Finite Group Databasebeta

← C2×#13072154 #14921247

Subgroups — C2×#13072154 #14921247

Order 2816.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic, complemented
4C22×#66990C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13072154C2116yesmaximal, direct product factor
8C2×#10622289C211yesmaximal, characteristic, complemented
9C2×#10622285C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622573C211yesmaximal, characteristic, complemented
12C2×#10622570C211yesmaximal, characteristic, complemented
13C2×#10622282C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622559C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic, complemented
24C24×Dic11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C22×C11×C22⋊C4C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C2×#66992—28no—
34C2×#66992C2218yescomplemented
35C2×#66990—28no—
36C2×#66990C2218yescomplemented
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2218yescomplemented
39C22×(C2×D11)⋊C4—28no—
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2218yescomplemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
51C22×Dic11⋊C4C2211yescharacteristic, complemented
52C22×Dic11⋊C4C2211yescharacteristic, complemented
53C22×Dic11⋊C4C2211yescharacteristic, complemented
54C22×Dic11⋊C4C2211yescharacteristic, complemented
55C22×C4×Dic11C2211yescharacteristic, complemented
56C2×#66937—28no—
57C2×#66937C2218yescomplemented
58C2×#66935—28no—
59C2×#66935C2218yescomplemented
60C11×#386C2218yescomplemented
61C2×C11×#95C2211yescharacteristic, complemented
62C2×C11×#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622573C2218yescomplemented
66#10622572C2218yescomplemented
67#10622570C2218yescomplemented
68#10622559C2218yescomplemented
69#10622289C2218yescomplemented
70#10622285C2218yescomplemented
71#10622282C2218yescomplemented
72#10622278C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—42no—
81C24×D11—42no—
82C24×D11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C24×D11C2311yescharacteristic
85C24×D11C2314yes—
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11C2314yes—
90C23×C4×C11—24no—
91C23×C4×C11—24no—
92C23×C4×C11—42no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2314yes—
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—42no—
108C22×C22⋊D11—42no—
109C22×C22⋊D11—42no—
110C22×C22⋊D11D418yescomplemented
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yescomplemented
115C23×Dic11—24no—
116C23×Dic11—24no—
117C23×Dic11—42no—
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2314yes—
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C22×D44—24no—
125C22×D44—24no—
126C22×D44—24no—
127C22×D44—24no—
128C22×D44—42no—
129C22×D44—42no—
130C22×D44C2314yes—
131C22×D44C2314yes—
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—42no—
135C22×C4×D11C2314yescomplemented
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—42no—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yescomplemented
141C2×C11×C22⋊C4C2314yescomplemented
142C2×C22⋊Dic11—24no—
143C2×C22⋊Dic11D418yescomplemented
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2314yescomplemented
146#66992—232no—
147#66990—232no—
148C4×C22⋊D11—232no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—232no—
159C2×(C2×D11)⋊C4D418yescomplemented
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yescomplemented
169C2×(C2×D11)⋊C4C2314yescomplemented
170C2×Dic11⋊C4—24no—
171C2×Dic11⋊C4—24no—
172C2×Dic11⋊C4—24no—
173C2×Dic11⋊C4—42no—
174C2×Dic11⋊C4C2314yescomplemented
175C2×Dic11⋊C4C2314yescomplemented
176C2×Dic11⋊C4C2314yescomplemented
177C2×Dic11⋊C4C2314yescomplemented
178C2×C4×Dic11—24no—
179C2×C4×Dic11C2314yescomplemented
180#66937—232no—
181#66935—232no—
182C11×#95C2314yescomplemented
183C11×#95C2314yescomplemented
184C11⋊#95C2314yescomplemented
185C11⋊#95C2314yescomplemented
186C2×#2424—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11C2×D414yes—
