Finite Group Databasebeta

← C2×#13074390 #14920127

Subgroups — C2×#13074390 #14920127

Order 2816.

4378 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66935C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
3#13074390C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622287C211yesmaximal, characteristic, complemented
7C2×#10622285C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
38C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C2×#66935—28no—
45C2×#66935C2218yes—
46C2×C22⋊C4×D11—28no—
47C2×C22⋊C4×D11C2218yescomplemented
48C11×#397C2218yescomplemented
49C2×C11×#95C2211yescharacteristic, complemented
50C2×C11×#95C2211yescharacteristic, complemented
51C2×C11×#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57#10622604C2218yescomplemented
58#10622602C2218yescomplemented
59#10622574C2218yescomplemented
60#10622572C2218yescomplemented
61#10622568C2218yescomplemented
62#10622565C2218yescomplemented
63#10622288C2218yescomplemented
64#10622287C2218yescomplemented
65#10622285C2218yescomplemented
66#10622281C2218yescomplemented
67#10622278C2218yescomplemented
68#10622278C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11—24no—
71C24×D11—24no—
72C24×D11—42no—
73C24×D11—42no—
74C24×D11—42no—
75C24×D11—42no—
76C24×D11D418yes—
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—24no—
99C22×D44—24no—
100C22×D44—42no—
101C22×D44—42no—
102C22×D44C2314yes—
103C22×D44C2314yes—
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11—42no—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11C2314yes—
111C22×C4×D11C2314yes—
112C2×C11×C4⋊C4—42no—
113C2×C11×C4⋊C4C2314yescomplemented
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—42no—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yescomplemented
145C2×(C2×D11)⋊C4C2314yescomplemented
146C2×(C2×D11)⋊C4C2314yescomplemented
147C2×(C2×D11)⋊C4C2314yescomplemented
148C2×C4⋊Dic11—42no—
149C2×C4⋊Dic11C2314yescomplemented
150C2×Dic11⋊C4—42no—
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4C2314yescomplemented
153C2×Dic11⋊C4C2314yescomplemented
154#66935—232no—
155C22⋊C4×D11—232no—
156C11×#95C2314yescomplemented
157C11×#95C2314yescomplemented
158C11×#95C2314yescomplemented
159C11⋊#95C2314yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162C11⋊#95C2314yescomplemented
163C11⋊#95C2314yescomplemented
164C2×#2622—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11C2×D414yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—232no—
185C23×D11—28no—
186C23×D11—28no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—416no—
195C23×D11—416no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—44no—
200C23×D11—416no—
201C23×D11—416no—
202C23×D11—416no—
203C23×D11—416no—
204C23×D11C2×D414yes—
205C23×D11C2×D414yes—
206C23×D11C2×D4116yes—
207C23×D11#4114yes—
208C23×D11#4114yes—
209C23×D11C2412yes—
210C23×D11C2412yes—
211C23×D11C2412yes—
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×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—416no—
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×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—28no—
263C2×D44—28no—
264C2×D44—44no—
265C2×D44—44no—
266C2×D44—416no—
267C2×D44—416no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—44no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11—44no—
274C2×C4×D11—416no—
275C2×C4×D11—416no—
276C11×C4⋊C4—44no—
277C11×C22⋊C4—28no—
278C11×C22⋊C4—28no—
279C11×C22⋊C4—44no—
280C22⋊Dic11—28no—
281C22⋊Dic11—44no—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—28no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294C4⋊Dic11—44no—
295Dic11⋊C4—44no—
296Dic11⋊C4—44no—
297C22×#120—111no—
298C23×C22⋊C4—111no—
299#2622—1116no—
300C2×#397—111no—
