Finite Group Databasebeta

← C2×#13072075 #14921206

Subgroups — C2×#13072075 #14921206

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×#66990C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13072075C2116yesmaximal, direct product factor
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622565C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic, complemented
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C2×C11×#123—28no—
25C2×C11×#123C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic, complemented
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic, complemented
35C22×C22⋊Dic11C2211yescharacteristic, complemented
36C2×#66990—28no—
37C2×#66990C2218yes—
38C2×C4×C22⋊D11—28no—
39C2×C4×C22⋊D11C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×Dic11⋊C4C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×C22⋊C4×D11—28no—
53C2×C22⋊C4×D11C2218yescomplemented
54#10622835C2218yescomplemented
55#10622826C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62#10622605C2218yescomplemented
63#10622603C2218yescomplemented
64#10622602C2218yescomplemented
65#10622600C2218yescomplemented
66#10622574C2218yescomplemented
67#10622569C2218yescomplemented
68#10622568C2218yescomplemented
69#10622565C2218yescomplemented
70#10622564C2218yescomplemented
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×D11C2314yes—
82C24×D11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—42no—
86C22×D4×C11C2314yes—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2314yescomplemented
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yes—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—42no—
115C22×C4×D11—42no—
116C22×C4×D11C2314yes—
117C22×C4×D11C2314yes—
118C11×#123—232no—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2314yescomplemented
122C2×C11×C4⋊C4C2314yescomplemented
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4D418yescomplemented
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yescomplemented
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—42no—
133C2×C22⋊Dic11—42no—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yescomplemented
138C2×C22⋊Dic11C2314yescomplemented
139#66990—232no—
140C4×C22⋊D11—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—42no—
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×C4⋊Dic11—42no—
158C2×C4⋊Dic11C2314yescomplemented
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4—42no—
161C2×Dic11⋊C4C2314yescomplemented
162C2×Dic11⋊C4C2314yescomplemented
163C2×C4×Dic11—24no—
164C2×C4×Dic11C2314yescomplemented
165C22⋊C4×D11—232no—
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×C11—22no—
184C24×C11—22no—
185C24×C11C2×D414yes—
186C24×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—232no—
195C23×D11—28no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—28no—
203C23×D11—28no—
204C23×D11—28no—
205C23×D11—28no—
206C23×D11—44no—
207C23×D11—44no—
208C23×D11—416no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11C2×D414yes—
215C23×D11#4114yes—
216C23×D11#4114yes—
217C23×D11#4114yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—44no—
223C2×D4×C11—416no—
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—28no—
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—28no—
239C22×C4×C11—44no—
240C22×C4×C11—416no—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—232no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—416no—
255C2×C22⋊D11C2×D4116yes—
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×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11C2×D414yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—416no—
287C2×C4×D11—416no—
288C11×C4⋊C4—28no—
289C11×C4⋊C4—28no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4C2×D4116yescomplemented
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11—44no—
297C22⋊Dic11—44no—
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—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—44no—
306C4⋊Dic11—44no—
307Dic11⋊C4—28no—
308Dic11⋊C4—44no—
309C4×Dic11—28no—
310C22×#123D1111yescharacteristic, complemented
311C22×#120—111no—
312C22×C4×D4—111no—
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—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11C22×D414yes—
353C23×C11C22×D412yes—
354C23×C11C22×D414yes—
355C23×C11C22×D412yes—
356C23×C11C2×#4112yes—
357C23×C11C2×#4112yes—
358C23×C11C2×#4112yes—
359C23×C11H(5,𝔽2)12yes—
360C23×C11H(5,𝔽2)12yes—