199C24×C11C2×D414yes—
200C24×C11#4114yes—
201C24×C11C2412yes—
202C24×C11C2412yes—
203C24×C11C2411yescharacteristic
204C23×D11—232no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—28no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—28no—
225C23×D11—28no—
226C23×D11—28no—
227C23×D11—28no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—416no—
231C23×D11—416no—
232C23×D11—416no—
233C23×D11—416no—
234C23×D11—416no—
235C23×D11—416no—
236C23×D11C2×D414yes—
237C23×D11C2×D414yes—
238C23×D11#4114yes—
239C23×D11C2412yes—
240C23×D11C2412yes—
241C23×D11C2412yes—
242C2×D4×C11—28no—
243C2×D4×C11—28no—
244C2×D4×C11—28no—
245C2×D4×C11—416no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—28no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—28no—
262C22×C4×C11—44no—
263C22×C4×C11—416no—
264C22×C4×C11C2×D414yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2412yes—
267C22×C4×C11C2412yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—232no—
274C2×C22⋊D11—28no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—28no—
279C2×C22⋊D11—44no—
280C2×C22⋊D11—44no—
281C2×C22⋊D11—44no—
282C2×C22⋊D11—416no—
283C2×C22⋊D11—416no—
284C2×C22⋊D11—416no—
285C2×C22⋊D11C2×D4116yescomplemented
286C22×Dic11—28no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—28no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—44no—
300C22×Dic11—416no—
301C22×Dic11C2×D414yes—
302C22×Dic11C2×D414yes—
303C22×Dic11C2×D414yes—
304C22×Dic11C2×D414yes—
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2412yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C2×D44—28no—
311C2×D44—28no—
312C2×D44—28no—
313C2×D44—28no—
314C2×D44—44no—
315C2×D44—44no—
316C2×D44—416no—
317C2×D44—416no—
318C2×C4×D11—28no—
319C2×C4×D11—28no—
320C2×C4×D11—44no—
321C2×C4×D11—416no—
322C11×C22⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—44no—
325C22⋊Dic11—28no—
326C22⋊Dic11C2×D4116yescomplemented
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4C2×D4116yescomplemented
337Dic11⋊C4—28no—
338Dic11⋊C4—28no—
339Dic11⋊C4—28no—
340Dic11⋊C4—44no—
341C4×Dic11—28no—
342C22×#121—111no—
343C22×#121—111no—
344C22×#120—111no—
345C22×#120—111no—
346C22×C4×D4—111no—
347C23×C22⋊C4—111no—
348#2424—1116no—
349C2×#396—111no—
350C2×#394—111no—
351C2×#394—111no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#388—111no—
355C2×#386—111no—
356C2×#386D1111yescharacteristic, complemented
357C2×#385—111no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—28no—
361C23×C11—28no—
362C23×C11—28no—
363C23×C11—28no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11#121116yescomplemented
383C23×C11C22×D414yes—
384C23×C11C22×D414yes—
385C23×C11C22×D412yes—
386C23×C11C22×D412yes—
387C23×C11C22×D412yes—
388C23×C11C2×#4114yes—
389C23×C11C2×#4112yes—
390C23×C11C2×#4112yes—
391C23×C11H(5,𝔽2)12yes—
392C23×C11H(5,𝔽2)12yes—
393C23×C11C2511yescharacteristic
394C22×D11—232no—
395C22×D11—28no—
396C22×D11—28no—
397C22×D11—28no—
398C22×D11—28no—
399C22×D11—28no—
400C22×D11—28no—
401C22×D11—28no—
402C22×D11—28no—
403C22×D11—28no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—416no—
423C22×D11—416no—
424C22×D11—416no—
425C22×D11—416no—
426C22×D11—4128no—
427C22×D11—416no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—416no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11—44no—
434C22×D11—44no—
435C22×D11—44no—
436C22×D11—44no—
437C22×D11—44no—
438C22×D11—44no—
439C22×D11—44no—
440C22×D11—44no—
441C22×D11C22×D414yes—
442C22×D11C22×D414yes—
443C22×D11C2×#4114yes—
444D4×C11—416no—
445C2×C4×C11—28no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—416no—
461C2×C4×C11—44no—
462C2×C4×C11—44no—
463C2×C4×C11—44no—
464C2×C4×C11—44no—
465C2×C4×C11C22×D414yes—
466C22⋊D11—232no—
467C22⋊D11—416no—
468C22⋊D11—416no—
469C22⋊D11—416no—
470C2×Dic11—28no—
471C2×Dic11—28no—
472C2×Dic11—28no—
473C2×Dic11—28no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—416no—
