Finite Group Databasebeta

← C2×#13073574 #14923791

Subgroups — C2×#13073574 #14923791

Order 2816.

4326 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4#13073574C2116yesmaximal, direct product factor
5C2×#10622597C211yesmaximal, characteristic, complemented
6C2×#10622565C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C2×C11×#121—28no—
28C2×C11×#121C2218yescomplemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C2×#66992—28no—
39C2×#66992—28no—
40C2×#66992C2218yescomplemented
41C2×#66992C2218yescomplemented
42C2×D4×Dic11—28no—
43C2×D4×Dic11C2218yescomplemented
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52#10622836C2218yescomplemented
53#10622833C2218yescomplemented
54#10622833C2218yescomplemented
55#10622826C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2218yescomplemented
65#10622603C2218yescomplemented
66#10622597C2218yescomplemented
67#10622574C2218yescomplemented
68#10622571C2218yescomplemented
69#10622565C2218yescomplemented
70#10622558C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—42no—
83C22×D4×C11D418yescomplemented
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C22×D4×C11C2314yes—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2314yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11—24no—
110C23×Dic11—42no—
111C23×Dic11—42no—
112C23×Dic11—42no—
113C23×Dic11—42no—
114C23×Dic11—42no—
115C23×Dic11D418yescomplemented
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2311yescharacteristic
120C23×Dic11C2314yes—
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2314yes—
125C23×Dic11C2314yes—
126C11×#121—232no—
127C2×C11×C4⋊C4—24no—
128C2×C11×C4⋊C4C2314yes—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—24no—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—24no—
136C2×C22⋊Dic11—24no—
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11—42no—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145#66992—232no—
146#66992—232no—
147D4×Dic11—232no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—42no—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×C4⋊Dic11—24no—
157C2×C4⋊Dic11C2314yes—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2543—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×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11C2×D414yes—
191C24×C11C2×D414yes—
192C24×C11C2×D414yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11C2412yes—
206C2×D4×C11—232no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C2×D4×C11—28no—
211C2×D4×C11—28no—
212C2×D4×C11—28no—
213C2×D4×C11—28no—
214C2×D4×C11—44no—
215C2×D4×C11—416no—
216C2×D4×C11—416no—
217C2×D4×C11C2×D4116yescomplemented
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—28no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—28no—
230C22×C4×C11—44no—
231C22×C4×C11—416no—
232C22×C4×C11C2×D414yes—
233C22×C4×C11#4114yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—416no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11—416no—
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—28no—
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—416no—
272C22×Dic11—44no—
273C22×Dic11—44no—
274C22×Dic11—44no—
275C22×Dic11—44no—
276C22×Dic11—44no—
277C22×Dic11—416no—
278C22×Dic11—416no—
279C22×Dic11C2×D414yes—
280C22×Dic11C2×D414yes—
281C22×Dic11C2×D4116yescomplemented
282C22×Dic11#4114yes—
283C22×Dic11C2412yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C11×C4⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11—28no—
298C22⋊Dic11—44no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—44no—
303C4⋊Dic11—28no—
304Dic11⋊C4—28no—
305Dic11⋊C4—28no—
306C4×Dic11—28no—
307C22×#121—111no—
308C22×#121—111no—
309C22×#121D1111yescharacteristic, complemented
310C22×C4×D4—111no—
311#2543—1116no—
312C2×#398—111no—
313C2×#397—111no—
314C2×#394—111no—
315C2×#392—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#386—111no—
322C22×#95—111no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—28no—
334C23×C11—28no—
335C23×C11—28no—
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—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11#121116yes—
361C23×C11C22×D414yes—
362C23×C11C22×D412yes—
363C23×C11C22×D414yes—
364C23×C11C22×D414yes—
365C23×C11C22×D412yes—
366C23×C11C2×#4114yes—
367C23×C11C2×#4112yes—
368C23×C11C2×#4112yes—
369C23×C11C2×#4112yes—
370C23×C11H(5,𝔽2)12yes—
371C23×C11H(5,𝔽2)12yes—
372C23×C11C2511yescharacteristic
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—44no—