361C23×C11C2511yescharacteristic
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—28no—
365C22×D11—28no—
366C22×D11—28no—
367C22×D11—28no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—232no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—28no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—416no—
383C22×D11—416no—
384C22×D11—416no—
385C22×D11—416no—
386C22×D11—4128no—
387C22×D11—416no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—416no—
393C22×D11#123116yescomplemented
394C22×D11C22×D414yes—
395C22×D11C2×#4114yes—
396C22×D11C2×#4114yes—
397C22×D11C2×#4114yes—
398D4×C11—416no—
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—44no—
416C2×C4×C11—44no—
417C2×C4×C11—44no—
418C2×C4×C11C22×D414yes—
419C2×C4×C11C22×D414yes—
420C22⋊D11—232no—
421C22⋊D11—416no—
422C2×Dic11—28no—
423C2×Dic11—22no—
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—44no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11C22×D414yes—
446C4×D11—416no—
447C4×D11—416no—
448C26—111no—
449C23×D4—111no—
450C23×D4—111no—
451C23×D4C2×D1111yescharacteristic
452C24×C4—111no—
453C24×C4—111no—
454C24×C4C2×D1111yescharacteristic, complemented
455C2×#123—28no—
456C2×#123C2×D1118yescomplemented
457C2×#120—118no—
458C2×#120—228no—
459C2×C4×D4—118no—
460C2×C4×D4—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—118no—
480C22×C22⋊C4—228no—
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C22⋊C4C2×D1111yescharacteristic, complemented
484C22×C42—111no—
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—24no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—416no—
511C22×C11—416no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11C2×#12314yes—
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—232no—
534C2×D11—24no—
535C2×D11—24no—
536C2×D11—24no—
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—24no—
542C2×D11—464no—
543C2×D11—42no—
544C2×D11—416no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11C2×#12318yescomplemented
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—42no—
575C22×D4—118no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—442no—
583C22×D4C22×D1114yes—
584C23×C4—24no—
585C23×C4—24no—
586C23×C4—42no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—114no—
594C23×C4—114no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—224no—
598C23×C4—224no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1114yescomplemented
607#123—232no—
608#120—2232no—
609C4×D4—2232no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—442no—
617C2×C4⋊C4—442no—
618C2×C4⋊C4C22×D1114yescomplemented
619C2×C4⋊C4C22×D1114yescomplemented
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—114no—
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—224no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
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—2232no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4—442no—
649C2×C22⋊C4C22⋊D1118yescomplemented
650C2×C22⋊C4C22×D1114yes—
651C2×C22⋊C4C22×D1114yes—
652C2×C22⋊C4C22×D1114yescomplemented
653C2×C42—114no—
654C2×C42—224no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
661C2×C11—44no—
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—28no—
672D11—44no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—114no—
686C24—114no—
687C24—114no—
688C24—112no—
689C24—114no—
690C24—112no—
691C24—228no—
692C24—228no—
693C24—228no—
694C24—228no—
695C24—2232no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—228no—
706C24—222no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24D4×D1114yes—
716C24C2×C22⋊D1114yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—44no—
723C2×D4—416no—
724C2×D4—1116no—
725C2×D4—2232no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—444no—
731C2×D4—4416no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—28no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—416no—
749C22×C4—114no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—112no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
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—228no—
776C22×C4—228no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—4416no—
780C22×C4—4416no—
781C22×C4C2×C22⋊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—28no—
790C4⋊C4—228no—
791C4⋊C4—444no—
792C4⋊C4—444no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—228no—
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—444no—
