Finite Group Databasebeta

← #14680452

Subgroups — #14680452

Order 2816.

1610 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66929C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13066870C212yesmaximal, complemented
4#13066866C212yesmaximal, complemented
5#13066862C212yesmaximal
6#13066858C212yesmaximal
7#13066852C212yesmaximal
8#13066851C212yesmaximal, complemented
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C22×C11×C4⋊C4C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2214yes—
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C2×#66929—24no—
22C2×#66929—24no—
23C2×#66929C418yescomplemented
24C11×#382—24no—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C4×C4⋊Dic11—24no—
32C24×D11C2311yescharacteristic
33C23×C4×C11C2314yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2311yescharacteristic
38C23×Dic11C2311yescharacteristic
39C23×Dic11C2311yescharacteristic
40C23×Dic11C2314yes—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4—44no—
43C2×C42×C11C2×C414yes—
44C2×C42×C11D414yes—
45C2×C42×C11D414yes—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—28no—
53C2×(C2×D11)⋊C4—44no—
54C2×(C2×D11)⋊C4—44no—
55C2×(C2×D11)⋊C4C2×C414yes—
56C2×(C2×D11)⋊C4C2×C414yes—
57C2×(C2×D11)⋊C4C2×C414yes—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11—28no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4C2×C414yes—
67C2×Dic11⋊C4C2×C414yes—
68C2×Dic11⋊C4C2×C414yes—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—44no—
71#66929—232no—
72C11×#95—24no—
73C11×#95—24no—
74C11⋊#95—24no—
75C11⋊#95—28no—
76C11⋊#95—44no—
77C11⋊#95—44no—
78#14291—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C23×D11—21no—
81C23×D11—21no—
82C23×D11—24no—
83C23×D11—22no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11—22no—
87C23×D11C22×C412yes—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×Dic11—24no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—24no—
121C22×Dic11—24no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11C22×C412yes—
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129C22×Dic11#4118yes—
130C11×C4⋊C4—48no—
131C42×C11C22⋊C4116yescomplemented
132(C2×D11)⋊C4—28no—
133(C2×D11)⋊C4—28no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—416no—
136C4⋊Dic11—216no—
137Dic11⋊C4—28no—
138Dic11⋊C4—28no—
139Dic11⋊C4—28no—
140C4×Dic11—48no—
141C22×#126—111no—
142C2×#382D1111yescharacteristic, complemented
143C2×C4×C4⋊C4—111no—
144#1441—112no—
145#1441—112no—
146#1439—112no—
147#1439—112no—
148#1437—112no—
149#1436—112no—
150C23×C11C23×C411yescharacteristic
151C23×C11C22×D411yescharacteristic
152C23×C11C22×D411yescharacteristic
153C23×C11C2×#4114yes—
154C23×C11H(5,𝔽2)12yes—
155C23×C11H(5,𝔽2)12yes—
156C23×C112−1+412yes—
157C23×C112−1+412yes—
158C22×D11—22no—
159C22×D11—24no—
160C22×D11—24no—
161C22×D11—24no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—44no—
171C22×D11—44no—
172C22×D11—44no—
173C22×D11—44no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—44no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11C2×C22⋊C414yes—
193C2×C4×C11C2×C22⋊C414yes—
194C2×C4×C11C2×C22⋊C414yes—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—28no—
202C2×Dic11—28no—
203C2×Dic11—28no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—44no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—44no—
213C2×Dic11—42no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×#126—118no—
217C2×#126—224no—
218C2×#126—224no—
219C22×C4⋊C4—111no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—111no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4C2×D1112yes—
224C22×C22⋊C4—111no—
225C22×C22⋊C4—111no—
226C22×C22⋊C4—111no—
227C22×C22⋊C4—114no—
228C22×C42—112no—
229C22×C42C2×D1111yescharacteristic
230#382—24no—
231C4×C4⋊C4—224no—
232C2×#95—114no—
233C2×#95—112no—
234C2×#95—114no—
235C2×#95—114no—
236C2×#95C2×D1112yes—
237C2×#95C2×D1112yes—
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11C4×#4112yes—
240C22×C11#52012yes—
241C22×C11#52012yes—
242C22×C11#52512yes—
243C22×C11#53212yes—
244C22×C11#53511yescharacteristic
245C22×C11#53511yescharacteristic
246C22×C11#53611yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11#53712yes—
249C22×C11#53712yes—
250C22×C11#53814yes—
251C22×C11#53914yes—
252C22×C11#54114yes—
253C22×C11#54214yes—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—48no—
