Finite Group Databasebeta

← #14909549

Subgroups — #14909549

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622770C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic, complemented
3#13070802C211yesmaximal, characteristic, complemented
4#13070800C212yesmaximal, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070718C212yesmaximal, complemented
7#13070716C212yesmaximal, complemented
8#13070528C211yesmaximal, characteristic, complemented
9#13070526C212yesmaximal, complemented
10#13070225C211yesmaximal, characteristic, complemented
11C11×#2184C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic, complemented
13C2×#66991—21no—
14C2×D8×D11C2211yescharacteristic, complemented
15C22×C8×D11C2211yescharacteristic
16D11×#121—21no—
17C2×C11×D16C2212yescomplemented
18C11×#466C2211yescharacteristic
19C2×#66896—21no—
20#10622770—21no—
21#10622770—21no—
22#10622770C2212yes—
23#10622770C2211yescharacteristic, complemented
24#10622770C2212yescomplemented
25C2×#66890C2212yescomplemented
26#10622728C2211yescharacteristic
27C2×#66882C2211yescharacteristic, complemented
28#10622651—21no—
29C2×#66862C2212yescomplemented
30#10622496C2211yescharacteristic, complemented
31D11×#107C2211yescharacteristic, complemented
32#10622388—21no—
33D11×#102—21no—
34C11×#357C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic, complemented
36#10622200C2212yescomplemented
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic, complemented
39#10622147C2212yescomplemented
40(C2×D11)⋊C16C2212yescomplemented
41#10622143C2212yescomplemented
42#10622128C2212yescomplemented
43C22×D4×C11—21no—
44C22×C22⋊D11—41no—
45C2×D4×D11—21no—
46C2×D4×D11—41no—
47C22×C4×D11D411yescharacteristic
48C2×C11×D8—21no—
49C2×C11×D8—42no—
50C2×C11×D8C2311yescharacteristic
51C2×C11×D8C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#121—21no—
54C2×C22⋊Dic11—41no—
55#66992—41no—
56#66991—22no—
57#66991—22no—
58#66991—21no—
59#66991—41no—
60#66991—41no—
61C2×#4323—21no—
62#66983—21no—
63C2×C4⋊Dic11—21no—
64C22×C11⋊C8D411yescharacteristic
65D8×D11—42no—
66C2×D88C2311yescharacteristic
67C2×C8×D11—42no—
68C2×C8×D11D411yescharacteristic
69C2×C8×D11D411yescharacteristic
70C2×C8×D11C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66948—21no—
73C4⋊C4×D11—21no—
74#66937—41no—
75C22⋊C4×D11—41no—
76C11×D16—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80#66896—22no—
81#66896—22no—
82#66896—21no—
83#66890—42no—
84#66885—21no—
85#66882—21no—
86#66882C2311yescharacteristic
87#66882C2312yes—
88C2×C11⋊C16C2312yes—
89#66873—21no—
90#66871—21no—
91#66862—42no—
92#33758—111nomaximal, Sylow
93C24×C11—41no—
94C23×D11—41no—
95C23×D11D811yescharacteristic
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—84no—
109C22×Dic11—41no—
110C22×Dic11D811yescharacteristic
111D4×D11—42no—
112D4×D11—42no—
113D4×D11—84no—
114C2×D44—21no—
115C2×D44—41no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11D811yescharacteristic
120C2×C4×D11D811yescharacteristic
121C2×C4×D11C2×D411yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C11×D8—22no—
124C11×D8—22no—
125C11×D8—22no—
126C11×D8—42no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C22⋊C4—41no—
132C22⋊Dic11—41no—
133C22⋊Dic11—42no—
134C22⋊Dic11—42no—
135#4323—42no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—22no—
140C4⋊Dic11—41no—
141Dic11⋊C4—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8C2×D411yescharacteristic
