Finite Group Databasebeta

← C2×#13071594 #14913261

Subgroups — C2×#13071594 #14913261

Order 2816.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66935C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
6#13071594C2116yesmaximal, direct product factor
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622564C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic, complemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic11C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46C2×#66946—28no—
47C2×#66946C2218yescomplemented
48C2×#66935C4116yescomplemented
49C2×#66935C2218yes—
50C2×C22⋊C4×D11—28no—
51C2×C22⋊C4×D11—28no—
52C2×C22⋊C4×D11C2218yescomplemented
53C2×C22⋊C4×D11C2218yescomplemented
54C2×C4×D44—28no—
55C2×C4×D44C2218yescomplemented
56C11×#388C2218yescomplemented
57C2×C11×#95C2211yescharacteristic, complemented
58C2×C11×#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63#10622602C2218yescomplemented
64#10622570C2218yescomplemented
65#10622569C2218yescomplemented
66#10622564C2218yescomplemented
67C4×(C2×D11)⋊C4C2218yescomplemented
68#10622281C2218yescomplemented
69#10622279C2218yescomplemented
70#10622278C2218yescomplemented
71#10622278C2218yescomplemented
72C25×C11C2311yescharacteristic
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11C2×C418yescomplemented
80C24×D11C2311yescharacteristic
81C24×D11C2314yes—
82C24×D11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11C2×C418yescomplemented
93C22×C22⋊D11C2314yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44C2×C418yescomplemented
104C22×D44C2×C418yescomplemented
105C22×D44C2314yes—
106C22×D44C2314yes—
107C22×C4×D11—24no—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—42no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11—42no—
121C22×C4×D11—42no—
122C22×C4×D11C2314yes—
123C22×C4×D11C2314yes—
124C22×C4×D11C2314yes—
125C22×C4×D11C2314yes—
126C22×C4×D11C2314yescomplemented
127C2×C11×C4⋊C4—24no—
128C2×C11×C4⋊C4C2314yescomplemented
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—24no—
131C2×C11×C22⋊C4C2×C418yescomplemented
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C11×C22⋊C4C2314yes—
135C2×C42×C11—24no—
136C2×C42×C11C2314yescomplemented
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11—24no—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4C2×C418yescomplemented
147C2×(C2×D11)⋊C4C2×C418yescomplemented
148C2×(C2×D11)⋊C4D418yescomplemented
149C2×(C2×D11)⋊C4D418yescomplemented
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yescomplemented
157C2×(C2×D11)⋊C4C2314yescomplemented
158C2×(C2×D11)⋊C4C2314yescomplemented
159C2×C4⋊Dic11—24no—
160C2×C4⋊Dic11C2314yescomplemented
161C2×Dic11⋊C4—42no—
162C2×Dic11⋊C4C2314yescomplemented
163C2×C4×Dic11—24no—
164C2×C4×Dic11—42no—
165C2×C4×Dic11C2314yescomplemented
166C2×C4×Dic11C2314yescomplemented
167#66946—232no—
168#66935C2×C4164yescomplemented
169C22⋊C4×D11—232no—
170C22⋊C4×D11—232no—
171C4×D44—232no—
172C11×#95C2314yescomplemented
173C11×#95C2314yescomplemented
174C11⋊#95C2314yescomplemented
175C11⋊#95C2314yescomplemented
176C11⋊#95C2314yescomplemented
177C11⋊#95C2314yescomplemented
178C2×#2358—111nomaximal, Sylow
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11C22×C414yes—
186C24×C11C2412yes—
187C24×C11C2411yescharacteristic
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—232no—
203C23×D11—232no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—28no—
207C23×D11—28no—
208C23×D11—416no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11—416no—
215C23×D11C22×C414yes—
216C23×D11C22×C414yes—
217C23×D11C22×C414yes—
218C23×D11C22×C4116yescomplemented
219C23×D11C2×D414yes—
220C23×D11C2×D414yes—
221C23×D11#4114yes—
222C23×D11#4114yes—
223C23×D11C2412yes—
224C23×D11C2412yes—
225C23×D11C2412yes—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11C22×C414yes—