486C2×Dic11—44no—
487C2×Dic11C22×D414yes—
488C2×Dic11C22×D414yes—
489C2×Dic11C22×D414yes—
490C2×Dic11C22×D414yes—
491D44—416no—
492D44—416no—
493C4×D11—416no—
494C26—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4—111no—
500C23×D4—111no—
501C23×D4C2×D1111yescharacteristic
502C24×C4—111no—
503C24×C4—111no—
504C24×C4C2×D1111yescharacteristic
505C2×#121—118no—
506C2×#121—118no—
507C2×#121—228no—
508C2×#121—228no—
509C2×#120—118no—
510C2×#120—118no—
511C2×#120—228no—
512C2×#120—228no—
513C2×C4×D4—118no—
514C2×C4×D4—228no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C4⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—118no—
532C22×C22⋊C4—228no—
533C22×C22⋊C4C2×D1111yescharacteristic
534C22×C22⋊C4C2×D1111yescharacteristic, complemented
535C22×C22⋊C4C2×D1111yescharacteristic, complemented
536C22×C42—111no—
537#396—118no—
538#394—118no—
539#394—118no—
540#392—118no—
541#390—118no—
542#388—118no—
543#386—118no—
544#386C2×D1118yescomplemented
545#385—118no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95C2×D1111yescharacteristic, complemented
549C2×#95C2×D1111yescharacteristic, complemented
550C22×C11—24no—
551C22×C11—232no—
552C22×C11—24no—
553C22×C11—24no—
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—88no—
565C22×C11C2×#12114yes—
566C22×C11C2×#12118yescomplemented
567C22×C11#52514yes—
568C22×C11#53814yes—
569C22×C11D4214yes—
570C22×C11D4214yes—
571C22×C11#54614yes—
572C22×C11#54614yes—
573C22×C11C23×D411yescharacteristic
574C22×C11C23×D411yescharacteristic
575C22×C11C23×D411yescharacteristic
576C22×C11C22×#4111yescharacteristic
577C22×C11C22×#4111yescharacteristic
578C22×C11C2×H(5,𝔽2)11yescharacteristic
579C22×C11C2×H(5,𝔽2)11yescharacteristic
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—24no—
586C2×D11—24no—
587C2×D11—24no—
588C2×D11—24no—
589C2×D11—464no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—416no—
594C2×D11—416no—
595C2×D11—416no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610Dic11—24no—
611Dic11—24no—
612Dic11—24no—
613Dic11—24no—
614Dic11—42no—
615C25—111no—
616C25—111no—
617C25—111no—
618C25—114no—
619C25—224no—
620C25—224no—
621C25—224no—
622C25—224no—
623C25—224no—
624C25—442no—
625C25—442no—
626C25C22×D1111yescharacteristic
627C25C22×D1111yescharacteristic
628C22×D4—24no—
629C22×D4—24no—
630C22×D4—24no—
631C22×D4—118no—
632C22×D4—114no—
633C22×D4—114no—
634C22×D4—114no—
635C22×D4—114no—
636C22×D4—114no—
637C22×D4—114no—
638C22×D4—224no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—224no—
643C22×D4—224no—
644C22×D4—224no—
645C22×D4—224no—
646C22×D4—224no—
647C22×D4—224no—
648C22×D4—224no—
649C22×D4—224no—
650C22×D4—442no—
651C22×D4—442no—
652C22×D4—442no—
653C22×D4—442no—
654C22×D4—442no—
655C22×D4C22×D1114yes—
656C23×C4—24no—
657C23×C4—24no—
658C23×C4—42no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—114no—
665C23×C4—114no—
666C23×C4—224no—
667C23×C4—224no—
668C23×C4—224no—
669C23×C4—224no—
670C23×C4—442no—
671C23×C4—442no—
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1114yes—
677C23×C4C22×D1111yescharacteristic
678#121—2232no—
679#121—2232no—
680#120—2232no—
681#120—2232no—
682C4×D4—2232no—
683C2×C4⋊C4—114no—
684C2×C4⋊C4—114no—
685C2×C4⋊C4—114no—
686C2×C4⋊C4—114no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—224no—
690C2×C4⋊C4—442no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—42no—
694C2×C22⋊C4—118no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—118no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—114no—
708C2×C22⋊C4—2232no—
709C2×C22⋊C4—224no—
710C2×C22⋊C4—224no—
711C2×C22⋊C4—224no—
712C2×C22⋊C4—224no—
713C2×C22⋊C4—224no—
714C2×C22⋊C4—224no—
715C2×C22⋊C4—224no—
716C2×C22⋊C4—224no—
717C2×C22⋊C4—224no—
718C2×C22⋊C4—224no—
719C2×C22⋊C4C22×D1114yes—
720C2×C22⋊C4C22×D1114yescomplemented
721C2×C22⋊C4C22×D1114yescomplemented
722C2×C42—114no—
723C2×C42—224no—
724#95—114no—
