Finite Group Databasebeta

← C2×#13072281 #14921198

Subgroups — C2×#13072281 #14921198

Order 2816.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C23×(C2×D11)⋊C4C211yesmaximal, characteristic
4C22×C22⋊C4×D11C211yesmaximal, characteristic
5#13072281C2116yesmaximal, direct product factor
6C2×#10622605C211yesmaximal, characteristic, complemented
7C2×#10622289C211yesmaximal, characteristic, complemented
8C2×#10622607C211yesmaximal, characteristic, complemented
9C2×#10622286C211yesmaximal, characteristic, complemented
10C2×#10622281C211yesmaximal, characteristic, complemented
11C2×#10622559C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622280C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic, complemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4—28no—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2218yes—
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×C4⋊Dic11C2211yescharacteristic, complemented
42C2×#66977—28no—
43C2×#66977C2218yescomplemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C2×#66949—28no—
51C2×#66949C2218yescomplemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yes—
54C11×#385C2218yescomplemented
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#10622607C2218yescomplemented
62#10622605C2218yescomplemented
63#10622602C2218yescomplemented
64#10622568C2218yes—
65#10622559C2218yescomplemented
66#10622555C2218yescomplemented
67#10622289C2218yescomplemented
68#10622286C2218yescomplemented
69#10622281C2218yescomplemented
70#10622280C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—42no—
77C24×D11—42no—
78C24×D11Q818yescomplemented
79C24×D11C2311yescharacteristic
80C24×D11C2314yes—
81C24×D11C2311yescharacteristic
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11—42no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2314yes—
91C23×C4×C11C2311yescharacteristic
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—42no—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
109C22×C4×D11C2314yes—
110C22×Dic22—24no—
111C22×Dic22—24no—
112C22×Dic22—42no—
113C22×Dic22C2314yescomplemented
114C2×C11×C4⋊C4—24no—
115C2×C11×C4⋊C4—42no—
116C2×C11×C4⋊C4C2314yescomplemented
117C2×C11×C4⋊C4C2314yescomplemented
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11D418yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—232no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
136C2×(C2×D11)⋊C4D418yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×C4⋊Dic11—24no—
148C2×C4⋊Dic11C2314yescomplemented
149#66977—232no—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—24no—
152C2×Dic11⋊C4—24no—
153C2×Dic11⋊C4—24no—
154C2×Dic11⋊C4—42no—
155C2×Dic11⋊C4—42no—
156C2×Dic11⋊C4C2314yescomplemented
157C2×Dic11⋊C4C2314yescomplemented
158C2×Dic11⋊C4C2314yescomplemented
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×Dic11⋊C4C2314yescomplemented
162#66949—232no—
163C22⋊C4×D11—232no—
164C11×#95C2314yescomplemented
165C11×#95C2314yescomplemented
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C2×#2437—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11C2×D414yes—
176C24×C11C2×Q814yes—
177C24×C11#4114yes—
178C24×C11C2412yes—
179C24×C11C2411yescharacteristic
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—232no—
185C23×D11—28no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—28no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—232no—
194C23×D11—28no—
195C23×D11—28no—
196C23×D11—416no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—416no—
200C23×D11—416no—
201C23×D11—416no—
202C23×D11—416no—
203C23×D11C2×D414yes—
204C23×D11C2×Q814yes—
205C23×D11C2×Q814yes—
206C23×D11C2×Q8116yescomplemented
207C23×D11#4114yes—
208C23×D11C2412yes—
209C23×D11C2412yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—28no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—28no—
229C22×C4×C11—44no—
230C22×C4×C11—416no—