241C22×C4×C11C22×C414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2×D414yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C2×C22⋊D11—416no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11C22×C4116yescomplemented
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×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11C22×C414yes—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—232no—
275C2×D44—232no—
276C2×D44—28no—
277C2×D44—28no—
278C2×D44—28no—
279C2×D44—28no—
280C2×D44C22×C4116yescomplemented
281C2×D44C22×C4116yescomplemented
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—416no—
298C2×C4×D11—416no—
299C2×C4×D11—416no—
300C2×C4×D11—416no—
301C2×C4×D11—416no—
302C11×C4⋊C4—28no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4C22×C4116yescomplemented
306C42×C11—28no—
307C22⋊Dic11—28no—
308C22⋊Dic11—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4C22×C4116yescomplemented
315(C2×D11)⋊C4C22×C4116yescomplemented
316(C2×D11)⋊C4C2×D4116yescomplemented
317(C2×D11)⋊C4C2×D4116yescomplemented
318C4⋊Dic11—28no—
319Dic11⋊C4—44no—
320C4×Dic11—28no—
321C4×Dic11—44no—
322C22×#120—111no—
323C22×C4×D4—111no—
324C22×C4×D4—111no—
325C23×C22⋊C4—111no—
326C23×C22⋊C4—111no—
327#2358—1116no—
328C2×#390—111no—
329C2×#388—111no—
330C2×#388D1111yescharacteristic, complemented
331C2×#386—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#385—111no—
335C2×#385—111no—
336C2×C4×C22⋊C4—111no—
337C2×C4×C22⋊C4—111no—
338C23×C11—28no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11C23×C414yes—
352C23×C11C23×C412yes—
353C23×C11C22×D412yes—
354C23×C11C22×D412yes—
355C23×C11C2×#4112yes—
356C23×C11C2×#4112yes—
357C23×C11H(5,𝔽2)12yes—
358C23×C11H(5,𝔽2)12yes—
359C23×C11C2511yescharacteristic
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—28no—
369C22×D11—28no—
370C22×D11—28no—
371C22×D11—28no—
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—28no—
381C22×D11—28no—
382C22×D11—28no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—232no—
390C22×D11—232no—
391C22×D11—416no—
392C22×D11—4128no—
393C22×D11—416no—
394C22×D11—416no—
395C22×D11—416no—
396C22×D11—416no—
397C22×D11—44no—
398C22×D11—44no—
399C22×D11—44no—
400C22×D11—44no—
401C22×D11C4×D4116yescomplemented
402C22×D11C4×D4116yescomplemented
403C22×D11C23×C414yes—
404C22×D11C23×C414yes—
405C22×D11C23×C414yes—
406C22×D11C22×D414yes—
407C22×D11C22×D414yes—
408C22×D11C2×#4114yes—
409C22×D11C2×#4114yes—
410C2×C4×C11—28no—
411C2×C4×C11—28no—
412C2×C4×C11—28no—
413C2×C4×C11—28no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—44no—
429C2×C4×C11—44no—
430C2×C4×C11C23×C414yes—
431C2×C4×C11C23×C414yes—
432C2×C4×C11C22×D414yes—
433C2×C4×C11C22×D414yes—
434C22⋊D11—416no—
435C2×Dic11—28no—
436C2×Dic11—28no—
437C2×Dic11—28no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—44no—
451C2×Dic11—44no—
452C2×Dic11C23×C414yes—
453C2×Dic11C22×D414yes—
454C2×Dic11C22×D414yes—
455D44—232no—
456D44—232no—
457C4×D11—416no—
458C4×D11—416no—
459C4×D11—416no—
460C4×D11—416no—
461C4×D11—416no—
462C26—111no—
463C23×D4—111no—
464C23×D4—111no—
465C23×D4—111no—
466C24×C4—111no—
467C24×C4—111no—
468C24×C4—111no—
469C24×C4—111no—
470C24×C4—111no—
471C2×#120—118no—
472C2×#120—1116no—
473C2×C4×D4—118no—
474C2×C4×D4—118no—
475C2×C4×D4—228no—
476C2×C4×D4—228no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4—111no—
479C22×C4⋊C4C2×D1111yescharacteristic, complemented
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—118no—
492C22×C22⋊C4—118no—
493C22×C22⋊C4—228no—
494C22×C22⋊C4—228no—
495C22×C22⋊C4C2×D1111yescharacteristic
496C22×C22⋊C4C2×D1111yescharacteristic
497C22×C22⋊C4C2×D1111yescharacteristic
498C22×C42—111no—
499C22×C42—111no—
500C22×C42C2×D1111yescharacteristic, complemented
501#390—118no—
