Finite Group Databasebeta

← C2×#13074388 #14920123

Subgroups — C2×#13074388 #14920123

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×#66990C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
3#13074388C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622835C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622568C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4C2211yescharacteristic, complemented
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic, complemented
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C2×#66990—28no—
34C2×#66990C2218yes—
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, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C2×C22⋊C4×D11—28no—
47C2×C22⋊C4×D11C2218yescomplemented
48C11×#394C2218yescomplemented
49C2×C11×#95C2211yescharacteristic, complemented
50#10622835C2218yescomplemented
51C2×C11⋊#95C2211yescharacteristic, complemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58#10622606C2218yescomplemented
59#10622602C2218yescomplemented
60#10622574C2218yescomplemented
61#10622572C2218yescomplemented
62#10622569C2218yescomplemented
63#10622569C2218yescomplemented
64#10622568C2218yescomplemented
65#10622566C2218yescomplemented
66#10622565C2218yescomplemented
67#10622288C2218yescomplemented
68#10622281C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11—24no—
72C24×D11—24no—
73C24×D11—42no—
74C24×D11—42no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11D418yes—
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C24×D11C2314yes—
81C22×D4×C11—24no—
82C22×D4×C11—42no—
83C22×D4×C11—42no—
84C22×D4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
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—42no—
116C2×C11×C22⋊C4—42no—
117C2×C11×C22⋊C4—42no—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yescomplemented
121C2×C11×C22⋊C4C2314yescomplemented
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yescomplemented
131C2×C22⋊Dic11C2314yescomplemented
132#66990—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)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
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×C4⋊Dic11—42no—
150C2×C4⋊Dic11C2314yescomplemented
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4—42no—
153C2×Dic11⋊C4C2314yescomplemented
154C2×Dic11⋊C4C2314yescomplemented
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×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11C2×D414yes—
179C24×C11C2412yes—
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—232no—
193C23×D11—28no—
194C23×D11—28no—
195C23×D11—416no—
196C23×D11—416no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—44no—
200C23×D11—44no—
201C23×D11—416no—
202C23×D11—416no—
203C23×D11—416no—
204C23×D11—416no—
205C23×D11C2×D414yes—
206C23×D11C2×D414yes—
207C23×D11C2×D4116yes—
208C23×D11#4114yes—
209C23×D11#4114yes—
210C23×D11C2412yes—
211C23×D11C2412yes—
212C2×D4×C11—28no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—416no—
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×C11—22no—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
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—416no—
243C2×C22⋊D11—416no—
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—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
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—44no—
279C11×C22⋊C4—44no—
280C11×C22⋊C4—44no—
281C22⋊Dic11—28no—
282C22⋊Dic11—28no—
283C22⋊Dic11—44no—
284C22⋊Dic11—44no—
285C22⋊Dic11—44no—
286(C2×D11)⋊C4—28no—
287(C2×D11)⋊C4—28no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
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×#397—111no—
304C2×#394—111no—
305C2×#394—111no—
306C2×#394—111no—
307C2×#394D1111yescharacteristic, complemented
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—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—44no—
330C23×C11—44no—
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×C11C22×D414yes—
341C23×C11C22×D412yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4112yes—
344C23×C11H(5,𝔽2)12yes—
345C23×C11H(5,𝔽2)12yes—
346C23×C11H(5,𝔽2)12yes—
347C23×C11H(5,𝔽2)12yes—
348C23×C11C2511yescharacteristic
349C22×D11—28no—
350C22×D11—28no—
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—28no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—232no—
369C22×D11—416no—
370C22×D11—416no—
371C22×D11—4128no—