301C2×#397—111no—
302C2×#397—111no—
303C2×#397D1111yescharacteristic, complemented
304C2×#394—111no—
305C2×#394—111no—
306C2×#394—111no—
307C2×#394—111no—
308C2×#386—111no—
309C2×#386—111no—
310C2×#385—111no—
311C2×#385—111no—
312C2×#379—111no—
313C23×C11—28no—
314C23×C11—28no—
315C23×C11—28no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11C22×D414yes—
327C23×C11C22×D412yes—
328C23×C11C2×#4112yes—
329C23×C11C2×#4112yes—
330C23×C11H(5,𝔽2)12yes—
331C23×C11H(5,𝔽2)12yes—
332C23×C11H(5,𝔽2)12yes—
333C23×C11H(5,𝔽2)12yes—
334C23×C11C2511yescharacteristic
335C22×D11—28no—
336C22×D11—28no—
337C22×D11—28no—
338C22×D11—28no—
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—232no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—416no—
363C22×D11—416no—
364C22×D11—4128no—
365C22×D11—416no—
366C22×D11—416no—
367C22×D11—416no—
368C22×D11—416no—
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#123116yes—
381C22×D11C22×D414yes—
382C22×D11C22×D414yes—
383C22×D11C2×#4114yes—
384C22×D11C2×#4114yes—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
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—22no—
402C2×C4×C11—22no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—44no—
407C2×C4×C11—44no—
408C2×C4×C11—44no—
409C22⋊D11—416no—
410C2×Dic11—22no—
411C2×Dic11—22no—
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—44no—
426C2×Dic11—44no—
427C2×Dic11—44no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430D44—416no—
431D44—416no—
432C4×D11—416no—
433C4×D11—416no—
434C26—111no—
435C23×D4—111no—
436C23×D4—111no—
437C23×D4—111no—
438C24×C4—111no—
439C24×C4—111no—
440C2×#120—118no—
441C2×#120—228no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—118no—
461C22×C22⋊C4—228no—
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4C2×D1111yescharacteristic
465#397—118no—
466#397—118no—
467#397—118no—
468#397C2×D1118yescomplemented
469#394—118no—
470#394—118no—
471#394—118no—
472#394—118no—
473#386—118no—
474#386—118no—
475#385—118no—
476#385—118no—
477#379—118no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95C2×D1111yescharacteristic, complemented
484C2×#95C2×D1111yescharacteristic, complemented
485C2×#95C2×D1111yescharacteristic, complemented
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—416no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11C2×#12314yes—
495C22×C11#53414yes—
496C22×C11#53414yes—
497C22×C11#53814yes—
498C22×C11#53814yes—
499C22×C11#53814yes—
500C22×C11#53814yes—
501C22×C11C23×D411yescharacteristic
502C22×C11C22×#4111yescharacteristic
503C22×C11C22×#4111yescharacteristic
504C22×C11C2×H(5,𝔽2)11yescharacteristic
505C22×C11C2×H(5,𝔽2)11yescharacteristic
506C22×C11C2×H(5,𝔽2)11yescharacteristic
507C22×C11C2×H(5,𝔽2)11yescharacteristic
508C2×D11—232no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—464no—
519C2×D11—416no—
520C2×D11—42no—
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—42no—
530C2×D11—42no—
531C2×D11—88no—
532C2×D11C2×#12318yes—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11—42no—
544C25—111no—
545C25—111no—
546C25—118no—
547C25—114no—
548C25—111no—
549C25—224no—
550C25—224no—
551C25—442no—
552C25—442no—
553C25—442no—
554C25—442no—
555C25C22×D1111yescharacteristic
556C22×D4—114no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—224no—
560C22×D4—224no—
561C22×D4—224no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—442no—
565C22×D4—442no—
566C22×D4—442no—
567C22×D4—442no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—114no—
574C23×C4—114no—
575C23×C4—224no—
576C23×C4—224no—
577C23×C4—442no—
578C23×C4—442no—
579C23×C4—442no—
580C23×C4—442no—
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1111yescharacteristic
