Finite Group Databasebeta

← #14763761

Subgroups — #14763761

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic, complemented
2#13071225C211yesmaximal, characteristic, complemented
3#13069574C212yesmaximal, complemented
4#13069544C212yesmaximal, complemented
5#13069055C212yesmaximal, complemented
6#13069045C212yesmaximal, complemented
7#13068626C212yesmaximal, complemented
8#13068616C212yesmaximal, complemented
9C2×C11×#540C211yesmaximal, characteristic
10C11×#540—24no—
11C11×#540C418yescomplemented
12C2×C11×#127C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C2×C11×#123—22no—
15C2×C11×#121—22no—
16C2×C11×#121C2212yes—
17C2×C4×D4×C11C2212yes—
18C2×C11×#117C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66896C2212yes—
22C2×#66896C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25#10622825C2212yes—
26#10622612—24no—
27#10622594—22no—
28#10622564—22no—
29#10622549C2211yescharacteristic
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11C2312yes—
41C23×C4×C11—22no—
42C23×C4×C11C2311yescharacteristic
43C11×#127—22no—
44C11×#127C2×C414yes—
45C11×#125—22no—
46C11×#125C2×C414yes—
47C11×#123—216no—
48C11×#121—24no—
49C11×#121—216no—
50C11×#121C2×C418yes—
51C4×D4×C11—24no—
52C4×D4×C11C2×C418yes—
53C11×#117C2×C414yes—
54C11×#117D414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4×Dic11—22no—
68C2×#4318—22no—
69C2×#4318—41no—
70C2×#4318—41no—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—41no—
73C22×C11⋊C8—41no—
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2312yes—
76#66896—42no—
77#66896—42no—
78#66896—42no—
79#66896—42no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C4⋊(C11⋊C8)—24no—
84C4⋊(C11⋊C8)—24no—
85#21897—111nomaximal, Sylow
86C24×C11—22no—
87C24×C11C2×D411yescharacteristic
88C2×D4×C11—28no—
89C2×D4×C11—28no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—82no—
96C2×D4×C11—82no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C2×D4×C11C22×C414yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—28no—
106C22×C4×C11—82no—
107C22×C4×C11—82no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11—22no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4C22⋊C418yes—
119C11×C4⋊C4C22×C414yes—
120C11×C22⋊C4—28no—
121C11×C22⋊C4—28no—
122C11×C22⋊C4C22⋊C418yes—
123C42×C11C22×C412yes—
124C42×C11C22×C412yes—
125C42×C11C2×D412yes—
126C42×C11C2×D412yes—
127C22⋊Dic11—82no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—82no—
133C4×Dic11—82no—
134#4318—44no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—44no—
142C2×#540D1111yescharacteristic
143C2×#424—111no—
144#2314—111no—
145#1989—112no—
146#1982—112no—
147#1895—112no—
148#1893—112no—
149#1804—112no—
150#1802—112no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—24no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11C2×C22⋊C412yes—
163C23×C11C22×D411yescharacteristic
164D4×C11—24no—
165D4×C11—24no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—88no—
169D4×C11—88no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—88no—
184C2×C4×C11C2×C22⋊C414yes—
185C2×C4×C11C2×C22⋊C414yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C23×C411yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×C4×C112−1+411yescharacteristic
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201C22×M16—111no—
202C23×C8—111no—
203#540—24no—
204#540Dic1118yescomplemented
205C2×#127C2×D1111yescharacteristic
206C2×#125C2×D1111yescharacteristic
207C2×#123—22no—
208C2×#121—22no—
209C2×#121C2×D1112yes—
210C2×C4×D4C2×D1112yes—
211C2×#117C2×D1111yescharacteristic
212#424—224no—
213C2×C4⋊C8—112no—
214C2×C4⋊C8—112no—
215C2×#102—112no—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102—112no—
219#388—222no—
220#387—222no—
221#384—111no—
222#382—111no—
223#380—112no—
224C4×C4⋊C4—112no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340—112no—
229C22×C11—22no—
230C22×C11—24no—
231C22×C11—42no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11C22×C22⋊C411yescharacteristic
242C22×C11#53711yescharacteristic
243C22×C11#53711yescharacteristic
244C22×C11#57612yes—
245C22×C11#57712yes—
246C4×C11—22no—
247C4×C11—24no—
248C4×C11—24no—