372C22×D11—416no—
373C22×D11—416no—
374C22×D11—416no—
375C22×D11—416no—
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—
385D4×C11—416no—
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—44no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C22⋊D11—416no—
407C22⋊D11—416no—
408C2×Dic11—22no—
409C2×Dic11—22no—
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—22no—
426C2×Dic11—44no—
427C2×Dic11—44no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C4×D11—416no—
433C4×D11—416no—
434C26—111no—
435C23×D4—111no—
436C23×D4—111no—
437C23×D4C2×D1111yescharacteristic
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—118no—
460C22×C22⋊C4—228no—
461C22×C22⋊C4C2×D1111yescharacteristic
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic, complemented
464C22×C22⋊C4C2×D1111yescharacteristic, complemented
465#397—118no—
466#397—118no—
467#397—118no—
468#397—118no—
469#394—118no—
470#394—118no—
471#394—118no—
472#394C2×D1118yescomplemented
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×#95—111no—
484C2×#95—111no—
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×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—88no—
502C22×C11C2×#12314yes—
503C22×C11#53414yes—
504C22×C11#53414yes—
505C22×C11#53814yes—
506C22×C11#53814yes—
507C22×C11#53814yes—
508C22×C11#53814yes—
509C22×C11C23×D411yescharacteristic
510C22×C11C22×#4111yescharacteristic
511C22×C11C22×#4111yescharacteristic
512C22×C11C2×H(5,𝔽2)11yescharacteristic
513C22×C11C2×H(5,𝔽2)11yescharacteristic
514C22×C11C2×H(5,𝔽2)11yescharacteristic
515C22×C11C2×H(5,𝔽2)11yescharacteristic
516C2×D11—232no—
517C2×D11—24no—
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—464no—
527C2×D11—416no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11C2×#12318yes—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536C4×C11—42no—
537C4×C11—42no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11—42no—
544C25—111no—
545C25—111no—
546C25—118no—
547C25—114no—
548C25—224no—
549C25—224no—
550C25—442no—
551C25—442no—
552C25—442no—
553C25—442no—
554C25C22×D1111yescharacteristic
555C25C22×D1111yescharacteristic
556C22×D4—24no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—224no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
565C22×D4—442no—
566C22×D4—442no—
567C22×D4C22×D1114yes—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—114no—
575C23×C4—114no—
576C23×C4—224no—
577C23×C4—224no—
578C23×C4—442no—
579C23×C4—442no—
580C23×C4—442no—
581C23×C4—442no—
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—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
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—224no—
622C2×C22⋊C4—442no—
623C2×C22⋊C4—442no—
624C2×C22⋊C4—442no—
625C2×C22⋊C4—442no—
626C2×C22⋊C4—442no—
627C2×C22⋊C4C22×D1114yes—
628C2×C22⋊C4C22×D1114yes—
629C2×C22⋊C4C22×D1114yescomplemented
630C2×C22⋊C4C22×D1114yescomplemented
631#95—114no—
632#95—114no—
633#95—114no—
634#95—114no—
635#95—114no—
636#95—114no—
637#95—114no—
638#95C22×D1114yescomplemented
639C2×C11—44no—
640C2×C11—82no—
641C2×C11#262218yescomplemented
642C2×C11C22×#12311yescharacteristic
643C2×C11C2×#53411yescharacteristic
644C2×C11C2×#53411yescharacteristic
645C2×C11C2×#53811yescharacteristic
646C2×C11C2×#53811yescharacteristic
647C2×C11C2×#53811yescharacteristic
648C2×C11C2×#53811yescharacteristic
649D11—28no—
650D11—44no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—114no—
665C24—114no—
666C24—114no—
667C24—112no—
668C24—114no—
669C24—112no—
670C24—1116no—
671C24—2232no—
672C24—228no—
673C24—228no—
674C24—222no—
675C24—222no—
676C24—222no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—4416no—
685C24—4416no—
686C24—444no—
687C24—444no—
688C24—444no—
689C24—444no—
690C24—4416no—
691C24—4416no—
692C24—4416no—
693C24—4416no—
694C24D4×D1114yes—
695C24C23×D1112yes—
696C24C23×D1112yes—
697C24C23×D1111yescharacteristic
698C2×D4—28no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—416no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—4416no—
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—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—228no—
732C22×C4—228no—
733C22×C4—222no—
734C22×C4—222no—
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—222no—
751C22×C4—444no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—444no—
755C22×C4—4416no—
756C22×C4—4416no—