144C2×C11⋊C8C2×D411yescharacteristic
145D88—22no—
146C8×D11—22no—
147C8×D11—22no—
148C8×D11—41no—
149C8×D11—41no—
150C11×C16—22no—
151C11⋊C16—22no—
152C2×#466—111no—
153C2×#466—111no—
154#2233—111no—
155#2233—112no—
156#2233—111no—
157#2218—112no—
158#2218—112no—
159#2184—112no—
160#2184—111no—
161#2184D1111yescharacteristic, complemented
162#2112—111no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11—82no—
168C23×C11C2×D811yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—82no—
174C22×D11—82no—
175C22×D11—82no—
176C22×D11C2×D811yescharacteristic
177C22×D11C2×D811yescharacteristic
178D4×C11—41no—
179D4×C11—42no—
180D4×C11—41no—
181D4×C11—42no—
182D4×C11—82no—
183D4×C11—82no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—41no—
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C22⋊D11—82no—
190C22⋊D11—82no—
191C22⋊D11—84no—
192C22⋊D11—82no—
193C22⋊D11—84no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—82no—
198C2×Dic11C2×D811yescharacteristic
199C2×Dic11C2×D811yescharacteristic
200D44—41no—
201D44—41no—
202D44—82no—
203C4×D11—21no—
204C4×D11—21no—
205C4×D11—21no—
206C4×D11—21no—
207C4×D11—41no—
208C4×D11—41no—
209C4×D11—82no—
210C8×C11—21no—
211C8×C11H(5,𝔽2)12yes—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C22×D8—111no—
215C22×D8C2×D1111yescharacteristic, complemented
216C23×C8—111no—
217C2×#121—221no—
218C2×#121—221no—
219C2×D16—112no—
220C2×D16C2×D1112yescomplemented
221C2×M32—112no—
222#466—112no—
223#466—111no—
224#466—112no—
225#466—111no—
226#466—111no—
227#466—221no—
228#466—221no—
229#466—221no—
230#466—221no—
231#466C2×D1111yescharacteristic
232C2×#107—111no—
233C2×#107—111no—
234C2×#102—221no—
235C2×#102—221no—
236#367—112no—
237#367—112no—
238#357—112no—
239#357—112no—
240#357—112no—
241#357C2×D1112yescomplemented
242C22⋊C16—111no—
243C22⋊C16—112no—
244C22⋊C16C2×D1111yescharacteristic, complemented
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—81no—
253C22×C11—164no—
254C22×C11#50912yes—
255C22×C11C22×D811yescharacteristic
256C2×D11—21no—
257C2×D11—21no—
258C2×D11—21no—
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—44no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—164no—
266C2×D11#50912yes—
267C4×C11—21no—
268C4×C11—81no—
269C4×C11#53411yescharacteristic
270C4×C11#57511yescharacteristic
271Dic11—21no—
272Dic11—21no—
273Dic11—81no—
274Dic11—82no—
275C22×D4—21no—
276C22×D4—221no—
277C22×D4—441no—
278C22×D4—441no—
279C23×C4—111no—
280C2×D8—21no—
281C2×D8—42no—
282C2×D8—111no—
283C2×D8—221no—
284C2×D8—442no—
285C2×D8C22×D1111yescharacteristic
286C2×D8C22×D1112yes—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8—111no—
292C22×C8—442no—
293C22×C8C22×D1111yescharacteristic
294#121—21no—
295#121—221no—
296#121—222no—
297#121—221no—
298#121—222no—
299#121—221no—
300#121—441no—
301#121—441no—
302#121—441no—
303#121—441no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C22⋊C4—441no—
307C2×C22⋊C4—441no—
308D16—42no—
309D16—442no—
310M32—442no—
311C2×C16—112no—
312C2×C16C22×D1112yes—
313#107—111no—
314#107—112no—
315#107—221no—
316#107—221no—
317#107C22×D1111yescharacteristic
318#102—21no—
319#102—221no—
320#102—221no—
321#102—222no—
322#102—222no—
323#102—221no—
324C2×C11—22no—
325C2×C11—161no—
326C2×C11—162no—
327C2×C11#318611yescharacteristic
328C2×C11C2×#50911yescharacteristic
329C2×C11C2×#50911yescharacteristic
330D11—22no—