257C2×D11—42no—
258C2×D11—82no—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—82no—
262C4×C11—24no—
263C4×C11—24no—
264C4×C11—24no—
265C4×C11—84no—
266Dic11—42no—
267Dic11—42no—
268Dic11—48no—
269Dic11—42no—
270C25—111no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—111no—
274C23×C4—114no—
275C23×C4C22×D1114yes—
276C23×C4C22×D1111yescharacteristic
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279#126—2232no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—114no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—228no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C22⋊C4—114no—
294C2×C22⋊C4—114no—
295C2×C22⋊C4—114no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—228no—
303C2×C22⋊C4—444no—
304C2×C22⋊C4—444no—
305C2×C42—224no—
306C2×C42—444no—
307C2×C42C4×D1114yes—
308C2×C42D4414yes—
309C2×C42C22⋊D1114yes—
310#95—24no—
311#95—24no—
312#95—228no—
313#95—224no—
314#95—444no—
315#95—444no—
316C2×C11#229711yescharacteristic
317C2×C11#231111yescharacteristic
318C2×C11#231111yescharacteristic
319C2×C11#233414yes—
320C2×C11#263612yes—
321C2×C11#263712yes—
322C2×C11#266212yes—
323C2×C11#266412yes—
324D11—82no—
325C24—112no—
326C24—221no—
327C24—222no—
328C24—222no—
329C24—224no—
330C24—222no—
331C24—222no—
332C24—221no—
333C24C23×D1111yescharacteristic
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—118no—
350C22×C4—224no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—222no—
355C22×C4—224no—
356C22×C4—222no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4—222no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—222no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4C2×C4×D1112yes—
368C22×C4C2×C4×D1112yes—
369C22×C4C2×C4×D1112yes—
370C22×C4C2×D4412yes—
371C22×C4C2×D4412yes—
372C22×C4C2×D4412yes—
373C22×C4C2×C22⋊D1112yes—
374C22×C4C2×C22⋊D1112yes—
375C22×C4C2×C22⋊D1112yes—
376C4⋊C4—48no—
377C4⋊C4—2216no—
378C4⋊C4—228no—
379C4⋊C4—228no—
380C4⋊C4—228no—
381C22⋊C4—228no—
382C22⋊C4—228no—
383C22⋊C4—228no—
384C22⋊C4—4416no—
385C42—448no—
386C42(C2×D11)⋊C4116yescomplemented
387C11#1429111yescharacteristic, complemented, Sylow
388C23—224no—
389C23—224no—
390C23—224no—
391C23—222no—
392C23—442no—
393C23—442no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—442no—
399C23—442no—
400C23—444no—
401C23—444no—
402C23—444no—
403C23—444no—
404C23C22×C4×D1111yescharacteristic
405C23C22×D4411yescharacteristic
406C23#6703712yes—
407C23#6704012yes—
408C23#41×D1114yes—
409C23#6704212yes—
410C23#6704312yes—
411C23C22×C22⋊D1111yescharacteristic
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—228no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—228no—
438C2×C4—228no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4C2×(C2×D11)⋊C414yes—
452C2×C4C2×(C2×D11)⋊C414yes—
453C2×C4C2×(C2×D11)⋊C414yes—
454C22—442no—
455C22—448no—
456C22—442no—
457C22—442no—
458C22—882no—
459C22—882no—
460C22—882no—
461C22—882no—
462C22#1062303512yes—
463C22#1062304112yes—
464C22#1062305312yes—
465C22#1062305412yes—
466C22#1062305512yes—
467C22#1062305611yescharacteristic
468C22#1062305711yescharacteristic
469C22#1062320014yes—
470C22#1062320914yes—
471C22#1062322314yes—
472C22#1062322714yes—
473C22C22×(C2×D11)⋊C411yescharacteristic
474C22#1062333611yescharacteristic
475C22#1062334711yescharacteristic
476C22#1062336312yes—
477C22#1062336412yes—
478C4—24no—
479C4—24no—
480C4—24no—
481C4—84no—
482C4—442no—
483C4—448no—
484C4—442no—
485C4—442no—
486C2—882no—
487C2#1307110411yescharacteristic
488C2#1307120411yescharacteristic
489C2#1307120911yescharacteristic
490C2#1307138714yes—
491C2#1307451512yes—
492C2#1307452612yes—
493C2#1307475512yes—
494C2#1307477712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#382C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#382D11
hypocenterC11#14291
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic11C2semidirect
3. #13066870C2semidirect
4. #13066866C2semidirect
8. #13066851C2semidirect
9. C2×C11×#382C2semidirect
23. C2×#66929C4semidirect
131. C42×C11C22⋊C4semidirect
142. C2×#382D11semidirect
386. C42(C2×D11)⋊C4semidirect
387. C11#14291semidirect

Maximal subgroups

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

subgroupindex
C22×#669292
C2×C4×C4⋊Dic112
#130668702
#130668662
#130668622
#130668582
#130668522
#130668512
C2×C11×#3822
#1429111