Finite Group Databasebeta

← #14770495

Subgroups — #14770495

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069415C212yesmaximal, complemented
4#13069411C211yesmaximal, characteristic, complemented
5#13069411C212yesmaximal, complemented
6#13069411C211yesmaximal, characteristic, complemented
7#13068600C212yesmaximal, complemented
8#13068596C211yesmaximal, characteristic, complemented
9#13068382C212yesmaximal, complemented
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, 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×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×C11×#117C2212yes—
24C22×C42×C11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622637—24no—
33Q8×C11⋊C8—24no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×#66867C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40C2×C4×C11⋊C8C2212yes—
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622162C2212yes—
43#10622162C2211yescharacteristic
44#10622162C2211yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11C2×C411yescharacteristic
47C22×D4×C11C2×C412yes—
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×C11D414yes—
59C4×Q8×C11D414yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C11×#117—24no—
65C11×#117—24no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C4⋊C4C2×C412yes—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C412yes—
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×C11C2311yescharacteristic
83C2×C42×C11C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)—24no—
93C22⋊(C11⋊C8)—24no—
94C22⋊(C11⋊C8)—42no—
95C22⋊(C11⋊C8)—42no—
96C22⋊(C11⋊C8)—42no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)—24no—
99C4⋊(C11⋊C8)—24no—
100C4⋊(C11⋊C8)—22no—
101#66867—24no—
102C4×C11⋊C8—22no—
103C4×C11⋊C8—24no—
104C4×C11⋊C8—22no—
105#22531—111nomaximal, Sylow
106C24×C11C22×C412yes—
107C24×C11C22×C411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C22⋊C414yes—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—42no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—41no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4C22⋊C414yes—
149C11×C4⋊C4C22⋊C418yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C42×C11C2×D414yes—
162C42×C11C2×D414yes—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8#4112yes—
180C2×C11⋊C8#4112yes—
181C2×#529D1111yescharacteristic
182C2×#446—111no—
183C2×C8×Q8—111no—
184#1955—112no—
185#1954—111no—
186#1954—111no—
187#1954—112no—
188#1798—112no—
189#1797—111no—
190#1750—112no—
191C4×C22⋊C8—111no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11#13112yes—
206C23×C11C23×C411yescharacteristic
207Q8×C11—28no—
208D4×C11—48no—
209D4×C11—44no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—44no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—44no—
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C2×C22⋊C414yes—
240C2×C4×C11C2×C22⋊C414yes—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11#13112yes—
243C2×C4×C11#13112yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C11⋊C8—22no—
251C11⋊C8—22no—
252C11⋊C8—41no—
253C11⋊C8—42no—
254C11⋊C8—41no—
255C11⋊C8—42no—
256#529—24no—
257#529—24no—
258C2×#126Dic1112yes—
259C2×#125Dic1111yescharacteristic
260C2×#124Dic1111yescharacteristic
261C2×#123Dic1112yes—
262C2×C22⋊Q8Dic1111yescharacteristic
263C2×#121Dic1111yescharacteristic
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4C2×D1111yescharacteristic
266C2×C4×D4C2×D1112yes—
267C2×#117C2×D1112yes—
268C22×C42C2×D1111yescharacteristic
269#446—224no—
270C8×Q8—224no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—111no—
273C2×C4⋊C8—112no—
274C2×C4⋊C8—112no—
275C2×C22⋊C8—111no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—111no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×#97—112no—
283C2×C4×C8—111no—
284C2×C4×C8—112no—
285C2×C4×C8—111no—
286#336—112no—
287#336—111no—
288#336—111no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11C4×#4111yescharacteristic
305C22×C11#52011yescharacteristic
306C22×C11C2×#13111yescharacteristic
307C22×C11C2×#13111yescharacteristic
308C22×C11C2×#13111yescharacteristic
309C22×C11#56811yescharacteristic
310C4×C11—24no—
311C4×C11—22no—
312C4×C11—24no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11#40814yes—
318C4×C11#54811yescharacteristic
319C4×C11#54811yescharacteristic
320C4×C11#55011yescharacteristic
321C4×C11#55011yescharacteristic
322C22×Q8C2×Dic1111yescharacteristic
323C22×D4C2×Dic1111yescharacteristic
324C22×D4C2×Dic1112yes—
