Finite Group Databasebeta

← C2×#13073581 #14923796

Subgroups — C2×#13073581 #14923796

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×#66948C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×C4×D44C211yesmaximal, characteristic, complemented
5#13073581C2116yesmaximal, direct product factor
6C2×#10622597C211yesmaximal, characteristic, complemented
7C2×#10622288C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C2×#66948—28no—
45C2×#66948C2218yescomplemented
46C2×#66937—28no—
47C2×#66937—28no—
48C2×#66937C2218yescomplemented
49C2×#66937C2218yescomplemented
50C2×C4×D44—28no—
51C2×C4×D44C2218yescomplemented
52C11×#388C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622597C2218yescomplemented
62#10622574C2218yescomplemented
63#10622573C2218yescomplemented
64#10622569C2218yescomplemented
65#10622569C2218yescomplemented
66#10622553C2218yescomplemented
67#10622288C2218yescomplemented
68#10622278C2218yescomplemented
69#10622278C2218yescomplemented
70D11×#95C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—24no—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44—24no—
104C22×D44—24no—
105C22×D44—42no—
106C22×D44D418yescomplemented
107C22×D44C2314yes—
108C22×D44C2314yes—
109C22×D44C2314yes—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—24no—
115C22×C4×D11—42no—
116C22×C4×D11—42no—
117C22×C4×D11—42no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11—42no—
121C22×C4×D11D418yescomplemented
122C22×C4×D11C2314yes—
123C22×C4×D11C2314yes—
124C22×C4×D11C2314yes—
125C22×C4×D11C2314yes—
126C2×C11×C4⋊C4—24no—
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4—24no—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C42×C11—24no—
135C2×C42×C11C2314yes—
136C2×C22⋊Dic11—42no—
137C2×C22⋊Dic11C2314yes—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yes—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160#66948—232no—
161#66937—232no—
162#66937—232no—
163C4×D44—232no—
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×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×D11C2×D414yes—
200C23×D11C2×D414yes—
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—22no—
220C22×C4×C11—22no—
221C22×C4×C11C2×D414yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11#4114yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—416no—
240C2×C22⋊D11—416no—
241C2×C22⋊D11—416no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
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×Dic11C2×D414yes—
256C22×Dic11#4114yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C2×D44—232no—
263C2×D44—28no—
264C2×D44—28no—
265C2×D44—28no—
266C2×D44—28no—
267C2×D44—28no—
268C2×D44—28no—
269C2×D44—28no—
270C2×D44—44no—
271C2×D44—416no—
272C2×D44—416no—
273C2×D44C2×D4116yescomplemented
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—416no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—416no—
287C2×C4×D11—416no—
288C2×C4×D11—416no—
289C2×C4×D11C2×D4116yescomplemented
290C11×C4⋊C4—28no—
291C11×C22⋊C4—28no—
292C11×C22⋊C4—28no—
293C11×C22⋊C4—28no—
294C42×C11—28no—
295C22⋊Dic11—44no—
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—
304C4⋊Dic11—28no—
305Dic11⋊C4—28no—
306Dic11⋊C4—28no—
307C22×#121—111no—
308C22×#121—111no—
309C22×#121—111no—
310C22×C4×D4—111no—
311#2543—1116no—
312C2×#398—111no—
313C2×#397—111no—
314C2×#394—111no—
315C2×#392—111no—
316C2×#388—111no—
317C2×#388D1111yescharacteristic, complemented
318C2×#386—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#386—111no—
322C22×#95—111no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11C22×D412yes—
338C23×C11C22×D412yes—
339C23×C11C2×#4112yes—
340C23×C11C2×#4112yes—
341C23×C11C2×#4112yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11C2511yescharacteristic
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—28no—
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—28no—
356C22×D11—28no—
357C22×D11—28no—
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—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#121116yes—
383C22×D11C22×D414yes—
384C22×D11C22×D414yes—
385C22×D11C22×D414yes—
386C22×D11C2×#4114yes—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
