Finite Group Databasebeta

← C2×#13072362 #14921506

Subgroups — C2×#13072362 #14921506

Order 2816.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic, complemented
2#13072362C2116yesmaximal, direct product factor
3C2×#10622599C211yesmaximal, characteristic, complemented
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622557C211yesmaximal, characteristic, complemented
8C2×#10622591C211yesmaximal, characteristic, complemented
9C2×#10622833C211yesmaximal, characteristic, complemented
10C2×#10622833C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622556C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C2×C11×#121—28no—
25C2×C11×#121C2218yes—
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C2×D4×Dic11—28no—
39C2×D4×Dic11C2218yescomplemented
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44#10622835C2218yescomplemented
45#10622833C2218yescomplemented
46#10622833C2218yescomplemented
47#10622833C2218yescomplemented
48#10622833C2218yescomplemented
49#10622823C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2218yescomplemented
63#10622599C2218yescomplemented
64#10622591C2218yescomplemented
65#10622566C2218yescomplemented
66#10622565C2218yescomplemented
67#10622557C2218yescomplemented
68#10622556C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—42no—
80C22×D4×C11D418yes—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C23×C4×C11—24no—
85C23×C4×C11—24no—
86C23×C4×C11—42no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×Dic11—24no—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—42no—
98C23×Dic11—42no—
99C23×Dic11—42no—
100C23×Dic11—42no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2314yes—
109C23×Dic11C2314yes—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2314yes—
112C11×#121—232no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11—42no—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137D4×Dic11—232no—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—42no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2444—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
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×C11C2×D414yes—
177C24×C11C2×D414yes—
178C24×C11#4114yes—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—232no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11—28no—
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—44no—
193C2×D4×C11—416no—
194C2×D4×C11—416no—
195C2×D4×C11C2×D4116yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—28no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—28no—
208C22×C4×C11—44no—
209C22×C4×C11—416no—
210C22×C4×C11C2×D414yes—
211C22×C4×C11#4114yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×Dic11—28no—
217C22×Dic11—28no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—28no—
223C22×Dic11—28no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—28no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—44no—
248C22×Dic11—416no—
249C22×Dic11—416no—
250C22×Dic11—416no—
251C22×Dic11#4114yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C11×C4⋊C4—28no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—28no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—28no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270C22⋊Dic11—44no—
271C22⋊Dic11—44no—
272C4⋊Dic11—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275C4×Dic11—28no—
276C22×#121D1111yescharacteristic
277C22×C4×D4—111no—
278#2444—1116no—
279C2×#400—111no—
280C2×#397—111no—
281C2×#397—111no—
282C2×#394—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×#385—111no—
290C2×#381—111no—
291C22×#95—111no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11#123116yes—
330C23×C11C22×D414yes—
331C23×C11C22×D414yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4114yes—
334C23×C11C2×#4114yes—
335C23×C11C2×#4112yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4112yes—
338C23×C11C2×#4112yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11C2511yescharacteristic
342D4×C11—232no—
343D4×C11—416no—
344D4×C11—416no—
345C2×C4×C11—28no—
346C2×C4×C11—28no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—416no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D414yes—
361C2×C4×C11C2×#4114yes—
362C2×Dic11—28no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—416no—
387C2×Dic11—416no—
388C2×Dic11—416no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—44no—
392C2×Dic11—44no—
393C2×Dic11—44no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11C2×#4114yes—
397C23×D4C2×D1111yescharacteristic
398C23×D4C2×D1111yescharacteristic
399C23×D4C2×D1111yescharacteristic
400C24×C4—111no—
401C24×C4—111no—
402C24×C4—111no—
403C24×C4C2×D1111yescharacteristic
404C2×#121—28no—
405C2×#121C2×D1118yes—
406C2×C4×D4—118no—
407C2×C4×D4—228no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4C2×D1111yescharacteristic
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C22⋊C4C2×D1111yescharacteristic
423C22×C42—111no—
424#400—118no—
425#397—118no—
426#397—118no—
427#394—118no—
428#388—118no—
429#387—118no—
430#386—118no—
431#386—118no—
432#386—118no—
433#386—118no—
434#385—118no—
435#381—118no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—118no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—232no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—416no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—88no—
472C22×C11C2×#12318yes—
473C22×C11C2×#12314yes—
474C22×C11#52914yes—
475C22×C11#53814yes—
476C22×C11#54614yes—
477C22×C11#54614yes—
478C22×C11#55314yes—
479C22×C11#55314yes—
480C22×C11C23×D411yescharacteristic
