Finite Group Databasebeta

← C2×#13072514 #14921292

Subgroups — C2×#13072514 #14921292

Order 2816.

4282 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×C4×D44C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13072514C2116yesmaximal, direct product factor
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622546C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622563C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yescomplemented
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
44C22×C4⋊Dic11C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66936—28no—
49C2×#66936C2218yescomplemented
50C2×(C22⋊D11)⋊C4—28no—
51C2×(C22⋊D11)⋊C4C2218yescomplemented
52C2×C4×D44—28no—
53C2×C4×D44C2218yescomplemented
54C11×#390C2218yescomplemented
55#10622836C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622607C2218yescomplemented
63#10622603C2218yescomplemented
64#10622573C2218yescomplemented
65#10622573C2218yescomplemented
66#10622569C2218yescomplemented
67#10622569C2218yescomplemented
68#10622564C2218yescomplemented
69#10622563C2218yescomplemented
70#10622546C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2314yes—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C2×C11×C4⋊C4—42no—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C42×C11—24no—
133C2×C42×C11C2314yes—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—24no—
136C2×C22⋊Dic11—42no—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140#66992—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4D418yescomplemented
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×C4⋊Dic11—24no—
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yes—
156C2×C4⋊Dic11C2314yes—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4D418yescomplemented
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11C2314yes—
163#66936—232no—
164(C22⋊D11)⋊C4—232no—
165C4×D44—232no—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2456—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#4114yes—
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×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11C2×D414yes—
203C23×D11#4114yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
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×C11C2×D414yes—
223C22×C4×C11C2×D414yes—
224C22×C4×C11#4114yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11—416no—
246C22×Dic11—28no—
247C22×Dic11—28no—
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×Dic11—22no—
263C22×Dic11—44no—
264C22×Dic11—416no—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D414yes—
267C22×Dic11C2×D414yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—232no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—416no—
285C2×C4×D11—416no—
286C11×C4⋊C4—44no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C42×C11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4C2×D4116yescomplemented
301C4⋊Dic11—28no—
302C4⋊Dic11—28no—
303Dic11⋊C4—28no—
304Dic11⋊C4C2×D4116yescomplemented
305C4×Dic11—28no—
306C22×#123—111no—
307C22×#121—111no—
308C22×C4×D4—111no—
309C22×C4×D4—111no—
310#2456—1116no—
311C2×#396—111no—
312C2×#392—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390D1111yescharacteristic, complemented
316C2×#388—111no—
317C2×#388—111no—
318C2×#387—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
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×D412yes—
350C23×C11C22×D412yes—
351C23×C11C2×#4114yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11C2511yescharacteristic
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11C22×D414yes—
385C22×D11C2×#4114yes—
386D4×C11—416no—
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—44no—
403C2×C4×C11—44no—
404C2×C4×C11C22×D414yes—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C2×#4114yes—
407C22⋊D11—232no—
408C22⋊D11—416no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C2×Dic11—28no—
412C2×Dic11—28no—
413C2×Dic11—28no—
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—416no—
430C2×Dic11—44no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C22×D414yes—
436D44—232no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4—111no—
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—228no—
452C2×C4×D4—118no—
453C2×C4×D4—118no—
454C2×C4×D4—228no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4C2×D1111yescharacteristic
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42C2×D1111yescharacteristic
476#396—118no—
477#392—118no—
478#392—118no—
479#392—118no—
480#390C2×D1118yescomplemented
481#388—118no—
482#388—118no—
483#387—118no—
484#386—118no—
485#386—118no—
486#385—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—88no—
509C22×C11#52514yes—
510C22×C11#52514yes—
511C22×C11#53814yes—
512C22×C11D4214yes—
513C22×C11#54614yes—
514C22×C11#55014yes—
515C22×C11#55314yes—
516C22×C11C23×D411yescharacteristic
517C22×C11C23×D411yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—416no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—42no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—114no—
562C22×D4—224no—
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—442no—
574C22×D4—442no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4C22×D1114yes—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—114no—
585C23×C4—114no—
586C23×C4—114no—
587C23×C4—224no—
588C23×C4—224no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603C4×D4—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—42no—