249C4×C11—44no—
250C4×C11#52011yescharacteristic
251C4×C11#52011yescharacteristic
252C4×C11#53511yescharacteristic
253C4×C11#53611yescharacteristic
254Dic11—82no—
255Dic11—82no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4C22×D1112yes—
259C23×C4—22no—
260C23×C4C22×D1111yescharacteristic
261C2×M16—222no—
262C2×M16—441no—
263C2×M16—441no—
264C22×C8—112no—
265C22×C8—112no—
266C22×C8—222no—
267C22×C8—441no—
268C22×C8—441no—
269#127—22no—
270#127C2×Dic1114yes—
271#125—22no—
272#125C2×Dic1114yes—
273#123—216no—
274#121—24no—
275#121—216no—
276#121C2×Dic1118yes—
277C4×D4—24no—
278C4×D4C2×Dic1118yes—
279#117C2×Dic1114yes—
280#117C22⋊D1114yes—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4C22⋊D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4C22⋊D1112yes—
291C2×C42—222no—
292C2×C42C22×D1111yescharacteristic
293C2×C42C22×D1111yescharacteristic
294C4⋊C8—224no—
295C4⋊C8—224no—
296#102—442no—
297#102—442no—
298#102—442no—
299#102—442no—
300#95—222no—
301#95—222no—
302#95—222no—
303C2×C11—42no—
304C2×C11—84no—
305C2×C11#231111yescharacteristic
306C2×C11#289712yes—
307C2×C11#325712yes—
308C2×C11#325911yescharacteristic
309C2×C11#326011yescharacteristic
310C24—22no—
311C24C2×C22⋊D1111yescharacteristic
312C2×D4—28no—
313C2×D4—28no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—82no—
320C2×D4—82no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4C22×Dic1114yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—28no—
330C22×C4—82no—
331C22×C4—82no—
332C22×C4—222no—
333C22×C4—222no—
334C22×C4C22×Dic1112yes—
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C2×C22⋊D1112yes—
337C22×C4C2×C22⋊D1112yes—
338C22×C4C2×C22⋊D1112yes—
339C22×C4C23×D1111yescharacteristic
340M16—444no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—444no—
348C4⋊C4—28no—
349C4⋊C4—22no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—882no—
355C4⋊C4C22⋊Dic1118yes—
356C4⋊C4C22×Dic1114yes—
357C22⋊C4—28no—
358C22⋊C4—28no—
359C22⋊C4—882no—
360C22⋊C4C22⋊Dic1118yes—
361C42—882no—
362C42C22×Dic1112yes—
363C42C22×Dic1112yes—
364C42C2×C22⋊D1112yes—
365C42C2×C22⋊D1112yes—
366C11#2189711yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—24no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23C2×C22⋊Dic1112yes—
379C23C22×C22⋊D1111yescharacteristic
380D4—24no—
381D4—24no—
382D4—42no—
383D4—42no—
384D4—88no—
385D4—88no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—88no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4C2×C22⋊Dic1114yes—
407C2×C4C2×C22⋊Dic1114yes—
408C2×C4C2×C22⋊Dic1112yes—
409C2×C4#6704211yescharacteristic
410C2×C4#6704211yescharacteristic
411C2×C4#6704311yescharacteristic
412C2×C4#6704311yescharacteristic
413C2×C4C23×Dic1111yescharacteristic
414C2×C4C22×C22⋊D1111yescharacteristic
415C8—442no—
416C8—442no—
417C22—22no—
418C22—24no—
419C22—42no—
420C22—41no—
421C22—41no—
422C22—44no—
423C22—44no—
424C22—44no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22#1062336411yescharacteristic
430C22#1062336411yescharacteristic
431C22#1062336612yes—
432C22#1062336712yes—
433C22C22×C22⋊Dic1111yescharacteristic
434C4—22no—
435C4—24no—
436C4—24no—
437C4—44no—
438C4—882no—
439C4—882no—
440C4#1062335611yescharacteristic
441C4#1062335811yescharacteristic
442C4#1062335811yescharacteristic
443C4#1062336111yescharacteristic
444C2—42no—
445C2—84no—
446C2#1307120811yescharacteristic
447C2#1307714212yes—
448C2#1308002112yes—
449C2#1308005111yescharacteristic
450C2#1308006211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#540C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#540D11
hypocenterC11#21897
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10622612C2semidirect
2. #13071225C2semidirect
3. #13069574C2semidirect
4. #13069544C2semidirect
5. #13069055C2semidirect
6. #13069045C2semidirect
7. #13068626C2semidirect
8. #13068616C2semidirect
11. C11×#540C4semidirect
204. #540Dic11semidirect
366. C11#21897semidirect

Maximal subgroups

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

subgroupindex
C2×#106226122
#130712252
#130695742
#130695442
#130690552
#130690452
#130686262
#130686162
C2×C11×#5402
#2189711