Finite Group Databasebeta

← C2×#13072072 #14921211

Subgroups — C2×#13072072 #14921211

Order 2816.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13072072C2116yesmaximal, direct product factor
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622553C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic, complemented
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C2×C4×D4×C11—28no—
25C2×C4×D4×C11C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic, complemented
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic, complemented
34C2×#66990—28no—
35C2×#66990C2218yes—
36C2×#66982—28no—
37C2×#66982C2218yescomplemented
38C22×(C2×D11)⋊C4—28no—
39C22×(C2×D11)⋊C4C2211yescharacteristic
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)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2218yescomplemented
50C22×Dic11⋊C4C2211yescharacteristic, complemented
51C22×Dic11⋊C4C2211yescharacteristic, complemented
52C22×Dic11⋊C4C2211yescharacteristic, complemented
53C22×Dic11⋊C4C2211yescharacteristic, complemented
54#10622833C2218yescomplemented
55#10622826C2218yescomplemented
56#10622823C2218yescomplemented
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#10622606C2218yescomplemented
64#10622605C2218yescomplemented
65#10622572C2218yescomplemented
66#10622572C2218yescomplemented
67#10622568C2218yescomplemented
68#10622555C2218yescomplemented
69#10622553C2218yescomplemented
70#10622553C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—42no—
79C24×D11—42no—
80C24×D11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C24×D11C2314yes—
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11D418yes—
86C22×D4×C11C2314yes—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11—24no—
91C23×C4×C11—42no—
92C23×C4×C11—42no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2314yes—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2314yescomplemented
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—42no—
105C22×C22⋊D11—42no—
106C22×C22⋊D11C2314yes—
107C22×C22⋊D11C2314yes—
108C23×Dic11—24no—
109C23×Dic11—24no—
110C23×Dic11—42no—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2314yes—
117C23×Dic11C2311yescharacteristic
118C4×D4×C11—232no—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4C2314yescomplemented
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yescomplemented
125C2×C42×C11—24no—
126C2×C42×C11C2314yescomplemented
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yescomplemented
134C2×C22⋊Dic11C2314yescomplemented
135#66990—232no—
136#66982—232no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—232no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4—42no—
147C2×(C2×D11)⋊C4D418yescomplemented
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4—42no—
161C2×Dic11⋊C4—42no—
162C2×Dic11⋊C4C2314yescomplemented
163C2×Dic11⋊C4C2314yescomplemented
164C2×Dic11⋊C4C2314yescomplemented
165C2×Dic11⋊C4C2314yescomplemented
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2418—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11C2×D414yes—
184C24×C11C2×D414yes—
185C24×C11#4114yes—
186C24×C11#4114yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—232no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—28no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—28no—
207C23×D11—28no—
208C23×D11—44no—
209C23×D11—44no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11—416no—
215C23×D11—416no—
216C23×D11C2×D414yes—
217C23×D11#4114yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×D4×C11—232no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11C2×D4116yes—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
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—28no—
234C22×C4×C11—28no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—28no—
240C22×C4×C11—28no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—416no—
244C22×C4×C11—416no—
245C22×C4×C11C2×D414yes—
246C22×C4×C11C2×D414yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—416no—
259C2×C22⋊D11—416no—
260C22×Dic11—28no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—28no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—44no—
280C22×Dic11—416no—
281C22×Dic11C2×D414yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C11×C4⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C42×C11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—44no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4C2×D4116yescomplemented
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308Dic11⋊C4—44no—
309Dic11⋊C4—44no—
310C22×#123—111no—
311C22×#120—111no—
312C22×C4×D4D1111yescharacteristic, complemented
313C23×C22⋊C4—111no—
314#2418—1116no—
315C2×#399—111no—
316C2×#397—111no—
317C2×#394—111no—
318C2×#394—111no—
319C2×#388—111no—
320C2×#388—111no—
321C2×#386—111no—
322C2×#386—111no—
323C2×#385—111no—
324C2×#380—111no—
325C2×#379—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—28no—
331C23×C11—28no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—28no—
337C23×C11—28no—
338C23×C11—28no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11#123116yescomplemented
350C23×C11C22×D412yes—
