Finite Group Databasebeta

← #14672469

Subgroups — #14672469

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic, complemented
2C2×#10622496C211yesmaximal, characteristic, complemented
3C2×#10622770C211yesmaximal, characteristic, complemented
4C2×#10622147C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66991—21no—
10C22×D88C2211yescharacteristic
11C22×C8×D11C2211yescharacteristic
12C2×#66948—21no—
13C22×C11×C16C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×#66896—21no—
16#10622770—22no—
17#10622770—22no—
18C2×#66890—22no—
19C2×#66890—22no—
20C2×#66890—22no—
21C2×#66882C2211yescharacteristic
22C22×C11⋊C16C2211yescharacteristic
23C2×#66873—21no—
24#10622496—22no—
25#10622496—22no—
26C11×#357—22no—
27#10622147—22no—
28(C2×D11)⋊C16—22no—
29C22×D4×C11—21no—
30C22×C22⋊D11—41no—
31C22×D44—21no—
32C22×D44—41no—
33C22×C4×D11D411yescharacteristic
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8D412yescomplemented
40C22×C8×C11C2311yescharacteristic
41C2×C11×C4⋊C4—21no—
42C2×C22⋊Dic11—41no—
43#66991—24no—
44#66991—42no—
45C2×(C2×D11)⋊C4—41no—
46C2×C4⋊Dic11—21no—
47C22×C11⋊C8D411yescharacteristic
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88—21no—
52C2×D88—21no—
53C2×D88D412yescomplemented
54C2×C8×D11—21no—
55C2×C8×D11—21no—
56C2×C8×D11—21no—
57C2×C8×D11—21no—
58C2×C8×D11—21no—
59C2×C8×D11—21no—
60#66948—24no—
61#66948—42no—
62C2×C11×C16—21no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C11×#107—21no—
66C11×#107D412yescomplemented
67#66896—24no—
68#66890—28no—
69#66882—21no—
70#66882D412yescomplemented
71C2×C11⋊C16—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16D412yescomplemented
74#66873—24no—
75#13304—111nomaximal, Sylow
76C24×C11—41no—
77C23×D11—41no—
78C23×D11D811yescharacteristic
79C2×D4×C11—22no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—44no—
88C2×C22⋊D11—82no—
89C2×C22⋊D11—82no—
90C22×Dic11—41no—
91C22×Dic11D811yescharacteristic
92C2×D44—22no—
93C2×D44—44no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—82no—
100C2×D44—82no—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—41no—
110C11×D8—41no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C22⋊Dic11—44no—
120(C2×D11)⋊C4—44no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126D88—22no—
127D88—22no—
128D88—41no—
129D88—41no—
130C8×D11—41no—
131C8×D11—41no—
132C8×D11—41no—
133C8×D11—41no—
134C11×C16—41no—
135C11⋊C16—22no—
136C22×D16—111no—
137C2×#466—111no—
138C2×#466—111no—
139C2×#357—111no—
140C2×#357D1111yescharacteristic, complemented
141C2×C22⋊C16—111no—
142#1380—111no—
143C23×C11—42no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11C2×D811yescharacteristic
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—42no—
158C22×D11—81no—
159C22×D11—81no—
160C22×D11—81no—
161C22×D11—81no—
162C22×D11—81no—
163C22×D11—81no—
164C22×D11D1612yescomplemented
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C22⋊D11—88no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—42no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185D44—42no—
186D44—42no—
187D44—88no—
188D44—81no—
189D44—81no—
190C4×D11—41no—
191C4×D11—41no—
192C4×D11—41no—
193C4×D11—41no—
194C8×C11#12011yescharacteristic
195C8×C11#12111yescharacteristic
196C8×C11#12111yescharacteristic
197C8×C11#12711yescharacteristic
198C11⋊C8—41no—
199C22×D8—111no—
200C22×D8C2×D1111yescharacteristic
201C23×C8—111no—
202C2×#121—221no—
203C2×#121—221no—
204C2×D16—222no—
205C2×D16—222no—
206C2×D16—222no—
207C22×C16—111no—
208C22×C16C2×D1111yescharacteristic
209#466—222no—
210#466—222no—
211#466—222no—
212#466—222no—
213C2×#107—111no—
214C2×#107C2×D1111yescharacteristic
215C2×#102—221no—
216C2×#102—221no—
217#357—22no—
218#357—222no—
219C22⋊C16—222no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—161no—
224C22×C11—161no—
225C22×C11—161no—
226C22×C11—161no—
227C22×C11#44711yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#46611yescharacteristic
230C22×C11C2×D1611yescharacteristic
231C22×C11#50811yescharacteristic
232C22×C11#50911yescharacteristic
233C22×C11#50911yescharacteristic
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—161no—
245C2×D11—161no—
246C2×D11—161no—
247C2×D11—161no—
248C4×C11—82no—
249C4×C11#39211yescharacteristic
250C4×C11#44911yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#46911yescharacteristic
253Dic11—41no—
254Dic11—82no—
255C22×D4—21no—
256C22×D4—221no—
257C22×D4—441no—
258C22×D4—441no—
259C23×C4—111no—