502#388—118no—
503#388C2×D1118yescomplemented
504#386—118no—
505#386—118no—
506#386—118no—
507#385—118no—
508#385—118no—
509C4×C22⋊C4—118no—
510C4×C22⋊C4—118no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95C2×D1111yescharacteristic, complemented
516C2×#95C2×D1111yescharacteristic, complemented
517C22×C11—24no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—416no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11C2×C4×D414yes—
526C22×C11C2×C4×D414yes—
527C22×C11#51814yes—
528C22×C11D4214yes—
529C22×C11#54614yes—
530C22×C11#54614yes—
531C22×C11#55114yes—
532C22×C11C24×C411yescharacteristic
533C22×C11C23×D411yescharacteristic
534C22×C11C23×D411yescharacteristic
535C22×C11C22×#4111yescharacteristic
536C22×C11C22×#4111yescharacteristic
537C22×C11C2×H(5,𝔽2)11yescharacteristic
538C22×C11C2×H(5,𝔽2)11yescharacteristic
539C2×D11—232no—
540C2×D11—232no—
541C2×D11—24no—
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—464no—
557C2×D11—416no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11C2×C4×D418yescomplemented
563C2×D11C2×C4×D418yescomplemented
564C4×C11—24no—
565C4×C11—24no—
566C4×C11—24no—
567C4×C11—24no—
568C4×C11—42no—
569C4×C11—42no—
570Dic11—24no—
571Dic11—24no—
572Dic11—24no—
573Dic11—42no—
574Dic11—42no—
575C25—111no—
576C25—111no—
577C25—111no—
578C25—118no—
579C25—114no—
580C25—224no—
581C25—224no—
582C25—224no—
583C25—224no—
584C25—442no—
585C25—442no—
586C25C22×D1111yescharacteristic
587C22×D4—118no—
588C22×D4—114no—
589C22×D4—118no—
590C22×D4—118no—
591C22×D4—114no—
592C22×D4—114no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—442no—
598C22×D4—442no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—111no—
604C23×C4—114no—
605C23×C4—114no—
606C23×C4—114no—
607C23×C4—114no—
608C23×C4—114no—
609C23×C4—224no—
610C23×C4—224no—
611C23×C4—224no—
612C23×C4—224no—
613C23×C4—224no—
614C23×C4—224no—
615C23×C4—224no—
616C23×C4—224no—
617C23×C4—224no—
618C23×C4—224no—
619C23×C4—442no—
620C23×C4—442no—
621C23×C4—442no—
622C23×C4—442no—
623C23×C4—442no—
624C23×C4C22×D1111yescharacteristic
625C23×C4C22×D1111yescharacteristic
626C23×C4C22×D1111yescharacteristic
627C23×C4C22×D1111yescharacteristic
628C23×C4C22×D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630#120—1164no—
631C4×D4—2232no—
632C4×D4—2232no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—224no—
637C2×C4⋊C4—442no—
638C2×C4⋊C4C22×D1114yescomplemented
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—118no—
642C2×C22⋊C4—118no—
643C2×C22⋊C4—118no—
644C2×C22⋊C4—118no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—114no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—2232no—
657C2×C22⋊C4—2232no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—224no—
660C2×C22⋊C4—224no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—442no—
665C2×C22⋊C4C4×D1118yescomplemented
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D1114yes—
668C2×C22⋊C4C22×D1114yes—
669C2×C42—24no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—224no—
673C2×C42—442no—
674C2×C42C22×D1114yescomplemented
675#95—114no—
676#95—114no—
677#95—114no—
678#95—114no—
679#95C22×D1114yescomplemented
680#95C22×D1114yescomplemented
681C2×C11—44no—
682C2×C11#235818yescomplemented
683C2×C11C22×C4×D411yescharacteristic
684C2×C11C22×C4×D411yescharacteristic
685C2×C11C2×#51811yescharacteristic
686C2×C11C2×D4211yescharacteristic
687C2×C11C2×#54611yescharacteristic
688C2×C11C2×#54611yescharacteristic
689C2×C11C2×#55111yescharacteristic
690D11—28no—
691D11—28no—
692D11—44no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—114no—
700C24—114no—
701C24—114no—
702C24—114no—
703C24—114no—
704C24—114no—
705C24—112no—
706C24—112no—
707C24—114no—
708C24—112no—
709C24—1116no—
710C24—228no—
711C24—228no—
712C24—2232no—
713C24—2232no—