806C22⋊C4—444no—
807C22⋊C4—444no—
808C22⋊C4C2×C22⋊D11116yescomplemented
809C42—228no—
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—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—1116no—
838C23—114no—
839C23—114no—
840C23—114no—
841C23—114no—
842C23—2232no—
843C23—228no—
844C23—228no—
845C23—228no—
846C23—228no—
847C23—228no—
848C23—228no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—228no—
854C23—228no—
855C23—222no—
856C23—228no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—4416no—
863C23—4416no—
864C23—4416no—
865C23—4416no—
866C23—4416no—
867C23—4416no—
868C23—44128no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23C2×D4×D1114yes—
874C23C2×D4×D1112yes—
875C23#6703712yes—
876C23#41×D1112yes—
877C23#41×D1112yes—
878C23#41×D1112yes—
879C23#6704212yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883D4—416no—
884D4—2232no—
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—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—114no—
906C2×C4—228no—
907C2×C4—222no—
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—4416no—
925C2×C4—4416no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4C22×C22⋊D1114yes—
932C2×C4C22×C22⋊D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—416no—
944C22—416no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—118no—
950C22—224no—
951C22—224no—
952C22—224no—
953C22—2232no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—4464no—
961C22—442no—
962C22—442no—
963C22—4416no—
964C22—442no—
965C22—442no—
966C22D11×#12314yes—
967C22#1062318514yes—
968C22#1062318814yes—
969C22#1062319014yes—
970C22D4×C22⋊D1114yes—
971C22#1062335914yes—
972C22#1062336014yes—
973C22C22×D4×D1111yescharacteristic
974C22C2×#6703711yescharacteristic
975C22C2×#41×D1111yescharacteristic
976C22C2×#41×D1111yescharacteristic
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—44no—
992C2—44no—
993C2—228no—
994C2—444no—
995C2#1307207518yesdirect product factor
996C2C2×D11×#12311yescharacteristic
997C2C2×#1062335911yescharacteristic
998C2C2×#1062318811yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062336011yescharacteristic
1001C2C2×#1062318511yescharacteristic
1002C2C2×#1062319011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC22×#123D11
hypocenterC11C2×#2418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. #13072075C2direct (N × H)
5. C2×#10622605C2semidirect
6. C2×#10622565C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622600C2semidirect
15. C2×#10622568C2semidirect
16. C22×C11×#123C2semidirect
19. C24×C4×C11C22semidirect
25. C2×C11×#123C22semidirect
26. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C4⋊C4C22semidirect
30. C22×C11×C22⋊C4C22semidirect
34. C22×C22⋊Dic11C22semidirect
35. C22×C22⋊Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
48. C22×C4⋊Dic11C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. #10622835C22semidirect
55. #10622826C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. #10622605C22semidirect
63. #10622603C22semidirect
64. #10622602C22semidirect
65. #10622600C22semidirect
66. #10622574C22semidirect
67. #10622569C22semidirect
68. #10622568C22semidirect
69. #10622565C22semidirect
70. #10622564C22semidirect
95. C23×C4×C11C23semidirect
121. C2×C11×C4⋊C4C23semidirect
122. C2×C11×C4⋊C4C23semidirect
125. C2×C11×C22⋊C4D4semidirect
128. C2×C11×C22⋊C4C23semidirect
137. C2×C22⋊Dic11C23semidirect
138. C2×C22⋊Dic11C23semidirect
158. C2×C4⋊Dic11C23semidirect
161. C2×Dic11⋊C4C23semidirect
162. C2×Dic11⋊C4C23semidirect
164. C2×C4×Dic11C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
292. C11×C22⋊C4C2×D4semidirect
310. C22×#123D11semidirect
393. C22×D11#123semidirect
454. C24×C4C2×D11semidirect
456. C2×#123C2×D11semidirect
464. C22×C4⋊C4C2×D11semidirect
465. C22×C4⋊C4C2×D11semidirect
483. C22×C22⋊C4C2×D11semidirect
548. C2×D11C2×#123semidirect
606. C23×C4C22×D11semidirect
618. C2×C4⋊C4C22×D11semidirect
619. C2×C4⋊C4C22×D11semidirect
649. C2×C22⋊C4C22⋊D11semidirect
652. C2×C22⋊C4C22×D11semidirect
663. C2×C11#2418semidirect
808. C22⋊C4C2×C22⋊D11semidirect
810. C11C2×#2418semidirect
995. C2#13072075direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
C22×C4×C22⋊D112
C22×C22⋊C4×D112
#130720752
C2×#106226052
C2×#106225652
C2×#106225742
C2×#106228352
C2×#106225642
C2×#106226032
C2×#106228262
C2×#106225692
C2×#106226022
C2×#106226002
C2×#106225682
C22×C11×#1232
C2×#241811