725#95—114no—
726#95C22×D1114yescomplemented
727#95C22×D1114yescomplemented
728C2×C11—28no—
729C2×C11—82no—
730C2×C11#242418yescomplemented
731C2×C11C22×#12111yescharacteristic
732C2×C11C2×#52511yescharacteristic
733C2×C11C2×#53811yescharacteristic
734C2×C11C2×D4211yescharacteristic
735C2×C11C2×D4211yescharacteristic
736C2×C11C2×#54611yescharacteristic
737C2×C11C2×#54611yescharacteristic
738D11—44no—
739D11—44no—
740D11—44no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—114no—
753C24—114no—
754C24—114no—
755C24—112no—
756C24—112no—
757C24—112no—
758C24—228no—
759C24—228no—
760C24—2232no—
761C24—222no—
762C24—228no—
763C24—222no—
764C24—222no—
765C24—222no—
766C24—222no—
767C24—222no—
768C24—222no—
769C24—222no—
770C24—222no—
771C24—222no—
772C24—222no—
773C24—222no—
774C24—222no—
775C24—222no—
776C24—222no—
777C24—222no—
778C24—222no—
779C24—222no—
780C24—228no—
781C24—228no—
782C24—444no—
783C24—444no—
784C24—4416no—
785C24—4416no—
786C24—4416no—
787C24—4416no—
788C24—4416no—
789C24—4416no—
790C24#433914yes—
791C24D4×D1114yes—
792C24D4×D1114yes—
793C24C23×D1112yes—
794C24C23×D1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—416no—
800C2×D4—1116no—
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—228no—
807C2×D4—228no—
808C2×D4—2232no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—444no—
815C2×D4—444no—
816C2×D4—4416no—
817C2×D4—4416no—
818C2×D4—444no—
819C2×D4—444no—
820C2×D4—444no—
821C2×D4—4416no—
822C2×D4—4416no—
823C2×D4—4416no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—28no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—28no—
840C22×C4—44no—
841C22×C4—416no—
842C22×C4—114no—
843C22×C4—114no—
844C22×C4—114no—
845C22×C4—114no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—228no—
852C22×C4—228no—
853C22×C4—222no—
854C22×C4—222no—
855C22×C4—222no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—222no—
860C22×C4—222no—
861C22×C4—222no—
862C22×C4—222no—
863C22×C4—228no—
864C22×C4—222no—
865C22×C4—228no—
866C22×C4—444no—
867C22×C4—4416no—
868C22×C4—444no—
869C22×C4—4416no—
870C22×C4D4×D1114yes—
871C22×C4C23×D1112yes—
872C22×C4C23×D1112yes—
873C22×C4C23×D1112yes—
874C22×C4C23×D1112yes—
875C22×C4C23×D1112yes—
876C4⋊C4—228no—
877C4⋊C4—228no—
878C4⋊C4—228no—
879C4⋊C4—444no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—44no—
883C22⋊C4—1116no—
884C22⋊C4—1116no—
885C22⋊C4—228no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—228no—
894C22⋊C4—228no—
895C42—228no—
896C11C2×#242411yescharacteristic, complemented, Sylow
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—114no—
922C23—114no—
923C23—114no—
924C23—2232no—
925C23—228no—
926C23—228no—
927C23—228no—
928C23—228no—
929C23—228no—
930C23—228no—
931C23—228no—
932C23—228no—
933C23—228no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—4416no—
953C23—4416no—
954C23—4416no—
955C23—4416no—
956C23—44128no—
957C23—4416no—
958C23—444no—
959C23—444no—
960C23—4416no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—444no—
965C23—444no—
966C23—444no—
967C23—444no—
968C23—444no—
969C23—444no—
970C23—444no—
971C23#66937116yescomplemented
972C23C2×#433914yes—
973C23C2×#433912yes—
974C23C2×D4×D1114yes—
975C23C2×D4×D1114yes—
976C23C2×D4×D1112yes—
977C23C2×D4×D1112yes—
978C23C2×D4×D1112yes—
979C23#6703712yes—
980C23#41×D1112yes—
981C23#6704212yes—
982C23C24×D1111yescharacteristic
983D4—416no—
984D4—2232no—
985D4—4416no—
986D4—4416no—
987D4—4416no—
988D4—4416no—
989D4—4416no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—416no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—114no—
1011C2×C4—114no—
1012C2×C4—114no—
1013C2×C4—114no—
1014C2×C4—228no—
1015C2×C4—228no—
1016C2×C4—228no—
1017C2×C4—228no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—4416no—
1030C2×C4—4416no—
1031C2×C4—444no—
1032C2×C4C2×D4×D1114yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—88no—
1048C22—224no—