714C24—228no—
715C24—228no—
716C24—222no—
717C24—222no—
718C24—222no—
719C24—222no—
720C24—222no—
721C24—222no—
722C24—222no—
723C24—222no—
724C24—222no—
725C24—222no—
726C24—222no—
727C24—222no—
728C24—222no—
729C24—222no—
730C24—4416no—
731C24—444no—
732C24—444no—
733C24—4416no—
734C24—4416no—
735C24—4416no—
736C24—4416no—
737C24C2×C4×D1114yes—
738C24C23×D1112yes—
739C24C23×D1111yescharacteristic
740C2×D4—1116no—
741C2×D4—1116no—
742C2×D4—1116no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—2232no—
746C2×D4—2232no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—4416no—
750C2×D4—444no—
751C2×D4—444no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—114no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—112no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—228no—
775C22×C4—228no—
776C22×C4—228no—
777C22×C4—228no—
778C22×C4—228no—
779C22×C4—228no—
780C22×C4—228no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—228no—
794C22×C4—228no—
795C22×C4—228no—
796C22×C4—444no—
797C22×C4—444no—
798C22×C4—444no—
799C22×C4—444no—
800C22×C4—444no—
801C22×C4—4416no—
802C22×C4—4416no—
803C22×C4—4416no—
804C22×C4—4416no—
805C22×C4—4416no—
806C22×C4C2×C4×D1114yes—
807C22×C4C2×C4×D1114yes—
808C22×C4D4×D1114yes—
809C22×C4D4×D1114yes—
810C22×C4C23×D1112yes—
811C22×C4C23×D1112yes—
812C22×C4C23×D1112yes—
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C4⋊C4—28no—
817C4⋊C4—228no—
818C4⋊C4—444no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—1116no—
822C22⋊C4—1116no—
823C22⋊C4—1116no—
824C22⋊C4—1116no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—444no—
832C22⋊C4C2×C4×D11116yescomplemented
833C42—28no—
834C42—228no—
835C42—444no—
836C11C2×#235811yescharacteristic, complemented, Sylow
837C23—28no—
838C23—28no—
839C23—28no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—1116no—
851C23—1116no—
852C23—114no—
853C23—114no—
854C23—114no—
855C23—114no—
856C23—114no—
857C23—114no—
858C23—114no—
859C23—2232no—
860C23—2232no—
861C23—228no—
862C23—228no—
863C23—228no—
864C23—228no—
865C23—228no—
866C23—228no—
867C23—228no—
868C23—228no—
869C23—228no—
870C23—228no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—228no—
880C23—228no—
881C23—228no—
882C23—228no—
883C23—228no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—4416no—
891C23—4416no—
892C23—4416no—
893C23—4416no—
894C23—4416no—
895C23—44128no—
896C23—444no—
897C23—444no—
898C23—444no—
899C23—444no—
900C23C22×C4×D1114yes—
901C23C22×C4×D1112yes—
902C23C2×D4×D1112yes—
903C23C2×D4×D1112yes—
904C23#41×D1112yes—
905C23#41×D1112yes—
906C23#6704212yes—
907C23#6704212yes—
908C23C24×D1111yescharacteristic
909D4—2232no—
910D4—2232no—
911D4—4416no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—114no—
933C2×C4—114no—
934C2×C4—114no—
935C2×C4—228no—
936C2×C4—228no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—228no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—4416no—
951C2×C4—4416no—
952C2×C4—4416no—
953C2×C4—4416no—
954C2×C4—4416no—
955C2×C4—444no—
956C2×C4—444no—
957C2×C4C22×C4×D1114yes—
958C2×C4C22×C4×D1114yes—
959C2×C4C2×D4×D1114yes—
960C2×C4C2×D4×D1114yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—416no—
969C22—118no—
970C22—118no—
971C22—224no—
972C22—224no—
973C22—224no—
974C22—224no—
975C22—224no—
976C22—224no—
977C22—224no—
978C22—224no—
979C22—224no—
980C22—224no—
981C22—224no—
982C22—224no—
983C22—2232no—
984C22—2232no—
985C22—224no—
986C22—224no—
987C22—224no—
988C22—4464no—
989C22—442no—
990C22—442no—
991C22—442no—
992C22—442no—
993C22—4416no—
994C22#1062305214yes—
995C22C4×D4×D1114yes—
996C22C4×D4×D1114yes—
997C22#1062314014yes—
998C22#1062318514yes—
999C22#1062320714yes—
1000C22#1062323614yes—
1001C22C23×C4×D1111yescharacteristic
1002C22C22×D4×D1111yescharacteristic