481C22×C11C22×#4111yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C22×#4111yescharacteristic
484C22×C11C22×#4111yescharacteristic
485C22×C11C2×H(5,𝔽2)11yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C25C22×D1111yescharacteristic
500C25C22×D1111yescharacteristic
501C25C22×D1111yescharacteristic
502C22×D4—24no—
503C22×D4—24no—
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—42no—
510C22×D4C22⋊D1118yes—
511C22×D4C22×D1114yes—
512C22×D4C22×D1114yes—
513C22×D4C22×D1114yes—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—42no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—114no—
526C23×C4—114no—
527C23×C4—114no—
528C23×C4—224no—
529C23×C4—224no—
530C23×C4—224no—
531C23×C4—224no—
532C23×C4—224no—
533C23×C4—442no—
534C23×C4—442no—
535C23×C4—442no—
536C23×C4—442no—
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1114yes—
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542#121—232no—
543C4×D4—2232no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4—442no—
551C2×C4⋊C4C22×D1114yes—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4—442no—
572C2×C22⋊C4C22×D1114yes—
573C2×C22⋊C4C22×D1114yes—
574C2×C42—114no—
575C2×C42—224no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—114no—
586#95—114no—
587#95—114no—
588C2×C11—28no—
589C2×C11—44no—
590C2×C11—82no—
591C2×C11#244418yescomplemented
592C2×C11C22×#12311yescharacteristic
593C2×C11C2×#52911yescharacteristic
594C2×C11C2×#53811yescharacteristic
595C2×C11C2×#54611yescharacteristic
596C2×C11C2×#54611yescharacteristic
597C2×C11C2×#55311yescharacteristic
598C2×C11C2×#55311yescharacteristic
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24#434114yes—
617C24#434114yes—
618C24C2×C22⋊D1114yes—
619C24C2×C22⋊D1114yes—
620C24C23×D1112yes—
621C24C23×D1112yes—
622C24C23×D1112yes—
623C24C23×D1111yescharacteristic
624C2×D4—232no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—416no—
634C2×D4—416no—
635C2×D4C2×C22⋊D11116yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—44no—
649C22×C4—416no—
650C22×C4—114no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—228no—
660C22×C4—228no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—228no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—228no—
686C22×C4—228no—
687C22×C4—444no—
688C22×C4—444no—
689C22×C4—444no—
690C22×C4—444no—
691C22×C4—4416no—
692C22×C4—4416no—
693C22×C4—4416no—
694C22×C4#434114yes—
695C22×C4C2×C22⋊D1114yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—28no—
701C4⋊C4—228no—
702C4⋊C4—228no—
703C4⋊C4—444no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—228no—
707C22⋊C4—228no—
708C22⋊C4—228no—
709C22⋊C4—228no—
710C22⋊C4—444no—
711C22⋊C4—444no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C22⋊C4—444no—
715C42—228no—
716C11C2×#244411yescharacteristic, complemented, Sylow
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23#66988116yes—
755C23C2×#434114yes—
756C23C2×#434114yes—
757C23C2×#434112yes—
758C23C2×#434112yes—
759C23C2×#434112yes—
760C23#6703712yes—
761C23#41×D1112yes—
762C23#6704212yes—
763C23C22×C22⋊D1114yes—
764C23C22×C22⋊D1114yes—
765C23C22×C22⋊D1112yes—
766C23C24×D1111yescharacteristic
767D4—232no—
768D4—416no—
769D4—416no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—114no—
786C2×C4—228no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—4416no—
811C2×C4—4416no—
812C2×C4—4416no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4—444no—
817C2×C4—444no—
818C2×C4—444no—
819C2×C4—444no—
820C2×C4C2×#434114yes—
821C2×C4C22×C22⋊D1114yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—232no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—416no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—88no—
845C22#1062313114yes—
846C22#1062313214yes—
847C22#1062314814yes—
848C22#1062314914yes—
849C22C2×#6698818yes—
850C22C2×#6698814yes—
851C22#1062333714yes—
852C22#1062336014yes—
853C22C22×#434111yescharacteristic
854C22C22×#434111yescharacteristic
855C22C22×#434111yescharacteristic
856C22C2×#6703711yescharacteristic
857C22C2×#41×D1111yescharacteristic
858C22C2×#6704211yescharacteristic
859C22C23×C22⋊D1111yescharacteristic
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—224no—
865C4—442no—
866C4—442no—
867C4—442no—
868C4—442no—
869C4—442no—
870C4—442no—
871C4—442no—
872C2—28no—
873C2—44no—
874C2—82no—
875C2#1307236218yesdirect product factor
876C2C22×#6698811yescharacteristic
877C2C2×#1062313111yescharacteristic
878C2C2×#1062314811yescharacteristic
879C2C2×#1062336011yescharacteristic
880C2C2×#1062333711yescharacteristic
881C2C2×#1062313211yescharacteristic
882C2C2×#1062314911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2444
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. #13072362C2direct (N × H)
3. C2×#10622599C2semidirect
4. C2×#10622565C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622591C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622556C2semidirect
15. C22×C11⋊#95C2semidirect
39. C2×D4×Dic11C22semidirect
44. #10622835C22semidirect
45. #10622833C22semidirect
46. #10622833C22semidirect
47. #10622833C22semidirect
48. #10622833C22semidirect
49. #10622823C22semidirect
62. C2×C11⋊#95C22semidirect
63. #10622599C22semidirect
64. #10622591C22semidirect
65. #10622566C22semidirect
66. #10622565C22semidirect
67. #10622557C22semidirect
68. #10622556C22semidirect
591. C2×C11#2444semidirect
716. C11C2×#2444semidirect
875. C2#13072362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130723622
C2×#106225992
C2×#106225652
C2×#106225662
C2×#106228352
C2×#106225572
C2×#106225912
C2×#106228332
C2×#106228232
C2×#106225562
C22×C11⋊#952
C22×C11×#1212
C2×#244411