Finite Group Databasebeta

← C2×#13072374 #14921669

Subgroups — C2×#13072374 #14921669

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66939C211yesmaximal, characteristic, complemented
3C22×#66936C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072374C2116yesmaximal, direct product factor
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66993—28no—
34C2×#66993C2218yes—
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×C4⋊Dic11C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66939—28no—
51C2×#66939C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C2×(C22⋊D11)⋊C4—28no—
55C2×(C22⋊D11)⋊C4C2218yescomplemented
56C11×#394C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622833C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622604C2218yescomplemented
63C4⋊C4×Dic11C2218yescomplemented
64#10622574C2218yescomplemented
65#10622572C2218yescomplemented
66#10622570C2218yescomplemented
67#10622570C2218yescomplemented
68#10622570C2218yescomplemented
69#10622278C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11D418yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2314yes—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—42no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—42no—
117C22×C4×D11C2314yes—
118C2×C11×C4⋊C4—24no—
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—24no—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4—42no—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2314yes—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—42no—
130C2×C22⋊Dic11—42no—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66993—232no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×C4⋊Dic11—24no—
150C2×C4⋊Dic11D418yescomplemented
151C2×C4⋊Dic11C2314yes—
152C2×C4⋊Dic11C2314yes—
153C2×Dic11⋊C4—24no—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2314yes—
159C2×C4×Dic11—24no—
160C2×C4×Dic11—24no—
161C2×C4×Dic11—24no—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66939—232no—
166#66936—232no—
167(C22⋊D11)⋊C4—232no—
168C11×#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2445—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×C11—22no—
186C24×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11C2×D414yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
209C2×D4×C11—416no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11C2×D414yes—
224C22×C4×C11#4114yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—416no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11C2×D4116yes—
246C22×Dic11—28no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—28no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—44no—
262C22×Dic11—416no—
263C22×Dic11C2×D414yes—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—28no—
275C2×D44—28no—
276C2×D44—44no—
277C2×D44—416no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—44no—
281C2×C4×D11—416no—
282C11×C4⋊C4—28no—
283C11×C22⋊C4—28no—
284C11×C22⋊C4—28no—
285C11×C22⋊C4—28no—
286C11×C22⋊C4—44no—
287C22⋊Dic11—28no—
288C22⋊Dic11—44no—
289C22⋊Dic11—44no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—44no—
295(C2×D11)⋊C4—44no—
296(C2×D11)⋊C4—44no—
297C4⋊Dic11—28no—
298C4⋊Dic11C2×D4116yescomplemented
299Dic11⋊C4—28no—
300Dic11⋊C4—28no—
301Dic11⋊C4—28no—
302C4×Dic11—28no—
303C4×Dic11—28no—
304C4×Dic11—28no—
305C22×#127—111no—
306C22×#123—111no—
307C22×#123—111no—
308C22×C4×D4—111no—
309#2445—1116no—
310C2×#394—111no—
311C2×#394—111no—
312C2×#394—111no—
313C2×#394D1111yescharacteristic, complemented
314C2×#390—111no—
315C2×#390—111no—
316C2×#390—111no—
317C2×#389—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×C4×C4⋊C4—111no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11C22×D414yes—
349C23×C11C22×D412yes—
350C23×C11C22×D412yes—
351C23×C11C2×#4112yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11H(5,𝔽2)12yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11C2511yescharacteristic
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—28no—
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—44no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11C22×D414yes—
385D4×C11—416no—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—44no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11C22×D414yes—
405C2×C4×C11C2×#4114yes—
406C22⋊D11—232no—
407C22⋊D11—416no—
408C22⋊D11—416no—
409C22⋊D11—416no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—416no—
426C2×Dic11—44no—
427C2×Dic11—44no—
428C2×Dic11—44no—
429C2×Dic11#123116yescomplemented
430C2×Dic11C22×D414yes—
431C2×Dic11C22×D414yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C2×#4114yes—
434C2×Dic11C2×#4114yes—
435D44—416no—
436C4×D11—416no—
437C23×D4—111no—
438C23×D4—111no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4C2×D1111yescharacteristic
443C24×C4—111no—
444C24×C4—111no—
445C2×#127—118no—
446C2×#127—228no—
447C2×#123—118no—
448C2×#123—118no—
449C2×#123—228no—
450C2×#123—228no—
451C2×C4×D4—118no—
452C2×C4×D4—228no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4C2×D1111yescharacteristic
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4C2×D1111yescharacteristic
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476#394—118no—
477#394—118no—
478#394—118no—
479#394C2×D1118yescomplemented
480#390—118no—
481#390—118no—
482#390—118no—
483#389—118no—
484#386—118no—
485#386—118no—
486C4×C4⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95C2×D1111yescharacteristic
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—416no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—88no—
507C22×C11C2×#12314yes—
508C22×C11#53214yes—
509C22×C11#54014yes—
510C22×C11D4214yes—
511C22×C11#54614yes—
512C22×C11#55014yes—
513C22×C11#55914yes—
514C22×C11C23×D411yescharacteristic
515C22×C11C23×D411yescharacteristic
516C22×C11C22×#4111yescharacteristic
517C22×C11C22×#4111yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C2×H(5,𝔽2)11yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—416no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—88no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11C2×#12318yescomplemented
548C25—111no—
549C25—111no—
550C25C22×D1111yescharacteristic
551C25C22×D1111yescharacteristic
552C22×D4—24no—
553C22×D4—24no—
554C22×D4—42no—
