Finite Group Databasebeta

← #14769886

Subgroups — #14769886

Order 2816.

1196 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069553C211yesmaximal, characteristic, complemented
4#13069553C211yesmaximal, characteristic, complemented
5#13068914C212yesmaximal, complemented
6#13068909C212yesmaximal, complemented
7#13068687C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10#13068313C212yesmaximal, complemented
11C2×C11×#529C211yesmaximal, characteristic
12C11×#529—24no—
13C11×#529—24no—
14C2×C11×#126C412yes—
15C2×C11×#125C411yescharacteristic
16C2×C11×#124C411yescharacteristic
17C2×C11×#123C412yes—
18C2×C11×C22⋊Q8C411yescharacteristic
19C2×C11×#121C411yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×C42×C11C2211yescharacteristic
25C22×#4318C2212yes—
26C23×C11⋊C8C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622625—24no—
33D4×C11⋊C8—24no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622162C2211yescharacteristic
39#10622162C2212yes—
40#10622162C2212yes—
41#10622162C2212yes—
42#10622162C2211yescharacteristic
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11C2×C412yes—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C11×#126—28no—
53C11×#125—24no—
54C11×#124—24no—
55C11×#123—28no—
56C11×C22⋊Q8—24no—
57C11×#121—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11D414yes—
63C4×D4×C11D414yes—
64C11×#117—24no—
65C11×#117—24no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C4⋊C4C2×C412yes—
68C2×C11×C4⋊C4C2×C412yes—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C412yes—
73C2×C11×C22⋊C4C2×C412yes—
74C2×C11×C22⋊C4C2×C412yes—
75C2×C11×C22⋊C4C2×C412yes—
76C2×C11×C22⋊C4C2×C412yes—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11C2×C411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2312yes—
83C2×C42×C11C2311yescharacteristic
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—42no—
87C22×C11⋊C8—24no—
88C22×C11⋊C8—24no—
89C22×C11⋊C8—42no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22⋊(C11⋊C8)—24no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)—42no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)—22no—
103C4×C11⋊C8—22no—
104C4×C11⋊C8—22no—
105#22474—111nomaximal, Sylow
106C24×C11C22×C412yes—
107C24×C11C22×C411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—42no—
116C2×D4×C11C22⋊C414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2411yescharacteristic
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4C22⋊C414yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4C22⋊C418yes—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163#4318—48no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—48no—
181C2×C11⋊C8#4112yes—
182C2×C11⋊C8#4112yes—
183C2×#529D1111yescharacteristic
184C2×#436—111no—
185C2×C8×D4—111no—
186#1984—111no—
187#1984—111no—
188#1870—112no—
189#1869—112no—
190#1818—112no—
191#1797—111no—
192C4×C22⋊C8—111no—
193#1729—112no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11C2×C22⋊C414yes—
207C23×C11#13112yes—
208C23×C11C23×C411yescharacteristic
209Q8×C11—44no—
210D4×C11—28no—
211D4×C11—48no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—44no—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C2×C22⋊C414yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11#13112yes—
245C2×C4×C11#13112yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C11⋊C8—22no—
253C11⋊C8—22no—
254C11⋊C8—42no—
255C11⋊C8—42no—
256C11⋊C8—41no—
257C11⋊C8—41no—
258C22×M16—112no—
259C23×C8—112no—
260#529—24no—
261#529—24no—
262C2×#126Dic1112yes—
263C2×#125Dic1111yescharacteristic
264C2×#124Dic1111yescharacteristic
265C2×#123Dic1112yes—
266C2×C22⋊Q8Dic1111yescharacteristic
267C2×#121Dic1111yescharacteristic
268C2×C4×Q8C2×D1111yescharacteristic
269C2×C4×D4C2×D1112yes—
270C2×C4×D4C2×D1111yescharacteristic
271C2×#117C2×D1112yes—
272C22×C42C2×D1111yescharacteristic
273#436—224no—
274C8×D4—224no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283C2×C4×C8—111no—
284#336—112no—
285#336—111no—
286#336—112no—
287#336—112no—
288#336—112no—
289#336—112no—
290#336—111no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11C4×#4111yescharacteristic
307C22×C11#52011yescharacteristic
308C22×C11C2×#13111yescharacteristic
309C22×C11C2×#13111yescharacteristic
310C22×C11C2×#13111yescharacteristic
311C22×C11#56811yescharacteristic
312C4×C11—24no—
313C4×C11—22no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11#40814yes—
320C4×C11#54611yescharacteristic
321C4×C11#54611yescharacteristic
322C4×C11#54711yescharacteristic
323C4×C11#54711yescharacteristic
324C22×Q8C2×Dic1111yescharacteristic
325C22×D4C2×Dic1112yes—
326C22×D4C2×Dic1111yescharacteristic
327C23×C4C2×Dic1111yescharacteristic