1003C22C22×D4×D1111yescharacteristic
1004C22C2×#41×D1111yescharacteristic
1005C22C2×#41×D1111yescharacteristic
1006C22C2×#6704211yescharacteristic
1007C22C2×#6704211yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—224no—
1015C4—224no—
1016C4—224no—
1017C4—442no—
1018C4—442no—
1019C2—44no—
1020C2—228no—
1021C2—228no—
1022C2—444no—
1023C2#1307159418yesdirect product factor
1024C2C2×C4×D4×D1111yescharacteristic
1025C2C2×C4×D4×D1111yescharacteristic
1026C2C2×#1062305211yescharacteristic
1027C2C2×#1062314011yescharacteristic
1028C2C2×#1062318511yescharacteristic
1029C2C2×#1062320711yescharacteristic
1030C2C2×#1062323611yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66935C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2358
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C22×#66946C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. C22×C22⋊C4×D11C2semidirect
6. #13071594C2direct (N × H)
7. C2×#10622570C2semidirect
8. C2×#10622564C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622602C2semidirect
14. C2×C4×(C2×D11)⋊C4C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#388C2semidirect
25. C23×C4×D11C22semidirect
26. C22×C11×C4⋊C4C22semidirect
30. C22×C42×C11C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×C4⋊Dic11C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×C4×Dic11C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66946C22semidirect
48. C2×#66935C4semidirect
52. C2×C22⋊C4×D11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
55. C2×C4×D44C22semidirect
56. C11×#388C22semidirect
57. C2×C11×#95C22semidirect
58. C2×C11×#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. #10622602C22semidirect
64. #10622570C22semidirect
65. #10622569C22semidirect
66. #10622564C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. #10622281C22semidirect
69. #10622279C22semidirect
70. #10622278C22semidirect
71. #10622278C22semidirect
79. C24×D11C2×C4semidirect
92. C22×C22⋊D11C2×C4semidirect
103. C22×D44C2×C4semidirect
104. C22×D44C2×C4semidirect
126. C22×C4×D11C23semidirect
128. C2×C11×C4⋊C4C23semidirect
131. C2×C11×C22⋊C4C2×C4semidirect
136. C2×C42×C11C23semidirect
146. C2×(C2×D11)⋊C4C2×C4semidirect
147. C2×(C2×D11)⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4D4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
156. C2×(C2×D11)⋊C4C23semidirect
157. C2×(C2×D11)⋊C4C23semidirect
158. C2×(C2×D11)⋊C4C23semidirect
160. C2×C4⋊Dic11C23semidirect
162. C2×Dic11⋊C4C23semidirect
165. C2×C4×Dic11C23semidirect
166. C2×C4×Dic11C23semidirect
168. #66935C2×C4semidirect
172. C11×#95C23semidirect
173. C11×#95C23semidirect
174. C11⋊#95C23semidirect
175. C11⋊#95C23semidirect
176. C11⋊#95C23semidirect
177. C11⋊#95C23semidirect
218. C23×D11C22×C4semidirect
253. C2×C22⋊D11C22×C4semidirect
280. C2×D44C22×C4semidirect
281. C2×D44C22×C4semidirect
305. C11×C22⋊C4C22×C4semidirect
314. (C2×D11)⋊C4C22×C4semidirect
315. (C2×D11)⋊C4C22×C4semidirect
316. (C2×D11)⋊C4C2×D4semidirect
317. (C2×D11)⋊C4C2×D4semidirect
330. C2×#388D11semidirect
401. C22×D11C4×D4semidirect
402. C22×D11C4×D4semidirect
479. C22×C4⋊C4C2×D11semidirect
500. C22×C42C2×D11semidirect
503. #388C2×D11semidirect
515. C2×#95C2×D11semidirect
516. C2×#95C2×D11semidirect
562. C2×D11C2×C4×D4semidirect
563. C2×D11C2×C4×D4semidirect
638. C2×C4⋊C4C22×D11semidirect
665. C2×C22⋊C4C4×D11semidirect
674. C2×C42C22×D11semidirect
679. #95C22×D11semidirect
680. #95C22×D11semidirect
682. C2×C11#2358semidirect
832. C22⋊C4C2×C4×D11semidirect
836. C11C2×#2358semidirect
1023. C2#13071594direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669352
C22×C4×D442
C22×#669462
C22×C22⋊C4×D112
#130715942
C2×#106225702
C2×#106225642
C2×#106222782
C2×#106225692
C2×#106222812
C2×#106226022
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×C11×#3882
C2×#235811