Finite Group Databasebeta

← #14656290

Subgroups — #14656290

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622686C211yesmaximal, characteristic
2C2×#10622461C211yesmaximal, characteristic, complemented
3C2×#10622688C211yesmaximal, characteristic, complemented
4#13069551C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4324—21no—
10C22×#4323—22no—
11C22×#4314—21no—
12C2×#66927C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×#66896—21no—
17C2×#66885—21no—
18#10622688—22no—
19#10622688—22no—
20#10622686—22no—
21#10622686—22no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622461—22no—
25#10622461—22no—
26C11×#331—22no—
27#10622188—22no—
28#10622123—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C22×Dic22D411yescharacteristic
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×#4324—24no—
44C2×#4324—42no—
45C2×#4324—42no—
46C2×#4323—28no—
47C2×#4323—44no—
48C2×#4323—44no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8D412yes—
54C2×#4314—24no—
55C2×#4314—42no—
56C2×#4314—42no—
57#66927—21no—
58#66927—21no—
59#66927—21no—
60#66927D412yes—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8D412yes—
69#66896—24no—
70#66885—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10262—111nomaximal, Sylow
76C24×C11—41no—
77C23×D11—41no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—82no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C2×D44—22no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—42no—
107C2×D44—41no—
108C2×D44—82no—
109C2×Dic22—21no—
110C2×Dic22—21no—
111C2×Dic22—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22D812yescomplemented
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—42no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4324—48no—
125#4323—416no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8SD1614yescomplemented
138#4314—48no—
139C2×#493—111no—
140C2×#460—111no—
141C2×#460—111no—
142#1984—111no—
143C2×#331—111no—
144C2×#331D1111yescharacteristic, complemented
145#1277—111no—
146C23×C11—42no—
147C23×C11—82no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—82no—
151C23×C11#12111yescharacteristic
152C22×D11—42no—
153C22×D11—82no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—82no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—44no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165D4×C11—81no—
166C2×C4×C11—22no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184D44—42no—
185D44—42no—
186D44—44no—
187D44—82no—
188D44—82no—
189D44—81no—
190D44—81no—
191D44—81no—
192D44—81no—
193Dic22—22no—
194Dic22—22no—
195Dic22—41no—
196Dic22—41no—
197C8×C11—42no—
198C8×C11—81no—
199C11⋊C8—24no—
200C11⋊C8—42no—
201C22×SD16—221no—
202C22×SD16—221no—
203C22×D8—222no—
204C2×#127—111no—
205C2×#127C2×D1111yescharacteristic
206C2×C4×Q8—111no—
207#493—222no—
208#493—222no—
209#460—222no—
210#460—222no—
211#460—222no—
212#460—222no—
213C2×C4⋊C8—111no—
214C2×C4⋊C8C2×D1111yescharacteristic
215C2×C4⋊C8C2×D1111yescharacteristic
216C2×#102—221no—
217C2×#102—221no—
218C2×C4×C8—111no—
219#336—222no—
220#331—22no—
221#331—222no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11—162no—
226C22×C11—162no—
227C22×C11#39211yescharacteristic
228C22×C11#46012yes—
229C22×C11#46611yescharacteristic
230C22×C11#46911yescharacteristic
231C22×C11#47212yes—
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—162no—
236C2×D11—162no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11#44711yescharacteristic
240C4×C11#44711yescharacteristic
241C4×C11#44911yescharacteristic
242C4×C11#44911yescharacteristic
243C4×C11#45012yes—
244C4×C11#49211yescharacteristic
245C4×C11#49611yescharacteristic
246Dic11—42no—
247Dic11—81no—
248C22×Q8—111no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—221no—
253C22×D4—221no—
254C22×D4—221no—
255C2×SD16—224no—
256C2×SD16—224no—
257C2×SD16—442no—
258C2×SD16—442no—
259C2×SD16—442no—
260C2×SD16—442no—
261C2×D8—228no—
262C2×D8—444no—
263C2×D8—444no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—112no—
267C22×C8—221no—
268#127—21no—
269#127—21no—