231C22×C4×C11C2×D414yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×Dic11—28no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—28no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—44no—
256C22×Dic11—416no—
257C22×Dic11C2×D414yes—
258C22×Dic11C2×D414yes—
259C22×Dic11C2×D414yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—416no—
273C2×C4×D11—416no—
274C2×Dic22—28no—
275C2×Dic22—28no—
276C2×Dic22—44no—
277C2×Dic22—416no—
278C11×C4⋊C4—28no—
279C11×C4⋊C4—44no—
280C11×C22⋊C4—28no—
281C11×C22⋊C4—28no—
282C22⋊Dic11—28no—
283C22⋊Dic11C2×D4116yes—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4C2×D4116yes—
294C4⋊Dic11—28no—
295Dic11⋊C4—28no—
296Dic11⋊C4—28no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299Dic11⋊C4—44no—
300Dic11⋊C4—44no—
301C22×C22⋊Q8—111no—
302C22×C22⋊Q8—111no—
303C23×C22⋊C4—111no—
304C23×C22⋊C4—111no—
305#2437—1116no—
306C2×#399—111no—
307C2×#396—111no—
308C2×#396—111no—
309C2×#393—111no—
310C2×#385—111no—
311C2×#385—111no—
312C2×#385—111no—
313C2×#385D1111yescharacteristic, complemented
314C2×#380—111no—
315C2×#380—111no—
316C2×#379—111no—
317C23×C11—28no—
318C23×C11—28no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C22⋊Q8116yescomplemented
328C23×C11C22×D414yes—
329C23×C11C22×D412yes—
330C23×C11C22×D412yes—
331C23×C11C22×Q814yes—
332C23×C11C22×Q812yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—232no—
352C22×D11—28no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—232no—
360C22×D11—416no—
361C22×D11—4128no—
362C22×D11—416no—
363C22×D11—416no—
364C22×D11—416no—
365C22×D11—416no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11C22⋊Q8116yescomplemented
371C22×D11C22×D414yes—
372C22×D11C22×Q814yes—
373C22×D11C22×Q814yes—
374C22×D11C2×#4114yes—
375C2×C4×C11—28no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—416no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11—44no—
399C2×C4×C11C22×D414yes—
400C2×Dic11—28no—
401C2×Dic11—28no—
402C2×Dic11—28no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—416no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11—44no—
422C2×Dic11C22×D414yes—
423C2×Dic11C22×D414yes—
424C2×Dic11C22×D414yes—
425C4×D11—416no—
426C4×D11—416no—
427Dic22—416no—
428C26—111no—
429C23×Q8—111no—
430C24×C4—111no—
431C24×C4—111no—
432C24×C4—111no—
433C24×C4C2×D1111yescharacteristic
434C2×C22⋊Q8—118no—
435C2×C22⋊Q8—118no—
436C2×C22⋊Q8—228no—
437C2×C22⋊Q8—228no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4C2×D1111yescharacteristic, complemented
446C22×C4⋊C4C2×D1111yescharacteristic, complemented
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—118no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—118no—
461C22×C22⋊C4—228no—
462C22×C22⋊C4—228no—
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465#399—118no—
466#396—118no—
467#396—118no—
468#393—118no—
469#385—118no—
470#385—118no—
471#385—118no—
472#385C2×D1118yescomplemented
473#380—118no—
474#380—118no—
475#379—118no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95C2×D1111yescharacteristic, complemented
481C2×#95C2×D1111yescharacteristic, complemented
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—232no—
485C22×C11—24no—
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11C2×C22⋊Q814yes—
490C22×C11C2×C22⋊Q814yes—
491C22×C11C2×C22⋊Q818yescomplemented
492C22×C11#54314yes—
493C22×C11D4214yes—
494C22×C11#54614yes—
495C22×C11#54614yes—
496C22×C11#55114yes—
497C22×C11C23×D411yescharacteristic
498C22×C11C23×D411yescharacteristic
499C22×C11C23×Q811yescharacteristic
500C22×C11C22×#4111yescharacteristic
501C22×C11C22×#4111yescharacteristic
502C22×C11C2×H(5,𝔽2)11yescharacteristic
503C22×C11C2×H(5,𝔽2)11yescharacteristic
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—232no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—464no—
515C2×D11—416no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11C2×C22⋊Q818yescomplemented
521C4×C11—24no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—24no—
529Dic11—24no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533C25—111no—