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—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11—44no—
408C2×C4×C11C22×D414yes—
409C2×C4×C11C22×D414yes—
410C2×C4×C11C2×#4114yes—
411C22⋊D11—416no—
412C22⋊D11—416no—
413C22⋊D11—416no—
414C2×Dic11—28no—
415C2×Dic11—28no—
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×Dic11C22×D414yes—
433C2×Dic11C2×#4114yes—
434D44—232no—
435D44—416no—
436D44—416no—
437C4×D11—416no—
438C4×D11—416no—
439C4×D11—416no—
440C4×D11—416no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C23×D4—111no—
446C23×D4—111no—
447C24×C4—111no—
448C24×C4—111no—
449C24×C4—111no—
450C24×C4—111no—
451C2×#121—118no—
452C2×#121—118no—
453C2×#121—118no—
454C2×#121—228no—
455C2×#121—228no—
456C2×#121—228no—
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⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C22⋊C4C2×D1111yescharacteristic
475C22×C42C2×D1111yescharacteristic
476#398—118no—
477#397—118no—
478#394—118no—
479#392—118no—
480#388—118no—
481#388C2×D1118yescomplemented
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—118no—
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—88no—
503C22×C11C2×#12114yes—
504C22×C11#53214yes—
505C22×C11#53414yes—
506C22×C11#54614yes—
507C22×C11#54614yes—
508C22×C11#55314yes—
509C22×C11#55314yes—
510C22×C11C23×D411yescharacteristic
511C22×C11C23×D411yescharacteristic
512C22×C11C22×#4111yescharacteristic
513C22×C11C22×#4111yescharacteristic
514C22×C11C22×#4111yescharacteristic
515C22×C11C2×H(5,𝔽2)11yescharacteristic
516C22×C11C2×H(5,𝔽2)11yescharacteristic
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—232no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—416no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—88no—
540C2×D11C2×#12118yes—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—24no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—42no—
547Dic11—24no—
548Dic11—24no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552C25—111no—
553C25—111no—
554C25—111no—
555C25C22×D1111yescharacteristic
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—118no—
560C22×D4—114no—
561C22×D4—114no—
562C22×D4—114no—
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—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—442no—
577C22×D4—442no—
578C22×D4—442no—
579C22×D4—442no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—118no—
583C23×C4—114no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—114no—
588C23×C4—114no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—224no—
595C23×C4—442no—
596C23×C4—442no—
597C23×C4—442no—
598C23×C4—442no—
599C23×C4—442no—
600C23×C4—442no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#121—2232no—
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—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—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—442no—
639C2×C22⋊C4—442no—
640C2×C22⋊C4C22×D1114yes—
641C2×C22⋊C4C22×D1114yes—
642C2×C22⋊C4C22×D1114yes—
643C2×C42—24no—
644C2×C42C22×D1114yes—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651#95C22×D1114yes—
652#95C22×D1114yes—
653C2×C11—82no—
654C2×C11#254318yescomplemented
655C2×C11C22×#12111yescharacteristic
656C2×C11C2×#53211yescharacteristic
657C2×C11C2×#53411yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#55311yescharacteristic
661C2×C11C2×#55311yescharacteristic
662D11—28no—
663D11—44no—
664D11—82no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—114no—
673C24—114no—
674C24—114no—
675C24—112no—
676C24—114no—
677C24—112no—
678C24—112no—
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—
693C24—222no—
694C24—222no—
695C24—222no—
696C24C23×D1112yes—
697C24C23×D1111yescharacteristic
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—228no—
712C2×D4—228no—
713C2×D4—444no—
714C2×D4—4416no—
715C2×D4—4416no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—444no—
719C2×D4—4416no—
720C2×D4—4416no—
721C2×D4—4416no—
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—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—1116no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—228no—
