Finite Group Databasebeta

← C2×#13072749 #14921357

Subgroups — C2×#13072749 #14921357

Order 2816.

4946 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×#67000C211yesmaximal, characteristic, complemented
2C22×#66935C211yesmaximal, characteristic
3C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13072749C2116yesmaximal, direct product factor
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622601C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C2×C11×C22⋊Q8—28no—
25C2×C11×C22⋊Q8C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#67000—28no—
33C2×#67000C2218yescomplemented
34C22×(C2×D11)⋊C4—28no—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
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)⋊C4C2218yescomplemented
46C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic11C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×#66935—28no—
53C2×#66935C2218yes—
54#10622844C2218yescomplemented
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#10622606C2218yescomplemented
63#10622604C2218yescomplemented
64#10622604C2218yescomplemented
65#10622603C2218yescomplemented
66#10622603C2218yescomplemented
67#10622601C2218yescomplemented
68#10622571C2218yescomplemented
69#10622568C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—42no—
78C24×D11—42no—
79C24×D11C2311yescharacteristic
80C24×D11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C24×D11C2314yes—
83C22×Q8×C11—24no—
84C22×Q8×C11—24no—
85C22×Q8×C11—42no—
86C22×Q8×C11C2314yescomplemented
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2314yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11C2314yes—
101C23×Dic11—24no—
102C23×Dic11—24no—
103C23×Dic11—42no—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2314yes—
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—42no—
115C22×D44—42no—
116C22×D44C2314yes—
117C22×D44C2314yes—
118C11×C22⋊Q8—232no—
119C2×C11×C4⋊C4—24no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4—24no—
122C2×C11×C4⋊C4C2314yescomplemented
123C2×C11×C4⋊C4C2314yescomplemented
124C2×C11×C4⋊C4C2314yescomplemented
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4D418yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11C2314yes—
131#67000—232no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—232no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4—42no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4D418yescomplemented
147C2×(C2×D11)⋊C4C2314yes—
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)⋊C4C2314yescomplemented
158C2×(C2×D11)⋊C4C2314yescomplemented
159C2×(C2×D11)⋊C4C2314yescomplemented
160C2×(C2×D11)⋊C4C2314yescomplemented
161C2×C4×Dic11—24no—
162C2×C4×Dic11—42no—
163C2×C4×Dic11C2314yescomplemented
164C2×C4×Dic11C2314yescomplemented
165#66935—232no—
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2472—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11C2×D414yes—
178C24×C11#4114yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—232no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—28no—
187C23×D11—22no—
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—28no—
197C23×D11—28no—
198C23×D11—28no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—28no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—44no—
208C23×D11—44no—
209C23×D11—416no—
210C23×D11—416no—
211C23×D11—416no—
212C23×D11—416no—
213C23×D11—416no—
214C23×D11—416no—
215C23×D11C2×D414yes—
216C23×D11#4114yes—
217C23×D11C2412yes—
218C23×D11C2412yes—
219C23×D11C2412yes—
220C2×Q8×C11—28no—
221C2×Q8×C11—28no—
222C2×Q8×C11—44no—
223C2×Q8×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—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—28no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—28no—
241C22×C4×C11—44no—
242C22×C4×C11—416no—
243C22×C4×C11C2×D414yes—
244C22×C4×C11C2×D414yes—
245C22×C4×C11C2×D414yes—
246C22×C4×C11C2412yes—
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—416no—
256C22×Dic11—28no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—28no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—44no—
273C22×Dic11—416no—
274C22×Dic11C2×D414yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C2×D44—28no—
281C2×D44—28no—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—416no—
287C2×D44—416no—
288C11×C4⋊C4—28no—
289C11×C4⋊C4—28no—
290C11×C4⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4C2×D4116yes—
293C22⋊Dic11—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
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)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4C2×D4116yescomplemented
308C4×Dic11—28no—
309C4×Dic11—44no—
310C22×#124—111no—
311C22×C22⋊Q8D1111yescharacteristic, complemented
312C22×#120—111no—
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394—111no—
318C2×#393—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#386—111no—
324C2×#379—111no—
325C2×C4×C22⋊C4—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#124116yescomplemented
337C23×C11C22×D412yes—
338C23×C11C22×D414yes—
339C23×C11C22×D412yes—
340C23×C11C2×#4114yes—