351C23×C11C22×D414yes—
352C23×C11C22×D414yes—
353C23×C11C22×D412yes—
354C23×C11C2×#4114yes—
355C23×C11C2×#4114yes—
356C23×C11C2×#4112yes—
357C23×C11C2×#4112yes—
358C23×C11C2×#4112yes—
359C23×C11H(5,𝔽2)12yes—
360C23×C11H(5,𝔽2)12yes—
361C23×C11C2511yescharacteristic
362C22×D11—232no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—28no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—416no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—416no—
385C22×D11—4128no—
386C22×D11—416no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—416no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11C22×D414yes—
397C22×D11C2×#4114yes—
398D4×C11—232no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—416no—
415C2×C4×C11—416no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11—44no—
419C2×C4×C11C22×D414yes—
420C2×C4×C11C22×D414yes—
421C22⋊D11—416no—
422C22⋊D11—416no—
423C2×Dic11—28no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—416no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11—44no—
447C2×Dic11C22×D414yes—
448C26—111no—
449C23×D4—111no—
450C23×D4—111no—
451C23×D4C2×D1111yescharacteristic
452C24×C4—111no—
453C24×C4C2×D1111yescharacteristic
454C24×C4C2×D1111yescharacteristic, complemented
455C2×#123—118no—
456C2×#123—228no—
457C2×#120—118no—
458C2×#120—228no—
459C2×C4×D4—28no—
460C2×C4×D4C2×D1118yescomplemented
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C4⋊C4—111no—
465C22×C4⋊C4C2×D1111yescharacteristic, complemented
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—118no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—228no—
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C22⋊C4C2×D1111yescharacteristic, complemented
484C22×C42C2×D1111yescharacteristic, complemented
485#399—118no—
486#397—118no—
487#394—118no—
488#394—118no—
489#388—118no—
490#388—118no—
491#386—118no—
492#386—118no—
493#385—118no—
494#380—118no—
495#379—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C22×C11—24no—
503C22×C11—232no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—24no—
509C22×C11—24no—
510C22×C11—24no—
511C22×C11—24no—
512C22×C11—42no—
513C22×C11—416no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11C2×#12314yes—
518C22×C11C2×#12318yescomplemented
519C22×C11#52514yes—
520C22×C11#53814yes—
521C22×C11D4214yes—
522C22×C11#54614yes—
523C22×C11#54614yes—
524C22×C11#55114yes—
525C22×C11C23×D411yescharacteristic
526C22×C11C23×D411yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C22×#4111yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C22×C11C2×H(5,𝔽2)11yescharacteristic
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—464no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—416no—
542C2×D11—416no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—42no—
552C4×C11—42no—
553C4×C11—42no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—114no—
563C25—224no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—442no—
569C25—442no—
570C25C22×D1111yescharacteristic
571C25C22×D1111yescharacteristic
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—114no—
575C22×D4—114no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—442no—
581C22×D4—442no—
582C22×D4C22⋊D1118yes—
583C22×D4C22×D1114yes—
584C23×C4—24no—
585C23×C4—24no—
586C23×C4—24no—
587C23×C4—24no—
588C23×C4—42no—
589C23×C4—42no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—114no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1114yes—
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1114yescomplemented
607#123—2232no—
608#120—2232no—
609C4×D4—232no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—224no—
617C2×C4⋊C4—442no—
618C2×C4⋊C4—442no—
619C2×C4⋊C4C22×D1114yescomplemented
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—118no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—114no—
635C2×C22⋊C4—114no—
636C2×C22⋊C4—114no—
637C2×C22⋊C4—2232no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—224no—
640C2×C22⋊C4—224no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—442no—
649C2×C22⋊C4—442no—
650C2×C22⋊C4—442no—
651C2×C22⋊C4C22×D1114yes—
652C2×C22⋊C4C22×D1114yescomplemented
653C2×C42—24no—
654C2×C42C22×D1114yescomplemented
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
661C2×C11—28no—
662C2×C11—44no—
663C2×C11#241818yescomplemented
664C2×C11C22×#12311yescharacteristic
665C2×C11C2×#52511yescharacteristic
666C2×C11C2×#53811yescharacteristic
667C2×C11C2×D4211yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#54611yescharacteristic
670C2×C11C2×#55111yescharacteristic
671D11—44no—
672D11—44no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—114no—
684C24—114no—
685C24—112no—
686C24—112no—
687C24—228no—
688C24—228no—
689C24—2232no—
690C24—228no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—228no—
704C24—228no—
705C24—444no—
706C24—444no—
707C24—4416no—
708C24—4416no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24#433914yes—
714C24#433914yes—
715C24C2×C22⋊D1114yes—
716C24C2×C22⋊D1114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×D4—232no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—228no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4—4416no—