387D4×C11—232no—
388D4×C11—416no—
389D4×C11—416no—
390C2×C4×C11—28no—
391C2×C4×C11—28no—
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—416no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C2×#4114yes—
407C22⋊D11—416no—
408C22⋊D11—416no—
409C22⋊D11—416no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—28no—
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—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—416no—
432C2×Dic11—416no—
433C2×Dic11—416no—
434C2×Dic11—44no—
435C2×Dic11—44no—
436C2×Dic11—44no—
437C2×Dic11—44no—
438C2×Dic11C22×D414yes—
439C2×Dic11C22×D414yes—
440C2×Dic11C2×#4114yes—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4C2×D1111yescharacteristic
445C23×D4C2×D1111yescharacteristic
446C23×D4C2×D1111yescharacteristic
447C24×C4—111no—
448C24×C4—111no—
449C24×C4—111no—
450C24×C4C2×D1111yescharacteristic
451C2×#121—28no—
452C2×#121—118no—
453C2×#121—118no—
454C2×#121—228no—
455C2×#121—228no—
456C2×#121C2×D1118yescomplemented
457C2×C4×D4—118no—
458C2×C4×D4—228no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C22⋊C4C2×D1111yescharacteristic
475C22×C42—111no—
476#398—118no—
477#397—118no—
478#394—118no—
479#392—118no—
480#388—118no—
481#388—118no—
482#386—118no—
483#386—118no—
484#386—118no—
485#386—118no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—118no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—24no—
500C22×C11—24no—
501C22×C11—232no—
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—416no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—88no—
518C22×C11C2×#12118yes—
519C22×C11C2×#12114yes—
520C22×C11#53214yes—
521C22×C11#53414yes—
522C22×C11#54614yes—
523C22×C11#54614yes—
524C22×C11#55314yes—
525C22×C11#55314yes—
526C22×C11C23×D411yescharacteristic
527C22×C11C23×D411yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C22×#4111yescharacteristic
530C22×C11C22×#4111yescharacteristic
531C22×C11C2×H(5,𝔽2)11yescharacteristic
532C22×C11C2×H(5,𝔽2)11yescharacteristic
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—88no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—42no—
544C4×C11—42no—
545Dic11—24no—
546Dic11—24no—
547Dic11—24no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552C25—111no—
553C25C22×D1111yescharacteristic
554C25C22×D1111yescharacteristic
555C25C22×D1111yescharacteristic
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—24no—
562C22×D4—24no—
563C22×D4—42no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—114no—
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×D4C22⋊D1118yescomplemented
577C22×D4C22×D1114yes—
578C22×D4C22×D1114yes—
579C22×D4C22×D1114yes—
580C23×C4—24no—
581C23×C4—24no—
582C23×C4—42no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—118no—
587C23×C4—114no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—114no—
593C23×C4—114no—
594C23×C4—224no—
595C23×C4—224no—
596C23×C4—224no—
597C23×C4—442no—
598C23×C4—442no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4—442no—
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1114yes—
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#121—232no—
608#121—2232no—
609#121—2232no—
610C4×D4—2232no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—114no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—224no—
617C2×C4⋊C4—224no—
618C2×C4⋊C4C22×D1114yes—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
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—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—442no—
640C2×C22⋊C4—442no—
641C2×C22⋊C4C22×D1114yes—
642C2×C22⋊C4C22×D1114yes—
643C2×C42—114no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651#95—114no—
652#95—114no—
653C2×C11—28no—
654C2×C11—44no—
655C2×C11—82no—
656C2×C11#254318yescomplemented
657C2×C11C22×#12111yescharacteristic
658C2×C11C2×#53211yescharacteristic
659C2×C11C2×#53411yescharacteristic
660C2×C11C2×#54611yescharacteristic
661C2×C11C2×#54611yescharacteristic
662C2×C11C2×#55311yescharacteristic
663C2×C11C2×#55311yescharacteristic
664D11—82no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—112no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24D4×D1114yes—
691C24#434114yes—
692C24C2×C22⋊D1114yes—
693C24C2×C22⋊D1114yes—
694C24C23×D1112yes—
695C24C23×D1112yes—
696C24C23×D1112yes—
697C24C23×D1111yescharacteristic
698C2×D4—232no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—44no—
707C2×D4—416no—