341C23×C11C2×#4114yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11C2×#4112yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11H(5,𝔽2)12yes—
347C23×C11C2511yescharacteristic
348C22×D11—232no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—28no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—416no—
375C22×D11—416no—
376C22×D11—416no—
377C22×D11—416no—
378C22×D11—416no—
379C22×D11—4128no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—416no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11C22×D414yes—
397C22×D11C2×#4114yes—
398Q8×C11—416no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
401C2×C4×C11—28no—
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—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—416no—
418C2×C4×C11—44no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11C22×D414yes—
422C2×C4×C11C22×D414yes—
423C2×C4×C11C22×D414yes—
424C22⋊D11—416no—
425C2×Dic11—28no—
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—416no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11C22×D414yes—
446D44—416no—
447D44—416no—
448C26—111no—
449C23×Q8C2×D1111yescharacteristic, complemented
450C23×D4—111no—
451C23×D4—111no—
452C23×D4—111no—
453C24×C4—111no—
454C24×C4C2×D1111yescharacteristic
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—28no—
458C2×C22⋊Q8C2×D1118yescomplemented
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4C2×D1111yescharacteristic, complemented
462C22×C4⋊C4C2×D1111yescharacteristic, complemented
463C22×C4⋊C4C2×D1111yescharacteristic, complemented
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
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—118no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—111no—
480C22×C22⋊C4—228no—
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C42—111no—
484C22×C42—111no—
485#397—118no—
486#394—118no—
487#394—118no—
488#393—118no—
489#390—118no—
490#388—118no—
491#388—118no—
492#386—118no—
493#386—118no—
494#379—118no—
495C4×C22⋊C4—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—232no—
509C22×C11#52514yes—
510C22×C11C2×#12414yes—
511C22×C11C2×#12418yescomplemented
512C22×C11#53814yes—
513C22×C11D4214yes—
514C22×C11#54614yes—
515C22×C11#54614yes—
516C22×C11#55114yes—
517C22×C11C23×D411yescharacteristic
518C22×C11C23×D411yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C22×#4111yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C22×C11C2×H(5,𝔽2)11yescharacteristic
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—464no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—416no—
540C2×D11—416no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—88no—
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—24no—
552C4×C11—42no—
553C4×C11—42no—
554C4×C11—42no—
555Dic11—24no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—111no—
561C25—111no—
562C25—111no—
563C25—114no—
564C25—224no—
565C25—224no—
566C25—224no—
567C25—224no—
568C25—224no—
569C25—442no—
570C25—442no—
571C25C22×D1111yescharacteristic
572C22×Q8—24no—
573C22×Q8—24no—
574C22×Q8—42no—
575C22×Q8C22×D1114yescomplemented
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—442no—
587C22×D4—442no—
588C23×C4—24no—
589C23×C4—24no—
590C23×C4—42no—
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×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—232no—
609#120—2232no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4C22×D1114yescomplemented
614C2×C4⋊C4C22×D1114yescomplemented
615C2×C4⋊C4C22×D1114yescomplemented
616C2×C22⋊C4—24no—
617C2×C22⋊C4—118no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
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—2232no—
634C2×C22⋊C4—224no—
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—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4C22⋊D1118yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—442no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
661C2×C11—28no—
662C2×C11#247218yescomplemented
663C2×C11C2×#52511yescharacteristic
664C2×C11C22×#12411yescharacteristic
665C2×C11C2×#53811yescharacteristic
666C2×C11C2×D4211yescharacteristic
667C2×C11C2×#54611yescharacteristic
668C2×C11C2×#54611yescharacteristic
669C2×C11C2×#55111yescharacteristic
670D11—44no—
671D11—44no—
672D11—82no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—114no—
678C24—114no—
679C24—112no—
680C24—112no—
681C24—112no—
682C24—228no—
683C24—228no—
684C24—2232no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—228no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24—222no—
693C24—222no—
694C24—222no—
695C24—222no—
696C24—222no—
697C24—222no—
698C24—222no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—228no—
703C24—222no—
704C24—222no—
705C24—228no—
706C24—222no—
707C24—444no—
708C24—444no—
709C24—4416no—
710C24—4416no—
711C24—4416no—
712C24—4416no—
713C24—4416no—
714C24—4416no—
715C24#434314yes—
716C24#434314yes—
717C24C2×C22⋊D1114yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—416no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—444no—
732C2×D4—444no—
733C2×D4—4416no—