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—112no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—221no—
269C2×D8—221no—
270C2×D8—221no—
271C2×D8D4412yescomplemented
272C22×C8—111no—
273C22×C8—221no—
274C22×C8—221no—
275C22×C8—221no—
276C22×C8—221no—
277C22×C8—221no—
278C22×C8—221no—
279C22×C8C22×D1111yescharacteristic
280#121—224no—
281#121—224no—
282#121—442no—
283#121—442no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—221no—
286C2×C22⋊C4—441no—
287C2×C22⋊C4—441no—
288D16—228no—
289C2×C16—21no—
290C2×C16—21no—
291C2×C16—21no—
292C2×C16—112no—
293C2×C16—221no—
294C2×C16—221no—
295#107—21no—
296#107—112no—
297#107—221no—
298#107C22⋊D1112yescomplemented
299#102—224no—
300#102—224no—
301C2×C11—162no—
302C2×C11#199911yescharacteristic
303C2×C11#218411yescharacteristic
304C2×C11#218411yescharacteristic
305C2×C11#218611yescharacteristic
306C2×C11#218611yescharacteristic
307C2×C11#221511yescharacteristic
308C2×C11#221811yescharacteristic
309D11—42no—
310D11—162no—
311C24—41no—
312C24—111no—
313C24—441no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—222no—
321C2×D4—444no—
322C2×D4—444no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—882no—
329C2×D4—882no—
330C2×D4—882no—
331C2×D4—882no—
332C22×C4—41no—
333C22×C4—111no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—441no—
341C22×C4D4×D1111yescharacteristic
342D8—22no—
343D8—22no—
344D8—41no—
345D8—41no—
346D8—222no—
347D8—222no—
348D8—441no—
349D8—441no—
350C2×C8—221no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—441no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8C2×D4411yescharacteristic
358C2×C8#433911yescharacteristic
359C2×C8D4×D1111yescharacteristic
360C2×C8D4×D1111yescharacteristic
361C2×C8D4×D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—41no—
365C4⋊C4—222no—
366C4⋊C4—441no—
367C22⋊C4—444no—
368C22⋊C4—444no—
369C16—41no—
370C16—222no—
371C11#1330411yescharacteristic, complemented, Sylow
372C23—42no—
373C23—81no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—112no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—442no—
387C23—881no—
388C23—881no—
389C23—881no—
390C23—881no—
391C23—881no—
392C23—881no—
393C23D8×D1111yescharacteristic
394D4—42no—
395D4—42no—
396D4—81no—
397D4—81no—
398D4—442no—
399D4—442no—
400D4—888no—
401D4—888no—
402D4—881no—
403D4—881no—
404C2×C4—42no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—442no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4#6693511yescharacteristic
418C2×C4#6693711yescharacteristic
419C2×C4#6696411yescharacteristic
420C2×C4#6696711yescharacteristic
421C2×C4#6696911yescharacteristic
422C2×C4#6699011yescharacteristic
423C8—441no—
424C8#6693511yescharacteristic
425C8#6693711yescharacteristic
426C8#6698311yescharacteristic
427C8#6699311yescharacteristic
428C22—82no—
429C22—82no—
430C22—82no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—161no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—882no—
443C22—882no—
444C22—882no—
445C22—1761no—
446C22—1761no—
447C22—1761no—
448C22—1761no—
449C22#1062238611yescharacteristic
450C22#1062238811yescharacteristic
451C22D11×D1611yescharacteristic
452C22#1062252411yescharacteristic
453C22#1062252711yescharacteristic
454C22#1062252911yescharacteristic
455C22#1062276911yescharacteristic
456C4—82no—
457C4—441no—
458C4—882no—
459C4#1062239411yescharacteristic
460C4#1062239511yescharacteristic
461C4#1062257311yescharacteristic
462C4#1062278511yescharacteristic
463C2—162no—
464C2—442no—
465C2—1762no—
466C2#1306961311yescharacteristic
467C2#1307052611yescharacteristic
468C2#1307052911yescharacteristic
469C2#1307053811yescharacteristic
470C2#1307054011yescharacteristic
471C2#1307070111yescharacteristic
472C2#1307071811yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
hypercenterC2×#357D11
hypocenterC11#13304
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C22×#66890C2semidirect
2. C2×#10622496C2semidirect
3. C2×#10622770C2semidirect
4. C2×#10622147C2semidirect
5. C2×(C2×D11)⋊C16C2semidirect
6. #13066707C2semidirect
7. C2×C11×#357C2semidirect
39. C2×C11×D8D4semidirect
53. C2×D88D4semidirect
66. C11×#107D4semidirect
70. #66882D4semidirect
73. C2×C11⋊C16D4semidirect
140. C2×#357D11semidirect
164. C22×D11D16semidirect
271. C2×D8D44semidirect
298. #107C22⋊D11semidirect
371. C11#13304semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
C2×#106224962
C2×#106227702
C2×#106221472
C2×(C2×D11)⋊C162
#130667072
C2×C11×#3572
#1330411