1049C22—224no—
1050C22—224no—
1051C22—224no—
1052C22—224no—
1053C22—224no—
1054C22—224no—
1055C22—224no—
1056C22—224no—
1057C22—4464no—
1058C22—442no—
1059C22—4416no—
1060C22—4416no—
1061C22—4416no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22C2×#6693714yes—
1074C22C2×#6693718yescomplemented
1075C22#1062307814yes—
1076C22#1062309114yes—
1077C22#1062312114yes—
1078C22#1062314014yes—
1079C22#1062314114yes—
1080C22#1062318514yes—
1081C22C22×#433911yescharacteristic
1082C22C22×D4×D1111yescharacteristic
1083C22C22×D4×D1111yescharacteristic
1084C22C22×D4×D1111yescharacteristic
1085C22C2×#6703711yescharacteristic
1086C22C2×#41×D1111yescharacteristic
1087C22C2×#6704211yescharacteristic
1088C4—24no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—224no—
1094C4—224no—
1095C4—224no—
1096C4—224no—
1097C4—442no—
1098C2—28no—
1099C2—82no—
1100C2—444no—
1101C2—444no—
1102C2—444no—
1103C2#1307215418yesdirect product factor
1104C2C22×#6693711yescharacteristic
1105C2C2×#1062307811yescharacteristic
1106C2C2×#1062309111yescharacteristic
1107C2C2×#1062312111yescharacteristic
1108C2C2×#1062314011yescharacteristic
1109C2C2×#1062314111yescharacteristic
1110C2C2×#1062318511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×#66992C2semidirect
3. C22×#66935C2semidirect
4. C22×#66990C2semidirect
5. C22×C4×C22⋊D11C2semidirect
6. C23×(C2×D11)⋊C4C2semidirect
7. #13072154C2direct (N × H)
8. C2×#10622289C2semidirect
9. C2×#10622285C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622573C2semidirect
12. C2×#10622570C2semidirect
13. C2×#10622282C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622559C2semidirect
16. C2×C11×#386C2semidirect
23. C23×C22⋊D11C22semidirect
27. C23×C4×D11C22semidirect
29. C22×C11×C22⋊C4C22semidirect
30. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
34. C2×#66992C22semidirect
36. C2×#66990C22semidirect
38. C2×C4×C22⋊D11C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
50. C22×(C2×D11)⋊C4C22semidirect
51. C22×Dic11⋊C4C22semidirect
52. C22×Dic11⋊C4C22semidirect
53. C22×Dic11⋊C4C22semidirect
54. C22×Dic11⋊C4C22semidirect
55. C22×C4×Dic11C22semidirect
57. C2×#66937C22semidirect
59. C2×#66935C22semidirect
60. C11×#386C22semidirect
61. C2×C11×#95C22semidirect
62. C2×C11×#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622573C22semidirect
66. #10622572C22semidirect
67. #10622570C22semidirect
68. #10622559C22semidirect
69. #10622289C22semidirect
70. #10622285C22semidirect
71. #10622282C22semidirect
72. #10622278C22semidirect
110. C22×C22⋊D11D4semidirect
114. C22×C22⋊D11C23semidirect
135. C22×C4×D11C23semidirect
140. C2×C11×C22⋊C4C23semidirect
141. C2×C11×C22⋊C4C23semidirect
143. C2×C22⋊Dic11D4semidirect
145. C2×C22⋊Dic11C23semidirect
159. C2×(C2×D11)⋊C4D4semidirect
168. C2×(C2×D11)⋊C4C23semidirect
169. C2×(C2×D11)⋊C4C23semidirect
174. C2×Dic11⋊C4C23semidirect
175. C2×Dic11⋊C4C23semidirect
176. C2×Dic11⋊C4C23semidirect
177. C2×Dic11⋊C4C23semidirect
179. C2×C4×Dic11C23semidirect
182. C11×#95C23semidirect
183. C11×#95C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
285. C2×C22⋊D11C2×D4semidirect
326. C22⋊Dic11C2×D4semidirect
336. (C2×D11)⋊C4C2×D4semidirect
356. C2×#386D11semidirect
382. C23×C11#121semidirect
534. C22×C22⋊C4C2×D11semidirect
535. C22×C22⋊C4C2×D11semidirect
544. #386C2×D11semidirect
548. C2×#95C2×D11semidirect
549. C2×#95C2×D11semidirect
566. C22×C11C2×#121semidirect
720. C2×C22⋊C4C22×D11semidirect
721. C2×C22⋊C4C22×D11semidirect
726. #95C22×D11semidirect
727. #95C22×D11semidirect
730. C2×C11#2424semidirect
896. C11C2×#2424semidirect
971. C23#66937semidirect
1074. C22C2×#66937semidirect
1103. C2#13072154direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669922
C22×#669352
C22×#669902
C22×C4×C22⋊D112
C23×(C2×D11)⋊C42
#130721542
C2×#106222892
C2×#106222852
C2×#106225722
C2×#106225732
C2×#106225702
C2×#106222822
C2×#106222782
C2×#106225592
C2×C11×#3862
C2×#242411