534C25—111no—
535C25—118no—
536C25—114no—
537C25—224no—
538C25—224no—
539C25—224no—
540C25—224no—
541C25—442no—
542C25—442no—
543C25C22×D1111yescharacteristic
544C22×Q8—114no—
545C22×Q8—224no—
546C22×Q8—224no—
547C22×Q8—442no—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—42no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—114no—
558C23×C4—114no—
559C23×C4—114no—
560C23×C4—224no—
561C23×C4—224no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—224no—
565C23×C4—224no—
566C23×C4—442no—
567C23×C4—442no—
568C23×C4—442no—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1114yes—
575C23×C4C22×D1111yescharacteristic
576C22⋊Q8—2232no—
577C22⋊Q8—2232no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—42no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—224no—
590C2×C4⋊C4—224no—
591C2×C4⋊C4—224no—
592C2×C4⋊C4—442no—
593C2×C4⋊C4—442no—
594C2×C4⋊C4C22×D1114yescomplemented
595C2×C4⋊C4C22×D1114yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—118no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—118no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—114no—
612C2×C22⋊C4—2232no—
613C2×C22⋊C4—2232no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—224no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—224no—
622C2×C22⋊C4—442no—
623C2×C22⋊C4—442no—
624C2×C22⋊C4C22×D1114yes—
625C2×C22⋊C4C22×D1114yes—
626#95—114no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95C22×D1114yescomplemented
631#95C22×D1114yescomplemented
632C2×C11—28no—
633C2×C11#243718yescomplemented
634C2×C11C22×C22⋊Q811yescharacteristic
635C2×C11C22×C22⋊Q811yescharacteristic
636C2×C11C2×#54311yescharacteristic
637C2×C11C2×D4211yescharacteristic
638C2×C11C2×#54611yescharacteristic
639C2×C11C2×#54611yescharacteristic
640C2×C11C2×#55111yescharacteristic
641D11—28no—
642D11—44no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—114no—
648C24—114no—
649C24—114no—
650C24—112no—
651C24—114no—
652C24—112no—
653C24—1116no—
654C24—228no—
655C24—2232no—
656C24—228no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—2232no—
662C24—228no—
663C24—222no—
664C24—228no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24—4416no—
671C24—444no—
672C24—444no—
673C24—4416no—
674C24—4416no—
675C24—4416no—
676C24—4416no—
677C24#433914yes—
678C24D4×D1114yes—
679C24Q8×D1114yes—
680C24C23×D1112yes—
681C24C23×D1111yescharacteristic
682C2×Q8—228no—
683C2×Q8—228no—
684C2×Q8—444no—
685C2×Q8—4416no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—416no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—228no—
717C22×C4—228no—
718C22×C4—228no—
719C22×C4—228no—
720C22×C4—228no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—228no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4—4416no—
740C22×C4—4416no—
741C22×C4—444no—
742C22×C4—4416no—
743C22×C4D4×D1114yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—228no—
753C4⋊C4—228no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C4⋊C4—444no—
758C4⋊C4—444no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—1116no—
762C22⋊C4—1116no—
763C22⋊C4—228no—
764C22⋊C4—228no—
765C22⋊C4—228no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—228no—
770C22⋊C4—228no—
771C22⋊C4—444no—
772C22⋊C4—444no—
773C11C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—1116no—
785C23—114no—
786C23—114no—
787C23—114no—
788C23—114no—
789C23—2232no—
790C23—228no—
791C23—228no—
792C23—228no—
793C23—228no—
794C23—228no—
795C23—228no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—228no—
801C23—2232no—
802C23—228no—
803C23—228no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—4416no—
811C23—4416no—
812C23—44128no—
813C23—4416no—
814C23—4416no—
815C23—4416no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23#66949116yescomplemented
821C23C2×#433914yes—
822C23C2×#433912yes—
823C23C2×D4×D1114yes—
824C23C2×D4×D1112yes—
825C23C2×D4×D1112yes—
826C23#6703712yes—
827C23C2×Q8×D1114yes—