328C23×C4C2×Dic1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1112yes—
331C2×M16—224no—
332C2×M16—224no—
333C2×M16—442no—
334C22×C8—111no—
335C22×C8—111no—
336C22×C8—112no—
337C22×C8—112no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—224no—
341C22×C8—224no—
342C22×C8—442no—
343#126—28no—
344#125—24no—
345#124—24no—
346#123—28no—
347C22⋊Q8—24no—
348#121—24no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4C22⋊D1114yes—
354C4×D4C22⋊D1114yes—
355#117—24no—
356#117—24no—
357C2×C4⋊C4C2×Dic1112yes—
358C2×C4⋊C4C2×Dic1112yes—
359C2×C4⋊C4C2×Dic1112yes—
360C2×C4⋊C4C2×Dic1111yescharacteristic
361C2×C4⋊C4C2×Dic1112yes—
362C2×C4⋊C4C2×Dic1111yescharacteristic
363C2×C22⋊C4C2×Dic1112yes—
364C2×C22⋊C4C2×Dic1112yes—
365C2×C22⋊C4C2×Dic1112yes—
366C2×C22⋊C4C2×Dic1112yes—
367C2×C22⋊C4C2×Dic1112yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42C2×Dic1111yescharacteristic
371C2×C42C2×Dic1111yescharacteristic
372C2×C42C22×D1111yescharacteristic
373C2×C42C22×D1112yes—
374C2×C42C22×D1111yescharacteristic
375C4⋊C8—222no—
376C4⋊C8—222no—
377C22⋊C8—222no—
378C22⋊C8—222no—
379C22⋊C8—224no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—222no—
383C4×C8—222no—
384C2×C11—44no—
385C2×C11—42no—
386C2×C11#233911yescharacteristic
387C2×C11C2×#40811yescharacteristic
388C2×C11#288011yescharacteristic
389C2×C11#296611yescharacteristic
390C2×C11#296911yescharacteristic
391C2×C11#299311yescharacteristic
392C2×C11#299411yescharacteristic
393C24C22×Dic1111yescharacteristic
394C24C22×Dic1112yes—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4C22⋊Dic1114yes—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—41no—
420C22×C4C22×Dic1111yescharacteristic
421C22×C4C22×Dic1111yescharacteristic
422C22×C4C22×Dic1112yes—
423C22×C4C22×Dic1112yes—
424C22×C4C22×Dic1111yescharacteristic
425C22×C4C22×Dic1111yescharacteristic
426C22×C4C22×Dic1112yes—
427C22×C4C22×Dic1111yescharacteristic
428C22×C4C2×C22⋊D1114yes—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C23×D1111yescharacteristic
431M16—448no—
432C2×C8—112no—
433C2×C8—112no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—448no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4C22⋊Dic1114yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4C22⋊Dic1118yes—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—21no—
466C42—22no—
467C42—22no—
468C42C2×C22⋊D1112yes—
469C42C2×C22⋊D1112yes—
470C11#2247411yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—22no—
478C23—22no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—21no—
483C23#6700112yes—
484C23C2×C22⋊Dic1114yes—
485C23C23×Dic1111yescharacteristic
486Q8—44no—
487D4—28no—
488D4—48no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—44no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4#6700112yes—
519C2×C4#6700112yes—
520C2×C4C2×C22⋊Dic1112yes—
521C2×C4C2×C22⋊Dic1114yes—
522C2×C4C2×C22⋊Dic1112yes—
523C2×C4#41×D1111yescharacteristic
524C2×C4#41×D1111yescharacteristic
525C2×C4#6704211yescharacteristic
526C2×C4#6704311yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—222no—
530C8—222no—
531C8—441no—
532C8—441no—
533C8—442no—
534C8—442no—
535C22—22no—
536C22—24no—
537C22—22no—
538C22—24no—
539C22—24no—
540C22—22no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22—41no—
546C22—42no—
547C22—41no—
548C22—42no—
549C22C2×#6700111yescharacteristic
550C22C2×#6700111yescharacteristic
551C22C2×#6700111yescharacteristic
552C22#1062335011yescharacteristic
553C22#41×Dic1111yescharacteristic
554C22#1062335811yescharacteristic
555C22C22×C22⋊Dic1111yescharacteristic
556C4—22no—
557C4—24no—
558C4—41no—
559C4—42no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4#1062284714yes—
564C4#1062335511yescharacteristic
565C4#1062335511yescharacteristic
566C4#1062336011yescharacteristic
567C4#1062336011yescharacteristic
568C2—42no—
569C2—44no—
570C2#1307144611yescharacteristic
571C2C2×#1062284711yescharacteristic
572C2#1307706511yescharacteristic
573C2#1307759211yescharacteristic
574C2#1307762111yescharacteristic
575C2#1307776511yescharacteristic
576C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#529C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#22474
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×D4×C11⋊C8C2semidirect
3. #13069553C2semidirect
4. #13069553C2semidirect
5. #13068914C2semidirect
6. #13068909C2semidirect
7. #13068687C2semidirect
8. #13068596C2semidirect
9. C4×C22⋊(C11⋊C8)C2semidirect
10. #13068313C2semidirect
470. C11#22474semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×D4×C11⋊C82
#130695532
#130689142
#130689092
#130686872
#130685962
C4×C22⋊(C11⋊C8)2
#130683132
C2×C11×#5292
#2247411