730C2×D4—4416no—
731C2×D4C2×C22⋊D11116yes—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—416no—
752C22×C4—416no—
753C22×C4—114no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—228no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—228no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—444no—
780C22×C4—4416no—
781C22×C4D4×D1114yes—
782C22×C4C2×C22⋊D1114yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—28no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C4⋊C4—444no—
792C4⋊C4—444no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—1116no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—228no—
804C22⋊C4—228no—
805C22⋊C4—228no—
806C22⋊C4—444no—
807C22⋊C4—444no—
808C22⋊C4—444no—
809C42—28no—
810C11C2×#241811yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—28no—
822C23—28no—
823C23—28no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—114no—
835C23—114no—
836C23—2232no—
837C23—228no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—228no—
842C23—228no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—4416no—
856C23—4416no—
857C23—4416no—
858C23—4416no—
859C23—4416no—
860C23—44128no—
861C23—444no—
862C23—444no—
863C23—4416no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23#66982116yescomplemented
871C23C2×#433914yes—
872C23C2×#433914yes—
873C23C2×#433912yes—
874C23C2×#433912yes—
875C23C2×D4×D1112yes—
876C23#6703712yes—
877C23#41×D1112yes—
878C23#6704212yes—
879C23C22×C22⋊D1114yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883D4—232no—
884D4—4416no—
885D4—4416no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—416no—
902C2×C4—416no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—114no—
907C2×C4—228no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—4416no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4C2×D4×D1114yes—
932C2×C4C22×C22⋊D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—232no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—416no—
947C22—42no—
948C22—224no—
949C22—224no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—224no—
954C22—4464no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—4416no—
960C22—4416no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22#1062307814yes—
966C22#1062308114yes—
967C22#1062308714yes—
968C22#1062309114yes—
969C22C2×#6698214yes—
970C22C2×#6698218yescomplemented
971C22D4×C22⋊D1114yes—
972C22#1062336014yes—
973C22C22×#433911yescharacteristic
974C22C22×#433911yescharacteristic
975C22C22×D4×D1111yescharacteristic
976C22C2×#6703711yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#6704211yescharacteristic
979C22C23×C22⋊D1111yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—224no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—28no—
992C2—44no—
993C2—444no—
994C2—444no—
995C2#1307207218yesdirect product factor
996C2C22×#6698211yescharacteristic
997C2C2×#1062307811yescharacteristic
998C2C2×#1062309111yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062336011yescharacteristic
1001C2C2×#1062308111yescharacteristic
1002C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
3. C23×(C2×D11)⋊C4C2semidirect
4. #13072072C2direct (N × H)
5. C2×#10622605C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622555C2semidirect
15. C2×#10622568C2semidirect
16. C22×C4×D4×C11C2semidirect
20. C24×C4×C11C22semidirect
25. C2×C4×D4×C11C22semidirect
26. C22×C11×C4⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C42×C11C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
37. C2×#66982C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×Dic11⋊C4C22semidirect
52. C22×Dic11⋊C4C22semidirect
53. C22×Dic11⋊C4C22semidirect
54. #10622833C22semidirect
55. #10622826C22semidirect
56. #10622823C22semidirect
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. #10622606C22semidirect
64. #10622605C22semidirect
65. #10622572C22semidirect
66. #10622572C22semidirect
67. #10622568C22semidirect
68. #10622555C22semidirect
69. #10622553C22semidirect
70. #10622553C22semidirect
99. C23×C4×C11C23semidirect
120. C2×C11×C4⋊C4C23semidirect
124. C2×C11×C22⋊C4C23semidirect
126. C2×C42×C11C23semidirect
133. C2×C22⋊Dic11C23semidirect
134. C2×C22⋊Dic11C23semidirect
147. C2×(C2×D11)⋊C4D4semidirect
162. C2×Dic11⋊C4C23semidirect
163. C2×Dic11⋊C4C23semidirect
164. C2×Dic11⋊C4C23semidirect
165. C2×Dic11⋊C4C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
305. (C2×D11)⋊C4C2×D4semidirect
312. C22×C4×D4D11semidirect
349. C23×C11#123semidirect
454. C24×C4C2×D11semidirect
460. C2×C4×D4C2×D11semidirect
465. C22×C4⋊C4C2×D11semidirect
483. C22×C22⋊C4C2×D11semidirect
484. C22×C42C2×D11semidirect
518. C22×C11C2×#123semidirect
606. C23×C4C22×D11semidirect
619. C2×C4⋊C4C22×D11semidirect
652. C2×C22⋊C4C22×D11semidirect
654. C2×C42C22×D11semidirect
663. C2×C11#2418semidirect
810. C11C2×#2418semidirect
870. C23#66982semidirect
970. C22C2×#66982semidirect
995. C2#13072072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669902
C23×(C2×D11)⋊C42
#130720722
C2×#106226052
C2×#106226062
C2×#106225722
C2×#106225532
C2×#106228332
C2×#106228262
C2×#106228232
C2×#106225552
C2×#106225682
C22×C4×D4×C112
C2×#241811