Finite Group Databasebeta

← #14908596

Subgroups — #14908596

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#466C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic, complemented
3#13070809C212yesmaximal, complemented
4#13070805C212yesmaximal, complemented
5#13070801C211yesmaximal, characteristic, complemented
6#13070797C211yesmaximal, characteristic, complemented
7#13070794C211yesmaximal, characteristic, complemented
8#13070403C212yesmaximal, complemented
9#13070330C212yesmaximal, complemented
10#13070225C211yesmaximal, characteristic, complemented
11C11×#2233C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×#121—21no—
15C2×#66945—21no—
16C11×#466C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic, complemented
18#10622770C2211yescharacteristic
19#10622728C2211yescharacteristic
20C2×#66882C2211yescharacteristic, complemented
21#10622651—21no—
22C2×#66872—21no—
23C2×#66862C2212yes—
24#10622496C2211yescharacteristic
25#10622493—21no—
26#10622493—21no—
27#10622493C2212yes—
28#10622493C2212yescomplemented
29D11×#107C2211yescharacteristic
30#10622388—21no—
31D11×#102—21no—
32C11×#367C2212yescomplemented
33C11×#357C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic, complemented
35#10622200C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic, complemented
37#10622147C2212yescomplemented
38(C2×D11)⋊C16C2212yescomplemented
39#10622142C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×D4×D11—21no—
44C2×D4×D11—41no—
45C22×C4×D11D411yescharacteristic
46C2×C11×D8C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#121—21no—
49C2×C11×C4⋊C4—21no—
50#66992—41no—
51#66991—21no—
52C2×#4323—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—41no—
55C2×C4⋊Dic11—21no—
56C2×C4×Dic11—41no—
57C22×C11⋊C8D411yescharacteristic
58D8×D11—24no—
59C2×D88C2311yescharacteristic
60C2×C8×D11—24no—
61C2×C8×D11D411yescharacteristic
62C2×C8×D11D411yescharacteristic
63C2×C8×D11C2311yescharacteristic
64C2×C8×D11C2311yescharacteristic
65#66948—21no—
66#66945—22no—
67#66945—22no—
68#66945—41no—
69#66945—41no—
70C4⋊C4×D11—21no—
71#66937—41no—
72C22⋊C4×D11—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2311yescharacteristic
76C11×#107C2312yes—
77C11×#102—21no—
78#66896—21no—
79#66885—21no—
80#66882—21no—
81#66882C2311yescharacteristic
82#66882C2312yes—
83C2×C11⋊C16C2312yes—
84#66873—21no—
85#66872—22no—
86#66872—22no—
87#66871—21no—
88#66862—24no—
89#33648—111nomaximal, Sylow
90C23×D11—41no—
91C23×D11D811yescharacteristic
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100C22×Dic11D811yescharacteristic
101D4×D11—42no—
102D4×D11—42no—
103D4×D11—84no—
104C2×D44—21no—
105C2×D44—41no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—41no—
109C2×C4×D11D811yescharacteristic
110C2×C4×D11D811yescharacteristic
111C2×C4×D11C2×D411yescharacteristic
112C2×C4×D11C2×D411yescharacteristic
113C11×D8—22no—
114C2×C8×C11—22no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C22⋊Dic11—41no—
122#4323—42no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130Dic11⋊C4—41no—
131C4×Dic11—42no—
132C4×Dic11—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136D88—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11—22no—
140C8×D11#4114yes—
141C11×C16—22no—
142C11⋊C16—22no—
143C2×#466—111no—
144C2×#427—111no—
145#2234—112no—
146#2234—112no—
147#2233—111no—
148#2233D1111yescharacteristic, complemented
149#2232—111no—
150#2232—111no—
151#2159—112no—
152#2140—112no—
153#2112—111no—
154C23×C11—41no—
155C23×C11C2×D811yescharacteristic
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—82no—
161C22×D11—82no—
162C22×D11—82no—
163C22×D11C2×D811yescharacteristic
164C22×D11C2×D811yescharacteristic
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—82no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C22⋊D11—82no—
176C22⋊D11—82no—
177C22⋊D11—82no—
178C2×Dic11—22no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—82no—
182C2×Dic11C2×D811yescharacteristic
183C2×Dic11C2×D811yescharacteristic
184D44—41no—
185D44—41no—
186D44—82no—
187C4×D11—22no—
188C4×D11—21no—
189C4×D11—21no—
190C4×D11—22no—
191C4×D11—82no—
192C4×D11#12312yes—
193C4×D11#13712yes—
194C8×C11—21no—
195C8×C11C2×#4112yes—
196C11⋊C8—21no—
197C11⋊C8#12312yes—
198C22×D8—111no—
199C23×C8—111no—
200C2×#121—221no—
201C2×#117—221no—
202C2×M32—112no—
203#466—111no—
204#466—111no—
205#466—111no—
206#466—221no—
207#466—221no—
208#466C2×D1111yescharacteristic
209#427—112no—
210#427—112no—
211#427—221no—
212#427—221no—
213C2×#107—111no—
214C2×#107—111no—
215C2×#107C2×D1111yescharacteristic, complemented
216C2×#106—221no—
217C2×#102—221no—
218#367—112no—
219#367C2×D1112yescomplemented
220#366—112no—
221#366—112no—