331D11—41no—
332D11—161no—
333C24—41no—
334C24—111no—
335C24—441no—
336C2×D4—21no—
337C2×D4—22no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—221no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—442no—
348C2×D4—441no—
349C2×D4—442no—
350C2×D4—441no—
351C2×D4—884no—
352C2×D4—884no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363D8—22no—
364D8—22no—
365D8—22no—
366D8—42no—
367D8—222no—
368D8—442no—
369C2×C8—22no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—441no—
375C2×C8—441no—
376C2×C8—441no—
377C2×C8D4×D1111yescharacteristic
378C2×C8C23×D1111yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C22⋊C4—41no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—442no—
388C22⋊C4—442no—
389C22⋊C4—441no—
390C16—22no—
391C16—222no—
392C11#3375811yescharacteristic, complemented, Sylow
393C23—41no—
394C23—42no—
395C23—82no—
396C23—82no—
397C23—82no—
398C23—111no—
399C23—111no—
400C23—222no—
401C23—222no—
402C23—441no—
403C23—441no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23D8×D1111yescharacteristic
408D4—42no—
409D4—41no—
410D4—42no—
411D4—41no—
412D4—82no—
413D4—82no—
414D4—441no—
415D4—441no—
416D4—882no—
417D4—882no—
418D4—884no—
419D4—884no—
420D4—882no—
421D4—882no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—111no—
426C2×C4—111no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—882no—
437C2×C4—882no—
438C2×C4D8×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C8—21no—
441C8—221no—
442C8—221no—
443C8#6703712yes—
444C22—21no—
445C22—21no—
446C22—82no—
447C22—81no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—82no—
452C22—112no—
453C22—164no—
454C22—221no—
455C22—221no—
456C22—221no—
457C22—221no—
458C22—221no—
459C22—444no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22—1764no—
464C22#1062252412yes—
465C22C2×D8×D1111yescharacteristic
466C4—21no—
467C4—81no—
468C4—221no—
469C4—221no—
470C4—882no—
471C4—881no—
472C4#1062312011yescharacteristic
473C4#1062330411yescharacteristic
474C2—22no—
475C2—162no—
476C2—161no—
477C2—222no—
478C2—441no—
479C2—1761no—
480C2#1307936511yescharacteristic
481C2D11×#50911yescharacteristic
482C2C2×#1062252411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33758
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. C2×#10622770C2semidirect
2. D11×#466C2semidirect
3. #13070802C2semidirect
4. #13070800C2semidirect
5. #13070799C2semidirect
6. #13070718C2semidirect
7. #13070716C2semidirect
8. #13070528C2semidirect
9. #13070526C2semidirect
10. #13070225C2semidirect
11. C11×#2184C2semidirect
12. C22×C11×D8C22semidirect
14. C2×D8×D11C22semidirect
17. C2×C11×D16C22semidirect
23. #10622770C22semidirect
24. #10622770C22semidirect
25. C2×#66890C22semidirect
27. C2×#66882C22semidirect
29. C2×#66862C22semidirect
30. #10622496C22semidirect
31. D11×#107C22semidirect
34. C11×#357C22semidirect
35. C11×C22⋊C16C22semidirect
36. #10622200C22semidirect
37. #10622200C22semidirect
38. C22⋊(C11⋊C16)C22semidirect
39. #10622147C22semidirect
40. (C2×D11)⋊C16C22semidirect
41. #10622143C22semidirect
42. #10622128C22semidirect
161. #2184D11semidirect
215. C22×D8C2×D11semidirect
220. C2×D16C2×D11semidirect
241. #357C2×D11semidirect
244. C22⋊C16C2×D11semidirect
392. C11#33758semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
D11×#4662
#130708022
#130708002
#130707992
#130707182
#130707162
#130705282
#130705262
#130702252
C11×#21842
#3375811