Finite Group Databasebeta

← C2×#13072278 #14921197

Subgroups — C2×#13072278 #14921197

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×#66950C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D11C211yesmaximal, characteristic
4C22×C22⋊C4×D11C211yesmaximal, characteristic
5#13072278C2116yesmaximal, direct product factor
6C2×#10622562C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622281C211yesmaximal, characteristic, complemented
10C2×#10622602C211yesmaximal, characteristic, complemented
11C2×#10622602C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622280C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic, complemented
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×C22⋊Dic11C2211yescharacteristic
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
40C22×C4⋊Dic11C2211yescharacteristic, complemented
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C2×#66950—28no—
47C2×#66950C2218yescomplemented
48C2×#66949—28no—
49C2×#66949C2218yescomplemented
50C2×C22⋊C4×D11—28no—
51C2×C22⋊C4×D11—28no—
52C2×C22⋊C4×D11C2218yes—
53C2×C22⋊C4×D11C2218yes—
54C11×#396C2218yescomplemented
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#10622602C2218yescomplemented
62#10622602C2218yescomplemented
63#10622602C2218yescomplemented
64#10622600C2218yescomplemented
65#10622568C2218yes—
66#10622562C2218yescomplemented
67#10622561C2218yescomplemented
68#10622560C2218yescomplemented
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×D11C2314yes—
80C24×D11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11C2314yes—
107C22×C4×D11C2314yes—
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—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⋊Dic11—42no—
129C2×C22⋊Dic11C2314yes—
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)⋊C4D418yes—
139C2×(C2×D11)⋊C4D418yes—
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×(C2×D11)⋊C4C2314yes—
148C2×C4⋊Dic11—24no—
149C2×C4⋊Dic11—24no—
150C2×C4⋊Dic11C2314yescomplemented
151C2×C4⋊Dic11C2314yescomplemented
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
160#66950—232no—
161#66949—232no—
162C22⋊C4×D11—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×C11—22no—
176C24×C11—22no—
177C24×C11C2×Q814yes—
178C24×C11C2412yes—
179C24×C11C2411yescharacteristic
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—232no—
189C23×D11—232no—
190C23×D11—28no—
191C23×D11—28no—
192C23×D11—28no—
193C23×D11—28no—
194C23×D11—416no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—416no—
198C23×D11—416no—
199C23×D11—416no—
200C23×D11—416no—
201C23×D11C2×D414yes—
202C23×D11C2×D414yes—
203C23×D11C2×Q814yes—
204C23×D11C2×Q814yes—
205C23×D11C2×Q8116yescomplemented
206C23×D11#4114yes—
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—22no—
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×C11C2×D414yes—
227C22×C4×C11C2×D414yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
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—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—28no—
265C2×C4×D11—28no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—416no—
271C2×C4×D11—416no—
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—28no—
280C11×C4⋊C4—44no—
281C11×C22⋊C4—28no—
282C11×C22⋊C4—28no—
283C11×C22⋊C4—44no—
284C22⋊Dic11—28no—
285C22⋊Dic11—28no—
286C22⋊Dic11—44no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4C2×D4116yes—
294(C2×D11)⋊C4C2×D4116yes—
295C4⋊Dic11—28no—
296C4⋊Dic11—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×#396D1111yescharacteristic, complemented
309C2×#393—111no—
310C2×#385—111no—
311C2×#385—111no—
312C2×#385—111no—
313C2×#385—111no—
314C2×#380—111no—
315C2×#380—111no—
316C2×#379—111no—
317C23×C11—28no—
318C23×C11—28no—
319C23×C11—28no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11C22×D412yes—
331C23×C11C22×D412yes—
332C23×C11C22×Q814yes—
333C23×C11C22×Q812yes—
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—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—232no—
360C22×D11—232no—
361C22×D11—416no—
362C22×D11—4128no—
363C22×D11—416no—
364C22×D11—416no—
365C22×D11—416no—
366C22×D11—416no—
367C22×D11C22⋊Q8116yescomplemented
368C22×D11C22⋊Q8116yescomplemented
369C22×D11C22×D414yes—
370C22×D11C22×D414yes—
371C22×D11C22×Q814yes—
372C22×D11C22×Q814yes—
373C22×D11C2×#4114yes—