222#357—112no—
223#357—112no—
224#357—112no—
225#357C2×D1112yescomplemented
226C22⋊C16—111no—
227C22⋊C16—112no—
228C22⋊C16C2×D1111yescharacteristic, complemented
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#50912yes—
235C22×C11C22×D811yescharacteristic
236C2×D11—21no—
237C2×D11—21no—
238C2×D11—21no—
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—44no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C2×D11—164no—
246C2×D11#48012yes—
247C4×C11—21no—
248C4×C11—81no—
249C4×C11—82no—
250C4×C11C2×#12311yescharacteristic
251C4×C11C2×#13711yescharacteristic
252Dic11—21no—
253Dic11—81no—
254Dic11—82no—
255Dic11#48012yes—
256C22×D4—221no—
257C22×D4—441no—
258C23×C4—111no—
259C2×D8—111no—
260C2×D8—224no—
261C2×D8—221no—
262C2×D8C22×D1111yescharacteristic
263C22×C8—111no—
264C22×C8—111no—
265C22×C8—111no—
266C22×C8—111no—
267C22×C8—111no—
268C22×C8—224no—
269C22×C8C22×D1111yescharacteristic
270#121—21no—
271#121—221no—
272#121—221no—
273#121—221no—
274#121—441no—
275#121—441no—
276#117—222no—
277#117—222no—
278#117—441no—
279#117—441no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C22⋊C4—441no—
284C2×C22⋊C4—441no—
285C2×C42—441no—
286M32—224no—
287C2×C16—112no—
288C2×C16C22×D1112yes—
289#107—21no—
290#107—112no—
291#107—111no—
292#107—221no—
293#107—221no—
294#107C22×D1112yes—
295#107C22×D1111yescharacteristic
296#106—222no—
297#106—222no—
298#102—21no—
299#102—221no—
300#102—221no—
301#102—221no—
302C2×C11—22no—
303C2×C11—161no—
304C2×C11C2×#48011yescharacteristic
305C2×C11C2×#50911yescharacteristic
306C2×C11#341411yescharacteristic
307D11—22no—
308D11—41no—
309D11—161no—
310C24—111no—
311C24—441no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—221no—
315C2×D4—441no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—884no—
322C22×C4—41no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4D4×D1111yescharacteristic
333D8—22no—
334D8—222no—
335D8—442no—
336C2×C8—22no—
337C2×C8—111no—
338C2×C8—114no—
339C2×C8—111no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8D4×D1111yescharacteristic
345C2×C8C23×D1111yescharacteristic
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—222no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—41no—
354C22⋊C4—441no—
355C22⋊C4—442no—
356C22⋊C4—442no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—442no—
360C42—442no—
361C16—22no—
362C16—222no—
363C11#3364811yescharacteristic, complemented, Sylow
364C23—41no—
365C23—111no—
366C23—111no—
367C23—222no—
368C23—222no—
369C23—441no—
370C23—441no—
371C23—882no—
372C23—882no—
373C23—882no—
374C23D8×D1111yescharacteristic
375D4—41no—
376D4—41no—
377D4—82no—
378D4—441no—
379D4—441no—
380D4—882no—
381D4—882no—
382D4—882no—
383D4—882no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—111no—
390C2×C4—112no—
391C2×C4—112no—
392C2×C4—111no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4D8×D1111yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C8—21no—
405C8—112no—
406C8—221no—
407C8#41×D1112yes—
408C22—21no—
409C22—21no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—112no—
414C22—221no—
415C22—221no—
416C22—221no—
417C22—221no—
418C22—221no—
419C22—444no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—1764no—
424C22#1062252712yes—
425C22C2×D8×D1111yescharacteristic
426C4—21no—
427C4—81no—
428C4—82no—
429C4—112no—
430C4—221no—
431C4—881no—
432C4—882no—
433C4D11×#12311yescharacteristic
434C4D11×#13711yescharacteristic
435C2—22no—
436C2—161no—
437C2—222no—
438C2—441no—
439C2—1761no—
440C2D11×#48011yescharacteristic
441C2C2×#1062252711yescharacteristic
442C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2233D11
hypocenterC11#33648
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. C2×#10622493C2semidirect
3. #13070809C2semidirect
4. #13070805C2semidirect
5. #13070801C2semidirect
6. #13070797C2semidirect
7. #13070794C2semidirect
8. #13070403C2semidirect
9. #13070330C2semidirect
10. #13070225C2semidirect
11. C11×#2233C2semidirect
17. C2×C11×#107C22semidirect
20. C2×#66882C22semidirect
28. #10622493C22semidirect
32. C11×#367C22semidirect
33. C11×#357C22semidirect
34. C11×C22⋊C16C22semidirect
35. #10622200C22semidirect
36. C22⋊(C11⋊C16)C22semidirect
37. #10622147C22semidirect
38. (C2×D11)⋊C16C22semidirect
39. #10622142C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
148. #2233D11semidirect
215. C2×#107C2×D11semidirect
219. #367C2×D11semidirect
225. #357C2×D11semidirect
228. C22⋊C16C2×D11semidirect
363. C11#33648semidirect

Maximal subgroups

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

subgroupindex
D11×#4662
C2×#106224932
#130708092
#130708052
#130708012
#130707972
#130707942
#130704032
#130703302
#130702252
C11×#22332
#3364811