Finite Group Databasebeta

← #14675396

Subgroups — #14675396

Order 2816.

1326 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×#10622590C211yesmaximal, characteristic
2C2×#10622263C212yesmaximal
3#13066851C212yesmaximal
4#13066850C212yesmaximal
5#13066849C212yesmaximal
6#13066848C211yesmaximal, characteristic
7#13066847C212yesmaximal
8#13066847C212yesmaximal
9C11×#1436C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622590C418yescomplemented
32#10622263C4116yescomplemented
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4—41no—
44C2×C11×C4⋊C4C2×C414yes—
45C2×C42×C11—41no—
46C2×C42×C11—42no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11—41no—
49C2×C4⋊Dic11C2×C414yes—
50C2×Dic11⋊C4—42no—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4C2×C418yes—
55C2×Dic11⋊C4C2×C418yes—
56C2×C4×Dic11—42no—
57C2×C4×Dic11—41no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11C2×C418yes—
62C2×C4×Dic11C2×C414yes—
63C11×#95—41no—
64C11×#95—42no—
65C11×#95C2×C418yes—
66C11⋊#95—42no—
67C11⋊#95—41no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95C2×C418yes—
72C11⋊#95C2×C418yes—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C418yes—
75C11⋊#95C2×C418yes—
76#13829—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C414yes—
104C22×C4×C11C22×C414yes—
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C412yes—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C22×C414yes—
130C22×Dic11C22×C414yes—
131C22×Dic11C22×C414yes—
132C22×Dic11C22×C414yes—
133C22×Dic11C22×C414yes—
134C22×Dic11C22×C414yes—
135C11×C4⋊C4—44no—
136C42×C11—44no—
137C4⋊Dic11—44no—
138Dic11⋊C4—48no—
139Dic11⋊C4—48no—
140C4×Dic11—44no—
141C4×Dic11—48no—
142C4×Dic11C42116yescomplemented
143C2×#382—112no—
144C2×#382—111no—
145#1436—112no—
146#1436—112no—
147#1436—112no—
148#1436—112no—
149#1436—112no—
150#1436—111no—
151#1436D1111yescharacteristic
152C23×C11C23×C411yescharacteristic
153C23×C11C23×C412yes—
154C23×C11H(5,𝔽2)11yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)12yes—
157C23×C11H(5,𝔽2)12yes—
158C23×C112−1+412yes—
159C23×C112−1+412yes—
160C23×C112−1+412yes—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11C2×C4214yes—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11C2×C4218yes—
218C22×C4⋊C4—112no—
219C22×C4⋊C4—112no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4C2×D1111yescharacteristic
222C22×C42—111no—
223C22×C42—112no—
224C22×C42—111no—
225C22×C42C2×D1111yescharacteristic
226#382—118no—
227#382—1116no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—111no—
238C2×#95C2×D1112yes—
239C2×#95C2×D1111yescharacteristic
240C2×#95C2×D1112yes—
241C22×C11C22×C4211yescharacteristic
242C22×C11#51811yescharacteristic
243C22×C11#51812yes—
244C22×C11#51911yescharacteristic
245C22×C11#51912yes—
246C22×C11#52012yes—
247C22×C11#52012yes—
248C22×C11#52012yes—
249C22×C11#52012yes—
250C22×C11#52012yes—
251C22×C11#52012yes—
252C22×C11H(3,𝔽4)11yescharacteristic
253C22×C11H(3,𝔽4)11yescharacteristic
254C22×C11#56212yes—
255C22×C11#56212yes—
256C22×C11#56212yes—
257C22×C11#56312yes—
258C22×C11#56311yescharacteristic
259C22×C11#56312yes—
260C22×C11#56311yescharacteristic
261C22×C11#56412yes—
262C4×C11—24no—
263C4×C11—44no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—44no—
267Dic11—28no—
268Dic11—44no—
269Dic11—44no—
270Dic11—44no—
271C23×C4—112no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4C22×D1112yes—
276C23×C4C22×D1112yes—
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—118no—
283C2×C4⋊C4—118no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4—442no—
288C2×C4⋊C4—442no—
289C2×C4⋊C4—441no—
290C2×C4⋊C4—441no—
291C2×C4⋊C4C4×D1114yes—
292C2×C42—42no—
293C2×C42—41no—
294C2×C42—114no—
295C2×C42—118no—
296C2×C42—442no—
297C2×C42—442no—
298C2×C42—441no—
299C2×C42—442no—
300C2×C42—442no—
301#95—42no—
302#95—41no—
303#95—118no—
304#95—118no—
305#95—118no—
306#95—118no—
307#95—118no—
308#95—442no—
309#95—442no—
310#95—441no—
311#95—442no—
312#95—442no—
313#95C4×D1118yes—
314C2×C11#227412yes—
315C2×C11#227411yescharacteristic
316C2×C11#237912yes—
317C2×C11#237911yescharacteristic
318C2×C11#237911yescharacteristic
319C2×C11#237912yes—
320C2×C11#238212yes—
321C2×C11#238212yes—
322C2×C11#238212yes—
323C24C23×D1111yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—114no—
348C22×C4—114no—
349C22×C4—114no—
350C22×C4—114no—
351C22×C4—114no—
352C22×C4—114no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4C2×C4×D1112yes—
376C22×C4C2×C4×D1112yes—
377C22×C4C2×C4×D1114yes—
378C22×C4C2×C4×D1114yes—
379C22×C4C2×C4×D1114yes—
380C22×C4C2×C4×D1112yes—
381C4⋊C4—44no—
382C4⋊C4—448no—
383C4⋊C4—448no—
384C4⋊C4—444no—
385C42—44no—
386C42—1116no—
387C42—444no—
388C42—448no—
389C11#1382911yescharacteristic, complemented, Sylow
390C23C22×C4×D1111yescharacteristic
391C23C22×C4×D1112yes—
392C23#6703711yescharacteristic
393C23#6703711yescharacteristic
394C23#6703712yes—
395C23#6704012yes—
396C23#6704212yes—
397C23#6704312yes—
398C23#6704312yes—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—118no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4C42×D1114yes—
456C22C2×C42×D1111yescharacteristic
457C22#1062301711yescharacteristic
458C22#1062303512yes—
459C22#1062304711yescharacteristic
460C22#1062305412yes—
461C22#1062307612yes—
462C22#1062307712yes—
463C22#1062307712yes—
464C22#1062307712yes—
465C22#1062310312yes—
466C22#1062310512yes—
467C22#1062312511yescharacteristic
468C22#1062315212yes—
469C22#1062317712yes—
470C22#1062317812yes—
471C22#1062318211yescharacteristic
472C22#1062319812yes—
473C22#1062321411yescharacteristic
474C22C11⋊#56412yes—
475C22#1062324312yes—
476C22#1062326611yescharacteristic
477C4—24no—
478C4—44no—
479C4—42no—
480C4—42no—
481C4—44no—
482C4—228no—
483C4—444no—
484C4—444no—
485C4—444no—
486C2#1307097012yes—
487C2#1307097111yescharacteristic
488C2#1307178512yes—
489C2#1307178611yescharacteristic
490C2#1307178811yescharacteristic
491C2#1307178912yes—
492C2#1307179812yes—
493C2#1307179912yes—
494C2#1307180012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#13829
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
31. #10622590C4semidirect
32. #10622263C4semidirect
142. C4×Dic11C42semidirect
389. C11#13829semidirect

Maximal subgroups

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

subgroupindex
C2×#106225902
C2×#106222632
#130668512
#130668502
#130668492
#130668482
#130668472
C11×#14362
#1382911