374C22×D11C2×#4114yes—
375C2×C4×C11—28no—
376C2×C4×C11—28no—
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—44no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11C22×D414yes—
398C2×C4×C11C22×D414yes—
399C2×Dic11—28no—
400C2×Dic11—28no—
401C2×Dic11—22no—
402C2×Dic11—22no—
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—44no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11C22×D414yes—
422C2×Dic11C22×D414yes—
423C4×D11—416no—
424C4×D11—416no—
425C4×D11—416no—
426C4×D11—416no—
427Dic22—416no—
428C26—111no—
429C23×Q8—111no—
430C24×C4—111no—
431C24×C4—111no—
432C24×C4—111no—
433C24×C4—111no—
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⋊C4C2×D1111yescharacteristic, complemented
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—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—118no—
459C22×C22⋊C4—118no—
460C22×C22⋊C4—228no—
461C22×C22⋊C4—228no—
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465#399—118no—
466#396—118no—
467#396C2×D1118yescomplemented
468#393—118no—
469#385—118no—
470#385—118no—
471#385—118no—
472#385—118no—
473#380—118no—
474#380—118no—
475#379—118no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95C2×D1111yescharacteristic, complemented
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—416no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11C2×C22⋊Q814yes—
491C22×C11C2×C22⋊Q814yes—
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—24no—
507C2×D11—24no—
508C2×D11—232no—
509C2×D11—232no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—464no—
519C2×D11C2×C22⋊Q818yescomplemented
520C2×D11C2×C22⋊Q818yescomplemented
521C4×C11—24no—
522C4×C11—24no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—24no—
529Dic11—42no—
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—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—114no—
555C23×C4—114no—
556C23×C4—114no—
557C23×C4—114no—
558C23×C4—224no—
559C23×C4—224no—
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×C4—442no—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575C23×C4C22×D1111yescharacteristic
576C22⋊Q8—2232no—
577C22⋊Q8—2232no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—42no—
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—442no—
592C2×C4⋊C4—442no—
593C2×C4⋊C4C22×D1114yescomplemented
594C2×C4⋊C4C22×D1114yescomplemented
595C2×C4⋊C4C22×D1114yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—118no—
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⋊C4C22×D1114yes—
624C2×C22⋊C4C22×D1114yes—
625C2×C22⋊C4C22×D1114yes—
626#95—114no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—114no—
631#95C22×D1114yescomplemented
632C2×C11—44no—
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—28no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—114no—
650C24—114no—
651C24—114no—
652C24—114no—
653C24—114no—
654C24—114no—
655C24—112no—
656C24—112no—
657C24—1116no—
658C24—228no—
659C24—228no—
660C24—2232no—
661C24—2232no—
662C24—228no—
663C24—228no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24—222no—
671C24—222no—
672C24—4416no—
673C24—444no—
674C24—444no—
675C24—4416no—
676C24—4416no—
677C24—4416no—
678C24—4416no—
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—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—114no—
703C22×C4—114no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—228no—
711C22×C4—228no—
712C22×C4—228no—
713C22×C4—228no—
714C22×C4—228no—
715C22×C4—228no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—228no—
733C22×C4—228no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4—444no—
738C22×C4—4416no—
739C22×C4—4416no—
740C22×C4—4416no—
741C22×C4—4416no—
742C22×C4D4×D1114yes—
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—28no—
752C4⋊C4—44no—
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—44no—
762C22⋊C4—1116no—
763C22⋊C4—1116no—
764C22⋊C4—228no—
765C22⋊C4—228no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—228no—
770C22⋊C4—228no—
771C22⋊C4—228no—
772C22⋊C4—444no—
773C11C2×#243711yescharacteristic, complemented, Sylow
774C23—28no—
775C23—28no—
776C23—28no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—1116no—
788C23—1116no—
789C23—114no—
790C23—114no—
791C23—114no—
792C23—114no—
793C23—114no—
794C23—114no—
795C23—2232no—
796C23—2232no—
797C23—228no—