606C2×C4⋊C4—118no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4C22×D1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—118no—
620C2×C22⋊C4—114no—
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—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—442no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—24no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42C22×D1114yes—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#245618yescomplemented
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#52511yescharacteristic
656C2×C11C2×#53811yescharacteristic
657C2×C11C2×D4211yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#55011yescharacteristic
660C2×C11C2×#55311yescharacteristic
661D11—44no—
662D11—44no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—114no—
677C24—114no—
678C24—112no—
679C24—112no—
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#433914yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—44no—
699C2×D4—416no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—2232no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—2232no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—4416no—
718C2×D4—4416no—
719C2×D4—4416no—
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—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—114no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—228no—
742C22×C4—228no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—222no—
746C22×C4—222no—
747C22×C4—222no—
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—228no—
761C22×C4—228no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—4416no—
765C22×C4—4416no—
766C22×C4—444no—
767C22×C4—4416no—
768C22×C4D4×D1114yes—
769C22×C4D4×D1114yes—
770C22×C4#434114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—44no—
777C4⋊C4—1116no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—228no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—1116no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C22⋊C4—444no—
794C42—28no—
795C42—228no—
796C11C2×#245611yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—114no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—228no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×#433914yes—
853C23C2×#433912yes—
854C23C2×D4×D1112yes—
855C23C2×D4×D1112yes—
856C23C2×#434112yes—
857C23#6703712yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C24×D1111yescharacteristic
861D4—416no—
862D4—2232no—
863D4—2232no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—22no—
871C2×C4—22no—
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—44no—
883C2×C4—44no—
884C2×C4—114no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4—228no—
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—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—4416no—
906C2×C4—4416no—
907C2×C4—4416no—
908C2×C4—444no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4C2×D4×D1114yes—
912C2×C4C2×D4×D1114yes—
913C2×C4C2×#434114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—416no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—88no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—224no—
934C22—224no—
935C22—224no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—4416no—
941C22—4416no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22#1062302114yes—
947C22#1062307814yes—
948C22#1062309614yes—
949C22#1062313714yes—
950C22#1062314014yes—
951C22#1062320914yes—
952C22#1062324914yes—
953C22C22×#433911yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×D4×D1111yescharacteristic
956C22C22×#434111yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#6704211yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—42no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—444no—
974C2—444no—
975C2#1307251418yesdirect product factor
976C2C2×#1062307811yescharacteristic
977C2C2×#1062313711yescharacteristic
978C2C2×#1062320911yescharacteristic
979C2C2×#1062314011yescharacteristic
980C2C2×#1062302111yescharacteristic
981C2C2×#1062324911yescharacteristic
982C2C2×#1062309611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
hypercenterC2×#390D11
hypocenterC11C2×#2456
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66992C2semidirect
3. C22×C4×D44C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13072514C2direct (N × H)
6. C2×#10622607C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622546C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622563C2semidirect
16. C2×C11×#390C2semidirect
36. C2×#66992C22semidirect
49. C2×#66936C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×C4×D44C22semidirect
54. C11×#390C22semidirect
55. #10622836C22semidirect
62. #10622607C22semidirect
63. #10622603C22semidirect
64. #10622573C22semidirect
65. #10622573C22semidirect
66. #10622569C22semidirect
67. #10622569C22semidirect
68. #10622564C22semidirect
69. #10622563C22semidirect
70. #10622546C22semidirect
146. C2×(C2×D11)⋊C4D4semidirect
158. C2×Dic11⋊C4D4semidirect
300. (C2×D11)⋊C4C2×D4semidirect
304. Dic11⋊C4C2×D4semidirect
315. C2×#390D11semidirect
480. #390C2×D11semidirect
653. C2×C11#2456semidirect
796. C11C2×#2456semidirect
975. C2#13072514direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669922
C22×C4×D442
C22×(C22⋊D11)⋊C42
#130725142
C2×#106226072
C2×#106225732
C2×#106228362
C2×#106225642
C2×#106226032
C2×#106225462
C2×#106225692
C2×#106225632
C2×C11×#3902
C2×#245611