587#120—2232no—
588C2×C4⋊C4—42no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—442no—
593C2×C4⋊C4—442no—
594C2×C4⋊C4—442no—
595C2×C4⋊C4C22×D1114yescomplemented
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—42no—
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—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—114no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—2232no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—224no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—442no—
622C2×C22⋊C4—442no—
623C2×C22⋊C4—442no—
624C2×C22⋊C4—442no—
625C2×C22⋊C4—442no—
626C2×C22⋊C4—442no—
627C2×C22⋊C4—442no—
628C2×C22⋊C4C22×D1114yes—
629C2×C22⋊C4C22×D1114yes—
630C2×C22⋊C4C22×D1114yes—
631#95—114no—
632#95—114no—
633#95—114no—
634#95—114no—
635#95—114no—
636#95C22×D1114yescomplemented
637#95C22×D1114yescomplemented
638#95C22×D1114yescomplemented
639C2×C11—44no—
640C2×C11#262218yescomplemented
641C2×C11C22×#12311yescharacteristic
642C2×C11C2×#53411yescharacteristic
643C2×C11C2×#53411yescharacteristic
644C2×C11C2×#53811yescharacteristic
645C2×C11C2×#53811yescharacteristic
646C2×C11C2×#53811yescharacteristic
647C2×C11C2×#53811yescharacteristic
648D11—28no—
649D11—44no—
650D11—82no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—114no—
658C24—114no—
659C24—114no—
660C24—112no—
661C24—114no—
662C24—112no—
663C24—1116no—
664C24—112no—
665C24—2232no—
666C24—228no—
667C24—228no—
668C24—222no—
669C24—222no—
670C24—222no—
671C24—222no—
672C24—222no—
673C24—222no—
674C24—222no—
675C24—222no—
676C24—222no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—4416no—
686C24—4416no—
687C24—444no—
688C24—444no—
689C24—444no—
690C24—444no—
691C24—4416no—
692C24—4416no—
693C24—4416no—
694C24—4416no—
695C24D4×D1114yes—
696C24C23×D1112yes—
697C24C23×D1111yescharacteristic
698C2×D4—228no—
699C2×D4—228no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—444no—
704C2×D4—444no—
705C2×D4—4416no—
706C2×D4—4416no—
707C2×D4—444no—
708C2×D4—444no—
709C2×D4—4416no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
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—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—228no—
734C22×C4—228no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—444no—
751C22×C4—444no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—4416no—
755C22×C4—4416no—
756C22×C4C23×D1112yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1112yes—
759C22×C4C23×D1112yes—
760C22×C4C23×D1112yes—
761C22×C4C23×D1112yes—
762C4⋊C4—44no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C4⋊C4—444no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—228no—
770C22⋊C4—228no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C22⋊C4—228no—
775C22⋊C4—228no—
776C22⋊C4—444no—
777C22⋊C4—444no—
778C22⋊C4—444no—
779C22⋊C4—444no—
780C22⋊C4—444no—
781C22⋊C4—444no—
782C22⋊C4—444no—
783C11C2×#262211yescharacteristic, complemented, Sylow
784C23—28no—
785C23—28no—
786C23—28no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—1116no—
798C23—114no—
799C23—114no—
800C23—114no—
801C23—114no—
802C23—2232no—
803C23—228no—
804C23—228no—
805C23—228no—
806C23—228no—
807C23—228no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—228no—
813C23—228no—
814C23—228no—
815C23—228no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—222no—
827C23—222no—
828C23—222no—
829C23—4416no—
830C23—4416no—
831C23—4416no—
832C23—4416no—
833C23—4416no—
834C23—4416no—
835C23—44128no—
836C23—444no—
837C23—444no—
838C23—444no—
839C23—444no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23C2×D4×D1114yes—
848C23C2×D4×D1112yes—
849C23#6703712yes—
850C23#41×D1112yes—
851C23#41×D1112yes—
852C23#6704212yes—
853C23#6704212yes—
