Finite Group Databasebeta

← #14680451

Subgroups — #14680451

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
1C2×#10622549C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13066869C212yesmaximal, complemented
4#13066869C212yesmaximal, complemented
5#13066861C212yesmaximal
6#13066861C212yesmaximal
7#13066853C212yesmaximal
8#13066848C212yesmaximal, complemented
9C22×C11×#126C211yesmaximal, characteristic
10C2×C11×#126—24no—
11C2×C11×#126—24no—
12C2×C11×#126C418yescomplemented
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2214yes—
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4×Dic11C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622549—24no—
31C4×C4⋊Dic11—24no—
32C25×C11C2311yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2314yes—
40C23×Dic11C2314yes—
41C11×#126—232no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2×C414yes—
50C2×C11×C4⋊C4C2×C414yes—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4C2×C414yes—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C11×C22⋊C4C2×C414yes—
60C2×C42×C11C2×C414yes—
61C2×C42×C11D414yes—
62C2×C42×C11D414yes—
63C2×C22⋊Dic11—28no—
64C2×C22⋊Dic11—44no—
65C2×C22⋊Dic11—44no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—28no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—44no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11—44no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—28no—
76C11⋊#95—44no—
77C11⋊#95—44no—
78#14291—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—21no—
81C24×C11—24no—
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11C22×C412yes—
87C24×C11C2411yescharacteristic
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—24no—
119C22×Dic11—24no—
120C22×Dic11—24no—
121C22×Dic11—24no—
122C22×Dic11—24no—
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11#4118yes—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—28no—
132C11×C4⋊C4—28no—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—28no—
136C42×C11C22⋊C4116yescomplemented
137C22⋊Dic11—416no—
138C4⋊Dic11—216no—
139C4⋊Dic11—48no—
140C4×Dic11—48no—
141C22×#126D1111yescharacteristic
142C2×#382—111no—
143C2×C4×C4⋊C4—111no—
144#1441—112no—
145#1441—112no—
146#1439—112no—
147#1439—112no—
148#1437—112no—
149#1436—112no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—24no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—44no—
163C23×C11—44no—
164C23×C11—44no—
165C23×C11—44no—
166C23×C11C23×C411yescharacteristic
167C23×C11C22×D411yescharacteristic
168C23×C11C22×D411yescharacteristic
169C23×C11C2×#4114yes—
170C23×C11H(5,𝔽2)12yes—
171C23×C11H(5,𝔽2)12yes—
172C23×C112−1+412yes—
173C23×C112−1+412yes—
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—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C2×C22⋊C414yes—
200C2×C4×C11C2×C22⋊C414yes—
201C2×C4×C11C2×C22⋊C414yes—
202C2×Dic11—28no—
203C2×Dic11—28no—
204C2×Dic11—28no—
205C2×Dic11—44no—
206C2×Dic11—44no—
207C2×Dic11—44no—
208C2×Dic11—44no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11—44no—
213C2×Dic11—44no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×#126—24no—
217C2×#126—24no—
218C2×#126Dic1118yescomplemented
219C22×C4⋊C4—112no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4C2×D1111yescharacteristic
222C22×C4⋊C4C2×D1111yescharacteristic
223C22×C4⋊C4C2×D1111yescharacteristic
224C22×C22⋊C4—114no—
225C22×C22⋊C4C2×D1111yescharacteristic
226C22×C22⋊C4C2×D1111yescharacteristic
227C22×C22⋊C4C2×D1111yescharacteristic
228C22×C42—112no—
229C22×C42C2×D1111yescharacteristic
230#382—224no—
231C4×C4⋊C4—224no—
232C2×#95—112no—
233C2×#95—114no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—114no—
237C2×#95—114no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—48no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11C22×C22⋊C411yescharacteristic
247C22×C11C4×#4112yes—
248C22×C11#52012yes—
249C22×C11#52012yes—
250C22×C11#52512yes—
251C22×C11#53212yes—
252C22×C11#53511yescharacteristic
253C22×C11#53511yescharacteristic
254C22×C11#53611yescharacteristic
255C22×C11#53611yescharacteristic
256C22×C11#53712yes—
257C22×C11#53712yes—
258C22×C11#53814yes—
259C22×C11#53914yes—
260C22×C11#54114yes—
261C22×C11#54214yes—
262C4×C11—24no—
263C4×C11—24no—