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—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—228no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C22⋊C4—228no—
775C22⋊C4—228no—
776C22⋊C4—228no—
777C22⋊C4—228no—
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—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—1116no—
812C23—114no—
813C23—114no—
814C23—114no—
815C23—114no—
816C23—2232no—
817C23—228no—
818C23—228no—
819C23—228no—
820C23—228no—
821C23—228no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—4416no—
837C23—4416no—
838C23—4416no—
839C23—4416no—
840C23—4416no—
841C23—4416no—
842C23—44128no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23C2×D4×D1114yes—
848C23C2×D4×D1112yes—
849C23#6703712yes—
850C23#6703712yes—
851C23#6703712yes—
852C23#41×D1112yes—
853C23#41×D1112yes—
854C23#6704212yes—
855C23C24×D1111yescharacteristic
856D4—416no—
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—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
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—4416no—
898C2×C4—4416no—
899C2×C4—444no—
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—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—88no—
921C22—118no—
922C22—224no—
923C22—224no—
924C22—224no—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—2232no—
929C22—224no—
930C22—224no—
931C22—224no—
932C22—4464no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—4416no—
938C22#1062312014yes—
939C22#1062313614yes—
940C22#1062314414yes—
941C22#1062314414yes—
942C22D11×#12314yes—
943C22#1062318814yes—
944C22#1062320914yes—
945C22C22×D4×D1111yescharacteristic
946C22C2×#6703711yescharacteristic
947C22C2×#6703711yescharacteristic
948C22C2×#6703711yescharacteristic
949C22C2×#41×D1111yescharacteristic
950C22C2×#41×D1111yescharacteristic
951C22C2×#6704211yescharacteristic
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—442no—
958C4—442no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4—442no—
963C2—44no—
964C2—82no—
965C2—228no—
966C2—444no—
967C2#1307438818yesdirect product factor
968C2C2×D11×#12311yescharacteristic
969C2C2×#1062313611yescharacteristic
970C2C2×#1062312011yescharacteristic
971C2C2×#1062314411yescharacteristic
972C2C2×#1062314411yescharacteristic
973C2C2×#1062320911yescharacteristic
974C2C2×#1062318811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66990C2
hypercenterC2×#394D11
hypocenterC11C2×#2622
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×D11C2semidirect
3. #13074388C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622566C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622835C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622568C2semidirect
16. C2×C11×#394C2semidirect
23. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
27. C22×C11×C22⋊C4C22semidirect
31. C22×C22⋊Dic11C22semidirect
32. C22×C22⋊Dic11C22semidirect
43. C22×C4⋊Dic11C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
47. C2×C22⋊C4×D11C22semidirect
48. C11×#394C22semidirect
49. C2×C11×#95C22semidirect
50. #10622835C22semidirect
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. C2×C11⋊#95C22semidirect
58. #10622606C22semidirect
59. #10622602C22semidirect
60. #10622574C22semidirect
61. #10622572C22semidirect
62. #10622569C22semidirect
63. #10622569C22semidirect
64. #10622568C22semidirect
65. #10622566C22semidirect
66. #10622565C22semidirect
67. #10622288C22semidirect
68. #10622281C22semidirect
113. C2×C11×C4⋊C4C23semidirect
120. C2×C11×C22⋊C4C23semidirect
121. C2×C11×C22⋊C4C23semidirect
130. C2×C22⋊Dic11C23semidirect
131. C2×C22⋊Dic11C23semidirect
150. C2×C4⋊Dic11C23semidirect
153. C2×Dic11⋊C4C23semidirect
154. 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
307. C2×#394D11semidirect
445. C22×C4⋊C4C2×D11semidirect
463. C22×C22⋊C4C2×D11semidirect
464. C22×C22⋊C4C2×D11semidirect
472. #394C2×D11semidirect
485. C2×#95C2×D11semidirect
595. C2×C4⋊C4C22×D11semidirect
629. C2×C22⋊C4C22×D11semidirect
630. C2×C22⋊C4C22×D11semidirect
638. #95C22×D11semidirect
641. C2×C11#2622semidirect
783. C11C2×#2622semidirect
967. C2#13074388direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669902
C22×C22⋊C4×D112
#130743882
C2×#106222882
C2×#106225652
C2×#106226062
C2×#106225662
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106225692
C2×#106222812
C2×#106226022
C2×#106225682
C2×C11×#3942
C2×#262211