270#127—21no—
271#127—112no—
272#127—221no—
273#127—221no—
274#127—221no—
275#127D4412yes—
276C4×Q8—221no—
277C4×Q8—221no—
278C4×Q8—221no—
279C4×Q8—221no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—221no—
282C2×C42—221no—
283C2×C42C22×D1111yescharacteristic
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—112no—
288C4⋊C8—221no—
289C4⋊C8C22⋊D1112yes—
290#102—224no—
291#102—224no—
292C4×C8—221no—
293C4×C8—221no—
294C2×C11—162no—
295C2×C11#166812yes—
296C2×C11#168812yes—
297C2×C11#199911yescharacteristic
298C2×C11#201411yescharacteristic
299C2×C11#201811yescharacteristic
300D11—162no—
301C24—41no—
302C24—441no—
303C2×Q8—112no—
304C2×Q8—221no—
305C2×Q8—221no—
306C2×Q8—221no—
307C2×Q8—221no—
308C2×Q8—221no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—42no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—82no—
322C2×D4—222no—
323C2×D4—222no—
324C2×D4—222no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—442no—
328C2×D4—441no—
329C2×D4—442no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—882no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4#433911yescharacteristic
338C22×C4D4×D1111yescharacteristic
339C22×C4D4×D1111yescharacteristic
340SD16—448no—
341SD16—448no—
342D8—4416no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—42no—
347C2×C8—41no—
348C2×C8—114no—
349C2×C8—222no—
350C2×C8—222no—
351C2×C8—222no—
352C2×C8—441no—
353C2×C8—441no—
354C4⋊C4—221no—
355C4⋊C4—221no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C42—441no—
359C42—441no—
360C42C2×D4411yescharacteristic
361C42D4×D1111yescharacteristic
362C42D4×D1111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C11#1026211yescharacteristic, complemented, Sylow
365C23—42no—
366C23—82no—
367C23—82no—
368C23—81no—
369C23—81no—
370C23—442no—
371C23—882no—
372C23—882no—
373C23—881no—
374C23—881no—
375C23#6693711yescharacteristic
376Q8—222no—
377Q8—222no—
378Q8—441no—
379Q8—441no—
380D4—42no—
381D4—44no—
382D4—42no—
383D4—82no—
384D4—82no—
385D4—81no—
386D4—81no—
387D4—81no—
388D4—81no—
389D4—442no—
390D4—442no—
391D4—444no—
392D4—882no—
393D4—882no—
394D4—881no—
395D4—881no—
396D4—881no—
397D4—881no—
398C2×C4—22no—
399C2×C4—222no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—442no—
404C2×C4#6693511yescharacteristic
405C2×C4#6693511yescharacteristic
406C2×C4#6693711yescharacteristic
407C2×C4D8×D1111yescharacteristic
408C2×C4#6696412yes—
409C2×C4#6696411yescharacteristic
410C2×C4SD16×D1112yes—
411C2×C4#6696711yescharacteristic
412C2×C4#6696911yescharacteristic
413C2×C4#6698311yescharacteristic
414C2×C4#6699011yescharacteristic
415C2×C4#6699311yescharacteristic
416C8—42no—
417C8—81no—
418C8—224no—
419C8—442no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22—162no—
424C22—162no—
425C22—882no—
426C22—882no—
427C22—882no—
428C22—1762no—
429C22—1762no—
430C22#1062236212yes—
431C22#1062237512yes—
432C22#1062238811yescharacteristic
433C22#1062239511yescharacteristic
434C22#1062257311yescharacteristic
435C4—21no—
436C4—21no—
437C4—442no—
438C4—881no—
439C4#1062238611yescharacteristic
440C4#1062238912yes—
441C4#1062239411yescharacteristic
442C4#1062276711yescharacteristic
443C4#1062276911yescharacteristic
444C4#1062278511yescharacteristic
445C4#1062278811yescharacteristic
446C2—162no—
447C2—1762no—
448C2#1306797512yes—
449C2#1306809912yes—
450C2#1306961311yescharacteristic
451C2#1306970511yescharacteristic
452C2#1306972411yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#121
prime radicalC2×#10622686C2
hypercenterC2×#331D11
hypocenterC11#10262
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×#10622461C2semidirect
3. C2×#10622688C2semidirect
4. #13069551C2semidirect
5. C2×#10622123C2semidirect
6. #13066450C2semidirect
7. C2×C11×#331C2semidirect
114. C2×Dic22D8semidirect
137. C2×C11⋊C8SD16semidirect
144. C2×#331D11semidirect
364. C11#10262semidirect

Maximal subgroups

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

subgroupindex
C2×#106226862
C2×#106224612
C2×#106226882
#130695512
C2×#106221232
#130664502
C2×C11×#3312
#1026211