555C22×D4—118no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—224no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
565C22×D4—224no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—442no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4C22×D1114yes—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—114no—
583C23×C4—114no—
584C23×C4—224no—
585C23×C4—224no—
586C23×C4—224no—
587C23×C4—224no—
588C23×C4—442no—
589C23×C4—442no—
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595#127—2232no—
596#123—2232no—
597#123—2232no—
598C4×D4—2232no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—118no—
601C2×C4⋊C4—114no—
602C2×C4⋊C4—114no—
603C2×C4⋊C4—114no—
604C2×C4⋊C4—114no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—224no—
607C2×C4⋊C4—224no—
608C2×C4⋊C4—224no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4C22×D1114yes—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—42no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
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—224no—
626C2×C22⋊C4—224no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—442no—
631C2×C22⋊C4—442no—
632C2×C22⋊C4—442no—
633C2×C22⋊C4—442no—
634C2×C22⋊C4—442no—
635C2×C22⋊C4C22×D1114yes—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—114no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—224no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95C22×D1114yes—
649C2×C11—44no—
650C2×C11—82no—
651C2×C11#244518yescomplemented
652C2×C11C22×#12311yescharacteristic
653C2×C11C2×#53211yescharacteristic
654C2×C11C2×#54011yescharacteristic
655C2×C11C2×D4211yescharacteristic
656C2×C11C2×#54611yescharacteristic
657C2×C11C2×#55011yescharacteristic
658C2×C11C2×#55911yescharacteristic
659D11—44no—
660D11—82no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—114no—
675C24—112no—
676C24—112no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24D4×D1114yes—
691C24C23×D1112yes—
692C24C23×D1112yes—
693C24C23×D1111yescharacteristic
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—416no—
698C2×D4—1116no—
699C2×D4—228no—
700C2×D4—2232no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—444no—
712C2×D4—4416no—
713C2×D4—4416no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—4416no—
717C2×D4—4416no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—114no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—112no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—228no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—444no—
760C22×C4—4416no—
761C22×C4—444no—
762C22×C4—4416no—
763C22×C4D4×D1114yes—
764C22×C4#434114yes—
765C22×C4C23×D1112yes—
766C22×C4C23×D1112yes—
767C22×C4C23×D1112yes—
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C4⋊C4—28no—
771C4⋊C4—1116no—
772C4⋊C4—228no—
773C4⋊C4—228no—
774C4⋊C4—228no—
775C4⋊C4—228no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—228no—
781C22⋊C4—228no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C22⋊C4—444no—
788C22⋊C4—444no—
789C22⋊C4—444no—
790C42—228no—
791C42—228no—
792C42—228no—
793C11C2×#244511yescharacteristic, complemented, Sylow
794C23—28no—
795C23—28no—
796C23—28no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—114no—
822C23—228no—
823C23—228no—
824C23—228no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23C2×D4×D1114yes—
850C23C2×D4×D1112yes—
851C23C2×D4×D1112yes—
852C23C2×#434112yes—
853C23#6703712yes—
854C23#41×D1112yes—
855C23#41×D1112yes—
856C23#6704212yes—
857C23C24×D1111yescharacteristic
858D4—416no—
859D4—2232no—
860D4—4416no—
861D4—4416no—
862D4—4416no—
863D4—4416no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—1116no—
883C2×C4—114no—
884C2×C4—114no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—228no—
889C2×C4—228no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—4416no—
904C2×C4—4416no—
905C2×C4—444no—
906C2×C4—444no—
907C2×C4—444no—
908C2×C4C2×D4×D1114yes—
909C2×C4C2×#434114yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—416no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—88no—
926C22—224no—
927C22—224no—
928C22—224no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—4416no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—888no—
942C22#1062312214yes—
943C22#1062312714yes—
944C22#1062313014yes—
945C22#1062314014yes—
946C22D11×#12314yes—
947C22#1062319414yes—
948C22#1062321214yes—
949C22C22×D4×D1111yescharacteristic
950C22C22×D4×D1111yescharacteristic
951C22C22×#434111yescharacteristic
952C22C2×#6703711yescharacteristic
953C22C2×#41×D1111yescharacteristic
954C22C2×#41×D1111yescharacteristic
955C22C2×#6704211yescharacteristic
956C4—24no—
957C4—24no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—118no—
962C4—224no—
963C4—224no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—44no—
968C2—82no—
969C2—444no—
970C2—882no—
971C2#1307237418yesdirect product factor
972C2C2×D11×#12311yescharacteristic
973C2C2×#1062312711yescharacteristic
974C2C2×#1062319411yescharacteristic
975C2C2×#1062314011yescharacteristic
976C2C2×#1062312211yescharacteristic
977C2C2×#1062313011yescharacteristic
978C2C2×#1062321211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#394D11
hypocenterC11C2×#2445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#66939C2semidirect
3. C22×#66936C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072374C2direct (N × H)
6. C2×#10622604C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622278C2semidirect
15. C2×C4⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
51. C2×#66939C22semidirect
53. C2×#66936C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. C11×#394C22semidirect
58. #10622833C22semidirect
62. #10622604C22semidirect
63. C4⋊C4×Dic11C22semidirect
64. #10622574C22semidirect
65. #10622572C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
68. #10622570C22semidirect
69. #10622278C22semidirect
70. #10622260C22semidirect
150. C2×C4⋊Dic11D4semidirect
298. C4⋊Dic11C2×D4semidirect
313. C2×#394D11semidirect
429. C2×Dic11#123semidirect
479. #394C2×D11semidirect
547. Dic11C2×#123semidirect
651. C2×C11#2445semidirect
793. C11C2×#2445semidirect
971. C2#13072374direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669392
C22×#669362
C22×(C22⋊D11)⋊C42
#130723742
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106225702
C2×#106222602
C2×#106228332
C2×#106222782
C2×C4⋊C4×Dic112
C2×C11×#3942
C2×#244511