264C4×C11—24no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268Dic11—48no—
269Dic11—84no—
270C25C22×D1111yescharacteristic
271C23×C4—114no—
272C23×C4—114no—
273C23×C4C22×D1111yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C23×C4C22×D1111yescharacteristic
276C23×C4C22×D1111yescharacteristic
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279#126—232no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—228no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—444no—
290C2×C4⋊C4C2×Dic1114yes—
291C2×C4⋊C4C2×Dic1114yes—
292C2×C4⋊C4C2×Dic1114yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—228no—
300C2×C22⋊C4—444no—
301C2×C22⋊C4—444no—
302C2×C22⋊C4C2×Dic1114yes—
303C2×C22⋊C4C2×Dic1114yes—
304C2×C22⋊C4C2×Dic1114yes—
305C2×C42—224no—
306C2×C42—444no—
307C2×C42C2×Dic1114yes—
308C2×C42C22⋊D1114yes—
309C2×C42C22⋊D1114yes—
310#95—228no—
311#95—224no—
312#95—224no—
313#95—224no—
314#95—444no—
315#95—444no—
316C2×C11—82no—
317C2×C11#229711yescharacteristic
318C2×C11#231111yescharacteristic
319C2×C11#231111yescharacteristic
320C2×C11#233414yes—
321C2×C11#263612yes—
322C2×C11#263712yes—
323C2×C11#266212yes—
324C2×C11#266412yes—
325C24—24no—
326C24—22no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—21no—
331C24—21no—
332C24C22×Dic1112yes—
333C24C23×D1111yescharacteristic
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—118no—
351C22×C4—224no—
352C22×C4—224no—
353C22×C4—224no—
354C22×C4—224no—
355C22×C4—224no—
356C22×C4—224no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4C22×Dic1112yes—
365C22×C4C22×Dic1112yes—
366C22×C4C22×Dic1112yes—
367C22×C4C22×Dic1112yes—
368C22×C4C22×Dic1112yes—
369C22×C4C22×Dic1112yes—
370C22×C4C2×C22⋊D1112yes—
371C22×C4C2×C22⋊D1112yes—
372C22×C4C2×C22⋊D1112yes—
373C22×C4C2×C22⋊D1112yes—
374C22×C4C2×C22⋊D1112yes—
375C22×C4C2×C22⋊D1112yes—
376C4⋊C4—28no—
377C4⋊C4—28no—
378C4⋊C4—28no—
379C4⋊C4—2216no—
380C4⋊C4—448no—
381C22⋊C4—28no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—4416no—
385C42—448no—
386C42C22⋊Dic11116yescomplemented
387C11#1429111yescharacteristic, complemented, Sylow
388C23—24no—
389C23—24no—
390C23—24no—
391C23—22no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—41no—
400C23—41no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23#41×D1114yes—
405C23#6704212yes—
406C23#6704212yes—
407C23#6704312yes—
408C23#6704312yes—
409C23C23×Dic1111yescharacteristic
410C23C22×C22⋊D1111yescharacteristic
411C23C22×C22⋊D1111yescharacteristic
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—228no—
438C2×C4—228no—
439C2×C4—228no—
440C2×C4—444no—
441C2×C4—444no—
442C2×C4—444no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4—444no—
447C2×C4—444no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4C2×C22⋊Dic1114yes—
452C2×C4C2×C22⋊Dic1114yes—
453C2×C4C2×C22⋊Dic1114yes—
454C22—42no—
455C22—48no—
456C22—42no—
457C22—42no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22#1062323214yes—
463C22#1062323514yes—
464C22#1062323814yes—
465C22#1062324114yes—
466C22#1062335611yescharacteristic
467C22#1062335611yescharacteristic
468C22#41×Dic1112yes—
469C22#1062335812yes—
470C22#1062335812yes—
471C22#1062335912yes—
472C22#1062336111yescharacteristic
473C22#1062336111yescharacteristic
474C22#1062336312yes—
475C22#1062336412yes—
476C22#1062336412yes—
477C22C22×C22⋊Dic1111yescharacteristic
478C4—24no—
479C4—24no—
480C4—24no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—448no—
485C4—884no—
486C2—82no—
487C2#1307110711yescharacteristic
488C2#1307120811yescharacteristic
489C2#1307120811yescharacteristic
490C2#1307139514yes—
491C2#1307451312yes—
492C2#1307452412yes—
493C2#1307475612yes—
494C2#1307477812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#126C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#126D11
hypocenterC11#14291
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C2×#10622549C2semidirect
2. C2×C4×C4⋊Dic11C2semidirect
3. #13066869C2semidirect
4. #13066869C2semidirect
8. #13066848C2semidirect
12. C2×C11×#126C4semidirect
136. C42×C11C22⋊C4semidirect
218. C2×#126Dic11semidirect
386. C42C22⋊Dic11semidirect
387. C11#14291semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
C2×C4×C4⋊Dic112
#130668692
#130668612
#130668532
#130668482
C22×C11×#1262
#1429111