Finite Group Databasebeta

← C2×#13072622 #14921616

Subgroups — C2×#13072622 #14921616

Order 2816.

4218 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×C4×D44C211yesmaximal, characteristic, complemented
5#13072622C2116yesmaximal, direct product factor
6C2×#10622274C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622284C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622281C211yesmaximal, characteristic, complemented
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66983—28no—
32C2×#66983C2218yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×C4⋊Dic11C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C2×#66937—28no—
49C2×#66937C2218yescomplemented
50C2×#66936—28no—
51C2×#66936C2218yescomplemented
52C2×C4×D44—28no—
53C2×C4×D44C2218yescomplemented
54C4×C11×C22⋊C4C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622826C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622574C2218yescomplemented
63#10622573C2218yescomplemented
64#10622553C2218yescomplemented
65#10622553C2218yescomplemented
66#10622552C2218yescomplemented
67#10622284C2218yescomplemented
68#10622281C2218yescomplemented
69#10622278C2218yescomplemented
70#10622274C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—42no—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2314yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
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—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—24no—
107C22×D44—24no—
108C22×D44—24no—
109C22×D44—42no—
110C22×D44—42no—
111C22×D44C2314yes—
112C22×D44C2314yes—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C2×C11×C22⋊C4—24no—
123C2×C11×C22⋊C4D418yescomplemented
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C42×C11—24no—
127C2×C42×C11—42no—
128C2×C42×C11C2314yes—
129C2×C42×C11C2314yes—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11C2314yes—
132#66983—232no—
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—42no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4D418yescomplemented
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×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11—24no—
156C2×C4⋊Dic11C2314yes—
157C2×C4⋊Dic11C2314yes—
158C2×C4⋊Dic11C2314yes—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4—24no—
161C2×Dic11⋊C4C2314yes—
162C2×Dic11⋊C4C2314yes—
163#66937—232no—
164#66936—232no—
165C4×D44—232no—
166C11×#95C2314yes—
167C11×#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2464—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11C2×D414yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
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—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11C2×D414yes—
202C23×D11#4114yes—
203C23×D11C2412yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
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—28no—
220C22×C4×C11—28no—
221C22×C4×C11—44no—
222C22×C4×C11—416no—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2×D414yes—
226C22×C4×C11#4114yes—
227C22×C4×C11#4114yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
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—44no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
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×Dic11C2×D414yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—232no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—28no—
272C2×D44—28no—
273C2×D44—28no—
274C2×D44—44no—
275C2×D44—44no—
276C2×D44—416no—
277C2×D44—416no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—416no—
285C2×C4×D11—416no—
286C11×C22⋊C4—28no—
287C11×C22⋊C4C2×D4116yescomplemented
288C42×C11—28no—
289C42×C11—44no—
290C22⋊Dic11—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4C2×D4116yescomplemented
301C4⋊Dic11—28no—
302C4⋊Dic11—28no—
303C4⋊Dic11—28no—
304Dic11⋊C4—28no—
305Dic11⋊C4—28no—
306C22×#123—111no—
307C22×#121—111no—
308C22×#121—111no—
309C22×C4×D4—111no—
310#2464—1116no—
311C2×#398—111no—
312C2×#394—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#385—111no—
321C2×C4×C22⋊C4D1111yescharacteristic, complemented
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11C22×D414yes—
336C23×C11C22×D412yes—
337C23×C11C22×D412yes—
338C23×C11C2×#4112yes—
339C23×C11C2×#4112yes—
340C23×C11C2×#4112yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11C2511yescharacteristic
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
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—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—44no—
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—
385C22×D11C2×#4114yes—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
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—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—416no—
405C2×C4×C11—44no—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C22×D414yes—
408C2×C4×C11C22×D414yes—
409C2×C4×C11C2×#4114yes—
410C2×C4×C11C2×#4114yes—
411C22⋊D11—416no—
412C22⋊D11—416no—
413C22⋊D11—416no—
414C2×Dic11—28no—
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—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—44no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C22×D414yes—
434D44—232no—
435D44—416no—
436D44—416no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C24×C4—111no—
446C24×C4—111no—
447C24×C4C2×D1111yescharacteristic
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—118no—
452C2×#121—228no—
453C2×#121—228no—
454C2×C4×D4—118no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊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⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42C2×D1111yescharacteristic
475C22×C42C2×D1111yescharacteristic
476#398—118no—
477#394—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#386—118no—
484#386—118no—
485#385—118no—
486C4×C22⋊C4C2×D1118yescomplemented
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95C2×D1111yescharacteristic
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11#52514yes—
502C22×C11#53214yes—
503C22×C11#54014yes—
504C22×C11D4214yes—
505C22×C11#54614yes—
506C22×C11#54614yes—
507C22×C11#55314yes—
508C22×C11C23×D411yescharacteristic
509C22×C11C23×D411yescharacteristic
510C22×C11C22×#4111yescharacteristic
