Finite Group Databasebeta

← C2×#13076622 #14959915

Subgroups — C2×#13076622 #14959915

Order 2816.

3322 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3#13076622C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622835C211yesmaximal, characteristic, complemented
12C2×#10622835C211yesmaximal, characteristic, complemented
13C2×#10622836C211yesmaximal, characteristic, complemented
14C2×#10622836C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yescomplemented
37C2×#66988—28no—
38C2×#66988C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C11×#392C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52#10622836C2218yescomplemented
53#10622836C2218yescomplemented
54#10622835C2218yescomplemented
55#10622835C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622574C2218yescomplemented
62#10622572C2218yescomplemented
63#10622572C2218yescomplemented
64#10622562C2218yescomplemented
65#10622561C2218yescomplemented
66#10622555C2218yescomplemented
67#10622289C2218yescomplemented
68#10622271C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—42no—
76C22×D4×C11—42no—
77C22×D4×C11—42no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11—42no—
81C22×D4×C11—42no—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C22×D4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C23×Dic11—42no—
102C23×Dic11—42no—
103C23×Dic11D418yescomplemented
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2314yes—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4—42no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66992—232no—
135#66988—232no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—42no—
138C2×(C2×D11)⋊C4—42no—
139C2×(C2×D11)⋊C4—42no—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×C4⋊Dic11—42no—
145C2×C4⋊Dic11C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—42no—
150C2×Dic11⋊C4—42no—
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2813—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
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×C11C2×D414yes—
186C24×C11C2412yes—
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×D11C2412yes—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11—416no—
208C2×D4×C11—416no—
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×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—416no—
236C2×C22⋊D11—416no—
237C2×C22⋊D11—416no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
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×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—416no—
258C22×Dic11—44no—
259C22×Dic11—44no—
260C22×Dic11C2×D414yes—
261C22×Dic11C2×D414yes—
262C22×Dic11C2×D4116yescomplemented
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C11×C22⋊C4—44no—
271C11×C22⋊C4—44no—
272C11×C22⋊C4—44no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—28no—
277C22⋊Dic11—44no—
278C22⋊Dic11—44no—
279C22⋊Dic11—44no—
280C22⋊Dic11—44no—
281(C2×D11)⋊C4—28no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4—44no—
284(C2×D11)⋊C4—44no—
285C4⋊Dic11—44no—
286Dic11⋊C4—28no—
287Dic11⋊C4—28no—
288Dic11⋊C4—28no—
289Dic11⋊C4—44no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292C22×#123—111no—
293C22×#121—111no—
294#2813—1116no—
295C2×#400—111no—
296C2×#399—111no—
297C2×#396—111no—
298C2×#396—111no—
299C2×#394—111no—
300C2×#394—111no—
301C2×#394—111no—
302C2×#394—111no—
303C2×#394—111no—
304C2×#392—111no—
305C2×#392—111no—
306C2×#392D1111yescharacteristic, complemented
307C2×#380—111no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
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×C11—44no—
336C23×C11—44no—
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×C11—44no—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11H(5,𝔽2)12yes—
352C23×C11H(5,𝔽2)12yes—
353C23×C11H(5,𝔽2)12yes—
354C23×C11H(5,𝔽2)12yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C112−1+412yes—
357C23×C11C2511yescharacteristic
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372D4×C11—416no—
373D4×C11—416no—
374D4×C11—416no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C22⋊D11—416no—
392C22⋊D11—416no—
393C22⋊D11—416no—
394C2×Dic11—28no—
395C2×Dic11—28no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—416no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11C22×D414yes—
422C2×Dic11C22×D414yes—
423C23×D4—111no—
424C23×D4—111no—
425C23×D4—111no—
426C23×D4C2×D1111yescharacteristic
427C23×D4C2×D1111yescharacteristic
428C23×D4C2×D1111yescharacteristic
429C24×C4—111no—
430C2×#123—118no—
431C2×#123—228no—
432C2×#121—118no—
433C2×#121—228no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456#400—118no—
457#399—118no—
458#396—118no—
459#396—118no—
460#394—118no—
461#394—118no—
462#394—118no—
463#394—118no—
464#394—118no—
465#392—118no—
466#392—118no—
467#392C2×D1118yescomplemented
468#380—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95C2×D1111yescharacteristic
475C22×C11—24no—
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—416no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—88no—
498C22×C11—88no—
499C22×C11#53414yes—
500C22×C11#53514yes—
501C22×C11#53714yes—
502C22×C11#56014yes—
503C22×C11#56014yes—
504C22×C11#56214yes—
505C22×C11#56214yes—
506C22×C11C23×D411yescharacteristic
507C22×C11C2×H(5,𝔽2)11yescharacteristic
508C22×C11C2×H(5,𝔽2)11yescharacteristic
509C22×C11C2×H(5,𝔽2)11yescharacteristic
510C22×C11C2×H(5,𝔽2)11yescharacteristic
511C22×C11C2×H(5,𝔽2)11yescharacteristic
512C22×C11C2×2−1+411yescharacteristic
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—88no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525Dic11—24no—