854C23#6704212yes—
855C23C24×D1111yescharacteristic
856D4—4416no—
857D4—4416no—
858D4—4416no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
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—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
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—4416no—
899C2×C4—4416no—
900C2×C4—444no—
901C2×C4—444no—
902C2×C4—444no—
903C2×C4—444no—
904C2×C4—444no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—416no—
913C22—118no—
914C22—224no—
915C22—224no—
916C22—224no—
917C22—224no—
918C22—224no—
919C22—224no—
920C22—2232no—
921C22—224no—
922C22—224no—
923C22—224no—
924C22—4464no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—4416no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—888no—
938C22#1062313614yes—
939C22D11×#12314yes—
940C22#1062318414yes—
941C22#1062318814yes—
942C22#1062320914yes—
943C22#1062323514yes—
944C22#1062323514yes—
945C22C22×D4×D1111yescharacteristic
946C22C2×#6703711yescharacteristic
947C22C2×#41×D1111yescharacteristic
948C22C2×#41×D1111yescharacteristic
949C22C2×#6704211yescharacteristic
950C22C2×#6704211yescharacteristic
951C22C2×#6704211yescharacteristic
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—442no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4—442no—
963C2—44no—
964C2—228no—
965C2—444no—
966C2—882no—
967C2#1307439018yesdirect product factor
968C2C2×D11×#12311yescharacteristic
969C2C2×#1062313611yescharacteristic
970C2C2×#1062318411yescharacteristic
971C2C2×#1062320911yescharacteristic
972C2C2×#1062318811yescharacteristic
973C2C2×#1062323511yescharacteristic
974C2C2×#1062323511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66935C2
hypercenterC2×#397D11
hypocenterC11C2×#2622
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×D11C2semidirect
3. #13074390C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622287C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#397C2semidirect
23. C22×C11×C4⋊C4C22semidirect
37. C22×(C2×D11)⋊C4C22semidirect
38. C22×(C2×D11)⋊C4C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×C4⋊Dic11C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
47. C2×C22⋊C4×D11C22semidirect
48. C11×#397C22semidirect
49. C2×C11×#95C22semidirect
50. C2×C11×#95C22semidirect
51. C2×C11×#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. #10622604C22semidirect
58. #10622602C22semidirect
59. #10622574C22semidirect
60. #10622572C22semidirect
61. #10622568C22semidirect
62. #10622565C22semidirect
63. #10622288C22semidirect
64. #10622287C22semidirect
65. #10622285C22semidirect
66. #10622281C22semidirect
67. #10622278C22semidirect
68. #10622278C22semidirect
113. C2×C11×C4⋊C4C23semidirect
144. C2×(C2×D11)⋊C4C23semidirect
145. C2×(C2×D11)⋊C4C23semidirect
146. C2×(C2×D11)⋊C4C23semidirect
147. C2×(C2×D11)⋊C4C23semidirect
149. C2×C4⋊Dic11C23semidirect
152. C2×Dic11⋊C4C23semidirect
153. C2×Dic11⋊C4C23semidirect
156. C11×#95C23semidirect
157. C11×#95C23semidirect
158. C11×#95C23semidirect
159. C11⋊#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
162. C11⋊#95C23semidirect
163. C11⋊#95C23semidirect
303. C2×#397D11semidirect
445. C22×C4⋊C4C2×D11semidirect
468. #397C2×D11semidirect
483. C2×#95C2×D11semidirect
484. C2×#95C2×D11semidirect
485. C2×#95C2×D11semidirect
595. C2×C4⋊C4C22×D11semidirect
636. #95C22×D11semidirect
637. #95C22×D11semidirect
638. #95C22×D11semidirect
640. C2×C11#2622semidirect
783. C11C2×#2622semidirect
967. C2#13074390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669352
C22×C22⋊C4×D112
#130743902
C2×#106222882
C2×#106225652
C2×#106222872
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222782
C2×#106222812
C2×#106226022
C2×#106225682
C2×C11×#3972
C2×#262211