798C23—228no—
799C23—228no—
800C23—228no—
801C23—228no—
802C23—228no—
803C23—228no—
804C23—228no—
805C23—228no—
806C23—228no—
807C23—228no—
808C23—228no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—4416no—
818C23—4416no—
819C23—44128no—
820C23—4416no—
821C23—4416no—
822C23—4416no—
823C23C2×D4×D1112yes—
824C23C2×D4×D1112yes—
825C23#6703712yes—
826C23C2×Q8×D1114yes—
827C23C2×Q8×D1112yes—
828C23#41×D1112yes—
829C23#41×D1112yes—
830C23#6704212yes—
831C23C24×D1111yescharacteristic
832Q8—4416no—
833C2×C4—28no—
834C2×C4—28no—
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—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—114no—
856C2×C4—114no—
857C2×C4—228no—
858C2×C4—228no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
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—4416no—
876C2×C4—4416no—
877C2×C4—4416no—
878C2×C4—4416no—
879C2×C4—444no—
880C2×C4—444no—
881C2×C4—444no—
882C2×C4—444no—
883C2×C4C2×D4×D1114yes—
884C2×C4C2×D4×D1114yes—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—42no—
889C22—416no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—118no—
894C22—118no—
895C22—224no—
896C22—224no—
897C22—2232no—
898C22—2232no—
899C22—224no—
900C22—224no—
901C22—224no—
902C22—224no—
903C22—224no—
904C22—224no—
905C22—224no—
906C22—224no—
907C22—224no—
908C22—224no—
909C22—4464no—
910C22#1062314014yes—
911C22#1062314114yes—
912C22#1062314314yes—
913C22D11×C22⋊Q814yes—
914C22D11×C22⋊Q814yes—
915C22#1062316514yes—
916C22#1062323614yes—
917C22C22×D4×D1111yescharacteristic
918C22C22×D4×D1111yescharacteristic
919C22C2×#6703711yescharacteristic
920C22C22×Q8×D1111yescharacteristic
921C22C2×#41×D1111yescharacteristic
922C22C2×#41×D1111yescharacteristic
923C22C2×#6704211yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—224no—
931C4—224no—
932C4—442no—
933C4—442no—
934C4—442no—
935C4—442no—
936C2—44no—
937C2—228no—
938C2—228no—
939C2#1307227818yesdirect product factor
940C2C2×D11×C22⋊Q811yescharacteristic
941C2C2×D11×C22⋊Q811yescharacteristic
942C2C2×#1062316511yescharacteristic
943C2C2×#1062314011yescharacteristic
944C2C2×#1062314111yescharacteristic
945C2C2×#1062314311yescharacteristic
946C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
2. C22×#66949C2semidirect
5. #13072278C2direct (N × H)
6. C2×#10622562C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622602C2semidirect
11. C2×#10622602C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622280C2semidirect
14. C2×#10622600C2semidirect
16. C2×C11×#396C2semidirect
22. C23×Dic22C22semidirect
23. C22×C11×C4⋊C4C22semidirect
24. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C4⋊C4C22semidirect
40. C22×C4⋊Dic11C22semidirect
41. C22×C4⋊Dic11C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
47. C2×#66950C22semidirect
49. C2×#66949C22semidirect
54. C11×#396C22semidirect
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. #10622602C22semidirect
62. #10622602C22semidirect
63. #10622602C22semidirect
64. #10622600C22semidirect
66. #10622562C22semidirect
67. #10622561C22semidirect
68. #10622560C22semidirect
69. #10622281C22semidirect
70. #10622280C22semidirect
78. C24×D11Q8semidirect
113. C22×Dic22C23semidirect
117. C2×C11×C4⋊C4C23semidirect
118. C2×C11×C4⋊C4C23semidirect
119. C2×C11×C4⋊C4C23semidirect
150. C2×C4⋊Dic11C23semidirect
151. C2×C4⋊Dic11C23semidirect
156. C2×Dic11⋊C4C23semidirect
157. C2×Dic11⋊C4C23semidirect
158. C2×Dic11⋊C4C23semidirect
159. C2×Dic11⋊C4C23semidirect
164. C11×#95C23semidirect
165. C11⋊#95C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
205. C23×D11C2×Q8semidirect
308. C2×#396D11semidirect
367. C22×D11C22⋊Q8semidirect
368. C22×D11C22⋊Q8semidirect
444. C22×C4⋊C4C2×D11semidirect
445. C22×C4⋊C4C2×D11semidirect
446. C22×C4⋊C4C2×D11semidirect
467. #396C2×D11semidirect
481. C2×#95C2×D11semidirect
519. C2×D11C2×C22⋊Q8semidirect
520. C2×D11C2×C22⋊Q8semidirect
593. C2×C4⋊C4C22×D11semidirect
594. C2×C4⋊C4C22×D11semidirect
595. C2×C4⋊C4C22×D11semidirect
631. #95C22×D11semidirect
633. C2×C11#2437semidirect
773. C11C2×#2437semidirect
939. C2#13072278direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669492
C22×C22⋊C4×D112
#130722782
C2×#106225622
C2×#106225612
C2×#106225602
C2×#106222812
C2×#106226022
C2×#106222802
C2×#106226002
C2×#106225682
C2×C11×#3962
C2×#243711