828C23C2×Q8×D1112yes—
829C23#41×D1112yes—
830C23#6704212yes—
831C23C24×D1111yescharacteristic
832Q8—4416no—
833C2×C4—28no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—114no—
858C2×C4—114no—
859C2×C4—114no—
860C2×C4—228no—
861C2×C4—228no—
862C2×C4—228no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—4416no—
879C2×C4—4416no—
880C2×C4—4416no—
881C2×C4—444no—
882C2×C4—444no—
883C2×C4—444no—
884C2×C4C2×D4×D1114yes—
885C22—24no—
886C22—232no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—118no—
893C22—224no—
894C22—2232no—
895C22—224no—
896C22—224no—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—224no—
901C22—224no—
902C22—224no—
903C22—4464no—
904C22—442no—
905C22—4416no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22C2×#6694914yes—
910C22C2×#6694918yescomplemented
911C22#1062308114yes—
912C22#1062308714yes—
913C22#1062312114yes—
914C22D11×C22⋊Q814yes—
915C22#1062316514yes—
916C22#1062318514yes—
917C22C22×#433911yescharacteristic
918C22C22×D4×D1111yescharacteristic
919C22C22×D4×D1111yescharacteristic
920C22C2×#6703711yescharacteristic
921C22C22×Q8×D1111yescharacteristic
922C22C2×#41×D1111yescharacteristic
923C22C2×#6704211yescharacteristic
924C4—24no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—224no—
931C4—224no—
932C4—224no—
933C4—442no—
934C4—442no—
935C4—442no—
936C2—28no—
937C2—228no—
938C2—444no—
939C2#1307228118yesdirect product factor
940C2C2×D11×C22⋊Q811yescharacteristic
941C2C22×#6694911yescharacteristic
942C2C2×#1062316511yescharacteristic
943C2C2×#1062312111yescharacteristic
944C2C2×#1062318511yescharacteristic
945C2C2×#1062308111yescharacteristic
946C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#385D11
hypocenterC11C2×#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66977C2semidirect
2. C22×#66949C2semidirect
5. #13072281C2direct (N × H)
6. C2×#10622605C2semidirect
7. C2×#10622289C2semidirect
8. C2×#10622607C2semidirect
9. C2×#10622286C2semidirect
10. C2×#10622281C2semidirect
11. C2×#10622559C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622280C2semidirect
14. C2×#10622555C2semidirect
16. C2×C11×#385C2semidirect
22. C23×Dic22C22semidirect
23. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C4⋊C4C22semidirect
41. C22×C4⋊Dic11C22semidirect
43. C2×#66977C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
46. C22×Dic11⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
51. C2×#66949C22semidirect
54. C11×#385C22semidirect
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. #10622607C22semidirect
62. #10622605C22semidirect
63. #10622602C22semidirect
65. #10622559C22semidirect
66. #10622555C22semidirect
67. #10622289C22semidirect
68. #10622286C22semidirect
69. #10622281C22semidirect
70. #10622280C22semidirect
78. C24×D11Q8semidirect
113. C22×Dic22C23semidirect
116. C2×C11×C4⋊C4C23semidirect
117. C2×C11×C4⋊C4C23semidirect
148. C2×C4⋊Dic11C23semidirect
156. C2×Dic11⋊C4C23semidirect
157. C2×Dic11⋊C4C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
161. C2×Dic11⋊C4C23semidirect
164. C11×#95C23semidirect
165. C11×#95C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
206. C23×D11C2×Q8semidirect
313. C2×#385D11semidirect
327. C23×C11C22⋊Q8semidirect
370. C22×D11C22⋊Q8semidirect
445. C22×C4⋊C4C2×D11semidirect
446. C22×C4⋊C4C2×D11semidirect
472. #385C2×D11semidirect
480. C2×#95C2×D11semidirect
481. C2×#95C2×D11semidirect
491. C22×C11C2×C22⋊Q8semidirect
520. C2×D11C2×C22⋊Q8semidirect
594. C2×C4⋊C4C22×D11semidirect
595. C2×C4⋊C4C22×D11semidirect
630. #95C22×D11semidirect
631. #95C22×D11semidirect
633. C2×C11#2437semidirect
773. C11C2×#2437semidirect
820. C23#66949semidirect
910. C22C2×#66949semidirect
939. C2#13072281direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#669492
C23×(C2×D11)⋊C42
C22×C22⋊C4×D112
#130722812
C2×#106226052
C2×#106222892
C2×#106226072
C2×#106222862
C2×#106222812
C2×#106225592
C2×#106226022
C2×#106222802
C2×#106225552
C2×#106225682
C2×C11×#3852
C2×#243711