325C23×C4C2×Dic1111yescharacteristic
326C23×C4C2×Dic1111yescharacteristic
327C23×C4C22×D1112yes—
328C23×C4C22×D1111yescharacteristic
329C22×C8—111no—
330C22×C8—111no—
331C22×C8—112no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8—112no—
335#126—28no—
336#125—24no—
337#124—24no—
338#123—28no—
339C22⋊Q8—24no—
340#121—24no—
341C4×Q8C22⋊D1114yes—
342C4×Q8C22⋊D1114yes—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—24no—
346C4×D4—24no—
347#117—24no—
348#117—24no—
349C2×C4⋊C4C2×Dic1112yes—
350C2×C4⋊C4C2×Dic1112yes—
351C2×C4⋊C4C2×Dic1111yescharacteristic
352C2×C4⋊C4C2×Dic1112yes—
353C2×C4⋊C4C2×Dic1111yescharacteristic
354C2×C4⋊C4C2×Dic1112yes—
355C2×C22⋊C4C2×Dic1112yes—
356C2×C22⋊C4C2×Dic1112yes—
357C2×C22⋊C4C2×Dic1112yes—
358C2×C22⋊C4C2×Dic1112yes—
359C2×C22⋊C4C2×Dic1112yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42C2×Dic1111yescharacteristic
363C2×C42C2×Dic1111yescharacteristic
364C2×C42C22×D1111yescharacteristic
365C2×C42C22×D1112yes—
366C2×C42C22×D1111yescharacteristic
367C4⋊C8—222no—
368C4⋊C8—224no—
369C4⋊C8—222no—
370C4⋊C8—224no—
371C22⋊C8—222no—
372C22⋊C8—224no—
373C22⋊C8—224no—
374C22⋊C8—222no—
375C22⋊C8—442no—
376C22⋊C8—442no—
377C22⋊C8—442no—
378#97—224no—
379C4×C8—222no—
380C4×C8—224no—
381C4×C8—222no—
382C2×C11—42no—
383C2×C11—82no—
384C2×C11#234111yescharacteristic
385C2×C11C2×#40811yescharacteristic
386C2×C11#288011yescharacteristic
387C2×C11#296611yescharacteristic
388C2×C11#296911yescharacteristic
389C2×C11#299311yescharacteristic
390C2×C11#299411yescharacteristic
391C24C22×Dic1112yes—
392C24C22×Dic1111yescharacteristic
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8C22⋊Dic1114yes—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—42no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—41no—
420C22×C4C22×Dic1111yescharacteristic
421C22×C4C22×Dic1111yescharacteristic
422C22×C4C22×Dic1111yescharacteristic
423C22×C4C22×Dic1112yes—
424C22×C4C22×Dic1111yescharacteristic
425C22×C4C22×Dic1112yes—
426C22×C4C22×Dic1112yes—
427C22×C4C22×Dic1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—112no—
430C2×C8—112no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—221no—
444C2×C8—222no—
445C2×C8—221no—
446C2×C8—222no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4C22⋊Dic1114yes—
452C4⋊C4C22⋊Dic1118yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—21no—
462C42C2×C22⋊D1112yes—
463C42C2×C22⋊D1112yes—
464C42C2×C22⋊D1114yes—
465C42C2×C22⋊D1114yes—
466C11#2253111yescharacteristic, complemented, Sylow
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23#6700112yes—
481C23C23×Dic1111yescharacteristic
482Q8—28no—
483D4—48no—
484D4—44no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4#6700112yes—
514C2×C4#6700112yes—
515C2×C4C2×C22⋊Dic1112yes—
516C2×C4C2×C22⋊Dic1114yes—
517C2×C4C2×C22⋊Dic1114yes—
518C2×C4C2×C22⋊Dic1112yes—
519C2×C4#41×D1111yescharacteristic
520C2×C4#41×D1111yescharacteristic
521C2×C4#6704211yescharacteristic
522C2×C4#6704311yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—222no—
526C8—222no—
527C8—442no—
528C8—441no—
529C8—441no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22C2×#6700111yescharacteristic
546C22C2×#6700111yescharacteristic
547C22C2×#6700111yescharacteristic
548C22#1062335011yescharacteristic
549C22#41×Dic1111yescharacteristic
550C22#1062335811yescharacteristic
551C22C22×C22⋊Dic1111yescharacteristic
552C4—24no—
553C4—22no—
554C4—24no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—42no—
559C4#1062284714yes—
560C4#1062336211yescharacteristic
561C4#1062336211yescharacteristic
562C4#1062336511yescharacteristic
563C4#1062336511yescharacteristic
564C2—42no—
565C2—82no—
566C2#1307145711yescharacteristic
567C2C2×#1062284711yescharacteristic
568C2#1307706511yescharacteristic
569C2#1307759211yescharacteristic
570C2#1307762111yescharacteristic
571C2#1307776511yescharacteristic
572C2#1307777611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#529C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#22531
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×#10622637C2semidirect
2. C2×Q8×C11⋊C8C2semidirect
3. #13069415C2semidirect
4. #13069411C2semidirect
5. #13069411C2semidirect
6. #13069411C2semidirect
7. #13068600C2semidirect
8. #13068596C2semidirect
9. #13068382C2semidirect
10. C4×C22⋊(C11⋊C8)C2semidirect
466. C11#22531semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
C2×Q8×C11⋊C82
#130694152
#130694112
#130686002
#130685962
#130683822
C4×C22⋊(C11⋊C8)2
C2×C11×#5292
#2253111