746C22×C4—228no—
747C22×C4—228no—
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—222no—
760C22×C4—222no—
761C22×C4—228no—
762C22×C4—228no—
763C22×C4—4416no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—4416no—
771C22×C4—4416no—
772C22×C4—4416no—
773C22×C4#433914yes—
774C22×C4D4×D1114yes—
775C22×C4D4×D1114yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
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—28no—
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—28no—
799C11C2×#254311yescharacteristic, complemented, Sylow
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—1116no—
815C23—114no—
816C23—114no—
817C23—114no—
818C23—114no—
819C23—228no—
820C23—228no—
821C23—228no—
822C23—228no—
823C23—228no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—228no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23—444no—
853C23—444no—
854C23—444no—
855C23—444no—
856C23C2×#433912yes—
857C23C2×D4×D1112yes—
858C23C2×D4×D1112yes—
859C23#41×D1112yes—
860C23#41×D1112yes—
861C23#6704212yes—
862C23#6704212yes—
863C23C24×D1111yescharacteristic
864D4—2232no—
865D4—4416no—
866D4—4416no—
867D4—4416no—
868D4—4416no—
869D4—4416no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—28no—
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—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—228no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—228no—
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—4416no—
909C2×C4—4416no—
910C2×C4—4416no—
911C2×C4—4416no—
912C2×C4—444no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4C2×#433914yes—
916C2×C4C2×D4×D1114yes—
917C2×C4C2×D4×D1114yes—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—88no—
926C22—118no—
927C22—224no—
928C22—224no—
929C22—224no—
930C22—224no—
931C22—2232no—
932C22—224no—
933C22—224no—
934C22—224no—
935C22—224no—
936C22—224no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—4416no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—888no—
950C22#1062306114yes—
951C22#1062307914yes—
952C22#1062308114yes—
953C22D11×#12114yes—
954C22#1062318414yes—
955C22#1062320714yes—
956C22#1062324014yes—
957C22C22×#433911yescharacteristic
958C22C22×D4×D1111yescharacteristic
959C22C22×D4×D1111yescharacteristic
960C22C2×#41×D1111yescharacteristic
961C22C2×#41×D1111yescharacteristic
962C22C2×#6704211yescharacteristic
963C22C2×#6704211yescharacteristic
964C4—24no—
965C4—24no—
966C4—24no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—224no—
971C4—224no—
972C4—442no—
973C4—442no—
974C4—442no—
975C2—82no—
976C2—228no—
977C2—444no—
978C2—882no—
979C2#1307358118yesdirect product factor
980C2C2×D11×#12111yescharacteristic
981C2C2×#1062307911yescharacteristic
982C2C2×#1062318411yescharacteristic
983C2C2×#1062320711yescharacteristic
984C2C2×#1062308111yescharacteristic
985C2C2×#1062306111yescharacteristic
986C2C2×#1062324011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
hypercenterC2×#388D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66937C2semidirect
3. C22×#66937C2semidirect
4. C22×C4×D44C2semidirect
5. #13073581C2direct (N × H)
6. C2×#10622597C2semidirect
7. C2×#10622288C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622569C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#388C2semidirect
45. C2×#66948C22semidirect
48. C2×#66937C22semidirect
49. C2×#66937C22semidirect
51. C2×C4×D44C22semidirect
52. C11×#388C22semidirect
61. #10622597C22semidirect
62. #10622574C22semidirect
63. #10622573C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
66. #10622553C22semidirect
67. #10622288C22semidirect
68. #10622278C22semidirect
69. #10622278C22semidirect
70. D11×#95C22semidirect
106. C22×D44D4semidirect
121. C22×C4×D11D4semidirect
273. C2×D44C2×D4semidirect
289. C2×C4×D11C2×D4semidirect
317. C2×#388D11semidirect
481. #388C2×D11semidirect
654. C2×C11#2543semidirect
799. C11C2×#2543semidirect
979. C2#13073581direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669372
C22×C4×D442
#130735812
C2×#106225972
C2×#106222882
C2×#106225742
C2×#106225732
C2×#106225532
C2×#106222782
C2×#106225692
C2×D11×#952
C2×C11×#3882
C2×#254311