526Dic11—24no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532C25—111no—
533C25C22×D1111yescharacteristic
534C25C22×D1111yescharacteristic
535C25C22×D1111yescharacteristic
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—42no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C22×D4—42no—
545C22×D4—114no—
546C22×D4—114no—
547C22×D4—114no—
548C22×D4—224no—
549C22×D4—224no—
550C22×D4—442no—
551C22×D4—442no—
552C22×D4—442no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4—442no—
557C22×D4C22×D1114yes—
558C22×D4C22×D1114yes—
559C22×D4C22×D1114yes—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—118no—
563C23×C4—114no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—442no—
570C23×C4—442no—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575#123—2232no—
576#121—2232no—
577C2×C4⋊C4—114no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—224no—
585C2×C4⋊C4—224no—
586C2×C4⋊C4—224no—
587C2×C4⋊C4—442no—
588C2×C4⋊C4—442no—
589C2×C4⋊C4—442no—
590C2×C4⋊C4—442no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—224no—
611C2×C22⋊C4—442no—
612C2×C22⋊C4—442no—
613C2×C22⋊C4—442no—
614C2×C22⋊C4—442no—
615C2×C22⋊C4—442no—
616C2×C22⋊C4—442no—
617C2×C22⋊C4—442no—
618C2×C22⋊C4C22×D1114yes—
619C2×C22⋊C4C22×D1114yes—
620C2×C22⋊C4C22×D1114yes—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95C22×D1114yes—
627C2×C11—44no—
628C2×C11—82no—
629C2×C11—82no—
630C2×C11#281318yescomplemented
631C2×C11C2×#53411yescharacteristic
632C2×C11C2×#53511yescharacteristic
633C2×C11C2×#53711yescharacteristic
634C2×C11C2×#56011yescharacteristic
635C2×C11C2×#56011yescharacteristic
636C2×C11C2×#56211yescharacteristic
637C2×C11C2×#56211yescharacteristic
638D11—82no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—112no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24D4×D1114yes—
668C24C23×D1112yes—
669C24C23×D1112yes—
670C24C23×D1112yes—
671C24C23×D1111yescharacteristic
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—416no—
682C2×D4—416no—
683C2×D4—416no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—444no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—4416no—
694C2×D4—4416no—
695C2×D4—4416no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—1116no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—4416no—
738C22×C4—444no—
739C22×C4—444no—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C4⋊C4—228no—
745C4⋊C4—228no—
746C4⋊C4—228no—
747C4⋊C4—444no—
748C4⋊C4—444no—
749C4⋊C4—444no—
750C4⋊C4—444no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—228no—
755C22⋊C4—228no—
756C22⋊C4—228no—
757C22⋊C4—228no—
758C22⋊C4—228no—
759C22⋊C4—444no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C11C2×#281311yescharacteristic, complemented, Sylow
767C23—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—444no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23C2×D4×D1114yes—
823C23C2×D4×D1112yes—
824C23#6703712yes—
825C23#6703712yes—
826C23#6703712yes—
827C23#6703712yes—
828C23#6703712yes—
829C23#6704312yes—
830C23C24×D1111yescharacteristic
831D4—416no—
832D4—416no—
833D4—416no—
834D4—4416no—
835D4—4416no—
836D4—4416no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—114no—
854C2×C4—114no—
855C2×C4—228no—
856C2×C4—228no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—4416no—
877C2×C4—444no—
878C2×C4—444no—
879C2×C4—444no—
880C2×C4—444no—
881C2×C4—444no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—416no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—88no—
905C22—88no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—888no—
914C22#1062312014yes—
915C22#1062312314yes—
916C22#1062312614yes—
917C22#1062312814yes—
918C22#1062315214yes—
919C22#1062315214yes—
920C22#1062325114yes—
921C22C22×D4×D1111yescharacteristic
922C22C2×#6703711yescharacteristic
923C22C2×#6703711yescharacteristic
924C22C2×#6703711yescharacteristic
925C22C2×#6703711yescharacteristic
926C22C2×#6703711yescharacteristic
927C22C2×#6704311yescharacteristic
928C4—42no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—224no—
933C4—224no—
934C4—442no—
935C4—442no—
936C4—442no—
937C4—442no—
938C4—442no—
939C2—44no—
940C2—82no—
941C2—82no—
942C2—882no—
943C2#1307662218yesdirect product factor
944C2C2×#1062312011yescharacteristic
945C2C2×#1062312311yescharacteristic
946C2C2×#1062312811yescharacteristic
947C2C2×#1062325111yescharacteristic
948C2C2×#1062312611yescharacteristic
949C2C2×#1062315211yescharacteristic
950C2C2×#1062315211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×#66992C2semidirect
3. #13076622C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622835C2semidirect
12. C2×#10622835C2semidirect
13. C2×#10622836C2semidirect
14. C2×#10622836C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#392C2semidirect
36. C2×#66992C22semidirect
38. C2×#66988C22semidirect
50. C11×#392C22semidirect
52. #10622836C22semidirect
53. #10622836C22semidirect
54. #10622835C22semidirect
55. #10622835C22semidirect
61. #10622574C22semidirect
62. #10622572C22semidirect
63. #10622572C22semidirect
64. #10622562C22semidirect
65. #10622561C22semidirect
66. #10622555C22semidirect
67. #10622289C22semidirect
68. #10622271C22semidirect
103. C23×Dic11D4semidirect
262. C22×Dic11C2×D4semidirect
306. C2×#392D11semidirect
467. #392C2×D11semidirect
630. C2×C11#2813semidirect
766. C11C2×#2813semidirect
943. C2#13076622direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×#669922
#130766222
C2×#106222712
C2×#106225622
C2×#106222892
C2×#106225612
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106225552
C2×C11×#3922
C2×#281311