708C2×D4—416no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—4416no—
719C2×D4—4416no—
720C2×D4—4416no—
721C2×D4C2×C22⋊D11116yescomplemented
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—28no—
733C22×C4—28no—
734C22×C4—44no—
735C22×C4—416no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—1116no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—228no—
748C22×C4—228no—
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—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—228no—
768C22×C4—4416no—
769C22×C4—444no—
770C22×C4—444no—
771C22×C4—444no—
772C22×C4—444no—
773C22×C4—444no—
774C22×C4—4416no—
775C22×C4—4416no—
776C22×C4#434114yes—
777C22×C4C2×C22⋊D1114yes—
778C22×C4C23×D1112yes—
779C22×C4C23×D1112yes—
780C22×C4C23×D1112yes—
781C22×C4C23×D1112yes—
782C4⋊C4—28no—
783C4⋊C4—228no—
784C4⋊C4—228no—
785C4⋊C4—228no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—228no—
792C22⋊C4—228no—
793C22⋊C4—228no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—444no—
797C22⋊C4—444no—
798C42—228no—
799C11C2×#254311yescharacteristic, complemented, Sylow
800C23—28no—
801C23—28no—
802C23—28no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—28no—
811C23—28no—
812C23—28no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23#66992116yes—
852C23C2×D4×D1114yes—
853C23C2×D4×D1112yes—
854C23C2×#434114yes—
855C23C2×#434112yes—
856C23C2×#434112yes—
857C23#6703712yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C22×C22⋊D1114yes—
861C23C22×C22⋊D1114yes—
862C23C22×C22⋊D1112yes—
863C23C24×D1111yescharacteristic
864D4—232no—
865D4—416no—
866D4—416no—
867D4—4416no—
868D4—4416no—
869D4—4416no—
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—416no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—228no—
889C2×C4—228no—
890C2×C4—228no—
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—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—4416no—
910C2×C4—4416no—
911C2×C4—4416no—
912C2×C4—444no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4—444no—
916C2×C4C2×#434114yes—
917C2×C4C22×C22⋊D1114yes—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—232no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—416no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—88no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—888no—
949C22#1062312714yes—
950C22#1062313214yes—
951C22#1062313614yes—
952C22#1062314914yes—
953C22C2×#6699218yes—
954C22C2×#6699214yes—
955C22#1062333714yes—
956C22#1062336014yes—
957C22C22×D4×D1111yescharacteristic
958C22C22×#434111yescharacteristic
959C22C22×#434111yescharacteristic
960C22C2×#6703711yescharacteristic
961C22C2×#41×D1111yescharacteristic
962C22C2×#6704211yescharacteristic
963C22C23×C22⋊D1111yescharacteristic
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—224no—
969C4—224no—
970C4—224no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—442no—
975C2—28no—
976C2—44no—
977C2—82no—
978C2—882no—
979C2#1307357418yesdirect product factor
980C2C22×#6699211yescharacteristic
981C2C2×#1062312711yescharacteristic
982C2C2×#1062313611yescharacteristic
983C2C2×#1062336011yescharacteristic
984C2C2×#1062333711yescharacteristic
985C2C2×#1062313211yescharacteristic
986C2C2×#1062314911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#66992C2semidirect
3. C22×D4×Dic11C2semidirect
4. #13073574C2direct (N × H)
5. C2×#10622597C2semidirect
6. C2×#10622565C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622571C2semidirect
15. C22×C11⋊#95C2semidirect
16. C22×C11×#121C2semidirect
28. C2×C11×#121C22semidirect
40. C2×#66992C22semidirect
41. C2×#66992C22semidirect
43. C2×D4×Dic11C22semidirect
52. #10622836C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
55. #10622826C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622603C22semidirect
66. #10622597C22semidirect
67. #10622574C22semidirect
68. #10622571C22semidirect
69. #10622565C22semidirect
70. #10622558C22semidirect
83. C22×D4×C11D4semidirect
115. C23×Dic11D4semidirect
217. C2×D4×C11C2×D4semidirect
281. C22×Dic11C2×D4semidirect
309. C22×#121D11semidirect
456. C2×#121C2×D11semidirect
576. C22×D4C22⋊D11semidirect
656. C2×C11#2543semidirect
721. C2×D4C2×C22⋊D11semidirect
799. C11C2×#2543semidirect
979. C2#13073574direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×D4×Dic112
#130735742
C2×#106225972
C2×#106225652
C2×#106225742
C2×#106228362
C2×#106225582
C2×#106226032
C2×#106228332
C2×#106228262
C2×#106225712
C22×C11⋊#952
C22×C11×#1212
C2×#254311