Finite Group Databasebeta

← #14911373

Subgroups — #14911373

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081035C211yesmaximal, characteristic, complemented
2#13080960C211yesmaximal, characteristic, complemented
3#13070897C211yesmaximal, characteristic, complemented
4#13070805C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070799C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070751C211yesmaximal, characteristic, complemented
10#13070716C211yesmaximal, characteristic, complemented
11D16×Dic11C211yesmaximal, characteristic, complemented
12#13070446C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070403C211yesmaximal, characteristic, complemented
15C11×#2218C211yesmaximal, characteristic, complemented
16#10623147—21no—
17#10623142—21no—
18C2×C11×D16C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622770C2211yescharacteristic
23#10622770C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622648—21no—
30#10622646—21no—
31C2×#66862C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622392—21no—
37#10622387—21no—
38#10622374—21no—
39#10622372—21no—
40C11×#367C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C11×#121—21no—
65#66992—41no—
66#66991—21no—
67#66991—21no—
68#66989—41no—
69#66988—41no—
70D4×Dic11—21no—
71D4×Dic11—21no—
72C4×C22⋊D11D411yescharacteristic
73#66979—21no—
74C2×C4⋊Dic11—21no—
75C2×C8×D11C2311yescharacteristic
76#66945—21no—
77C4⋊C4×D11—21no—
78#66941—21no—
79#66941—21no—
80#66938—41no—
81#66936—41no—
82#66931—41no—
83#66930—41no—
84C11×D16—22no—
85C11×M32—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#102—21no—
91C11×#102—21no—
92#66896—21no—
93#66896—21no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66871—21no—
110#66871—21no—
111#66871—21no—
112#66862—22no—
113#33921—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11D811yescharacteristic
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125#4341—84no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—41no—
129C2×Dic22—41no—
130C11×D8—21no—
131C11×D8—21no—
132C11×D8—21no—
133C11×D8—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11D811yescharacteristic
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4D811yescharacteristic
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C8×D11—21no—
165C8×D11—21no—
166C11×C16—21no—
167C11×C16#4112yescomplemented
168C11⋊C16—21no—
169C11⋊C16—21no—
170#3341—111no—
171#3334—111no—
172#2254—111no—
173#2234—111no—
174#2234—111no—
175#2233—111no—
176#2233—111no—
177#2226—111no—
178#2224—111no—
179#2218—111no—
180#2218D1111yescharacteristic, complemented
181C4×D16—111no—
182#2169—111no—
183#2159—111no—
184#2159—111no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11C2×D811yescharacteristic
188C22×D11C2×D811yescharacteristic
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—82no—
194D4×C11—161no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—22no—
202C22⋊D11—82no—
203C22⋊D11—161no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—82no—
209C2×Dic11—82no—
210C2×Dic11—82no—
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C4×D11—21no—
215C4×D11—21no—
216C4×D11—82no—
217Dic22—82no—
218Dic22—161no—
219C8×C11—21no—
220C8×C11C2×#4111yescharacteristic
221C8×C112−1+411yescharacteristic
222C11⋊C8—21no—
223C11⋊C8—21no—
224#555—221no—
225#547—221no—
226C2×D16C2×D1111yescharacteristic
227C2×M32—111no—
228C2×M32C2×D1111yescharacteristic
229#500—111no—
230#500—111no—
231#482—221no—
232#482—221no—
233#480—221no—
234#480—221no—
235#476—221no—
236#474—221no—
237#466—111no—
238#466—111no—
239#466C2×D1111yescharacteristic
240#466C2×D1111yescharacteristic
241C4×D8—111no—
242C4×D8—111no—
243C8×D4—111no—
244#427—111no—
245#427—111no—
246C2×#107—111no—
247C2×#107—111no—
248#367—111no—
249#367—111no—
250#367—111no—
251#367—111no—
252#367—111no—
253#367C2×D1111yescharacteristic
254#366—111no—
255#366—111no—
256#366—111no—
257C4⋊C16—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264C22⋊C16—111no—
265C22⋊C16—111no—
266C4×C16—111no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11C22×D811yescharacteristic