734C2×D4—4416no—
735C2×D4—4416no—
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—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—44no—
754C22×C4—416no—
755C22×C4—114no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—228no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—228no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—444no—
778C22×C4—4416no—
779C22×C4D4×D1114yes—
780C22×C4C2×C22⋊D1114yes—
781C22×C4C2×C22⋊D1114yes—
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—1116no—
793C22⋊C4—228no—
794C22⋊C4—228no—
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—444no—
804C22⋊C4—444no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4C2×C22⋊D11116yes—
808C42—228no—
809C42—444no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—114no—
822C23—114no—
823C23—2232no—
824C23—228no—
825C23—228no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—4416no—
850C23—4416no—
851C23—4416no—
852C23—4416no—
853C23—4416no—
854C23—44128no—
855C23—444no—
856C23—444no—
857C23—444no—
858C23—4416no—
859C23—444no—
860C23—444no—
861C23—444no—
862C23—444no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23#67000116yescomplemented
872C23C2×D4×D1112yes—
873C23#6703712yes—
874C23C2×#434314yes—
875C23C2×#434314yes—
876C23C2×#434312yes—
877C23C2×#434312yes—
878C23#41×D1112yes—
879C23#6704212yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883Q8—416no—
884D4—4416no—
885D4—4416no—
886D4—4416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
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—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—416no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—114no—
910C2×C4—228no—
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×C4C2×D4×D1114yes—
931C2×C4C22×C22⋊D1114yes—
932C2×C4C22×C22⋊D1114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—232no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—224no—
941C22—224no—
942C22—224no—
943C22—224no—
944C22—224no—
945C22—224no—
946C22—4464no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22—4416no—
953C22—4416no—
954C22—442no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—888no—
965C22#1062315814yes—
966C22#1062316114yes—
967C22#1062316814yes—
968C22#1062317514yes—
969C22D4×C22⋊D1114yes—
970C22C2×#6700014yes—
971C22C2×#6700018yescomplemented
972C22#1062336014yes—
973C22C22×D4×D1111yescharacteristic
974C22C2×#6703711yescharacteristic
975C22C22×#434311yescharacteristic
976C22C22×#434311yescharacteristic
977C22C2×#41×D1111yescharacteristic
978C22C2×#6704211yescharacteristic
979C22C23×C22⋊D1111yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—28no—
992C2—444no—
993C2—444no—
994C2—882no—
995C2#1307274918yesdirect product factor
996C2C2×#1062315811yescharacteristic
997C2C22×#6700011yescharacteristic
998C2C2×#1062317511yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062336011yescharacteristic
1001C2C2×#1062316111yescharacteristic
1002C2C2×#1062316811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
3. C23×(C2×D11)⋊C4C2semidirect
4. #13072749C2direct (N × H)
5. C2×#10622606C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622568C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
18. C23×Q8×C11C22semidirect
25. C2×C11×C22⋊Q8C22semidirect
26. C22×C11×C4⋊C4C22semidirect
27. C22×C11×C4⋊C4C22semidirect
28. C22×C11×C4⋊C4C22semidirect
33. C2×#67000C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×(C2×D11)⋊C4C22semidirect
47. C22×(C2×D11)⋊C4C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
50. C22×C4×Dic11C22semidirect
51. C22×C4×Dic11C22semidirect
54. #10622844C22semidirect
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. #10622606C22semidirect
63. #10622604C22semidirect
64. #10622604C22semidirect
65. #10622603C22semidirect
66. #10622603C22semidirect
67. #10622601C22semidirect
68. #10622571C22semidirect
69. #10622568C22semidirect
70. C22⋊C4×Dic11C22semidirect
86. C22×Q8×C11C23semidirect
122. C2×C11×C4⋊C4C23semidirect
123. C2×C11×C4⋊C4C23semidirect
124. C2×C11×C4⋊C4C23semidirect
146. C2×(C2×D11)⋊C4D4semidirect
157. C2×(C2×D11)⋊C4C23semidirect
158. C2×(C2×D11)⋊C4C23semidirect
159. C2×(C2×D11)⋊C4C23semidirect
160. C2×(C2×D11)⋊C4C23semidirect
163. C2×C4×Dic11C23semidirect
164. C2×C4×Dic11C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
307. (C2×D11)⋊C4C2×D4semidirect
311. C22×C22⋊Q8D11semidirect
336. C23×C11#124semidirect
449. C23×Q8C2×D11semidirect
458. C2×C22⋊Q8C2×D11semidirect
461. C22×C4⋊C4C2×D11semidirect
462. C22×C4⋊C4C2×D11semidirect
463. C22×C4⋊C4C2×D11semidirect
511. C22×C11C2×#124semidirect
575. C22×Q8C22×D11semidirect
613. C2×C4⋊C4C22×D11semidirect
614. C2×C4⋊C4C22×D11semidirect
615. C2×C4⋊C4C22×D11semidirect
662. C2×C11#2472semidirect
810. C11C2×#2472semidirect
871. C23#67000semidirect
971. C22C2×#67000semidirect
995. C2#13072749direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669352
C23×(C2×D11)⋊C42
#130727492
C2×#106226062
C2×#106226042
C2×#106228442
C2×#106226012
C2×#106226032
C2×#106228262
C2×#106225712
C2×#106225682
C2×C22⋊C4×Dic112
C22×C11×C22⋊Q82
C2×#247211