteristic
667C2×C11C2×D4211yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#54611yescharacteristic
670C2×C11C2×#55111yescharacteristic
671D11—44no—
672D11—44no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—114no—
685C24—114no—
686C24—112no—
687C24—112no—
688C24—228no—
689C24—228no—
690C24—2232no—
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—228no—
705C24—228no—
706C24—444no—
707C24—444no—
708C24—4416no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24#433914yes—
715C24D4×D1114yes—
716C24#434114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—444no—
723C2×Q8—4416no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—416no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—228no—
732C2×D4—444no—
733C2×D4—444no—
734C2×D4—4416no—
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—28no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—28no—
752C22×C4—44no—
753C22×C4—416no—
754C22×C4—114no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—228no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—228no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—444no—
781C22×C4—4416no—
782C22×C4D4×D1114yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—228no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—1116no—
795C22⋊C4—1116no—
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—228no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4—444no—
808C42—228no—
809C42—444no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—114no—
836C23—114no—
837C23—2232no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—228no—
842C23—228no—
843C23—228no—
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—44128no—
862C23—444no—
863C23—444no—
864C23—4416no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23#66938116yescomplemented
872C23C2×#433914yes—
873C23C2×#433912yes—
874C23C2×D4×D1114yes—
875C23C2×D4×D1112yes—
876C23C2×D4×D1112yes—
877C23C2×#434114yes—
878C23C2×#434112yes—
879C23#6703712yes—
880C23#41×D1112yes—
881C23#6704212yes—
882C23C24×D1111yescharacteristic
883Q8—4416no—
884D4—416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
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—22no—
902C2×C4—416no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—114no—
908C2×C4—114no—
909C2×C4—114no—
910C2×C4—228no—
911C2×C4—228no—
912C2×C4—228no—
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—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—4416no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4—444no—
932C2×C4C2×D4×D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—232no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—88no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—4464no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—4416no—
961C22—4416no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22C2×#6693814yes—
966C22C2×#6693818yescomplemented
967C22#1062308114yes—
968C22#1062308714yes—
969C22#1062312114yes—
970C22#1062313714yes—
971C22#1062314814yes—
972C22#1062318514yes—
973C22C22×#433911yescharacteristic
974C22C22×D4×D1111yescharacteristic
975C22C22×D4×D1111yescharacteristic
976C22C22×#434111yescharacteristic
977C22C2×#6703711yescharacteristic
978C22C2×#41×D1111yescharacteristic
979C22C2×#6704211yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—224no—
987C4—224no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—28no—
992C2—82no—
993C2—444no—
994C2—444no—
995C2#1307274718yesdirect product factor
996C2C2×#1062313711yescharacteristic
997C2C22×#6693811yescharacteristic
998C2C2×#1062314811yescharacteristic
999C2C2×#1062312111yescharacteristic
1000C2C2×#1062318511yescharacteristic
1001C2C2×#1062308111yescharacteristic
1002C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#386D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66977C2semidirect
4. C23×(C2×D11)⋊C4C2semidirect
5. #13072747C2direct (N × H)
6. C2×#10622288C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622283C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622568C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#386C2semidirect
23. C23×Dic22C22semidirect
25. C22×C11×C22⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
29. C22×C22⋊Dic11C22semidirect
30. C22×C22⋊Dic11C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×C4⋊Dic11C22semidirect
47. C2×#66977C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×C4×Dic11C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×#66938C22semidirect
54. C11×#386C22semidirect
55. C2×C11×#95C22semidirect
56. C2×C11×#95C22semidirect
57. #10622833C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622574C22semidirect
63. #10622572C22semidirect
64. #10622570C22semidirect
65. #10622568C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. #10622288C22semidirect
68. #10622286C22semidirect
69. #10622283C22semidirect
70. #10622282C22semidirect
117. C22×Dic22C23semidirect
122. C2×C11×C22⋊C4C23semidirect
123. C2×C11×C22⋊C4C23semidirect
130. C2×C22⋊Dic11C23semidirect
131. C2×C22⋊Dic11C23semidirect
143. C2×(C2×D11)⋊C4D4semidirect
155. C2×C4⋊Dic11C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
163. C2×C4×Dic11C23semidirect
164. C2×C4×Dic11C23semidirect
166. C11×#95C23semidirect
167. C11×#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
304. (C2×D11)⋊C4C2×D4semidirect
323. C2×#386D11semidirect
350. C23×C11#124semidirect
481. C22×C22⋊C4C2×D11semidirect
482. C22×C22⋊C4C2×D11semidirect
493. #386C2×D11semidirect
500. C2×#95C2×D11semidirect
501. C2×#95C2×D11semidirect
519. C22×C11C2×#124semidirect
649. C2×C22⋊C4C22×D11semidirect
650. C2×C22⋊C4C22×D11semidirect
659. #95C22×D11semidirect
660. #95C22×D11semidirect
663. C2×C11#2472semidirect
810. C11C2×#2472semidirect
871. C23#66938semidirect
966. C22C2×#66938semidirect
995. C2#13072747direct (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×#669772
C22×#669902
C23×(C2×D11)⋊C42
#130727472
C2×#106222882
C2×#106225742
C2×#106225722
C2×#106222862
C2×#106225702
C2×#106222832
C2×#106222822
C2×#106228332
C2×#106225682
C2×C22⋊C4×Dic112
C2×C11×#3862
C2×#247211