277C2×D11—21no—
278C2×D11—21no—
279C2×D11—21no—
280C4×C11—21no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11#54711yescharacteristic
284C4×C11#57811yescharacteristic
285Dic11—21no—
286Dic11—21no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290Dic11—81no—
291Dic11#50912yes—
292C2×#41—441no—
293C2×D8C22×D1111yescharacteristic
294C2×D8C22×D1111yescharacteristic
295C22×C8—111no—
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#124—441no—
300#124—441no—
301#123—441no—
302#123—441no—
303C22⋊Q8—441no—
304#121—21no—
305#121—21no—
306#121—221no—
307#121—221no—
308#121—441no—
309C4×D4—111no—
310C4×D4—221no—
311C4×D4—221no—
312#117—221no—
313#117—221no—
314#117—441no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317D16—22no—
318M32—22no—
319M32—222no—
320C2×C16—111no—
321C2×C16—111no—
322C2×C16C22×D1111yescharacteristic
323C2×C16C22×D1111yescharacteristic
324#107—111no—
325#107—111no—
326#107—111no—
327#107—111no—
328#107—221no—
329#107—221no—
330#107—221no—
331#107—221no—
332#107C22×D1111yescharacteristic
333#107C22×D1111yescharacteristic
334#106—221no—
335#106—221no—
336C4⋊C8—111no—
337#102—21no—
338#102—21no—
339#102—221no—
340#102—221no—
341#102—221no—
342#102—221no—
343C22⋊C8—111no—
344C22⋊C8—111no—
345C4×C8—111no—
346C2×C11—41no—
347C2×C11—161no—
348C2×C11—161no—
349C2×C11#333411yescharacteristic
350C2×C11C2×#50911yescharacteristic
351C2×C11#341611yescharacteristic
352D11—41no—
353#41—884no—
354C2×Q8—441no—
355C2×Q8—441no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—111no—
361C2×D4—441no—
362C2×D4—441no—
363C22×C4—111no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4D4×D1111yescharacteristic
369D8—21no—
370D8—21no—
371D8—21no—
372D8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—111no—
376C2×C8—111no—
377C2×C8—221no—
378C2×C8—221no—
379C2×C8D4×D1111yescharacteristic
380C2×C8C23×D1111yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—111no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—111no—
395C22⋊C4—111no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—111no—
403C42—441no—
404C42—441no—
405C16—21no—
406C16—221no—
407C16—221no—
408C16#434112yescomplemented
409C11#3392111yescharacteristic, complemented, Sylow
410C23—41no—
411C23—41no—
412C23—111no—
413C23D8×D1111yescharacteristic
414Q8—882no—
415Q8—1761no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—222no—
423D4—882no—
424D4—1761no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—111no—
430C2×C4—111no—
431C2×C4—111no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—882no—
439C2×C4—882no—
440C2×C4—882no—
441C2×C4—882no—
442C2×C4D8×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C8—21no—
445C8—221no—
446C8—221no—
447C8C2×#434111yescharacteristic
448C8#6704311yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—221no—
459C22—221no—
460C22—221no—
461C22C2×D8×D1111yescharacteristic
462C4—21no—
463C4—81no—
464C4—81no—
465C4—112no—
466C4—221no—
467C4—221no—
468C4—881no—
469C4—881no—
470C4—881no—
471C4—881no—
472C4#1062314211yescharacteristic
473C4#1062330211yescharacteristic
474C2—41no—
475C2—161no—
476C2—161no—
477C2—441no—
478C2#1308096011yescharacteristic
479C2D11×#50911yescharacteristic
480C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #13081035C2semidirect
2. #13080960C2semidirect
3. #13070897C2semidirect
4. #13070805C2semidirect
5. #13070804C2semidirect
6. #13070800C2semidirect
7. #13070799C2semidirect
8. #13070761C2semidirect
9. #13070751C2semidirect
10. #13070716C2semidirect
11. D16×Dic11C2semidirect
12. #13070446C2semidirect
13. #13070404C2semidirect
14. #13070403C2semidirect
15. C11×#2218C2semidirect
167. C11×C16#41semidirect
180. #2218D11semidirect
408. C16#4341semidirect
409. C11#33921semidirect

Maximal subgroups

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

subgroupindex
#130810352
#130809602
#130708972
#130708052
#130708042
#130708002
#130707992
#130707612
#130707512
#130707162
D16×Dic112
#130704462
#130704042
#130704032
C11×#22182
#3392111