511C22×C11C22×#4111yescharacteristic
512C22×C11C22×#4111yescharacteristic
513C22×C11C2×H(5,𝔽2)11yescharacteristic
514C22×C11C2×H(5,𝔽2)11yescharacteristic
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—416no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—24no—
544C4×C11—42no—
545Dic11—24no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25—111no—
553C25C22×D1111yescharacteristic
554C22×D4—114no—
555C22×D4—114no—
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—224no—
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—224no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4—442no—
578C23×C4—24no—
579C23×C4—24no—
580C23×C4—42no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—114no—
587C23×C4—114no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—442no—
593C23×C4—442no—
594C23×C4C22×D1111yescharacteristic
595C23×C4C22×D1114yes—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603#121—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—118no—
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—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4D4418yescomplemented
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—24no—
642C2×C42—42no—
643C2×C42C22×D1114yes—
644C2×C42C22×D1114yes—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95C22×D1114yes—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11#246418yescomplemented
653C2×C11C2×#52511yescharacteristic
654C2×C11C2×#53211yescharacteristic
655C2×C11C2×#54011yescharacteristic
656C2×C11C2×D4211yescharacteristic
657C2×C11C2×#54611yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#55311yescharacteristic
660D11—44no—
661D11—44no—
662D11—82no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—114no—
670C24—114no—
671C24—112no—
672C24—112no—
673C24—112no—
674C24—222no—
675C24—222no—
676C24—222no—
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—
690C24—222no—
691C24—222no—
692C24—222no—
693C24C2×D4414yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—228no—
697C2×D4—228no—
698C2×D4—2232no—
699C2×D4—228no—
700C2×D4—228no—
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—444no—
711C2×D4—444no—
712C2×D4—4416no—
713C2×D4—4416no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—4416no—
718C2×D4—4416no—
719C2×D4—4416no—
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—22no—
732C22×C4—22no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—44no—
736C22×C4—416no—
737C22×C4—114no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
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—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—4416no—
764C22×C4—4416no—
765C22×C4C2×D4414yes—
766C22×C4C2×D4414yes—
767C22×C4#433914yes—
768C22×C4#433914yes—
769C22×C4D4×D1114yes—
770C22×C4C23×D1112yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—228no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—228no—
781C22⋊C4—28no—
782C22⋊C4—1116no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C22⋊C4C2×D44116yescomplemented
794C42—28no—
795C42—44no—
796C11C2×#246411yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—114no—
811C23—114no—
812C23—228no—
813C23—228no—
814C23—228no—
815C23—228no—
816C23—228no—
817C23—228no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
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—444no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C22×D4414yes—
853C23C22×D4412yes—
854C23C2×#433912yes—
855C23C2×#433912yes—
856C23C2×D4×D1112yes—
857C23#6703712yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C24×D1111yescharacteristic
861D4—2232no—
862D4—4416no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—416no—
886C2×C4—44no—
887C2×C4—114no—
888C2×C4—228no—
889C2×C4—222no—
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×C4—444no—
909C2×C4C22×D4414yes—
910C2×C4C22×D4414yes—
911C2×C4C2×#433914yes—
912C2×C4C2×#433914yes—
913C2×C4C2×D4×D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—416no—
922C22—224no—
923C22—224no—
924C22—224no—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—4416no—
937C22—4416no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062300814yes—
947C22#1062302114yes—
948C22#1062306114yes—
949C22#1062307814yes—
950C22D4×D4414yes—
951C22#1062308514yes—
952C22#1062309314yes—
953C22C23×D4411yescharacteristic
954C22C22×#433911yescharacteristic
955C22C22×#433911yescharacteristic
956C22C22×D4×D1111yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#6704211yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—24no—
965C4—42no—
966C4—224no—
967C4—442no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—444no—
973C2—444no—
974C2—882no—
975C2#1307262218yesdirect product factor
976C2C2×#1062307811yescharacteristic
977C2C2×#1062300811yescharacteristic
978C2C2×#1062309311yescharacteristic
979C2C2×D4×D4411yescharacteristic
980C2C2×#1062302111yescharacteristic
981C2C2×#1062308511yescharacteristic
982C2C2×#1062306111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2464
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66983C2semidirect
3. C22×#66937C2semidirect
4. C22×C4×D44C2semidirect
5. #13072622C2direct (N × H)
6. C2×#10622274C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622281C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
32. C2×#66983C22semidirect
49. C2×#66937C22semidirect
51. C2×#66936C22semidirect
53. C2×C4×D44C22semidirect
54. C4×C11×C22⋊C4C22semidirect
57. #10622826C22semidirect
62. #10622574C22semidirect
63. #10622573C22semidirect
64. #10622553C22semidirect
65. #10622553C22semidirect
66. #10622552C22semidirect
67. #10622284C22semidirect
68. #10622281C22semidirect
69. #10622278C22semidirect
70. #10622274C22semidirect
123. C2×C11×C22⋊C4D4semidirect
142. C2×(C2×D11)⋊C4D4semidirect
287. C11×C22⋊C4C2×D4semidirect
300. (C2×D11)⋊C4C2×D4semidirect
321. C2×C4×C22⋊C4D11semidirect
486. C4×C22⋊C4C2×D11semidirect
638. C2×C22⋊C4D44semidirect
652. C2×C11#2464semidirect
793. C22⋊C4C2×D44semidirect
796. C11C2×#2464semidirect
975. C2#13072622direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669832
C22×#669372
C22×C4×D442
#130726222
C2×#106222742
C2×#106225742
C2×#106222842
C2×#106225732
C2×#106225522
C2×#106225532
C2×#106228262
C2×#106222782
C2×#106222812
C2×C4×C11×C22⋊C42
C2×#246411